Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000175: Integer partitions ⟶ ℤ
Values
=>
Cc0005;cc-rep-1
Cc0002;cc-rep-2
Cc0002;cc-rep
[1,2,3]=>[1,0,1,0,1,0]=>[2,1]=>[1]=>0
[1,3,2]=>[1,0,1,1,0,0]=>[1,1]=>[1]=>0
[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[3,2,1]=>[2,1]=>1
[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>[2,2,1]=>[2,1]=>1
[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>[3,1,1]=>[1,1]=>0
[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[2,1,1]=>[1,1]=>0
[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>[3,2]=>[2]=>0
[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[2]=>0
[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[3,1]=>[1]=>0
[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[2,1]=>[1]=>0
[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,1]=>[1]=>0
[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>[1,1]=>[1]=>0
[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[3,2,1]=>3
[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]=>[2,2,1]=>2
[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]=>[3,1,1]=>2
[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[2,1,1]=>2
[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]=>[3,2]=>1
[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]=>[3,2]=>1
[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]=>[2,2]=>0
[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]=>[2,2]=>0
[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]=>[3,1]=>1
[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]=>[3,1]=>1
[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]=>[2,1]=>1
[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]=>[2,1]=>1
[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]=>[1,1]=>0
[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]=>[1,1]=>0
[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]=>[1,1]=>0
[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]=>[1,1]=>0
[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]=>[3]=>0
[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[3]=>0
[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[2]=>0
[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]=>[2]=>0
[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2]=>0
[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2]=>0
[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]=>[3]=>0
[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[3]=>0
[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[2]=>0
[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]=>[2]=>0
[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2]=>0
[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2]=>0
[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[1]=>0
[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]=>[1]=>0
[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[1]=>0
[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]=>[1]=>0
[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]=>[1]=>0
[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]=>[1]=>0
[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[1]=>0
[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,3,6,2,5,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[1,4,2,6,3,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,4,2,6,5,3]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,4,6,2,5,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,4,6,5,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,4,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]=>[4,3,2]=>3
[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]=>[3,3,2]=>2
[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]=>[4,2,2]=>2
[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]=>[3,2,2]=>2
[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]=>[2,2,2]=>0
[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]=>[2,2,2]=>0
[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]=>[4,3,1]=>3
[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]=>[3,3,1]=>2
[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]=>[4,2,1]=>3
[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]=>[3,2,1]=>3
[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]=>[2,2,1]=>2
[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]=>[2,2,1]=>2
[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,3,6,1,5,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,3,6,4,1,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,3,6,5,1,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]=>[4,1,1]=>2
[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[3,1,1]=>2
[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,4,1,6,5,3]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]=>[4,1,1]=>2
[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[3,1,1]=>2
[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]=>[2,1,1]=>2
[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]=>[2,1,1]=>2
[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,4,6,1,5,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,1,4,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,1,4,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,1,5,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,3,1,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,3,1,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,3,4,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,3,5,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,5,1,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]=>[4,3]=>1
[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]=>[4,3]=>1
[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]=>[3,3]=>0
[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[3,3]=>0
[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]=>[4,2]=>1
[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[4,2]=>1
[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[3,2]=>1
[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]=>[3,2]=>1
[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[2,2]=>0
[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[2,2]=>0
[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[2,2]=>0
[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[2,2]=>0
[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,6,2,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,6,4,5,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]=>[4,3]=>1
[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]=>[4,3]=>1
[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]=>[3,3]=>0
[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[3,3]=>0
[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]=>[4,2]=>1
[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[4,2]=>1
[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[3,2]=>1
[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]=>[3,2]=>1
[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[2,2]=>0
[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[2,2]=>0
[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[2,2]=>0
[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[2,2]=>0
[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,6,4,1,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]=>[4,1]=>1
[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[4,1]=>1
[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[3,1]=>1
[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]=>[3,1]=>1
[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]=>[4,1]=>1
[3,4,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[4,1]=>1
[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[3,1]=>1
[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]=>[3,1]=>1
[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]=>[2,1]=>1
[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]=>[2,1]=>1
[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]=>[2,1]=>1
[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]=>[2,1]=>1
[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]=>[2,1]=>1
[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]=>[2,1]=>1
[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,4,6,2,1,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1]=>0
[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1]=>0
[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1]=>0
[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1]=>0
[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1]=>0
[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[1,1]=>0
[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,2,1,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,2,4,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4]=>0
[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4]=>0
[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[3]=>0
[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3]=>0
[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,1,2,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4]=>0
[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4]=>0
[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[3]=>0
[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3]=>0
[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,1,3,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2]=>0
[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2]=>0
[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2]=>0
[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2]=>0
[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2]=>0
[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2]=>0
[4,1,6,2,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,6,2,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4]=>0
[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4]=>0
[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[3]=>0
[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3]=>0
[4,2,1,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4]=>0
[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4]=>0
[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[3]=>0
[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3]=>0
[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2]=>0
[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2]=>0
[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2]=>0
[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2]=>0
[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2]=>0
[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2]=>0
[4,2,6,1,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4]=>0
[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4]=>0
[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[3]=>0
[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3]=>0
[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4]=>0
[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4]=>0
[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[3]=>0
[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3]=>0
[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3]=>0
[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2]=>0
[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2]=>0
[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2]=>0
[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2]=>0
[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2]=>0
[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2]=>0
[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1]=>0
[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[1]=>0
[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1]=>0
[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[1]=>0
[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1]=>0
[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1]=>0
[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1]=>0
[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[1]=>0
[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1]=>0
[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[1]=>0
[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1]=>0
[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1]=>0
[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1]=>0
[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[1]=>0
[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1]=>0
[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[1]=>0
[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1]=>0
[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1]=>0
[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1]=>0
[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1]=>0
[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1]=>0
[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1]=>0
[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1]=>0
[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1]=>0
[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[1,2,3,4,5,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2,1]=>[5,4,3,2,1]=>10
[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2,1]=>[4,4,3,2,1]=>9
[1,2,3,4,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2,1]=>[4,4,3,2,1]=>9
[1,2,3,4,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[1,2,3,4,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2,1]=>[5,3,3,2,1]=>9
[1,2,3,5,4,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2,1]=>[5,3,3,2,1]=>9
[1,2,3,5,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2,1]=>[4,3,3,2,1]=>9
[1,2,3,5,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2,1]=>[4,3,3,2,1]=>9
[1,2,3,5,7,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[1,2,3,5,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,6,4,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,6,7,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,7,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,3,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2,1]=>[5,4,2,2,1]=>9
[1,2,4,3,5,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2,1]=>[5,4,2,2,1]=>9
[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2,1]=>[4,4,2,2,1]=>8
[1,2,4,3,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2,1]=>[4,4,2,2,1]=>8
[1,2,4,3,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[1,2,4,3,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[1,2,4,5,3,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2,1]=>[5,3,2,2,1]=>9
[1,2,4,5,3,7,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2,1]=>[5,3,2,2,1]=>9
[1,2,4,5,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2,1]=>[4,3,2,2,1]=>9
[1,2,4,5,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2,1]=>[4,3,2,2,1]=>9
[1,2,4,5,7,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]=>[4,3,2,2,1]=>9
[1,2,4,5,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]=>[4,3,2,2,1]=>9
[1,2,4,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,6,3,7,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,6,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,7,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,7,3,6,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,7,5,3,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,7,5,6,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,7,6,3,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,4,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[1,2,5,3,4,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[1,2,5,3,6,4,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,3,6,7,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,3,7,4,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,3,7,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,4,3,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[1,2,5,4,3,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[1,2,5,4,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,4,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,4,7,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,4,7,6,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,5,6,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,6,3,7,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,6,4,3,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,6,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,6,7,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,7,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,7,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,7,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,7,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,5,7,6,4,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,3,4,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,3,5,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,3,7,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,3,7,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,4,3,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,4,7,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,4,7,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,5,3,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,5,7,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,7,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,7,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,7,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,7,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,6,7,5,4,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,3,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,3,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,4,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,4,6,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,5,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,6,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,1]=>[5,4,3,1,1]=>9
[1,3,2,4,5,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1,1]=>[5,4,3,1,1]=>9
[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1,1]=>[4,4,3,1,1]=>8
[1,3,2,4,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1,1]=>[4,4,3,1,1]=>8
[1,3,2,4,7,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[1,3,2,4,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1,1]=>[5,3,3,1,1]=>8
[1,3,2,5,4,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[1,3,2,5,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1,1]=>[4,3,3,1,1]=>8
[1,3,2,5,6,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1]=>8
[1,3,2,5,7,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[1,3,2,5,7,6,4]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,6,4,7,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,6,7,5,4]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,7,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,7,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,7,5,6,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,7,6,4,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,2,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,4,2,5,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,1]=>[5,4,2,1,1]=>9
[1,3,4,2,5,7,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1,1]=>[5,4,2,1,1]=>9
[1,3,4,2,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1,1]=>[4,4,2,1,1]=>8
[1,3,4,2,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]=>[4,4,2,1,1]=>8
[1,3,4,2,7,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[1,3,4,2,7,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[1,3,4,5,2,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,1]=>[5,3,2,1,1]=>9
[1,3,4,5,2,7,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]=>[5,3,2,1,1]=>9
[1,3,4,5,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]=>[4,3,2,1,1]=>9
[1,3,4,5,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[1,3,4,5,7,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[1,3,4,5,7,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[1,3,4,6,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,6,2,7,5]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,6,7,2,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,6,7,5,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,7,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,7,5,2,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,7,5,6,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,7,6,2,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,4,7,6,5,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,3,5,2,4,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[1,3,5,2,4,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[1,3,5,2,6,4,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,2,6,7,4]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,2,7,4,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,2,7,6,4]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,4,2,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[1,3,5,4,2,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[1,3,5,4,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,4,6,7,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,4,7,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,4,7,6,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,5,6,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,6,2,7,4]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,6,4,2,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,6,7,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,7,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,7,4,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,7,4,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,7,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,5,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,3,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,2,4,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,2,5,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,2,5,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,2,7,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,2,7,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,4,2,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,4,2,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,4,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,4,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,4,7,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,4,7,5,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,5,2,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,5,2,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,5,4,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,5,7,4,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,7,2,5,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,7,4,2,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,7,4,5,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,7,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,6,7,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,4,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,5,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,4,2,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,4,5,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,5,2,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,5,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,5,4,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,2,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,4,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,5,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1,1]=>[5,4,1,1,1]=>7
[1,4,2,3,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,2,3,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,2,3,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,2,3,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,2,5,3,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]=>[5,3,1,1,1]=>7
[1,4,2,5,3,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]=>[5,3,1,1,1]=>7
[1,4,2,5,6,3,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,2,5,6,7,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,2,5,7,3,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,2,5,7,6,3]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,2,6,3,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,6,3,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,6,5,3,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,6,5,7,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,6,7,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,6,7,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,7,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,7,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,7,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,7,5,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,7,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,2,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,2,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1,1]=>[5,4,1,1,1]=>7
[1,4,3,2,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[1,4,3,2,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,3,2,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,3,2,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,3,2,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,4,3,5,2,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]=>[5,3,1,1,1]=>7
[1,4,3,5,2,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]=>[5,3,1,1,1]=>7
[1,4,3,5,6,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,3,5,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,3,5,7,2,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,3,5,7,6,2]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,4,3,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,6,2,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,6,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,6,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,6,7,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,7,2,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,7,5,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,7,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,7,6,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,3,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,5,2,3,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[1,4,5,2,3,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[1,4,5,2,6,3,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,2,6,7,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,2,7,3,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,2,7,6,3]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,3,2,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[1,4,5,3,2,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[1,4,5,3,6,2,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,3,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,3,7,2,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,3,7,6,2]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,4,5,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,6,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,6,3,2,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,6,3,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,6,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,6,7,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,7,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,7,3,2,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,7,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,7,6,2,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,5,7,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,2,3,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,2,5,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,2,5,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,2,7,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,2,7,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,3,2,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,3,2,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,3,5,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,3,7,2,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,3,7,5,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,5,2,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,5,2,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,5,3,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,5,3,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,5,7,3,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,7,2,5,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,7,3,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,7,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,7,5,2,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,7,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,3,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,5,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,5,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,6,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,3,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,3,2,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,3,5,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,5,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,5,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,5,3,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,5,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,5,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,6,2,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,6,3,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,6,5,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,2,3,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,2,3,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,3,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,3,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,3,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,4,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,2,4,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,2,4,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,4,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,4,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,4,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,2,6,3,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,6,3,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,6,4,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,6,4,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,6,7,3,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,6,7,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,7,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,7,3,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,7,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,7,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,7,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,2,7,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,2,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,3,2,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,3,2,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,2,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,2,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,2,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,4,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,3,4,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,3,4,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,4,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,4,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,4,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,3,6,2,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,6,2,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,6,4,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,6,4,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,6,7,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,6,7,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,2,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,2,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,4,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,2,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,4,2,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,4,2,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,2,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,2,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,2,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,3,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,4,3,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,5,4,3,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,3,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,3,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,3,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,4,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,6,2,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,6,3,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,6,7,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,7,2,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,7,2,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,7,3,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,7,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,7,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,4,7,6,3,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,2,3,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,2,4,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,2,4,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,2,7,3,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,2,7,4,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,3,2,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,3,2,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,3,4,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,3,7,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,3,7,4,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,4,2,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,4,2,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,4,3,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,4,3,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,4,7,3,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,7,2,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,7,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,7,3,4,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,7,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,6,7,4,3,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,3,2,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,3,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,3,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,3,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,6,3,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,6,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,3,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,3,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,3,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,3,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,4,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,4,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,4,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,4,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,4,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,7,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,7,3,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,7,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,7,4,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,7,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,7,5,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,2,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,2,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,2,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,2,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,4,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,4,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,4,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,4,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,5,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,5,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,5,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,5,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,5,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,2,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,4,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,5,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,2,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,2,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,2,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,2,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,3,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,3,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,3,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,7,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,7,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,7,3,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,7,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,7,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,7,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,2,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,2,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,2,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,2,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,3,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,3,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,3,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,3,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,3,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,4,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,4,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,4,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,7,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,7,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,7,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,7,4,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,2,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,2,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,2,5,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,3,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,3,5,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,2,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,3,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,4,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,4,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,4,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,6,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,6,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,6,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,6,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,2,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,2,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,2,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,2,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,2,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,5,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,2,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,2,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,3,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,3,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,5,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,5,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,6,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,6,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,2,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,2,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,2,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,2,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[2,1,3,4,5,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2]=>[5,4,3,2]=>6
[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2]=>[4,4,3,2]=>5
[2,1,3,4,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2]=>[4,4,3,2]=>5
[2,1,3,4,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[2,1,3,4,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2]=>[5,3,3,2]=>5
[2,1,3,5,4,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[2,1,3,5,6,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2]=>[4,3,3,2]=>5
[2,1,3,5,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]=>[4,3,3,2]=>5
[2,1,3,5,7,4,6]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[2,1,3,5,7,6,4]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,6,4,7,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,6,7,5,4]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,7,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,7,5,4,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,7,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,7,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2]=>[5,4,2,2]=>5
[2,1,4,3,5,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2]=>[5,4,2,2]=>5
[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[2,1,4,3,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[2,1,4,3,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[2,1,4,3,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[2,1,4,5,3,6,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2]=>[5,3,2,2]=>5
[2,1,4,5,3,7,6]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[2,1,4,5,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]=>[4,3,2,2]=>5
[2,1,4,5,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]=>[4,3,2,2]=>5
[2,1,4,5,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[2,1,4,5,7,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[2,1,4,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,6,3,7,5]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,6,7,5,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,7,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,7,3,6,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,7,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,7,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,7,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,1,4,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[2,1,5,3,4,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[2,1,5,3,6,4,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,3,6,7,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,3,7,4,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,3,7,6,4]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,4,3,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[2,1,5,4,3,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[2,1,5,4,6,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,4,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,4,7,3,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,4,7,6,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,1,5,6,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,6,3,7,4]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,6,4,3,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,6,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,6,7,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,7,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,7,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,7,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,7,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,1,5,7,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,3,4,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,3,5,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,3,7,4,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,3,7,5,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,4,3,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,4,7,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,4,7,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,5,3,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,7,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,7,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,7,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,7,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,1,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,5,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1]=>[5,4,3,1]=>6
[2,3,1,4,5,7,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1]=>[5,4,3,1]=>6
[2,3,1,4,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1]=>[4,4,3,1]=>5
[2,3,1,4,6,7,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]=>[4,4,3,1]=>5
[2,3,1,4,7,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[2,3,1,4,7,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[2,3,1,5,4,6,7]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1]=>[5,3,3,1]=>5
[2,3,1,5,4,7,6]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]=>[5,3,3,1]=>5
[2,3,1,5,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]=>[4,3,3,1]=>5
[2,3,1,5,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]=>[4,3,3,1]=>5
[2,3,1,5,7,4,6]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[2,3,1,5,7,6,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[2,3,1,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,6,4,7,5]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,6,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,6,7,5,4]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,7,4,6,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,7,5,4,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,7,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,7,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,3,1,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1]=>[5,4,2,1]=>6
[2,3,4,1,5,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]=>[5,4,2,1]=>6
[2,3,4,1,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]=>[4,4,2,1]=>5
[2,3,4,1,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]=>[4,4,2,1]=>5
[2,3,4,1,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[2,3,4,1,7,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]=>[5,3,2,1]=>6
[2,3,4,5,1,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]=>[5,3,2,1]=>6
[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[2,3,4,5,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[2,3,4,5,7,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[2,3,4,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,6,7,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,7,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,7,5,1,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,7,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,7,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,3,4,7,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,3,5,1,4,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[2,3,5,1,4,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[2,3,5,1,6,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,1,6,7,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,1,7,4,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,1,7,6,4]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,4,1,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[2,3,5,4,1,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[2,3,5,4,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,4,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,4,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,4,7,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[2,3,5,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,6,1,7,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,6,4,1,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,6,7,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,7,1,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,7,1,6,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,7,4,1,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,7,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,7,6,1,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,3,5,7,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,3,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,1,5,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,1,5,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,1,7,4,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,1,7,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,4,1,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,4,1,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,4,7,1,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,4,7,5,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,5,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,5,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,5,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,5,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,5,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,7,1,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,7,4,1,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,7,4,5,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,7,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,3,6,7,5,4,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,1,5,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,1,6,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,4,1,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,4,5,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,4,5,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,4,6,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,5,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,5,6,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,6,1,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,6,1,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,6,4,1,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,6,4,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,4,1,3,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[2,4,1,3,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[2,4,1,3,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[2,4,1,3,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[2,4,1,3,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[2,4,1,3,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[2,4,1,5,3,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[2,4,1,5,3,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[2,4,1,5,6,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[2,4,1,5,6,7,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[2,4,1,5,7,3,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[2,4,1,5,7,6,3]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[2,4,1,6,3,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,6,5,3,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,6,5,7,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,6,7,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,6,7,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,7,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,7,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,7,5,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,7,5,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,7,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,1,7,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,1,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[2,4,3,1,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[2,4,3,1,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[2,4,3,1,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[2,4,3,1,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[2,4,3,1,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[2,4,3,5,1,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[2,4,3,5,1,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[2,4,3,5,6,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[2,4,3,5,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[2,4,3,5,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[2,4,3,5,7,6,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[2,4,3,6,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,6,1,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,6,7,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,7,1,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,7,5,1,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,7,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,7,6,1,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,3,7,6,5,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,4,5,1,3,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[2,4,5,1,3,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[2,4,5,1,6,3,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,1,6,7,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,1,7,3,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,1,7,6,3]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,3,1,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[2,4,5,3,1,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[2,4,5,3,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,3,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,3,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,3,7,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[2,4,5,6,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,6,1,7,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,6,3,1,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,6,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,6,7,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,7,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,7,3,1,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,7,3,6,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,7,6,1,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,7,6,3,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,1,3,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,1,5,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,1,5,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,1,7,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,1,7,5,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,3,1,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,3,1,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,3,5,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,3,7,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,3,7,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,5,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,5,1,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,5,3,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,5,7,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,7,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,7,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,7,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,7,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,4,6,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,5,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,3,5,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,3,6,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,3,6,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,5,1,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,5,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,3,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,3,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,1,3,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,5,1,3,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,1,3,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,3,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,3,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,3,7,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,4,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,5,1,4,3,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,1,4,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,4,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,4,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,4,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,1,6,3,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,6,3,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,6,4,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,6,4,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,6,7,3,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,6,7,4,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,7,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,7,3,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,7,4,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,7,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,7,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,1,7,6,4,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,1,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,5,3,1,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,3,1,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,1,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,1,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,1,7,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,4,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,5,3,4,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,3,4,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,4,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,4,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,4,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,3,6,1,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,6,1,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,6,4,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,6,4,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,6,7,1,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,6,7,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,7,1,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,7,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,7,4,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,7,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,7,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,3,7,6,4,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,1,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,5,4,1,3,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,4,1,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,1,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,1,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,1,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,3,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,5,4,3,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,4,3,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,3,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,3,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,3,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,6,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,6,1,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,6,3,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,6,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,6,7,3,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,7,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,7,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,7,3,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,7,3,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,7,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,4,7,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,6,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,1,3,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,1,4,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,1,4,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,1,7,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,1,7,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,3,1,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,3,1,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,3,4,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,3,7,1,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,3,7,4,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,4,1,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,4,1,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,4,3,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,4,7,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,7,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,7,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,7,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,7,4,1,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,7,4,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,3,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,4,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,4,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,3,1,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,3,4,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,3,4,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,3,6,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,4,3,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,6,1,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,6,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,6,4,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,6,4,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,3,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,3,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,3,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,3,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,4,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,4,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,4,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,4,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,4,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,4,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,5,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,5,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,5,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,5,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,5,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,5,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,7,3,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,7,4,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,7,4,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,7,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,7,5,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,4,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,4,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,4,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,4,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,4,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,5,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,5,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,5,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,5,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,7,1,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,7,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,7,4,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,7,4,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,7,5,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,7,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,1,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,1,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,1,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,1,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,1,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,1,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,3,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,3,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,3,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,3,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,5,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,5,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,5,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,7,1,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,7,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,7,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,7,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,7,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,4,7,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,1,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,1,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,1,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,1,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,1,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,4,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,4,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,4,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,4,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,7,1,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,7,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,7,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,7,4,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,4,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,3,1,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,3,4,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,3,5,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,3,5,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,4,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,4,1,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,4,5,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,4,5,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,5,1,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,5,4,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,4,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,4,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,4,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,5,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,5,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,5,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,5,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,1,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,5,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,6,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,6,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,6,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,6,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,6,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,1,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,1,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,3,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,3,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,3,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,3,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,6,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,6,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,1,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,1,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3]=>[5,4,3]=>3
[3,1,2,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]=>[4,4,3]=>2
[3,1,2,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[3,1,2,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,1,2,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]=>[5,3,3]=>2
[3,1,2,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[3,1,2,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]=>[4,3,3]=>2
[3,1,2,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[3,1,2,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,1,2,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,1,2,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,1,2,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,1,2,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,1,2,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,1,2,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,1,2,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,2,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,2,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,2,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,2,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,2,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,4,2,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]=>[5,4,2]=>3
[3,1,4,2,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[3,1,4,2,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]=>[4,4,2]=>2
[3,1,4,2,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[3,1,4,2,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,1,4,2,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,1,4,5,2,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]=>[5,3,2]=>3
[3,1,4,5,2,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[3,1,4,5,6,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]=>[4,3,2]=>3
[3,1,4,5,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[3,1,4,5,7,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,1,4,5,7,6,2]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,1,4,6,2,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[3,3,2]=>2
[3,1,4,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,1,4,6,5,2,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[3,3,2]=>2
[3,1,4,6,5,7,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,1,4,6,7,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,1,4,6,7,5,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,1,4,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,1,4,7,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,1,4,7,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,1,4,7,5,6,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,1,4,7,6,2,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,1,4,7,6,5,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,1,5,2,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,1,5,2,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,1,5,2,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,1,5,2,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,1,5,2,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,5,2,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,5,4,2,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,1,5,4,2,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,1,5,4,6,2,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,1,5,4,6,7,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,1,5,4,7,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,5,4,7,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,5,6,2,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,1,5,6,2,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,1,5,6,4,2,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,1,5,6,4,7,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,1,5,6,7,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,1,5,6,7,4,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,1,5,7,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,5,7,2,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,5,7,4,2,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,5,7,4,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,5,7,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,5,7,6,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,6,2,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,6,2,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,6,2,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,6,2,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,1,6,2,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,1,6,4,2,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,6,4,2,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,6,4,5,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,6,4,5,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,6,4,7,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,1,6,4,7,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,1,6,5,2,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,6,5,2,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,6,5,4,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,6,5,4,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,6,5,7,2,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,1,6,5,7,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,1,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,1,6,7,2,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,1,6,7,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,1,6,7,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,1,6,7,5,2,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,1,6,7,5,4,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,1,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,2,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,2,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,2,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,2,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,5,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,5,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,6,2,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,5,4,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,6,5,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3]=>[5,4,3]=>3
[3,2,1,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[3,2,1,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]=>[4,4,3]=>2
[3,2,1,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[3,2,1,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,2,1,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,2,1,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]=>[5,3,3]=>2
[3,2,1,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[3,2,1,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]=>[4,3,3]=>2
[3,2,1,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[3,2,1,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,2,1,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,2,1,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,2,1,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,2,1,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,2,1,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,2,1,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,2,1,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,2,1,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,1,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,1,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,1,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,1,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,1,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]=>[5,4,2]=>3
[3,2,4,1,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[3,2,4,1,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]=>[4,4,2]=>2
[3,2,4,1,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[3,2,4,1,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,2,4,1,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]=>[5,3,2]=>3
[3,2,4,5,1,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]=>[4,3,2]=>3
[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[3,2,4,5,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,2,4,5,7,6,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,2,4,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[3,3,2]=>2
[3,2,4,6,1,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,2,4,6,5,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[3,3,2]=>2
[3,2,4,6,5,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,2,4,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,2,4,6,7,5,1]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,2,4,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,4,7,1,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,4,7,5,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,4,7,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,4,7,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,4,7,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,5,1,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,2,5,1,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,2,5,1,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,2,5,1,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,2,5,1,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,2,5,1,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,2,5,4,1,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,2,5,4,1,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,2,5,4,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,2,5,4,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,2,5,4,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,2,5,4,7,6,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,2,5,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,2,5,6,1,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,2,5,6,4,1,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,2,5,6,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,2,5,6,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,2,5,6,7,4,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,2,5,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,2,5,7,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,2,5,7,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,2,5,7,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,2,5,7,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,2,5,7,6,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,2,6,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,2,6,1,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,6,1,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,2,6,1,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,6,1,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,1,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,4,1,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,2,6,4,1,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,2,6,4,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,6,4,7,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,4,7,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,5,1,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,2,6,5,1,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,2,6,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,6,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,5,7,4,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,6,7,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,6,7,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,6,7,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,6,7,5,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,6,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,4,1,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,4,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,4,5,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,4,5,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,4,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,5,4,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,5,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,6,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]=>[5,4,1]=>3
[3,4,1,2,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[3,4,1,2,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]=>[4,4,1]=>2
[3,4,1,2,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[3,4,1,2,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,4,1,2,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,4,1,5,2,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]=>[5,3,1]=>3
[3,4,1,5,2,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[3,4,1,5,6,2,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]=>[4,3,1]=>3
[3,4,1,5,6,7,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[3,4,1,5,7,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,4,1,5,7,6,2]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,4,1,6,2,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[3,3,1]=>2
[3,4,1,6,2,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[3,4,1,6,5,2,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[3,3,1]=>2
[3,4,1,6,5,7,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[3,4,1,6,7,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[3,4,1,6,7,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[3,4,1,7,2,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,7,2,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,7,5,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,7,5,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,7,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,7,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]=>[5,4,1]=>3
[3,4,2,1,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[3,4,2,1,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]=>[4,4,1]=>2
[3,4,2,1,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[3,4,2,1,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,4,2,1,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]=>[5,3,1]=>3
[3,4,2,5,1,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]=>[4,3,1]=>3
[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[3,4,2,5,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,4,2,5,7,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,4,2,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[3,3,1]=>2
[3,4,2,6,1,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[3,4,2,6,5,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[3,3,1]=>2
[3,4,2,6,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[3,4,2,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[3,4,2,6,7,5,1]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[3,4,2,7,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,2,7,1,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,2,7,5,1,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,2,7,5,6,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,2,7,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,2,7,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]=>[5,2,1]=>3
[3,4,5,1,2,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[3,4,5,1,6,2,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]=>[4,2,1]=>3
[3,4,5,1,6,7,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[3,4,5,1,7,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[3,4,5,1,7,6,2]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[3,4,5,2,1,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]=>[5,2,1]=>3
[3,4,5,2,1,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]=>[4,2,1]=>3
[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[3,4,5,2,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[3,4,5,2,7,6,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]=>[3,2,1]=>3
[3,4,5,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[3,4,5,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]=>[3,2,1]=>3
[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[3,4,5,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[3,4,5,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,4,5,7,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,4,5,7,2,1,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,4,5,7,2,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,4,5,7,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,4,5,7,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,4,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,4,6,1,2,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,6,1,5,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,4,6,1,5,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,6,1,7,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,4,6,1,7,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,4,6,2,1,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,4,6,2,1,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,6,2,5,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,4,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,6,2,7,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,4,6,2,7,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,4,6,5,1,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,4,6,5,1,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,4,6,5,2,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,4,6,5,7,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,4,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[3,4,6,7,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[3,4,6,7,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[3,4,6,7,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[3,4,6,7,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[3,4,6,7,5,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[3,4,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,1,5,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,2,5,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,2,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,2,6,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,5,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,5,6,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,7,6,5,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,1,2,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,5,1,2,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,1,2,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,1,2,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,5,1,2,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,1,2,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,1,4,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,5,1,4,2,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,1,4,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,1,4,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,5,1,4,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,1,4,7,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,1,6,2,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,1,6,2,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,1,6,4,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,1,6,4,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,1,6,7,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,5,1,6,7,4,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,5,1,7,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,1,7,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,1,7,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,1,7,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,1,7,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,1,7,6,4,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,2,1,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,5,2,1,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,2,1,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,2,1,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,5,2,1,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,2,1,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,2,4,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,5,2,4,1,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,2,4,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,2,4,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,5,2,4,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,2,4,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,2,6,1,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,2,6,1,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,2,6,4,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,2,6,4,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,2,6,7,1,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,5,2,6,7,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,5,2,7,1,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,2,7,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,2,7,4,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,2,7,4,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,2,7,6,1,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,2,7,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,4,1,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,5,4,1,2,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,4,1,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,4,1,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,5,4,1,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,4,1,7,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,4,2,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,5,4,2,1,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,4,2,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,4,2,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,5,4,2,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,4,2,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,4,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,4,6,1,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,4,6,2,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,4,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,4,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,5,4,6,7,2,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,5,4,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,4,7,1,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,4,7,2,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,4,7,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,4,7,6,1,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,4,7,6,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,5,6,1,2,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,6,1,4,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,5,6,1,4,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,6,1,7,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,5,6,1,7,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,5,6,2,1,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,5,6,2,1,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,6,2,4,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,5,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,6,2,7,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,5,6,2,7,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,5,6,4,1,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,5,6,4,1,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,5,6,4,2,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,6,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,5,6,4,7,2,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,5,6,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,5,6,7,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,5,6,7,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,5,6,7,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,5,6,7,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,5,6,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,5,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,1,6,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,1,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,2,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,2,1,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,4,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,4,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,6,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,6,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,1,2,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,1,2,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,1,2,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,1,2,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,1,2,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,1,4,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,1,4,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,1,4,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,1,4,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,1,4,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,1,4,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,1,5,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,1,5,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,1,5,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,1,5,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,1,5,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,1,5,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,1,7,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,1,7,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,1,7,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,1,7,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,1,7,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,1,7,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,2,1,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,2,1,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,2,1,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,2,1,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,2,1,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,2,1,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,2,4,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,2,4,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,2,4,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,2,4,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,2,4,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,2,5,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,2,5,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,2,5,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,2,5,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,2,5,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,2,7,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,2,7,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,2,7,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,2,7,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,2,7,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,2,7,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,4,1,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,1,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,1,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,4,1,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,4,2,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,2,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,4,2,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,2,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,4,2,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,4,2,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,4,5,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,5,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,4,5,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,5,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,4,5,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,4,7,1,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,4,7,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,4,7,2,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,4,7,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,4,7,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,4,7,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,5,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,5,1,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,1,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,5,1,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,1,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,1,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,2,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,5,2,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,2,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,5,2,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,2,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,2,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,4,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,5,4,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,5,4,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,4,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,4,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,5,7,1,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,5,7,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,5,7,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,5,7,4,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,5,7,4,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,7,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,1,4,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,1,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,2,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,2,1,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,2,4,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,2,5,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,2,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,4,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,4,2,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,4,2,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,4,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,4,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,5,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,5,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,2,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,2,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,4,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,4,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,5,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,6,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,6,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,1,6,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,1,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,4,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,5,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,5,1,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,5,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,5,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,6,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,2,6,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,1,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,1,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,5,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,2,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,4,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,4,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,4,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,4,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,1,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,1,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,1,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,1,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,4,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,4,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,4,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,5,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[5,4]=>1
[4,1,2,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[5,4]=>1
[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[4,4]=>0
[4,1,2,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[4,4]=>0
[4,1,2,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,1,2,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,1,2,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[5,3]=>1
[4,1,2,5,3,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[5,3]=>1
[4,1,2,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[4,3]=>1
[4,1,2,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3]=>1
[4,1,2,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,1,2,5,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,1,2,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,1,2,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,1,2,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,1,2,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,1,2,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,1,2,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,1,2,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,2,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,2,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,2,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,2,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,2,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[5,4]=>1
[4,1,3,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[5,4]=>1
[4,1,3,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[4,4]=>0
[4,1,3,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[4,4]=>0
[4,1,3,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,1,3,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,1,3,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[5,3]=>1
[4,1,3,5,2,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[5,3]=>1
[4,1,3,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[4,3]=>1
[4,1,3,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3]=>1
[4,1,3,5,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,1,3,5,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,1,3,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,1,3,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,1,3,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,1,3,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,1,3,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,1,3,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,1,3,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,7,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,5,2,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[5,2]=>1
[4,1,5,2,3,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2]=>1
[4,1,5,2,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[4,2]=>1
[4,1,5,2,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,2]=>1
[4,1,5,2,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,1,5,2,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,1,5,3,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[5,2]=>1
[4,1,5,3,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2]=>1
[4,1,5,3,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[4,2]=>1
[4,1,5,3,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,2]=>1
[4,1,5,3,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,1,5,3,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,1,5,6,2,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,2]=>1
[4,1,5,6,2,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,2]=>1
[4,1,5,6,3,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,2]=>1
[4,1,5,6,3,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,2]=>1
[4,1,5,6,7,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,1,5,6,7,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,1,5,7,2,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,5,7,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,5,7,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,5,7,3,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,5,7,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,5,7,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,6,2,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,2,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,6,2,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,2,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,6,2,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,6,2,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,6,3,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,3,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,6,3,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,3,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,6,3,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,6,3,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,6,5,2,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,5,2,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,6,5,3,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,5,3,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,6,5,7,2,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,6,5,7,3,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,6,7,2,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,6,7,2,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,6,7,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,6,7,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,6,7,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,6,7,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,7,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,2,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,2,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,3,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,3,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,3,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,3,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,2,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,3,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,6,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,6,2,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,6,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,6,3,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[5,4]=>1
[4,2,1,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[5,4]=>1
[4,2,1,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[4,4]=>0
[4,2,1,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[4,4]=>0
[4,2,1,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,1,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,1,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[5,3]=>1
[4,2,1,5,3,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[5,3]=>1
[4,2,1,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[4,3]=>1
[4,2,1,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3]=>1
[4,2,1,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,2,1,5,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,2,1,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,2,1,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,2,1,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,2,1,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,2,1,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,2,1,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,2,1,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,3,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[5,4]=>1
[4,2,3,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[5,4]=>1
[4,2,3,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[4,4]=>0
[4,2,3,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[4,4]=>0
[4,2,3,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,3,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[5,3]=>1
[4,2,3,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[5,3]=>1
[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[4,3]=>1
[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3]=>1
[4,2,3,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,2,3,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,2,3,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,2,3,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,2,3,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,2,3,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,2,3,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,2,3,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,2,3,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,3,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,3,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,3,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,3,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,3,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,5,1,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[5,2]=>1
[4,2,5,1,3,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2]=>1
[4,2,5,1,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[4,2]=>1
[4,2,5,1,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,2]=>1
[4,2,5,1,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,2,5,1,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,2,5,3,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[5,2]=>1
[4,2,5,3,1,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2]=>1
[4,2,5,3,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[4,2]=>1
[4,2,5,3,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,2]=>1
[4,2,5,3,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,2,5,3,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,2,5,6,1,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,2]=>1
[4,2,5,6,1,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,2]=>1
[4,2,5,6,3,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,2]=>1
[4,2,5,6,3,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,2]=>1
[4,2,5,6,7,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,2,5,6,7,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,2,5,7,1,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,5,7,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,5,7,3,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,5,7,3,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,5,7,6,1,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,5,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,6,1,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,2,6,1,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,6,1,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,2,6,1,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,6,1,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,6,1,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,6,3,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,2,6,3,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,6,3,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,2,6,3,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,6,3,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,6,3,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,6,5,1,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,2,6,5,1,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,6,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,2,6,5,3,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,6,5,7,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,6,5,7,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,6,7,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,6,7,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,6,7,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,6,7,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,6,7,5,1,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,7,1,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,1,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,1,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,5,1,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,5,1,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,5,3,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,5,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,5,6,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,6,1,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[5,4]=>1
[4,3,1,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[5,4]=>1
[4,3,1,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[4,4]=>0
[4,3,1,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[4,4]=>0
[4,3,1,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,1,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,1,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[5,3]=>1
[4,3,1,5,2,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[5,3]=>1
[4,3,1,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[4,3]=>1
[4,3,1,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3]=>1
[4,3,1,5,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,3,1,5,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,3,1,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,3,1,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,1,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,3,1,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,1,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,3,1,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,3,1,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,7,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[5,4]=>1
[4,3,2,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[5,4]=>1
[4,3,2,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[4,4]=>0
[4,3,2,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[4,4]=>0
[4,3,2,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,2,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,2,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[5,3]=>1
[4,3,2,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[5,3]=>1
[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[4,3]=>1
[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3]=>1
[4,3,2,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,3,2,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,3,2,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,3,2,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,2,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3]=>0
[4,3,2,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,2,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,3,2,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,3,2,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[5,2]=>1
[4,3,5,1,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2]=>1
[4,3,5,1,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[4,2]=>1
[4,3,5,1,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,2]=>1
[4,3,5,1,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,3,5,1,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[5,2]=>1
[4,3,5,2,1,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2]=>1
[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[4,2]=>1
[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,2]=>1
[4,3,5,2,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,3,5,2,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,2]=>1
[4,3,5,6,1,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,2]=>1
[4,3,5,6,2,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,2]=>1
[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,2]=>1
[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,3,5,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,3,5,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,5,7,1,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,5,7,2,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,5,7,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,5,7,6,1,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,5,7,6,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,6,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,3,6,1,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,6,1,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,3,6,1,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,6,1,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,6,1,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,6,2,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,3,6,2,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,6,2,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,3,6,2,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,6,2,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,6,2,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,6,5,1,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,3,6,5,1,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,6,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[2,2]=>0
[4,3,6,5,2,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,6,5,7,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,6,7,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,6,7,2,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,6,7,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,6,7,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,6,7,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,1,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,1,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,1,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,5,1,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,5,2,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,5,6,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,6,2,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,6,5,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,1]=>1
[4,5,1,2,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,1,2,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[4,1]=>1
[4,5,1,2,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,1]=>1
[4,5,1,2,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,1,2,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,1,3,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,1]=>1
[4,5,1,3,2,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,1,3,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[4,1]=>1
[4,5,1,3,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,1]=>1
[4,5,1,3,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,1,3,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,1,6,2,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,1]=>1
[4,5,1,6,2,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,1,6,3,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,1]=>1
[4,5,1,6,3,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,1,6,7,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,5,1,6,7,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,5,1,7,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,1,7,2,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,1,7,3,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,1,7,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,1,7,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,1,7,6,3,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,2,1,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,1]=>1
[4,5,2,1,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,2,1,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[4,1]=>1
[4,5,2,1,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,1]=>1
[4,5,2,1,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,2,1,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,2,3,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,1]=>1
[4,5,2,3,1,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[4,1]=>1
[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,1]=>1
[4,5,2,3,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,2,3,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,2,6,1,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,1]=>1
[4,5,2,6,1,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,2,6,3,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,1]=>1
[4,5,2,6,3,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,2,6,7,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,5,2,6,7,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,5,2,7,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,2,7,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,2,7,3,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,2,7,3,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,2,7,6,1,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,2,7,6,3,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,3,1,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,1]=>1
[4,5,3,1,2,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,3,1,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[4,1]=>1
[4,5,3,1,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,1]=>1
[4,5,3,1,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,3,1,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,1]=>1
[4,5,3,2,1,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,3,2,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[4,1]=>1
[4,5,3,2,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,1]=>1
[4,5,3,2,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,3,2,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,1]=>1
[4,5,3,6,1,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,3,6,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,1]=>1
[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,5,3,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,5,3,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,3,7,1,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,3,7,2,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,3,7,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,3,7,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,3,7,6,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[2,1]=>1
[4,5,6,1,2,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[2,1]=>1
[4,5,6,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[2,1]=>1
[4,5,6,1,3,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[2,1]=>1
[4,5,6,1,7,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,5,6,1,7,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,5,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[2,1]=>1
[4,5,6,2,1,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[2,1]=>1
[4,5,6,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[2,1]=>1
[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[2,1]=>1
[4,5,6,2,7,1,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,5,6,2,7,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,5,6,3,1,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[2,1]=>1
[4,5,6,3,1,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[2,1]=>1
[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[2,1]=>1
[4,5,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[2,1]=>1
[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,5,6,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,6,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,6,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,1,2,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,1,3,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,1,3,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,1,6,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,2,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,2,3,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,2,3,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,2,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,6,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,6,1,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,6,2,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,1,2,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,1,2,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,1,2,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,1,2,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,1,2,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,1,3,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,1,3,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,1,3,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,1,3,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,1,3,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,1,3,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,1,5,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,1,5,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,1,5,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,1,5,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,1,5,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,1,7,2,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,1,7,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,1,7,3,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,1,7,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,1,7,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,1,7,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,2,1,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,2,1,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,1,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,2,1,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,2,3,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,2,3,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,3,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,3,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,2,3,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,2,5,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,2,5,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,5,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,2,5,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,5,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,2,5,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,2,7,1,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,2,7,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,2,7,3,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,2,7,3,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,2,7,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,2,7,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,3,1,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,1,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,3,1,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,1,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,3,1,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,3,1,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,3,2,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,2,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,3,2,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,2,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,3,2,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,3,2,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,3,5,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,5,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,3,5,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,5,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,3,5,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,3,7,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,3,7,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,3,7,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,3,7,2,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,3,7,5,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,3,7,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,5,1,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,5,1,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,1,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,5,1,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,1,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,5,1,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,5,2,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,5,2,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,2,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,5,2,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,2,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,5,2,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,5,3,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,5,3,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[1,1]=>0
[4,6,5,3,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,3,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,5,3,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,5,7,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,5,7,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,5,7,2,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,5,7,3,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,5,7,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,1,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,1,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,1,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,2,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,2,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,2,5,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,3,1,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,3,2,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,3,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,3,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,5,1,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,5,3,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,3,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,3,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,5,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,5,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,5,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,5,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,6,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,1,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,1,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,1,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,5,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,5,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,5,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,5,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,1,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,2,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,2,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,5,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,5,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,6,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,6,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,6,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,2,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,2,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,2,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,2,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,3,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,3,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,3,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,3,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,6,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,2,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,2,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,2,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,3,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,5,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,5,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,1,2,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,1,2,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,1,2,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,1,2,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,3,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,1,2,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,1,2,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,1,2,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,1,2,4,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,4,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,1,2,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,1,2,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,1,2,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,1,2,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,1,2,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,1,2,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,2,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,2,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,2,7,4,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,2,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,2,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,3,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,1,3,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,1,3,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,1,3,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,1,3,2,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,3,2,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,3,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,1,3,4,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,1,3,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,1,3,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,1,3,4,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,3,4,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,3,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,1,3,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,1,3,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,1,3,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,1,3,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,1,3,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,1,3,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,3,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,3,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,3,7,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,3,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,3,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,4,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,1,4,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,1,4,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,1,4,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,1,4,2,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,4,2,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,4,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,1,4,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,1,4,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,1,4,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,1,4,3,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,4,3,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,1,4,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,1,4,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,1,4,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,1,4,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,1,4,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,1,4,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,1,4,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,4,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,4,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,4,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,4,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,4,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,6,2,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,1,6,2,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,1,6,2,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,1,6,2,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,1,6,2,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,2,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,3,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,1,6,3,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,1,6,3,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,1,6,3,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,1,6,3,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,3,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,4,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,1,6,4,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,1,6,4,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,1,6,4,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,1,6,4,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,4,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,7,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,6,7,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,6,7,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,6,7,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,6,7,4,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,6,7,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,7,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,2,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,2,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,2,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,3,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,3,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,3,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,6,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,6,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,2,1,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,2,1,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,2,1,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,2,1,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,1,3,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,2,1,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,2,1,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,2,1,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,2,1,4,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,1,4,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,1,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,2,1,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,2,1,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,2,1,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,2,1,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,2,1,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,2,1,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,4,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,2,3,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,2,3,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,2,3,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,2,3,1,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,3,1,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,3,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,2,3,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,2,3,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,3,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,3,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,2,3,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,2,3,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,2,3,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,2,3,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,2,3,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,2,3,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,7,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,2,4,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,2,4,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,2,4,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,2,4,1,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,4,1,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,4,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,2,4,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,2,4,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,2,4,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,2,4,3,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,4,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,2,4,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,2,4,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,2,4,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,2,4,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,2,4,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,2,4,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,2,4,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,6,1,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,2,6,1,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,2,6,1,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,2,6,1,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,2,6,1,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,2,6,1,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,2,6,3,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,2,6,3,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,2,6,3,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,2,6,3,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,2,6,3,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,2,6,3,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,2,6,4,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,2,6,4,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,2,6,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,2,6,4,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,2,6,4,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,2,6,4,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,2,6,7,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,6,7,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,6,7,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,6,7,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,6,7,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,6,7,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,7,1,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,1,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,3,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,3,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,3,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,3,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,3,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,6,1,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,6,1,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,6,3,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,6,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,3,1,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,3,1,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,3,1,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,3,1,2,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,2,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,3,1,4,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,3,1,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,3,1,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,3,1,4,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,4,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,3,1,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,3,1,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,3,1,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,3,1,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,3,1,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,3,1,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,1,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,1,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,1,7,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,1,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,1,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,3,2,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,3,2,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,3,2,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,3,2,1,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,2,1,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,2,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,3,2,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,3,2,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,2,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,2,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,3,2,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,3,2,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,3,2,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,3,2,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,3,2,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,3,2,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,7,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,3,4,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,3,4,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,3,4,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,3,4,1,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,4,1,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,4,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,3,4,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,3,4,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,3,4,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,3,4,2,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,4,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,3,4,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,3,4,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,3,4,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,7,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,6,1,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,3,6,1,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,3,6,1,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,3,6,1,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,3,6,1,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,1,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,2,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,3,6,2,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,3,6,2,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,3,6,2,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,3,6,2,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,2,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,4,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,3,6,4,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,3,6,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,3,6,4,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,3,6,4,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,4,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,7,1,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,6,7,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,6,7,2,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,6,7,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,6,7,4,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,6,7,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,7,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,1,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,1,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,2,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,4,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,6,2,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,4,1,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,4,1,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,4,1,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,4,1,2,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,1,2,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,1,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,4,1,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,4,1,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,4,1,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,4,1,3,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,1,3,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,1,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,4,1,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,4,1,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,4,1,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,4,1,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,4,1,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,4,1,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,4,2,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,4,2,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,4,2,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,4,2,1,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,2,1,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,2,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,4,2,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,4,2,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,4,2,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,4,2,3,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,2,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,2,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,4,2,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,4,2,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,4,2,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,4,2,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,4,2,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,4,2,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,4,3,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,4,3,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,4,3,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,4,3,1,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,1,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5]=>0
[5,4,3,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[5]=>0
[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[4]=>0
[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4]=>0
[5,4,3,2,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,4,3,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,4,3,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[3]=>0
[5,4,3,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[3]=>0
[5,4,3,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,4,3,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3]=>0
[5,4,3,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,7,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,4,6,1,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,4,6,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,4,6,1,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,4,6,1,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,4,6,1,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,4,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,4,6,2,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,4,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,4,6,2,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,4,6,2,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,4,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,4,6,3,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2]=>0
[5,4,6,3,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2]=>0
[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,4,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2]=>0
[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,6,7,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,6,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,1,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,1,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,2,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,2,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,3,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,6,1,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,6,2,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,7,6,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,1,2,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,1,2,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,1,2,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,1,2,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,1,3,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,1,3,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,1,3,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,1,3,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,1,3,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,1,4,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,1,4,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,1,4,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,1,4,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,1,7,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,1,7,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,1,7,3,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,1,7,3,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,1,7,4,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,2,1,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,2,1,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,2,1,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,2,1,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,2,3,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,2,3,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,2,3,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,2,4,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,2,4,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,2,4,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,2,4,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,2,4,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,2,7,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,7,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,7,3,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,7,3,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,7,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,7,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,3,1,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,3,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,3,1,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,3,1,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,3,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,3,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,3,2,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,3,2,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,3,4,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,3,7,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,3,7,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,3,7,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,3,7,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,3,7,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,3,7,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,4,1,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,4,1,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,4,1,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,4,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,4,2,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,4,2,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1]=>0
[5,6,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[1]=>0
[5,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[1]=>0
[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,4,7,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,2,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,3,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,3,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,6,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,6,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,3,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,3,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,3,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,3,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,4,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,2,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,2,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,2,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,3,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,6,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,6,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,6,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,6,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,2,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,2,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,4,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,4,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,7,4,8,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,6,7,4,8,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[6,7,4,5,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,4,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,6,4,7,8,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[6,4,5,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,4,6,7,8,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,5,6,7,8,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,5,8,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,4,3,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,6,7,4,3,8,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[6,7,4,5,3,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,5,4,7,3,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,4,5,7,3,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,4,6,7,3,8,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[4,5,6,7,3,8,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[6,5,4,3,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,5,3,4,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,4,5,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,4,3,6,7,8,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[5,3,4,6,7,8,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[4,3,5,6,7,8,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[3,4,5,6,7,8,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[6,7,5,8,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,7,8,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,5,7,4,8,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,4,5,8,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,5,6,7,8,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,7,8,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,4,3,2,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,7,4,3,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,7,4,5,3,2,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,5,7,3,2,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,5,6,7,3,2,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[6,5,7,3,4,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,5,4,3,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,5,3,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,4,6,3,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[4,5,6,3,7,2,8,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,2,1]=>3
[6,5,3,4,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,6,3,4,7,2,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[6,4,3,5,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,4,5,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,4,3,6,7,2,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[4,5,3,6,7,2,8,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,1]=>3
[3,4,5,6,7,2,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[6,7,5,4,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,7,4,2,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,6,7,4,2,3,8,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[6,7,4,5,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,4,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,6,4,7,2,3,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[6,4,5,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,4,6,7,2,3,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[4,5,6,7,2,3,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[6,7,5,3,2,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,7,3,2,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,6,7,2,3,4,8,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[6,7,4,3,2,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,3,2,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,2,3,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,4,3,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,6,3,2,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[4,5,6,3,2,7,8,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[5,2,1]=>3
[6,5,3,4,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,4,5,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,3,6,2,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[4,3,5,6,2,7,8,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]=>[5,3,2]=>3
[3,4,5,6,2,7,8,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]=>[5,3,2,1]=>6
[6,5,4,2,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,6,4,2,3,7,8,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[6,4,5,2,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,6,2,3,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[4,5,6,2,3,7,8,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[5,2,1]=>3
[6,5,3,2,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,2,3,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,3,4,5,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,3,2,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,5,3,2,6,7,8,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[5,4,1]=>3
[5,3,4,2,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,3,5,2,6,7,8,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[5,4,2]=>3
[3,4,5,2,6,7,8,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1]=>[5,4,2,1]=>6
[5,4,2,3,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,5,2,3,6,7,8,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[5,4,1]=>3
[5,3,2,4,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[5,2,3,4,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,3,2,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[3,4,2,5,6,7,8,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1]=>[5,4,3,1]=>6
[4,2,3,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[3,2,4,5,6,7,8,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[2,3,4,5,6,7,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[6,7,8,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,5,7,4,8,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,4,5,8,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,4,7,8,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,6,4,7,8,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,4,6,7,8,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,5,6,7,8,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,5,7,4,3,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,6,7,4,3,8,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[6,7,4,5,3,8,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,5,4,7,3,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,6,4,7,3,8,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[6,4,5,7,3,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,4,6,7,3,8,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[4,5,6,7,3,8,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[6,5,4,3,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,6,4,3,7,8,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,4,6,3,7,8,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[4,5,6,3,7,8,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[5,6,3,4,7,8,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[6,4,3,5,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,4,5,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,4,3,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[4,5,3,6,7,8,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[5,3,4,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[4,3,5,6,7,8,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[3,4,5,6,7,8,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[6,7,8,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,5,4,8,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,7,4,8,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,6,7,4,8,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,4,6,7,8,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,5,6,7,8,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,4,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,7,4,8,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,6,7,4,8,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[6,7,4,5,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,4,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,6,4,7,8,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[6,4,5,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,4,6,7,8,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,5,6,7,8,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,5,8,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,8,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,5,7,8,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,8,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,5,4,3,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,7,4,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,7,4,3,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,4,5,3,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,4,7,3,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,6,4,7,3,2,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,4,6,7,3,2,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[4,5,6,7,3,2,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[3,2,1]=>3
[6,7,5,3,4,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,7,3,4,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,7,3,4,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,4,3,5,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,4,3,7,2,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,6,4,3,7,2,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[5,4,6,3,7,2,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[5,4,3,6,7,2,1,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[3,4,5,6,7,2,1,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]=>[4,3,2,1]=>6
[6,7,5,4,2,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,6,7,4,2,3,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,4,5,2,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,4,7,2,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,6,4,7,2,3,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,4,6,7,2,3,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[4,5,6,7,2,3,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[3,2,1]=>3
[6,5,7,3,2,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,7,3,2,4,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,5,2,3,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,7,2,3,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,7,2,3,4,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,4,3,2,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,4,2,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,4,2,3,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,2,4,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,2,3,4,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,4,3,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,6,4,3,2,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[5,4,6,3,2,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[5,6,3,4,2,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[6,3,4,5,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,4,3,6,2,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[4,5,3,6,2,7,1,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[5,3,1]=>3
[5,3,4,6,2,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[4,3,5,6,2,7,1,8]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]=>[5,3,2]=>3
[5,4,6,2,3,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[6,5,3,2,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,2,3,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,3,2,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,2,3,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,4,3,2,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[5,4,2,3,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[4,5,2,3,6,7,1,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]=>[5,4,1]=>3
[5,2,3,4,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[4,3,2,5,6,7,1,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]=>[5,4,3]=>3
[3,4,2,5,6,7,1,8]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]=>[5,4,3,1]=>6
[4,2,3,5,6,7,1,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]=>[5,4,3]=>3
[3,2,4,5,6,7,1,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2]=>[5,4,3,2]=>6
[2,3,4,5,6,7,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1]=>[5,4,3,2,1]=>10
[6,7,5,4,3,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,4,6,7,3,1,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[4,5,6,7,3,1,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[3,2,1]=>3
[6,5,7,3,4,1,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,7,3,4,5,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,4,3,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,4,5,3,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,6,3,4,7,1,2,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[6,4,3,5,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,3,4,5,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,3,5,6,7,1,2,8]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]=>[4,3,2]=>3
[3,4,5,6,7,1,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]=>[4,3,2,1]=>6
[6,5,7,4,2,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,4,6,7,2,1,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[4,5,6,7,2,1,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[3,2,1]=>3
[5,6,7,4,1,2,3,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[5,6,4,7,1,2,3,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,4,6,7,1,2,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[4,5,6,7,1,2,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[3,2,1]=>3
[6,7,5,2,3,1,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,7,2,3,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,7,2,3,1,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[5,6,7,3,1,2,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,5,2,1,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,6,7,2,1,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,5,1,2,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,7,1,2,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,7,1,2,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[6,7,4,3,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,4,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,4,2,3,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,2,4,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,2,3,4,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,4,1,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,2,1,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,2,3,1,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,1,2,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,1,2,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,4,3,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[5,4,6,3,2,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[4,5,6,3,2,1,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]=>[6,2,1]=>3
[6,5,3,4,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,3,4,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,3,4,5,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,4,3,6,2,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[3,4,5,6,2,1,7,8]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1]=>[6,3,2,1]=>6
[5,4,6,2,3,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,6,3,2,4,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,5,2,3,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,2,3,4,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,4,3,2,5,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,3,4,5,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,4,3,2,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[3,4,5,2,6,1,7,8]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1]=>[6,4,2,1]=>6
[5,3,2,4,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,2,3,4,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[4,3,2,5,6,1,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]=>[6,4,3]=>3
[4,2,3,5,6,1,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]=>[6,4,3]=>3
[3,2,4,5,6,1,7,8]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2]=>[6,4,3,2]=>6
[2,3,4,5,6,1,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1]=>[6,4,3,2,1]=>10
[6,5,4,3,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,4,3,1,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,4,5,3,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,4,6,3,1,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,6,3,4,1,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,4,3,5,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,4,3,6,1,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[3,4,5,6,1,2,7,8]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1]=>[6,3,2,1]=>6
[6,5,4,2,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,4,2,1,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,4,5,2,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,4,6,2,1,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[4,5,6,2,1,3,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]=>[6,2,1]=>3
[6,5,4,1,2,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,5,6,1,2,3,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]=>[6,2,1]=>3
[6,5,3,2,1,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,3,2,1,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[5,6,2,1,3,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[6,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,4,3,2,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,3,4,2,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,4,3,1,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,4,2,1,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,4,1,2,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,3,2,1,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,3,1,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,3,1,2,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,1,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,1,2,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,4,3,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,3,4,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[4,3,5,2,1,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]=>[6,5,2]=>3
[3,4,5,2,1,6,7,8]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1]=>[6,5,2,1]=>6
[5,4,2,3,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,3,2,4,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,2,3,4,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[4,3,2,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]=>[6,5,3]=>3
[4,2,3,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]=>[6,5,3]=>3
[3,2,4,5,1,6,7,8]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2]=>[6,5,3,2]=>6
[2,3,4,5,1,6,7,8]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1]=>[6,5,3,2,1]=>10
[5,4,3,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,3,4,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[4,3,5,1,2,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]=>[6,5,2]=>3
[3,4,5,1,2,6,7,8]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1]=>[6,5,2,1]=>6
[5,4,2,1,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,4,1,2,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,3,2,1,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,2,3,1,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,3,1,2,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,2,1,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[4,3,2,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]=>[6,5,4]=>3
[3,4,2,1,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1]=>[6,5,4,1]=>6
[4,2,3,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]=>[6,5,4]=>3
[3,2,4,1,5,6,7,8]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2]=>[6,5,4,2]=>6
[4,3,1,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]=>[6,5,4]=>3
[3,4,1,2,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1]=>[6,5,4,1]=>6
[4,2,1,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]=>[6,5,4]=>3
[4,1,2,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]=>[6,5,4]=>3
[6,8,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,8,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,5,8,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,8,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,6,8,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,6,8,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,6,8,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,6,7,8,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,5,8,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,7,8,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[6,5,4,8,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,6,5,8,7,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,5,6,8,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[5,7,6,4,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,7,6,5,8,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,6,7,5,8,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[5,4,7,6,8,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,5,7,6,8,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,6,5,7,8,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,8,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,7,6,8,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,5,8,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,8,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,5,6,8,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[3,7,6,5,8,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,6,7,5,8,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,5,7,6,8,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[3,5,6,7,8,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[4,3,8,7,6,5,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,6,7,8,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,4,8,7,6,5,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,6,7,8,5,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[5,4,3,8,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,3,7,8,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,5,3,7,8,6,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[3,5,4,7,8,6,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[4,3,5,7,8,6,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,4,5,8,7,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,7,8,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[6,5,4,3,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,4,3,8,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,6,3,8,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[4,3,6,5,8,7,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,4,3,6,8,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,5,3,6,8,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,3,5,6,8,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,4,5,6,8,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[5,7,6,4,3,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,7,6,5,3,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,4,7,6,3,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[3,7,6,5,4,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,5,7,6,4,8,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,5,6,7,4,8,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[4,3,7,6,5,8,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,4,7,6,5,8,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,4,6,7,5,8,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[4,5,3,7,6,8,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[3,5,4,7,6,8,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[4,3,5,7,6,8,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,4,5,7,6,8,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[3,6,5,4,7,8,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[3,5,6,4,7,8,2,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[4,3,6,5,7,8,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,4,6,5,7,8,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[3,5,4,6,7,8,2,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[2,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,6,8,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,7,8,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,8,7,6,4,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,7,5,8,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,5,7,8,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,6,7,8,4,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,4,8,7,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,7,8,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,6,8,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,7,8,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,5,4,8,7,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,4,7,8,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,4,5,7,8,6,3,1]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,6,5,4,8,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,5,6,4,8,7,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,4,6,5,8,7,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,5,6,8,7,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,7,6,5,4,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,7,5,4,8,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,6,7,4,8,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,4,7,6,5,8,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,6,7,5,8,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,5,4,7,6,8,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,5,4,7,8,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,5,6,4,7,8,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,4,6,5,7,8,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,5,4,6,7,8,3,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,4,5,6,7,8,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,2,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,8,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,2,5,7,8,6,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[3,2,6,7,5,8,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[3,2,5,7,6,8,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[3,2,5,6,7,8,4,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]=>[4,3,2,2]=>5
[2,3,8,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,6,7,8,5,4,1]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,3,5,8,7,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,5,7,8,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,6,5,8,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,3,5,6,8,7,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]=>[4,3,2,2,1]=>9
[2,3,7,6,5,8,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,5,7,6,8,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,5,6,7,8,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]=>[4,3,2,2,1]=>9
[4,3,2,8,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,2,7,8,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[4,3,2,6,8,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,4,2,8,7,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,4,2,7,8,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[2,4,3,8,7,6,5,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,6,8,7,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,3,6,7,8,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1]=>8
[3,2,4,8,7,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,2,4,7,8,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[2,3,4,8,7,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,6,8,7,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[2,3,4,7,6,8,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,6,7,8,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1]=>[4,3,3,2,1]=>9
[5,4,3,2,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,3,2,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,5,3,2,8,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,5,4,2,7,8,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[4,3,5,2,8,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,4,5,2,7,8,6,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]=>[4,4,2,1]=>5
[2,5,4,3,8,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,5,4,3,7,8,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,4,5,3,8,7,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[2,4,5,3,7,8,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]=>[4,4,2,1,1]=>8
[3,2,5,4,7,8,6,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[2,3,5,4,8,7,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,5,4,7,8,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1]=>[4,4,2,2,1]=>8
[4,3,2,5,8,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,3,2,5,7,8,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[3,4,2,5,8,7,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[3,4,2,5,7,8,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]=>[4,4,3,1]=>5
[2,4,3,5,8,7,6,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[3,2,4,5,7,8,6,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]=>[4,4,3,2]=>5
[2,3,4,5,8,7,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,5,7,8,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1]=>[4,4,3,2,1]=>9
[6,5,4,3,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,5,3,2,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,4,6,3,2,8,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[4,5,6,3,2,8,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[3,6,5,4,2,8,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,5,6,4,2,8,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[4,3,6,5,2,8,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[5,4,3,6,2,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[4,5,3,6,2,8,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[2,6,5,4,3,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,4,6,5,3,8,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,5,6,3,8,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]=>[5,3,2,1,1]=>9
[3,2,6,5,4,8,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[2,3,5,6,4,8,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1]=>[5,3,2,2,1]=>9
[4,3,2,6,5,8,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[3,4,2,6,5,8,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[5,3,3,1]=>5
[2,4,3,6,5,8,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[3,2,4,6,5,8,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[2,3,4,6,5,8,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]=>[5,3,3,2,1]=>9
[5,4,3,2,6,8,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,5,3,2,6,8,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[2,5,4,3,6,8,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,4,5,3,6,8,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]=>[5,4,2,1,1]=>9
[3,2,5,4,6,8,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]=>[5,4,2,2]=>5
[4,3,2,5,6,8,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[3,4,2,5,6,8,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]=>[5,4,3,1]=>6
[2,4,3,5,6,8,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1]=>[5,4,3,1,1]=>9
[3,2,4,5,6,8,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]=>[5,4,3,2]=>6
[2,3,4,5,6,8,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1]=>[5,4,3,2,1]=>10
[5,7,6,4,3,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,7,6,5,3,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,6,7,5,3,2,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[4,6,5,7,3,2,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,7,6,4,2,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,6,7,4,2,8,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[4,3,7,6,5,2,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,6,7,5,2,8,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,4,7,6,5,2,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,4,6,7,5,2,8,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[5,4,3,7,6,2,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,5,3,7,6,2,8,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[3,5,4,7,6,2,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,4,5,7,6,2,8,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[4,6,5,3,7,2,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,6,5,4,7,2,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[3,5,6,4,7,2,8,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[4,3,6,5,7,2,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,4,6,5,7,2,8,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]=>[4,2,2,1]=>5
[3,5,4,6,7,2,8,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[2,7,6,5,4,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,7,4,3,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,6,7,4,3,8,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,4,6,7,5,3,8,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,5,4,7,6,3,8,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,4,6,5,7,3,8,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,5,4,6,7,3,8,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,4,5,6,7,3,8,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,2,7,6,5,4,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,7,5,4,8,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]=>[3,2,2,2]=>3
[3,2,5,7,6,4,8,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,2,6,5,7,4,8,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,2,5,6,7,4,8,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]=>[4,3,2,2]=>5
[2,3,7,6,5,4,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,5,7,6,4,8,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,5,6,7,4,8,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1]=>[4,3,2,2,1]=>9
[4,3,2,7,6,5,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,2,6,7,5,8,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,3,3]=>2
[3,4,2,7,6,5,8,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[3,4,2,6,7,5,8,1]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]=>[4,3,3,1]=>5
[2,4,3,7,6,5,8,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,6,7,5,8,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1]=>[4,3,3,1,1]=>8
[3,2,4,7,6,5,8,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[2,3,4,7,6,5,8,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,6,7,5,8,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1]=>[4,3,3,2,1]=>9
[5,4,3,2,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,5,4,2,7,6,8,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[4,3,5,2,7,6,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[3,4,5,2,7,6,8,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]=>[4,4,2,1]=>5
[2,5,4,3,7,6,8,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[3,2,5,4,7,6,8,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[2,3,5,4,7,6,8,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]=>[4,4,2,2,1]=>8
[4,3,2,5,7,6,8,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[3,4,2,5,7,6,8,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1]=>[4,4,3,1]=>5
[2,4,3,5,7,6,8,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1]=>[4,4,3,1,1]=>8
[3,2,4,5,7,6,8,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2]=>[4,4,3,2]=>5
[2,3,4,5,7,6,8,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,6,5,4,2,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[3,5,6,4,2,7,8,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[3,4,6,5,2,7,8,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[3,5,4,6,2,7,8,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[2,6,5,4,3,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,5,6,4,3,7,8,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,4,6,5,3,7,8,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,5,4,6,3,7,8,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]=>[5,3,1,1,1]=>7
[2,4,5,6,3,7,8,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1]=>[5,3,2,1,1]=>9
[3,2,5,6,4,7,8,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]=>[5,3,2,2]=>5
[2,3,6,5,4,7,8,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,5,6,4,7,8,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1]=>[5,3,2,2,1]=>9
[4,3,2,6,5,7,8,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[3,4,2,6,5,7,8,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1]=>[5,3,3,1]=>5
[2,4,3,6,5,7,8,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,3,4,6,5,7,8,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1]=>[5,3,3,2,1]=>9
[3,5,4,2,6,7,8,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[2,5,4,3,6,7,8,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,4,5,3,6,7,8,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1]=>[5,4,2,1,1]=>9
[3,2,5,4,6,7,8,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]=>[5,4,2,2]=>5
[2,3,5,4,6,7,8,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1]=>[5,4,2,2,1]=>9
[2,4,3,5,6,7,8,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1]=>[5,4,3,1,1]=>9
[1,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,6,8,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,8,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,8,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,8,7,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,6,5,8,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,5,8,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,7,6,8,4,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,7,8,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,6,7,8,4,3,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,4,8,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,7,8,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,6,8,7,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,4,6,7,8,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,5,4,7,8,6,3,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,5,8,7,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,4,5,7,8,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,6,5,4,8,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,4,6,5,8,7,3,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,5,4,6,8,7,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,7,6,5,4,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,6,5,8,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,6,7,5,8,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,6,5,4,7,8,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,4,6,7,8,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,4,5,6,7,8,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[1,3,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,8,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,6,8,7,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,3,6,7,8,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,3,5,8,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,8,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,6,8,7,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[4,3,2,2,1,1]=>13
[1,3,6,7,5,8,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,3,5,7,6,8,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,6,5,7,8,4,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,4,3,8,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,3,7,8,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,3,6,8,7,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[1,4,3,7,6,8,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,3,4,8,7,6,5,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,5,4,3,8,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,4,5,3,8,7,6,2]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[1,3,4,5,7,8,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1,1]=>[4,4,3,2,1,1]=>13
[1,6,5,4,3,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,6,4,3,8,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,4,6,5,3,8,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[1,3,4,5,6,8,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1,1]=>[5,4,3,2,1,1]=>14
[1,7,6,5,4,3,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,5,4,3,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,5,7,4,3,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,6,7,5,3,8,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,5,6,4,7,3,8,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,4,6,5,7,3,8,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,5,4,6,7,3,8,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,4,5,6,7,3,8,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[1,6,5,4,3,7,8,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,4,3,6,7,8,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]=>[5,4,1,1,1,1]=>9
[1,4,5,3,6,7,8,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1,1]=>[5,4,2,1,1,1]=>12
[1,4,3,5,6,7,8,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1,1]=>[5,4,3,1,1,1]=>12
[1,3,4,5,6,7,8,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,1]=>[5,4,3,2,1,1]=>14
[2,1,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,8,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,8,7,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,7,6,8,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,7,8,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,5,8,7,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,5,7,8,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,6,5,8,7,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,1,5,6,8,7,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,3,2,2,2]=>7
[2,1,7,6,5,8,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,7,5,8,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,5,7,6,8,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,6,5,7,8,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,1,5,6,7,8,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2]=>[4,3,2,2,2]=>7
[2,1,4,8,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,4,7,8,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,4,5,8,7,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]=>[4,4,3,2,2]=>8
[2,1,7,6,5,4,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,7,5,4,8,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,5,4,6,7,8,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2]=>[5,4,2,2,2]=>7
[2,1,4,5,6,7,8,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2]=>[5,4,3,2,2]=>9
[1,2,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,8,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,6,7,8,5,4,3]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,5,8,7,6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,6,5,8,7,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,7,6,5,8,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,5,6,7,8,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2,1]=>[4,3,2,2,2,1]=>12
[1,2,4,8,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,4,5,6,8,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2,1]=>[5,4,3,2,2,1]=>14
[1,2,7,6,5,4,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,5,6,7,4,8,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2,1]=>[4,3,2,2,2,1]=>12
[1,2,6,5,4,7,8,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]=>[5,2,2,2,2,1]=>9
[1,2,5,4,6,7,8,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2,1]=>[5,4,2,2,2,1]=>12
[1,2,4,5,6,7,8,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2,1]=>[5,4,3,2,2,1]=>14
[3,2,1,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,7,8,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,6,8,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[3,2,1,7,6,8,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,6,7,8,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]=>[4,3,3,3]=>3
[2,3,1,8,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[1,3,2,8,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[2,1,3,8,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,7,8,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,5,6,7,8,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2]=>[5,4,3,3,2]=>9
[1,2,3,8,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,6,7,8,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2,1]=>[4,3,3,3,2,1]=>12
[1,2,3,7,6,5,8,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,6,7,5,8,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2,1]=>[4,3,3,3,2,1]=>12
[1,2,3,6,5,7,8,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2,1]=>[5,3,3,3,2,1]=>12
[4,3,2,1,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,3,2,1,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[3,4,2,1,8,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[3,2,4,1,8,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[2,3,4,1,8,7,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[4,4,4,2,1]=>7
[1,3,4,2,8,7,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]=>[4,4,4,2,1,1]=>11
[3,2,1,4,7,8,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]=>[4,4,4,3]=>3
[2,3,1,4,8,7,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]=>[4,4,4,3,1]=>7
[5,4,3,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,4,3,2,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[4,5,3,2,1,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[3,5,4,2,1,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[4,3,5,2,1,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[2,3,4,5,1,8,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1]=>[5,5,3,2,1]=>9
[1,4,5,3,2,8,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1,1]=>[5,5,2,1,1,1]=>11
[4,3,2,1,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]=>[5,5,4]=>2
[2,3,4,1,5,8,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1]=>[5,5,4,2,1]=>9
[1,4,3,2,5,7,8,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1,1]=>[5,5,4,1,1,1]=>11
[3,2,1,4,5,7,8,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3]=>[5,5,4,3]=>5
[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,6,4,3,2,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[4,6,5,3,2,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[5,4,6,3,2,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[4,5,6,3,2,1,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,2,1]=>3
[3,6,5,4,2,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,5,6,4,2,1,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[6,2,1,1]=>5
[4,3,6,5,2,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[3,4,6,5,2,1,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]=>[6,2,2,1]=>5
[5,4,3,6,2,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[4,5,3,6,2,1,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1]=>3
[4,3,5,6,2,1,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,3,2]=>3
[3,4,5,6,2,1,8,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1]=>[6,3,2,1]=>6
[2,6,5,4,3,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,5,6,4,3,1,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[6,2,1,1,1]=>7
[5,4,3,2,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[4,5,3,2,6,1,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[6,4,1]=>3
[3,4,5,2,6,1,8,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1]=>[6,4,2,1]=>6
[2,3,4,5,6,1,8,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1]=>[6,4,3,2,1]=>10
[1,6,5,4,3,2,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,5,6,4,3,2,8,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1,1]=>[6,2,1,1,1,1]=>9
[2,1,6,5,4,3,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]=>[6,2,2,2,2]=>4
[5,4,3,2,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[3,4,5,2,1,6,8,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1]=>[6,5,2,1]=>6
[2,3,4,5,1,6,8,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1]=>[6,5,3,2,1]=>10
[5,7,6,4,3,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,7,6,5,3,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,6,7,5,3,2,1,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[5,4,7,6,3,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[4,5,7,6,3,2,1,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[4,6,5,7,3,2,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[3,5,7,6,4,2,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,6,7,4,2,1,8]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]=>[3,2,1,1]=>5
[4,3,7,6,5,2,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,4,7,6,5,2,1,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[5,4,3,7,6,2,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,5,3,7,6,2,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[3,5,4,7,6,2,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[4,3,5,7,6,2,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[3,6,5,4,7,2,1,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[3,5,6,4,7,2,1,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[4,2,1,1]=>5
[4,3,6,5,7,2,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[2,7,6,5,4,3,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,7,5,4,3,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,7,6,4,3,1,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,6,7,4,3,1,8]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,4,6,7,5,3,1,8]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,5,4,7,6,3,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,6,4,7,3,1,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,5,4,6,7,3,1,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,4,5,6,7,3,1,8]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,2,7,6,5,4,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,7,5,4,1,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[3,2,5,7,6,4,1,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[3,2,6,5,7,4,1,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[2,3,7,6,5,4,1,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,6,7,5,4,1,8]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]=>[3,2,2,2,1]=>7
[4,3,2,6,7,5,1,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[3,4,2,7,6,5,1,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[3,3,3,1]=>3
[2,3,4,7,6,5,1,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,6,7,5,1,8]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1]=>[4,3,3,2,1]=>9
[5,4,3,2,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[4,5,3,2,7,6,1,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[3,5,4,2,7,6,1,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[4,3,5,2,7,6,1,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[2,3,4,5,7,6,1,8]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,6,5,4,2,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,5,6,4,2,7,1,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,2,1,1]=>5
[3,4,6,5,2,7,1,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,2,2,1]=>5
[3,5,4,6,2,7,1,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[1,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,5,4,3,2,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,5,7,4,3,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,6,7,4,3,2,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,4,7,6,5,3,2,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,6,7,5,3,2,8]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,5,4,7,6,3,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,6,4,7,3,2,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,3,7,6,5,4,2,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,5,3,6,7,2,8]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1,1]=>[5,4,2,1,1,1]=>12
[2,1,7,6,5,4,3,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,7,6,5,4,3,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,2,1,7,6,5,4,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[5,4,3,2,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[3,6,5,4,2,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,3,6,5,2,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[2,4,5,6,3,1,7,8]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1]=>[6,3,2,1,1]=>9
[2,3,6,5,4,1,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]=>[6,2,2,2,1]=>7
[2,3,5,6,4,1,7,8]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1]=>[6,3,2,2,1]=>9
[2,3,4,6,5,1,7,8]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1]=>[6,3,3,2,1]=>9
[1,6,5,4,3,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,4,5,6,3,2,7,8]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1,1]=>[6,3,2,1,1,1]=>12
[2,5,4,3,1,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]=>[6,5,1,1,1]=>7
[2,4,5,3,1,6,7,8]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1]=>[6,5,2,1,1]=>9
[2,3,5,4,1,6,7,8]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1]=>[6,5,2,2,1]=>9
[1,4,5,3,2,6,7,8]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1,1]=>[6,5,2,1,1,1]=>12
[2,1,5,4,3,6,7,8]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2]=>[6,5,2,2,2]=>7
[2,4,3,1,5,6,7,8]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1]=>[6,5,4,1,1]=>9
[1,2,3,7,5,6,8,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,5,6,7,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,5,7,6,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,6,7,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,4,8,5,6,7,3]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,4,8,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,6,4,5,7,8,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]=>[5,2,2,2,2,1]=>9
[1,2,7,4,5,6,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,4,5,6,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,4,6,7,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,4,7,6,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,5,4,6,3,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,5,4,6,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,5,4,6,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,5,4,7,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,5,6,4,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,5,6,7,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,6,5,7,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,7,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,2,8,5,7,6,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,3,2,8,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,3,2,8,6,7,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,3,4,2,8,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]=>[4,4,4,2,1,1]=>11
[1,3,4,8,5,6,7,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,3,4,8,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,3,4,8,6,7,5,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,3,7,4,5,6,2,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,4,5,6,8,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,4,5,6,7,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,4,6,5,7,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,4,6,7,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,5,4,6,7,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,5,4,7,6,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,5,6,7,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,5,7,6,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,6,5,7,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,7,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,3,8,5,6,7,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,3,8,5,7,6,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,3,8,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,3,8,6,7,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,3,4,6,7,8,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]=>[5,4,1,1,1,1]=>9
[1,5,3,4,8,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,6,3,4,5,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,3,4,5,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,3,4,5,6,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,4,5,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,4,5,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,4,6,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,4,7,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,4,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,3,5,4,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,3,5,4,6,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,5,4,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,5,4,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,5,6,4,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,5,6,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,5,7,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,6,5,4,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,6,5,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,5,4,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,5,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,6,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,3,5,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,4,3,5,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,4,3,5,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,3,5,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,3,6,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,3,6,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,3,6,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,5,3,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,4,5,3,2,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,4,5,3,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,4,5,3,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,5,3,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,5,6,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,5,6,3,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,5,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,6,5,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,6,5,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,6,5,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,7,6,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,4,3,6,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,4,3,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,3,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,3,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,6,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,7,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,4,5,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,4,5,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,4,5,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,5,4,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,3,8,5,6,7,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,8,5,7,6,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,8,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,8,6,7,5,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,4,5,8,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]=>[4,4,3,2,2]=>8
[2,1,4,8,5,6,7,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,4,8,5,7,6,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,4,8,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,4,8,6,7,5,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,6,4,5,3,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]=>[6,2,2,2,2]=>4
[2,1,8,4,5,6,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,4,5,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,4,6,5,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,4,6,5,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,4,6,7,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,4,7,6,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,4,6,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,4,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,5,6,4,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,6,4,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,6,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,7,6,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,7,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,3,1,8,5,6,7,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,3,1,8,6,7,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,3,4,1,8,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[4,4,4,2,1]=>7
[2,3,4,5,8,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,7,5,6,1,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,5,6,8,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,5,6,7,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,5,7,6,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,6,7,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,5,4,8,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,6,4,5,1,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]=>[6,2,2,2,1]=>7
[2,3,6,4,5,7,8,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,6,4,5,8,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,7,4,5,6,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,4,5,6,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,4,6,5,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,4,6,7,5,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,5,4,6,1,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,5,4,6,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,5,4,6,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,5,6,4,1,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,5,6,4,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,5,6,4,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,5,6,7,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,5,7,6,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,3,5,8,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[2,4,3,7,5,6,8,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,8,5,6,7,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,8,5,7,6,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,8,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,8,6,7,5,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,5,3,4,1,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]=>[6,5,1,1,1]=>7
[2,5,3,4,6,7,8,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,5,3,4,6,8,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,5,3,4,7,6,8,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,5,3,4,8,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,5,3,4,8,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,6,3,4,5,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,3,4,5,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,3,4,5,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,7,3,4,5,6,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,4,5,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,4,5,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,5,4,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,3,5,4,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,3,5,4,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,3,5,4,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,7,3,5,4,6,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,5,4,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,3,5,6,4,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,5,6,7,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,5,7,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,3,6,5,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,7,5,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,7,6,5,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,4,3,8,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,6,4,3,5,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,4,3,5,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,4,3,5,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,7,4,3,5,6,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,5,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,5,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,3,6,5,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,6,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,6,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,7,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,5,3,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,4,5,3,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,4,5,3,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,4,5,3,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,4,5,3,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,5,6,3,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,5,6,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,5,6,3,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,5,6,7,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,6,5,3,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,6,5,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,6,5,3,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,7,6,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,4,3,6,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,3,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,3,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,4,6,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,6,7,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,7,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,4,5,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,4,6,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,1,7,5,6,4,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,5,6,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,5,7,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,4,1,8,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,2,4,5,8,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[3,2,4,7,5,6,8,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[3,2,4,8,5,6,7,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,2,4,8,6,7,5,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,2,5,4,8,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,2,7,4,5,6,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,4,5,6,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,4,6,5,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,4,6,5,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,4,6,5,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,5,4,6,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,5,4,6,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,5,4,7,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,5,6,4,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,5,6,4,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,5,6,4,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,5,7,6,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,6,5,7,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,7,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,3,1,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]=>[5,5,4]=>2
[4,2,3,1,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,2,3,1,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,2,3,5,6,8,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[4,2,3,5,8,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,2,3,6,5,8,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,2,3,7,5,6,1,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,2,3,7,5,6,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,2,3,8,5,6,7,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,3,8,5,7,6,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,3,7,6,5,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,2,3,8,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,3,8,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,2,3,4,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,2,3,4,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,2,3,4,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,3,4,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,2,3,4,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,2,3,4,8,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,3,4,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,2,3,4,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,3,4,5,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,3,5,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,3,5,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,3,5,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,2,3,5,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,2,4,3,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,2,4,3,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,2,4,3,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[5,2,4,3,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,4,3,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,2,4,3,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,2,4,3,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[5,2,4,3,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,2,4,3,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,2,4,3,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,2,4,3,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,4,5,3,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,4,5,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,4,5,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,5,4,3,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,5,4,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,5,4,3,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,2,5,4,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,3,2,1,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,3,2,7,5,6,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,2,8,5,6,7,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,2,8,5,7,6,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,2,8,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,3,2,4,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,3,2,4,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[5,3,2,4,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,2,4,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,3,2,4,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,3,2,5,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,3,2,5,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,2,5,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,3,2,5,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,2,5,4,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,3,4,2,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,3,4,2,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,3,4,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,4,2,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,3,4,2,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,3,4,2,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,3,4,2,8,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,3,4,2,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,4,5,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,4,5,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,5,4,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,5,4,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,3,5,4,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,5,4,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,4,3,2,8,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,4,3,2,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,3,2,5,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,3,5,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,3,4,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,4,1,6,3,8,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,6,1,3,8,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,1,6,8,3,5,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,6,1,8,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,8,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,7,1,3,5,8]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,1,6,3,7,8,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,6,1,3,7,8,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,1,6,7,3,8,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,6,1,7,3,8,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,7,1,3,8,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,1,6,7,8,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,6,1,7,8,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,7,1,8,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,7,8,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,1,7,3,5,8,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,7,1,3,5,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,1,7,3,8,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,7,1,3,8,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,1,4,7,8,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,4,1,7,8,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,7,1,8,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,7,8,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,1,5,7,3,8,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1]=>[4,4,3,1,1]=>8
[2,4,5,1,7,3,8,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1]=>[4,4,2,1,1]=>8
[2,4,5,7,1,3,8,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,4,5,1,7,8,3,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]=>[4,4,2,1,1]=>8
[2,4,5,7,1,8,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,4,5,7,8,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,1,4,8,3,5,6,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,4,1,8,3,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,8,1,3,5,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,1,4,5,8,3,6,7]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]=>[4,4,3,2,2]=>8
[2,4,1,5,8,3,6,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[2,4,5,1,8,3,6,7]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[2,4,1,5,6,8,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1]=>[5,4,3,1,1]=>9
[2,4,5,1,6,8,3,7]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]=>[5,4,2,1,1]=>9
[2,4,5,6,1,8,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]=>[5,3,2,1,1]=>9
[2,4,5,6,8,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,4,1,3,5,6,7,8]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1]=>[6,5,4,1,1]=>9
[2,4,5,1,3,6,7,8]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1]=>[6,5,2,1,1]=>9
[2,4,5,6,1,3,7,8]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1]=>[6,3,2,1,1]=>9
[2,4,5,6,7,1,3,8]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,4,1,5,6,7,8,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1]=>[5,4,3,1,1]=>9
[2,4,5,6,1,7,8,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1]=>[5,3,2,1,1]=>9
[2,4,5,6,7,1,8,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,4,5,6,7,8,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,5,6,1,3,4,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[6,2,1,1,1]=>7
[2,5,1,3,6,8,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,5,1,6,3,8,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]=>[5,3,1,1,1]=>7
[2,5,6,1,3,8,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,1,5,6,8,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,3,2,2,2]=>7
[2,5,1,6,8,3,4,7]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,5,6,8,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,5,6,1,3,7,4,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,5,1,6,7,3,4,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,5,6,1,7,3,4,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,1,5,3,6,7,8,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2]=>[5,4,2,2,2]=>7
[2,5,1,3,6,7,8,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,5,1,6,3,7,8,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]=>[5,3,1,1,1]=>7
[2,5,6,1,3,7,8,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,5,1,6,7,3,8,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,5,6,7,1,3,8,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,1,5,6,7,8,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2]=>[4,3,2,2,2]=>7
[2,5,1,6,7,8,3,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,5,6,1,7,8,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,5,6,7,1,8,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,5,6,7,8,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,5,1,3,7,4,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,5,1,7,3,4,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,7,1,3,4,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,1,3,7,8,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,1,5,7,3,8,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,5,1,7,3,8,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,7,1,3,8,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,1,5,7,8,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,5,1,7,8,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,7,1,8,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,7,8,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,3,5,1,7,4,8,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,5,7,1,4,8,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,5,7,1,8,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,5,1,3,8,4,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,1,5,8,3,4,6,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,5,1,8,3,4,6,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,8,1,3,4,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,3,5,1,8,4,6,7]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,5,8,1,4,6,7]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,5,1,6,8,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1]=>[5,4,2,2,1]=>9
[2,3,5,6,1,8,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1]=>[5,3,2,2,1]=>9
[2,3,5,6,8,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]=>[4,3,2,2,1]=>9
[2,1,5,3,4,6,7,8]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2]=>[6,5,2,2,2]=>7
[2,5,1,3,4,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]=>[6,5,1,1,1]=>7
[2,3,5,1,4,6,7,8]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1]=>[6,5,2,2,1]=>9
[2,3,5,6,1,4,7,8]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1]=>[6,3,2,2,1]=>9
[2,3,5,1,6,7,8,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1]=>[5,4,2,2,1]=>9
[2,3,5,6,1,7,8,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1]=>[5,3,2,2,1]=>9
[2,3,5,6,7,1,8,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1]=>[4,3,2,2,1]=>9
[2,3,5,6,7,8,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]=>[4,3,2,2,1]=>9
[2,6,1,3,7,4,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,1,6,7,3,4,8,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,1,7,3,4,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,7,1,3,4,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,1,6,3,7,8,4,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,6,1,3,7,8,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,1,6,7,3,8,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,1,7,3,8,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,7,1,3,8,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,1,6,7,8,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,1,7,8,3,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,7,1,8,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,8,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,1,7,3,4,5,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,7,1,3,4,5,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,1,3,4,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,3,6,7,1,4,5,8]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,6,1,3,4,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,3,6,1,4,7,8,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,6,7,1,4,8,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,1,3,6,7,8,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2]=>[4,3,3,3,2]=>7
[2,3,6,1,7,8,4,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,3,6,7,1,8,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,3,6,7,8,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,1,6,3,8,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,6,1,3,8,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,1,6,8,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,1,8,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,8,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,1,3,4,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,3,6,1,4,8,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,6,1,8,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,3,6,8,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,1,6,3,4,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]=>[6,2,2,2,2]=>4
[2,6,1,3,4,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,3,4,6,1,8,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]=>[5,3,3,2,1]=>9
[2,3,4,6,8,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[2,6,1,3,4,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,3,6,1,4,5,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]=>[6,2,2,2,1]=>7
[2,3,4,6,1,5,7,8]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1]=>[6,3,3,2,1]=>9
[2,3,4,6,7,1,5,8]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1]=>[4,3,3,2,1]=>9
[2,3,4,6,1,7,8,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1]=>[5,3,3,2,1]=>9
[2,3,4,6,7,8,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1]=>[4,3,3,2,1]=>9
[2,1,7,3,8,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,1,3,8,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,8,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,1,8,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,3,4,8,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,3,7,1,4,8,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,1,3,7,8,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,3,1,7,8,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,3,7,8,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,1,7,3,4,5,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,1,3,4,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,7,1,4,5,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,4,7,1,5,8,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,1,8,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,8,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,1,7,3,4,5,6,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,1,3,4,5,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,7,1,4,5,6,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,4,7,1,5,6,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,5,7,1,6,8]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,5,7,1,8,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,5,7,8,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,1,8,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,3,8,4,5,6,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,3,1,8,4,5,6,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,3,8,1,4,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,1,4,8,5,6,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]=>[4,4,4,3,1]=>7
[2,3,4,1,8,5,6,7]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[4,4,4,2,1]=>7
[2,3,4,8,1,5,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,1,5,8,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1]=>[5,5,4,2,1]=>9
[2,3,4,5,1,8,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1]=>[5,5,3,2,1]=>9
[2,3,4,5,8,1,6,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,5,6,8,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1]=>[5,4,3,2,1]=>10
[3,4,6,1,2,5,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]=>[6,2,2,1]=>5
[3,1,4,6,2,8,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[3,4,1,6,2,8,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[5,3,3,1]=>5
[3,1,4,6,8,2,5,7]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[3,4,1,6,8,2,5,7]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[3,4,6,8,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,4,6,1,2,7,5,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,2,2,1]=>5
[3,4,6,7,1,2,5,8]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]=>[3,2,2,1]=>5
[3,1,4,6,2,7,8,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2]=>[5,3,3,2]=>5
[3,4,1,6,2,7,8,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1]=>[5,3,3,1]=>5
[3,4,6,1,2,7,8,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[3,1,4,6,7,2,8,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2]=>[4,3,3,2]=>5
[3,4,1,6,7,2,8,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]=>[4,3,3,1]=>5
[3,4,6,1,7,2,8,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]=>[4,2,2,1]=>5
[3,4,6,7,1,2,8,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[3,1,4,6,7,8,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]=>[4,3,3,2]=>5
[3,4,1,6,7,8,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]=>[4,3,3,1]=>5
[3,4,6,1,7,8,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[3,4,6,7,1,8,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[3,4,6,7,8,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[3,1,4,7,2,5,8,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[3,4,1,7,2,5,8,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[3,4,7,1,2,5,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,1,4,7,2,8,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[3,4,7,1,8,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,8,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,4,5,7,1,2,6,8]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]=>[3,3,2,1]=>5
[3,1,4,5,7,2,8,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2]=>[4,4,3,2]=>5
[3,4,1,5,7,2,8,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1]=>[4,4,3,1]=>5
[3,4,5,7,1,2,8,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[3,1,4,5,7,8,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]=>[4,4,3,2]=>5
[3,4,1,5,7,8,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]=>[4,4,3,1]=>5
[3,4,5,1,7,8,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]=>[4,4,2,1]=>5
[3,4,5,7,1,8,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,7,8,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[3,1,4,2,8,5,6,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,4,1,2,8,5,6,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[3,1,4,8,2,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,4,1,8,2,5,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,4,8,1,2,5,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,1,4,5,8,2,6,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[3,4,1,5,8,2,6,7]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[3,4,5,8,1,2,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,1,2,6,8,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1]=>[6,5,2,1]=>6
[3,4,5,1,6,2,8,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1]=>[6,4,2,1]=>6
[3,4,5,6,1,2,8,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1]=>[6,3,2,1]=>6
[3,1,4,5,6,8,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]=>[5,4,3,2]=>6
[3,4,1,5,6,8,2,7]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]=>[5,4,3,1]=>6
[3,4,5,6,1,8,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]=>[5,3,2,1]=>6
[3,4,5,6,8,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[3,1,4,2,5,6,7,8]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2]=>[6,5,4,2]=>6
[3,1,4,5,2,6,7,8]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2]=>[6,5,3,2]=>6
[3,4,5,1,6,2,7,8]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1]=>[6,4,2,1]=>6
[3,1,4,5,6,7,2,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2]=>[5,4,3,2]=>6
[3,4,1,5,6,7,2,8]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]=>[5,4,3,1]=>6
[3,1,4,5,6,7,8,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[3,4,1,5,6,7,8,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1]=>[5,4,3,1]=>6
[3,4,5,1,6,7,8,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1]=>[5,4,2,1]=>6
[3,4,5,6,1,7,8,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]=>[5,3,2,1]=>6
[3,4,5,6,7,1,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[3,5,1,6,2,4,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[6,3,1,1]=>5
[3,5,6,1,2,4,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[6,2,1,1]=>5
[3,1,5,2,6,8,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]=>[5,4,2,2]=>5
[3,5,1,2,6,8,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[3,1,5,6,2,8,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[3,5,6,1,2,8,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[3,1,5,6,8,2,4,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[3,5,1,6,8,2,4,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[3,5,6,1,8,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,8,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[3,5,6,1,2,4,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[6,2,1,1]=>5
[3,5,1,6,2,7,4,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[3,5,6,1,2,7,4,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,2,1,1]=>5
[3,5,1,6,7,2,4,8]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]=>[4,3,1,1]=>5
[3,5,6,1,7,2,4,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,7,1,2,4,8]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]=>[3,2,1,1]=>5
[3,1,5,2,6,7,8,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]=>[5,4,2,2]=>5
[3,5,1,2,6,7,8,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[3,1,5,6,2,7,8,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]=>[5,3,2,2]=>5
[3,5,1,6,2,7,8,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[3,5,6,1,2,7,8,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[3,1,5,6,7,2,8,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]=>[4,3,2,2]=>5
[3,5,1,6,7,2,8,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[3,5,6,1,7,2,8,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,7,1,2,8,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[3,1,5,6,7,8,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]=>[4,3,2,2]=>5
[3,5,1,6,7,8,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[3,5,6,1,7,8,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,7,1,8,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[3,5,6,7,8,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[3,1,5,2,7,4,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[3,5,1,2,7,4,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[3,1,5,7,2,4,8,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,5,1,7,2,4,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,1,2,4,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,1,5,2,7,8,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[3,5,1,2,7,8,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[3,1,5,7,2,8,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[3,5,1,7,2,8,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,1,2,8,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,1,5,7,8,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[3,5,1,7,8,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,8,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,5,1,2,7,4,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[3,1,5,7,2,4,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[3,5,1,7,2,4,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,1,2,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[1,3,5,7,2,8,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,8,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[3,1,5,2,8,4,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,5,1,2,8,4,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,1,5,8,2,4,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,5,1,8,2,4,6,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,5,1,2,4,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[1,3,5,8,2,4,6,7]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,6,8,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[4,3,2,2,1,1]=>13
[3,1,6,2,7,4,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,6,1,2,7,4,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[3,6,1,7,2,4,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[3,6,7,1,2,4,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[3,6,1,2,7,8,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[3,1,6,7,2,8,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[3,6,1,7,2,8,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[3,6,7,1,2,8,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[3,6,1,7,8,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,6,7,8,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,1,6,2,7,4,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[3,1,6,7,2,4,5,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[3,6,7,1,2,4,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[3,6,1,2,4,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,1,6,2,4,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[3,6,1,2,4,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[1,3,6,7,2,4,8,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[3,1,2,6,7,8,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]=>[4,3,3,3]=>3
[1,3,6,2,7,8,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,3,6,7,8,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[3,1,6,2,8,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[3,1,6,8,2,4,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,6,1,8,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,1,6,2,4,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,6,1,2,4,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,6,1,2,4,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,6,1,2,4,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,1,7,2,8,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,7,1,2,8,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,1,7,8,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,7,8,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,2,4,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,1,2,7,4,8,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[1,3,7,2,4,8,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,2,7,8,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[1,3,7,2,8,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,8,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,7,2,4,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,7,1,2,4,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,2,4,5,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,2,4,7,8,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]=>[4,4,4,3]=>3
[1,3,4,7,8,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,1,7,2,4,5,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,7,1,2,4,5,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,1,2,7,4,5,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[1,3,7,2,4,5,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,2,4,5,7,8,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3]=>[5,5,4,3]=>5
[1,3,4,5,7,8,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1,1]=>[4,4,3,2,1,1]=>13
[3,1,8,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,1,2,4,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,1,2,8,4,5,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[1,3,2,8,4,5,6,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,3,8,2,4,5,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,4,2,8,5,6,7]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]=>[4,4,4,2,1,1]=>11
[1,3,4,8,2,5,6,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,3,4,5,6,8,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1,1]=>[5,4,3,2,1,1]=>14
[4,5,1,2,6,3,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[6,4,1]=>3
[4,1,5,6,2,3,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,3,2]=>3
[4,5,1,6,2,3,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1]=>3
[4,5,6,1,2,3,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,2,1]=>3
[4,1,5,2,6,8,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[4,5,1,2,6,8,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[4,1,5,6,2,8,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[4,5,1,6,2,8,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[4,5,6,1,2,8,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[4,1,5,6,8,2,3,7]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[4,5,1,6,8,2,3,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,5,6,1,8,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[4,5,6,8,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[4,5,1,6,2,3,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]=>[6,3,1]=>3
[4,5,1,2,6,7,3,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]=>[5,4,1]=>3
[4,5,1,6,2,7,3,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[5,3,1]=>3
[4,5,6,1,2,7,3,8]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]=>[5,2,1]=>3
[4,1,5,6,7,2,3,8]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]=>[4,3,2]=>3
[4,5,1,6,7,2,3,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]=>[4,3,1]=>3
[4,5,6,1,7,2,3,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]=>[4,2,1]=>3
[4,1,5,2,6,7,8,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[5,4,2]=>3
[4,5,1,2,6,7,8,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[5,4,1]=>3
[4,5,1,6,2,7,8,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]=>[5,3,1]=>3
[4,5,6,1,2,7,8,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[5,2,1]=>3
[4,1,5,6,7,2,8,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]=>[4,3,2]=>3
[4,5,1,6,7,2,8,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,1]=>3
[4,5,6,1,7,2,8,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,2,1]=>3
[4,5,6,7,1,2,8,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[4,1,5,6,7,8,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[4,5,1,6,7,8,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[4,5,6,1,7,8,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[4,5,6,7,1,8,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[4,1,5,2,7,3,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,5,1,2,7,3,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[4,5,1,7,2,3,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,5,7,1,2,3,8,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,1,5,2,7,8,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[4,5,1,2,7,8,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[4,1,5,7,2,8,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[4,5,1,7,2,8,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,5,7,1,2,8,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,1,7,8,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[4,5,7,8,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,1,5,2,7,3,6,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[4,5,1,2,7,3,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[4,1,5,7,2,3,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,5,1,7,2,3,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,1,2,5,7,3,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[1,4,5,7,2,3,8,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[4,1,2,5,7,8,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[1,4,5,7,8,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[4,1,5,2,8,3,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,5,1,2,8,3,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,5,1,8,2,3,6,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,8,1,2,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,1,5,2,3,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[4,5,1,2,3,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[1,4,5,2,3,8,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1,1]=>[5,5,2,1,1,1]=>11
[4,1,2,5,8,3,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[1,4,5,2,8,3,6,7]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[4,1,2,5,6,8,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[1,4,5,6,8,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[4,1,2,5,3,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]=>[6,5,3]=>3
[1,4,5,2,3,6,7,8]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1,1]=>[6,5,2,1,1,1]=>12
[4,1,2,5,6,3,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]=>[6,4,3]=>3
[4,1,2,5,6,7,3,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]=>[5,4,3]=>3
[1,4,5,2,6,7,3,8]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1,1]=>[5,4,2,1,1,1]=>12
[1,4,5,6,7,2,3,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[4,1,2,5,6,7,8,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[1,4,2,5,6,7,8,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1,1]=>[5,4,3,1,1,1]=>12
[1,4,5,2,6,7,8,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1,1]=>[5,4,2,1,1,1]=>12
[1,4,5,6,7,2,8,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[1,4,5,6,7,8,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[4,1,6,2,7,3,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,1,6,7,2,3,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[4,6,1,7,2,3,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[4,6,7,1,2,3,8,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[4,6,1,2,7,8,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,6,1,7,2,8,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,6,7,1,2,8,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[4,6,1,7,8,2,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[4,6,7,1,8,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,8,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,1,6,2,7,3,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,6,1,2,7,3,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,1,6,7,2,3,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[4,6,1,7,2,3,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,6,7,1,2,3,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[4,1,6,2,3,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[4,6,1,2,3,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,1,2,6,7,3,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[1,4,6,7,2,3,5,8]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,1,6,2,3,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[4,1,2,6,3,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[4,1,2,6,7,3,8,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,3,3]=>2
[1,4,6,2,7,3,8,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,4,6,2,7,8,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,4,6,7,2,8,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,4,6,7,8,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,1,6,2,8,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,6,1,2,8,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,1,6,8,2,3,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,6,1,8,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,8,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,1,6,2,3,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,6,1,2,3,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,1,2,6,3,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[1,4,6,2,3,8,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[1,4,2,6,8,3,5,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[1,4,6,2,8,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,4,6,8,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,1,6,2,3,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,6,1,2,3,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,1,6,2,3,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,6,1,2,3,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[4,1,7,2,8,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,7,1,2,8,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,1,7,8,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,7,1,8,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,8,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,1,7,2,3,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,7,1,2,3,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[1,4,2,7,3,8,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,7,2,3,8,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,2,7,8,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[1,4,2,7,8,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,7,2,8,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,7,8,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,7,2,3,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,1,2,7,3,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[1,4,7,2,3,5,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,2,3,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[4,1,7,2,3,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,1,2,7,3,5,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[1,4,7,2,3,5,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,2,3,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]=>[5,5,4]=>2
[1,4,2,3,5,7,8,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1,1]=>[5,5,4,1,1,1]=>11
[4,1,8,2,3,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,2,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,2,8,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,4,2,8,3,5,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,8,2,3,5,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,2,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[1,2,4,8,3,5,6,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,4,5,6,8,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2,1]=>[5,4,3,2,2,1]=>14
[5,1,6,2,7,3,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,6,1,2,7,3,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,1,6,7,2,3,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,6,1,7,2,3,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,7,1,2,3,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,1,6,2,7,8,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,6,1,2,7,8,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,1,6,7,2,8,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,6,1,7,2,8,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,7,1,2,8,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,1,6,7,8,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,6,1,7,8,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,7,1,8,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,1,6,2,7,3,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[5,6,1,2,7,3,4,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[5,6,1,7,2,3,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,1,6,2,3,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[5,1,2,6,3,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,1,2,6,7,3,4,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[1,5,6,2,7,3,4,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,5,6,7,2,3,4,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,1,6,2,3,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,6,1,2,3,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[5,1,2,6,3,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[1,5,6,2,3,7,8,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[5,1,2,6,7,3,8,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[1,5,6,7,2,3,8,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,1,2,6,7,8,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[1,5,6,2,7,8,3,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,5,6,7,2,8,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,5,6,7,8,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,1,6,2,8,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,6,1,2,8,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,1,8,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,8,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,1,6,2,3,8,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,6,1,2,3,8,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,1,2,6,3,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[1,5,2,6,3,8,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,5,6,2,3,8,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[5,1,2,6,8,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[1,5,2,6,8,3,4,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,5,6,2,8,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,5,6,8,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,1,6,2,3,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,6,1,2,3,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[1,5,6,2,3,4,8,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1,1]=>[6,2,1,1,1,1]=>9
[5,1,2,3,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,1,6,2,3,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,1,2,6,3,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,1,2,3,6,4,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,1,2,3,6,7,4,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[5,1,2,3,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[1,5,2,3,6,7,8,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]=>[5,4,1,1,1,1]=>9
[1,2,5,3,6,7,8,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2,1]=>[5,4,2,2,2,1]=>12
[1,2,5,6,3,7,8,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2,1]=>[5,3,2,2,2,1]=>12
[1,2,5,6,7,3,8,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2,1]=>[4,3,2,2,2,1]=>12
[1,2,5,6,7,8,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2,1]=>[4,3,2,2,2,1]=>12
[5,1,7,2,8,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,7,1,2,8,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,1,7,8,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,7,8,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,1,2,7,3,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[1,5,2,7,3,8,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,2,3,8,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,2,7,8,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[1,5,2,7,8,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,2,8,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,8,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,7,2,3,4,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,7,1,2,3,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,1,2,7,3,4,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[1,5,2,7,3,4,8,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,2,3,4,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,2,3,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,1,2,3,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,5,2,3,7,8,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,5,7,8,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[5,1,7,2,3,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,7,1,2,3,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,5,2,7,3,4,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,2,3,4,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,2,3,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,1,8,2,3,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,1,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,2,8,3,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,2,8,3,4,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,2,3,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,5,2,3,8,4,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,5,8,3,4,6,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[5,1,2,3,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,2,3,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[6,1,7,2,8,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,1,2,8,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,1,7,8,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,1,8,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,1,7,2,3,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,7,1,2,3,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,1,2,7,3,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,6,2,7,3,8,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,7,2,3,8,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,2,7,8,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,6,2,7,8,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,7,2,8,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,8,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,2,3,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,7,1,2,3,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,1,2,7,3,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,6,2,7,3,4,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,7,2,3,4,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,2,3,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,6,2,3,7,4,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,1,2,3,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[1,6,2,3,7,8,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,2,6,7,3,8,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,6,7,8,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,1,7,2,3,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,1,2,7,3,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,6,2,7,3,4,5,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,7,2,3,4,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,2,3,7,4,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,1,2,3,4,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[1,6,2,3,4,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,1,2,3,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[1,6,2,3,4,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,2,6,3,4,7,8,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]=>[5,2,2,2,2,1]=>9
[1,2,3,6,4,7,8,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2,1]=>[5,3,3,3,2,1]=>12
[1,2,3,6,7,4,8,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2,1]=>[4,3,3,3,2,1]=>12
[1,2,3,6,7,8,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2,1]=>[4,3,3,3,2,1]=>12
[6,1,8,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,2,8,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,2,8,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,8,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,2,3,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,2,3,8,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,2,6,3,8,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,6,8,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,1,2,3,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,6,2,3,4,8,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,1,2,3,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[1,6,2,3,4,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,2,3,4,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,7,2,8,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,3,8,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,8,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,8,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,2,3,4,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,4,8,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,2,3,4,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,4,5,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,7,4,5,8,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,7,2,3,4,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,4,5,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,4,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,8,4,5,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[5,3,2,6,1,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,4,5,2,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,4,6,2,1,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[3,6,1,5,4,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[4,6,5,1,3,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[5,6,4,3,1,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[6,7,4,3,8,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,7,4,3,1,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,7,5,1,3,8,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,1,5,4,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,5,4,8,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,8,1,5,4,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,1,3,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,4,3,1,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,3,7,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,7,3,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,7,1,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,1,7,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,6,7,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,8,6,7,4,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,6,8,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,7,1,6,8,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,1,8,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,6,8,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,7,2,1,8,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,4,7,2,8,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,2,7,8,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,3,2,7,1,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,2,1,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[3,4,1,2,8,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[5,3,2,8,1,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,2,8,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,2,7,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,8,2,1,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,1,2,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,1,8,2,7,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,1,5,8,3,7,6,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,6,8,7,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,6,1,8,7,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,6,8,1,7,2,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,5,8,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,7,8,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,8,1,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,7,1,8,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,8,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,8,1,7,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,5,4,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,3,2,5,4,7,6,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,5,4,3,2,7,6,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,7,4,3,6,5,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[2,1,10,5,4,7,6,9,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[8,9,5,6,3,4,10,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[6,1]=>[1]=>0
[8,3,2,7,6,5,4,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[2,1,10,7,6,5,4,9,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,9,6,5,8,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[4,9,10,1,7,8,5,6,2,3]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,8,9,10,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[2,1,10,5,4,9,8,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[7,10,5,9,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,10,1,2,9,8,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,1,10,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[3,10,1,9,8,7,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,5,1,3,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]=>[6,5,2]=>3
[5,2,4,1,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[4,2,6,1,3,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[5,3,6,1,2,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[6,2,4,1,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,3,5,1,2,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,2,7,1,3,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,7,1,2,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,4,7,1,2,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,2,7,1,3,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,3,7,1,2,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,4,7,1,2,3,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[3,2,8,1,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,8,1,3,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,8,1,3,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,1,2,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,5,7,1,4,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[4,2,5,7,1,3,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,3,5,7,1,2,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[5,2,4,7,1,3,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,3,4,7,1,2,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,2,6,7,1,3,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[5,2,6,7,1,3,4,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[5,3,6,7,1,2,4,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[6,2,5,7,1,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,3,5,7,1,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,2,5,8,1,4,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,2,5,8,1,3,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,3,5,8,1,2,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,2,4,8,1,3,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,6,8,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,2,6,8,1,3,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,3,6,8,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,2,6,8,1,3,4,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,2,4,8,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,4,8,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,5,8,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,5,8,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,5,8,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,2,7,8,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,3,7,8,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,3,7,8,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,4,7,8,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,2,7,8,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,3,7,8,1,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,4,7,8,1,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,6,2,5,1,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,6,2,5,1,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[4,6,3,5,1,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[5,6,2,4,1,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[3,7,2,5,1,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,5,1,2,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,2,4,1,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,4,1,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[3,7,2,6,1,4,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,6,1,2,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,2,6,1,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,6,1,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,7,2,5,1,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[4,8,2,5,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,4,1,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,4,1,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,2,6,1,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,6,1,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,6,1,2,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,6,1,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,4,1,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,4,1,2,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,5,1,2,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,5,1,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,2,7,1,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,7,1,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,7,1,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,7,1,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,7,1,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,1,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,7,1,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,7,1,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,3,2,6,1,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,4,2,6,1,3,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[6,3,2,5,1,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,4,2,5,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,5,2,4,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,3,2,7,1,5,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[5,3,2,7,1,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,4,3,7,1,2,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,3,2,7,1,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,4,2,7,1,3,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,4,3,7,1,2,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,2,7,1,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,3,7,1,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[4,3,2,8,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,3,2,8,1,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,3,8,1,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,2,8,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,8,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,3,8,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,2,8,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,8,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,6,2,5,8,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[4,6,3,5,8,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,6,2,4,8,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,7,2,5,8,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,7,3,5,8,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,2,4,8,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,3,4,8,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,7,2,6,8,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,6,8,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,2,6,8,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,4,6,8,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,3,4,8,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,3,5,8,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,8,2,5,7,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,5,7,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,5,7,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,4,7,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,2,6,7,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,3,6,7,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,6,7,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,6,7,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,6,7,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,5,7,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,5,7,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,3,2,6,8,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,3,2,6,8,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,2,6,8,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,3,6,8,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,3,2,5,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,3,5,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,2,4,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,3,2,7,8,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,3,2,7,8,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,4,2,7,8,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,4,3,7,8,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[6,4,2,7,8,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,4,3,7,8,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,5,2,7,8,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,3,7,2,6,1,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,3,7,2,6,1,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,4,7,2,6,1,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,3,7,2,5,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,4,7,3,5,1,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,3,8,2,6,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,8,2,6,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,2,6,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,3,6,1,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,8,2,5,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,2,5,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,3,5,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,2,4,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,3,4,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,8,2,7,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,8,2,7,1,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,2,7,1,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,3,7,1,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,8,2,7,1,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,2,7,1,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,3,7,1,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,2,7,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,3,2,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,4,3,2,7,1,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,3,2,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,4,2,7,1,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,4,3,2,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,5,3,2,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,4,2,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,4,3,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,8,3,7,2,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,7,2,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,2,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,3,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,7,2,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,7,2,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,7,3,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,3,8,2,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,3,8,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,8,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,8,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,3,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,1,2,3,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,1,2,8,3,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,1,2,5,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,2,5,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,1,2,8,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,2,8,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,2,7,6,3,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,1,2,5,8,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,1,2,8,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,8,2,4,7,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,2,6,4,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,2,7,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,2,6,4,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,1,5,2,8,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,1,8,2,6,7,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,4,2,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,4,2,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,1,5,2,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,8,2,3,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,5,2,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,1,4,2,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,4,2,7,3,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,1,4,2,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,1,4,2,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,4,2,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[3,1,4,8,2,7,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,1,8,5,2,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,5,2,4,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,6,2,4,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,6,2,4,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,5,2,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,1,8,5,2,7,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,6,2,7,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,5,2,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[6,1,4,5,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,4,5,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[3,1,4,8,6,2,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,1,4,8,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,1,4,7,6,2,8,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[3,1,8,5,6,2,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,5,7,2,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,7,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,5,6,2,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,1,4,5,8,7,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[3,1,4,8,6,7,2,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,1,8,5,6,7,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,1,3,4,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,3,6,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,3,7,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,3,6,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,1,3,8,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,8,1,3,6,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,1,8,3,7,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,8,1,5,3,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,5,3,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,6,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,6,3,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,1,5,3,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,1,5,3,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,6,3,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,1,5,3,7,8,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,4,1,8,6,3,5,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,1,8,7,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,1,7,6,3,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,8,1,5,6,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,5,7,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,7,6,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,5,6,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,1,5,8,7,3,6]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[2,4,1,8,6,7,3,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,8,1,5,6,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,1,2,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,1,2,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,3,1,2,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,1,2,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,3,1,2,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,3,1,2,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,1,2,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[6,4,1,2,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,1,2,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,8,1,2,3,7,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,1,2,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,1,2,7,3,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,8,1,2,6,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,2,7,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,1,2,6,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,4,1,2,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,4,1,2,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,8,1,2,6,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,1,2,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,3,1,8,2,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,7,2,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,1,6,2,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,3,1,8,2,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,6,2,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[6,3,1,5,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,1,5,2,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,8,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,1,5,2,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,1,5,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,8,1,5,2,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,1,5,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,3,1,5,8,2,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,3,1,5,7,2,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[4,3,1,8,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,8,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,7,6,2,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,1,5,6,8,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[4,3,1,5,8,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,3,1,8,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,5,6,7,8,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[2,3,8,1,4,7,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,1,6,4,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,1,7,4,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,1,6,4,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,5,1,8,7,4,6]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,8,1,6,7,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,4,1,3,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,1,3,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,1,3,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,4,1,3,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,1,3,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,5,1,3,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,1,3,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,1,3,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,5,1,3,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,1,3,7,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,5,1,3,7,8,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,5,4,1,8,3,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,5,4,1,7,3,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,8,4,1,6,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,1,7,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,1,6,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,1,6,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,1,7,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,1,6,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,4,1,6,8,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[2,5,4,1,8,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,8,4,1,6,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,1,6,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,4,1,6,7,8,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]=>[5,4,1,1,1]=>7
[6,3,4,1,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,4,1,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,7,1,2,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,3,5,1,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,8,1,2,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,5,1,2,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,8,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,4,1,2,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,8,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,5,1,2,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,4,1,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,8,4,1,2,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,1,2,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,4,1,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,3,4,1,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,4,1,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,3,4,1,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,3,4,1,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,4,1,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[2,3,4,8,1,7,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,8,5,1,4,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,5,1,4,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,6,1,4,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,6,5,1,8,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,8,5,1,7,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,6,1,7,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,6,5,1,7,8,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,8,4,5,1,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,5,1,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,6,1,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,8,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,6,1,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,5,1,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,5,1,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,5,1,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,4,5,1,7,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,6,1,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,5,1,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,5,1,7,8,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[6,3,4,5,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,4,5,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[2,3,4,8,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,6,1,8,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,8,5,6,1,4,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,5,7,1,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,7,6,1,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,7,5,6,1,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,4,5,6,1,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,5,7,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,7,6,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,5,6,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,4,5,8,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,8,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,8,5,6,7,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,4,5,6,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[7,1,2,3,4,5,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[7,1,2,3,4,5,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[6,1,2,3,4,9,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[5,5]=>0
[6,1,2,3,4,7,9,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,6,5]=>[6,5]=>1
[6,1,2,3,4,9,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[5,5]=>0
[6,1,2,3,4,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[5,1,2,3,9,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,1,2,3,9,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,1,2,3,6,7,8,9,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]=>[6,5,4]=>3
[4,1,2,9,3,5,8,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[4,1,2,9,3,8,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[7,1,2,8,3,4,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,3]=>[3]=>0
[4,1,2,8,9,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[4,1,2,9,6,7,8,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,1,9,2,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,8,2,4,5,6,9,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,9,2,4,5,8,6,7]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,1,4,2,3,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[3,1,4,9,2,5,6,7,8]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,4,9,2,5,8,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,9,8,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[7,1,4,5,2,3,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[7,1,4,9,2,3,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,1,9,6,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,1,8,9,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,1,4,8,9,2,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,8,9,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[7,1,4,5,6,2,8,9,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[3,1,4,9,8,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,9,8,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,4,9,6,7,8,2,5]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,9,5,6,7,8,2,4]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,9,1,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,3,4,5,6,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,3,4,5,9,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[2,9,1,3,4,5,8,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,3,4,5,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[2,9,1,3,4,8,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,3,9,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,1,3,8,7,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,1,3,6,7,8,4,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,1,8,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,6,3,4,8,9,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[2,8,1,9,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,1,8,6,7,3,4,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,1,5,6,7,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,1,2,4,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[5,3,1,2,6,7,8,9,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]=>[6,5,4]=>3
[7,4,1,2,3,5,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[6,4,1,2,3,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[5,9,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,2,3,4,6,9,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,1,2,3,4,8,9,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1]=>[6,1,1]=>2
[7,6,1,2,3,4,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[7,6,1,2,3,4,8,9,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[5,6,1,2,3,9,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[5,9,1,2,3,8,4,6,7]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,1,2,9,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,9,1,2,6,3,4,7,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,1,2,6,7,8,9,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]=>[6,5,4]=>3
[4,3,1,9,2,5,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[6,9,1,5,2,3,4,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,3,9,1,4,5,6,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,8,1,4,5,6,9,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,1,4,5,8,6,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,1,4,7,8,5,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,1,8,7,4,5,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,8,1,6,7,4,9,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,1,6,7,8,4,5]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,9,4,1,3,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,5,1,3,4,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,9,1,3,4,5,7,8]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,9,7,1,3,4,5,6,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,4,1,6,3,5,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,4,1,9,3,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,4,1,6,3,8,5,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,8,1,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,5,1,6,7,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,4,1,2,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[6,9,4,1,2,3,5,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,1,2,3,5,9,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1]=>0
[6,9,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,1,2,3,4,9,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1]=>0
[6,7,9,1,2,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,9,8,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,8,1,2,3,4,9,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1]=>[2,1]=>1
[7,8,9,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,5,1,6,2,3,9,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1]=>0
[5,3,4,1,9,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,3,4,1,6,7,8,9,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]=>[6,5,4]=>3
[2,3,4,9,1,5,6,7,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,4,9,1,5,8,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,4,9,1,7,8,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,1,4,6,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,6,1,4,5,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,8,1,4,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,5,1,7,4,6,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,6,1,7,8,4,5]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,9,4,5,1,3,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,4,5,1,3,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[2,9,8,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,9,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,8,9,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,6,5,1,7,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,3,4,5,1,2,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[7,3,4,8,1,2,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,3]=>[3]=>0
[7,3,8,9,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[7,8,4,6,1,2,3,9,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1]=>0
[7,8,9,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,6,5,1,2,3,9,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1]=>0
[6,3,4,5,1,7,9,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,6,5]=>[6,5]=>1
[6,3,4,5,1,9,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[5,5]=>0
[6,3,4,5,1,7,8,9,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[2,3,4,9,6,1,5,7,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,4,9,7,1,5,6,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,4,9,6,1,8,5,7]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,4,9,7,1,8,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,6,1,4,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,8,5,6,1,4,9,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,5,6,1,8,4,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,8,4,5,6,1,3,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,9,5,7,1,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,9,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,7,5,6,1,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,3,4,5,6,1,9,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[7,3,4,5,6,1,8,9,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[2,3,4,9,6,7,1,5,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,6,7,1,4,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,5,6,8,1,4,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,9,4,5,6,7,1,3,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,4,5,6,8,1,3,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,4,5,8,7,1,3,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,4,8,6,7,1,3,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,8,5,6,7,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,4,5,6,7,1,9,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,4,9,6,7,8,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,6,7,8,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,9,4,5,6,7,8,1,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,2,6,1,4,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[6,3,1,1]=>5
[3,5,2,6,4,1,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[6,3,1,1]=>5
[3,5,2,7,4,8,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[3,5,2,7,4,8,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[4,5,7,2,3,8,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,7,2,3,8,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,6,2,3,1,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,2,1]=>3
[4,5,6,2,1,3,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,2,1]=>3
[3,5,1,6,4,2,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[6,3,1,1]=>5
[4,5,6,1,3,2,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,2,1]=>3
[4,5,6,3,1,2,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,2,1]=>3
[4,5,7,3,2,8,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,7,3,2,8,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,6,7,3,8,2,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,3,8,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,3,8,1,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,5,7,3,1,8,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,7,1,3,8,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,5,1,7,4,8,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[2,1,5,7,4,8,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,5,7,4,8,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[3,3,2,2,2]=>6
[3,5,1,7,4,8,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[4,5,7,1,3,8,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,7,3,1,8,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,6,7,3,8,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,3,8,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,3,8,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[5,6,7,8,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,6,7,1,8,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,6,1,7,8,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,1,6,7,8,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,6,7,8,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,6,1,7,8,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[4,6,7,1,8,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[5,6,7,8,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,5,7,2,1,8,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,6,7,2,8,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,2,8,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,2,8,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,6,2,7,8,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,6,2,7,8,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,6,2,7,8,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,5,2,7,1,8,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[3,5,2,7,1,8,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[3,6,2,7,8,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,6,2,7,8,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,6,2,7,8,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[4,6,7,2,8,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,2,8,5,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,6,7,2,8,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,5,7,2,1,8,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,7,1,2,8,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,5,1,7,2,8,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[2,1,5,7,3,8,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,6,7,8,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,6,1,7,8,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[4,6,7,1,8,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[5,6,7,8,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,6,7,1,8,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[3,6,1,7,8,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,1,6,7,8,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,6,1,7,8,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[4,6,7,1,8,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[5,6,7,8,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,10,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,10,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,5,8,7,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,7,4,5,8,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[2,6,7,4,5,1,8,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,6,7,4,5,2,3,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,4,7,6,2,3,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,5,4,7,6,1,8,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,5,4,7,6,8,1,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[4,5,3,7,8,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[5,4,3,8,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,3,7,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,4,8,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,5,6,8,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,2,5,6,1,8,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[4,2,5,6,8,1,7,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[5,2,4,8,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,4,5,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,4,5,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,4,8,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,3,2,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,1,3,8,2,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,8,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,3,1,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,3,8,1,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,8,2,1,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,2,8,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,5,2,7,8,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[2,5,3,7,1,6,8,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,5,3,7,2,6,4,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,7,3,2,5,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,6,7,3,1,5,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,6,7,2,1,8,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[6,5,8,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,1,8,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,1,7,2,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,1,8,2,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,2,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,2,1,3,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,2,1,8,3,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,1,3,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,1,6,2,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,3,1,5,2,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,5,1,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,4,6,1,2,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[2,1,6,5,3,4,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]=>[6,2,2,2,2]=>4
[3,6,1,5,2,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[4,6,5,1,2,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[5,6,4,1,2,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[6,5,4,1,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,7,4,1,8,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,7,4,1,2,8,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,7,5,1,2,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,1,5,2,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,5,3,8,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,3,7,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,8,1,5,2,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,1,2,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,4,1,2,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,1,7,2,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,1,7,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,6,7,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,8,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,6,8,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,7,1,6,8,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,1,8,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,6,8,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,7,1,2,8,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,4,7,1,8,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,1,7,8,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,3,1,7,2,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,1,2,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[3,4,1,2,8,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[6,3,1,8,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,8,1,2,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,1,2,7,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,1,8,2,7,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,1,5,8,3,7,4,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,6,8,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,6,1,8,7,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,6,8,1,7,2,3,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,8,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,8,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,7,1,8,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,8,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,8,1,7,6,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,7,3,8,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,4,7,3,5,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,4,7,2,5,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,2,7,6,1,3,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,4,2,7,6,1,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,4,3,7,6,8,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,4,3,7,8,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[6,4,8,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,3,8,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,3,6,8,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,2,6,7,1,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[5,4,2,6,7,1,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[5,3,2,6,1,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,3,2,6,1,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[5,3,2,6,1,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[5,4,2,6,8,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,2,8,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,2,5,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,2,8,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,2,6,1,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[4,3,2,1,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,3,2,8,1,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,8,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,2,1,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,2,8,1,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,2,7,8,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,2,7,1,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,3,2,7,1,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,3,2,7,1,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,3,7,2,1,5,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,3,7,2,1,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,3,7,2,1,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,4,7,2,8,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,5,7,8,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,5,8,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,7,2,1,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,3,7,2,1,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,3,7,2,1,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,3,2,7,1,4,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,4,2,8,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,8,2,1,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,2,8,1,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,2,1,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,3,2,1,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,3,2,8,1,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,8,2,1,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,2,1,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,1,8,4,7,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,4,7,2,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,3,2,7,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,8,3,2,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,2,3,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,2,3,7,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,2,8,3,7,6,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,2,8,3,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,1,8,3,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,1,3,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,3,1,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,4,7,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,4,7,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,4,7,5,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,6,8,4,7,1,5,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,3,1,7,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,1,3,7,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,1,8,3,7,6,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,2,5,8,3,7,6,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[2,5,3,8,1,7,6,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,4,8,7,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,5,4,8,7,6,1,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,3,4,8,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,4,8,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,3,8,1,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,3,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,1,2,3,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,1,3,2,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,3,1,2,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,3,8,1,2,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,1,8,2,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,3,8,2,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,3,8,2,7,6,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,4,8,7,2,6,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,4,8,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,1,8,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,1,7,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,7,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,8,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,8,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,1,8,7,2,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,1,5,8,7,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[1,4,5,8,7,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,3,5,8,2,7,6,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[3,1,5,8,2,7,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,6,8,1,2,7,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,6,8,2,1,7,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,6,8,2,7,1,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,8,3,7,5,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,5,3,8,7,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,2,8,7,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,5,2,8,1,7,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,1,4,2,8,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,2,5,8,1,7,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,2,5,8,7,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,3,5,8,7,6,1,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,4,5,8,7,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,4,5,8,7,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,3,5,8,1,7,6,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[5,1,3,2,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[6,1,3,2,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,1,4,2,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,1,4,2,6,3,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[2,1,6,3,5,4,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]=>[6,2,2,2,2]=>4
[4,1,6,2,5,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[6,2,5,1,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,2,6,1,4,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,2,7,1,4,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,2,8,1,4,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,1,4,3,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,7,1,4,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,1,7,2,5,3,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,7,2,5,4,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,3,5,4,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,3,5,4,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,8,2,5,4,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,8,2,5,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,8,2,6,3,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,2,6,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,2,6,4,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,8,3,6,4,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,3,6,4,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,7,2,6,3,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,1,7,2,6,3,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,2,7,1,5,3,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,8,1,5,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,5,2,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,1,4,2,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,1,3,2,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,1,3,2,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,1,4,2,8,5,7,6]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[4,1,3,2,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,1,3,2,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,1,3,2,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,4,2,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,4,2,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,1,5,2,8,3,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,1,5,2,8,4,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[2,1,6,3,8,4,7,5]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[3,1,6,2,8,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,2,8,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,1,6,2,8,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,1,5,2,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,7,3,8,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,2,8,3,7,1,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,8,3,7,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,3,7,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,4,7,2,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,8,4,7,3,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,4,8,3,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,7,4,8,2,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,1,7,3,8,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,1,7,3,8,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,4,2,6,8,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[5,3,6,2,8,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,3,6,2,4,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,7,3,8,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,3,8,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,5,2,6,3,8,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[4,5,2,1,6,8,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[5,3,1,6,8,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,6,2,8,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,5,6,1,4,8,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[4,1,5,6,3,8,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[4,5,1,6,3,8,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[4,5,6,3,2,8,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[6,7,4,8,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,8,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,1,8,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,7,1,5,8,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,3,7,8,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,5,1,7,8,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[6,7,4,3,8,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,4,8,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,8,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,7,3,8,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,6,7,3,1,8,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,1,7,3,8,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,1,6,7,3,8,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[6,4,7,1,8,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,8,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,2,8,4,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,2,8,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,1,7,4,8,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,1,6,7,3,2,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,6,1,7,3,2,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,7,3,2,1,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,7,3,2,8,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,2,7,3,8,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,2,7,3,1,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,2,1,7,3,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[6,1,7,4,2,8,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,7,2,1,8,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,7,3,1,8,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,7,1,5,2,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,7,4,2,1,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,4,2,8,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,4,2,8,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,6,7,2,8,4,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,2,8,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,2,1,8,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[5,7,3,8,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,4,7,8,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,7,8,1,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,4,7,8,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[5,7,3,8,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,6,7,2,8,5,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,8,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,8,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[6,4,7,8,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,4,7,8,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,1,5,7,8,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[5,3,7,8,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,7,2,8,5,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,4,1,7,8,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,1,6,2,7,8,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,6,2,1,7,8,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,6,2,7,1,8,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,2,7,8,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,7,2,8,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,6,7,2,1,8,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,1,7,2,8,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,1,6,7,2,8,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[6,4,7,1,8,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,6,7,1,8,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[6,7,8,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[4,6,7,8,1,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[5,1,6,7,8,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,6,1,7,8,4,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,7,1,8,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,3,2,7,4,1,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[2,4,5,3,7,1,8,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1]=>[4,4,2,1,1]=>8
[4,5,3,7,2,1,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,3,6,7,2,8,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[4,3,6,7,2,8,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[4,5,3,7,1,8,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,1,5,3,7,2,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[5,3,4,7,1,2,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,3,6,7,8,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[1,6,4,7,8,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,4,7,8,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,5,6,7,8,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[3,1,5,6,7,8,4,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]=>[4,3,2,2]=>5
[4,6,1,7,8,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[3,6,7,1,4,8,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[6,2,4,1,7,8,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[2,6,7,1,4,8,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,3,6,7,8,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[1,5,3,6,7,8,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[3,5,6,7,8,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[3,5,6,7,8,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[5,2,7,1,3,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,1,7,8,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,5,2,7,8,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[4,2,6,7,8,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[4,2,6,7,8,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,6,2,7,4,8,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[3,6,2,7,4,8,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[3,7,4,2,1,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,7,3,4,2,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,2,1,3,5,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,3,2,7,1,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,6,2,7,1,8,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[6,7,3,8,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,4,7,8,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,6,4,7,8,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,6,2,7,8,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[6,2,7,1,3,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,3,1,7,8,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,6,1,7,8,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,1,2,6,7,8,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[5,2,6,7,8,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,2,6,7,8,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[2,5,6,7,8,4,1,3]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,5,2,6,7,8,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,6,4,7,8,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,7,1,3,8,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,7,8,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,3,8,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,4,7,8,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,5,2,3,7,6,1,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[6,4,3,7,2,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,5,6,3,4,8,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[4,6,2,7,3,5,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[3,2,6,7,4,5,1,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[4,7,2,6,5,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,6,2,4,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,7,5,4,8,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,2,4,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,6,5,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,6,5,1,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,2,6,5,8,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[5,1,6,2,4,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[6,1,5,4,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,8,6,7,4,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,7,8,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,7,2,8,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,2,7,8,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,2,1,7,8,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[3,2,8,7,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,2,7,1,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,6,8,4,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,8,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,7,8,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,2,8,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,2,6,8,4,1,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,6,2,8,3,1,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,6,8,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,5,8,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,7,3,8,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,3,7,8,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[6,4,3,8,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,2,3,8,1,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,2,5,4,8,1,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[4,5,2,3,1,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[6,4,3,1,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,5,8,3,7,6,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,5,1,3,2,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,6,1,2,3,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[4,6,2,1,3,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,2,6,1,4,8,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,2,7,1,8,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,7,2,1,8,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,1,2,8,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,1,8,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[1,6,8,7,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,8,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,1,7,2,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,2,7,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,1,7,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,1,7,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,2,8,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,1,8,2,7,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,8,7,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,6,2,4,8,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[4,5,1,2,3,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[4,6,1,2,3,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[1,6,5,3,4,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,1,5,2,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,1,2,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,1,2,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,4,1,2,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,4,1,2,7,3,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,4,1,7,2,3,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,4,1,8,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,7,5,3,8,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,3,7,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,3,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,8,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,2,8,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,1,7,2,8,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,1,2,7,8,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[1,4,3,8,7,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,1,2,8,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,2,8,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,1,8,2,7,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,6,2,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[4,7,1,6,2,3,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,8,1,6,2,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,7,2,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,2,7,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,2,7,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,8,2,7,4,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,5,8,3,7,4,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,8,7,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,8,7,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,1,7,2,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,6,1,2,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,7,8,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,2,5,4,7,1,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[4,2,5,3,7,6,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,2,5,3,7,1,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,3,5,2,7,1,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,3,6,2,7,5,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,3,6,2,7,1,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,3,6,1,7,2,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,3,5,1,7,2,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[3,1,5,4,7,2,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[3,1,5,4,7,6,8,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[4,1,5,3,7,6,8,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,3,5,1,7,6,8,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,3,6,1,7,5,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,3,6,5,7,1,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[5,3,6,4,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,3,6,4,7,1,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,3,6,1,7,4,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,1,6,3,7,4,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[4,1,6,3,7,5,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,1,6,4,7,5,8,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,1,6,4,7,2,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,3,7,2,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[5,1,6,3,7,2,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,3,6,1,7,2,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,3,6,2,7,1,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,3,6,2,7,4,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,2,6,3,7,4,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,2,6,3,7,1,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,2,6,1,7,3,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[4,2,5,1,7,3,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,2,6,1,7,3,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,2,6,3,7,1,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,2,6,3,7,5,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,2,6,4,7,5,8,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,2,6,4,7,1,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,2,6,1,7,4,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,2,5,1,7,4,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[3,2,5,1,7,6,8,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[3,2,6,1,7,5,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,2,6,5,7,1,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[4,2,6,5,7,3,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,2,6,5,7,1,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,2,6,1,7,5,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[4,2,5,1,7,6,8,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[4,1,5,2,7,6,8,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,2]=>2
[3,1,5,2,7,6,8,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]=>[4,4,2,2]=>4
[3,1,6,2,7,5,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,2,7,5,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[5,1,6,2,7,4,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,2,6,1,7,4,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,2,6,4,7,1,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,2,6,4,7,3,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,4,6,2,7,3,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,4,6,2,7,1,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,4,6,1,7,2,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,1,6,4,7,2,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[4,1,6,5,7,2,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[3,1,6,5,7,2,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[3,1,6,5,7,4,8,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,5,7,3,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,2,2]=>2
[5,1,6,4,7,3,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,4,6,1,7,3,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[5,4,6,3,7,1,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[4,2]=>1
[3,7,5,2,4,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,4,5,7,3,1,8,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]=>[3,3,2,1,1]=>8
[5,7,4,3,2,1,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,6,8,3,2,7,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,6,3,2,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[1,4,6,7,3,2,8,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[5,4,7,3,1,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[1,7,4,5,3,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,1,4,2,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,7,4,2,1,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,6,3,8,7,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[1,7,4,8,6,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,5,8,7,4,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,1,5,8,6,7,4,2]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,8,1,6,7,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,6,4,1,8,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,7,6,8,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,1,6,4,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,7,3,5,6,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,6,7,5,8,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[3,7,6,5,8,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,5,7,2,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,3,5,7,6,8,1,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,1,6,5,7,8,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[4,2,2,2,2]=>4
[4,2,7,6,8,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,2,6,8,7,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,8,2,4,6,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,6,4,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,2,6,1,4,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[5,3,7,2,1,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,7,3,2,1,5,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,8,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,8,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,8,2,1,7,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,1,8,7,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,1,7,8,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,6,8,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,8,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,8,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,8,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,7,8,6,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,3,1,2,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,6,3,5,1,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,8,1,4,5,7,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,2,4,5,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[2,6,1,4,5,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[6,1,2,4,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,6,3,2,1,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[5,4,3,6,1,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,3,1,4,5,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,8,7,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,7,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,8,4,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,1,8,7,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,8,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[5,6,3,8,1,7,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,7,6,4,5,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,1,8,4,7,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,8,4,7,6,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,8,3,5,6,7,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,1,8,3,5,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,4,2,5,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,3,8,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,1,5,8,4,6,7,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,4,8,3,6,7,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[6,4,3,8,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,1,8,2,5,6,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,8,1,5,6,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,8,2,5,6,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,2,3,5,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,2,1,5,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,1,3,5,6,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,3,2,4,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,8,3,4,6,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,8,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,7,3,8,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,7,8,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,8,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,6,3,8,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,8,3,6,2,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,2,6,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,3,8,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,5,8,4,7,6,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,2,4,7,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,7,6,4,5,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,3,6,1,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,1,7,6,5,8,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,3,6,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,8,3,5,2,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,4,1,5,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,1,2,5,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,8,1,5,6,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,2,8,5,6,7,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,4,1,8,5,6,7,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[4,1,2,8,5,6,7,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,5,3,2,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,3,5,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,3,1,8,5,6,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,4,8,5,6,7,2]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[6,5,3,7,2,8,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,7,4,5,8,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,7,2,4,5,8,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,1,7,4,8,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,5,7,4,8,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,6,3,7,1,8,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[3,8,7,4,5,2,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,4,8,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,7,1,4,8,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,3,1,8,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,6,3,5,8,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,3,8,1,2,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,7,8,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,2,5,1,6,8,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]=>[5,4,2,2]=>5
[3,6,2,5,4,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,5,2,4,7,1,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[3,5,8,2,4,7,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,5,8,3,7,6,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,2,6,5,3,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[5,4,2,1,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[6,3,5,1,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,1,5,3,8,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,1,6,4,3,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,4,3,2,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,4,3,8,2,7,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,6,2,8,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,7,6,2,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[6,4,3,1,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,4,7,5,8,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,8,5,7,4,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,8,7,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,4,5,8,7,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,5,4,8,7,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[6,4,3,8,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,3,7,1,8,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,8,3,7,6,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,8,6,5,3,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,6,3,7,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,6,1,8,7,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,8,7,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,2,8,7,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,6,4,8,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,1,6,3,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,1,7,5,3,2,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,5,3,2,8,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,6,3,8,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,7,6,3,1,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,5,2,1,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,2,7,4,1,8,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,7,2,6,3,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,4,8,6,3,7,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,8,6,2,4,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,7,2,1,4,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[4,3,7,8,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,8,2,5,7,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,8,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,2,6,8,1,7,5,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,4,8,2,7,1,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,1,5,7,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,7,1,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,2,6,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,8,1,7,5,2,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,1,6,8,2,7,4,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,5,2,8,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,7,1,8,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,8,2,7,6,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,8,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,7,2,8,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,7,1,8,6,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,8,1,7,5,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,2,3,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,4,2,7,3,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,2,7,6,4,5,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[4,7,2,6,3,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,6,2,3,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,6,5,2,3,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,5,2,8,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,2,3,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,6,3,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,6,4,1,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,8,5,2,7,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,2,1,7,8,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[3,2,8,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,8,7,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,6,8,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,8,2,3,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,2,8,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,3,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,5,2,3,1,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[5,4,2,3,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[6,4,2,1,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,4,2,8,7,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,8,2,7,3,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,5,1,2,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,2,1,3,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,2,6,1,4,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,2,7,1,8,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,7,2,1,8,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,6,8,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,8,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,1,7,2,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,2,1,7,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,1,7,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,1,8,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,1,8,2,7,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,8,7,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,7,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,5,1,2,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,3,5,6,1,2,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,3,2]=>3
[6,3,7,5,1,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,2,7,1,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,6,1,5,4,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[6,4,3,5,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,3,1,4,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,7,4,6,2,8,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,4,7,8,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,1,8,5,7,3,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,2,4,6,7,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,4,8,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,1,4,6,8,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[2,5,4,6,7,1,8,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,4,6,3,7,5,8,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[4,1,6,3,8,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,7,4,2,8,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,5,8,4,1,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,4,8,3,7,6,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[6,3,7,4,1,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,1,8,2,7,6,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,8,1,6,7,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,7,2,6,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,7,2,3,8,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,8,2,1,7,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,1,3,6,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,7,2,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,3,8,7,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,8,7,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,4,1,8,5,7,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[4,4,4,2,1]=>7
[5,3,6,1,8,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,6,2,8,7,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[2,8,6,5,4,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,3,6,1,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,1,8,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,5,3,6,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,7,3,5,2,1,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[2,7,4,1,6,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,1,2,8,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,1,5,8,7,6,3]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[4,1,2,5,8,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[6,4,2,1,5,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,4,1,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,3,1,5,7,6,8,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[3,1,4,5,6,8,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]=>[5,4,3,2]=>6
[4,5,2,6,3,1,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1]=>3
[6,5,2,1,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,2,7,4,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,7,5,2,8,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,6,3,2,4,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[3,6,2,4,1,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[2,6,1,3,5,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[6,7,2,3,4,8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,1,7,3,8,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,5,7,3,8,6,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,6,7,4,1,8,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[5,6,3,7,4,8,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[2,1,6,7,4,8,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,8,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,3,7,4,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,7,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,7,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,6,3,1,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,1,6,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,1,2,7,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,2,5,7,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,3,5,2,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,3,2,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,4,2,8,5,7,6,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,4,1,8,7,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[4,3,1,8,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,4,8,6,5,7,2]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,7,5,6,8,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,7,1,6,8,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,2,1,8,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,6,2,5,8,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,6,2,8,4,3,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,7,2,8,1,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,8,7,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,7,8,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,7,8,4,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,3,8,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,1,7,8,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,5,8,4,6,3,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[6,5,3,8,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,4,8,3,5,6,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,1,8,3,6,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,4,8,1,7,2,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,1,8,2,4,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,8,1,4,6,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,8,2,5,1,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,8,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,4,8,3,5,7,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[6,8,2,4,3,5,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,2,3,5,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,2,1,4,6,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,1,3,4,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,1,6,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,1,6,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,6,7,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,7,6,1,4,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,4,1,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[2,8,5,3,4,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,4,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,4,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,6,1,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,6,1,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,6,7,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,4,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,4,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,4,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,7,2,4,6,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[6,5,2,7,3,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,2,8,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,2,8,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,8,2,1,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,6,2,1,8,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[3,5,7,6,1,4,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,4,1,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,4,6,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[6,5,2,7,3,1,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,5,2,6,3,1,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]=>[6,3,1]=>3
[6,5,2,7,3,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,1,6,7,4,3,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,1,2,6,4,8,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[5,1,2,8,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,6,8,7,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,5,2,8,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,2,3,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,1,2,3,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,1,2,3,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,1,2,3,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,1,2,8,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,6,8,2,3,1,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,5,8,2,4,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,2,4,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,2,8,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,2,7,3,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,1,6,7,4,3,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[5,1,6,8,7,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,7,8,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,1,8,3,6,5,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,3,6,2,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,4,8,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,1,4,8,6,5,2,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[4,1,6,7,8,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[4,1,6,5,7,3,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,5,2,6,3,7,1,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[5,3,1]=>3
[4,5,2,7,3,8,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[3,5,6,2,4,8,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[3,5,6,2,4,8,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[3,7,5,6,8,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,2,8,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,1,2,5,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,1,2,3,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[4,5,2,7,3,8,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,1,6,7,8,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[4,1,2,6,8,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,1,2,5,6,8,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[4,5,2,6,3,7,8,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]=>[5,3,1]=>3
[6,4,1,2,5,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[2,4,8,1,5,7,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,8,1,7,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,1,4,7,2,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,2,1,7,5,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[2,1,8,7,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,3,8,2,6,4,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,3,7,1,6,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,3,6,2,7,4,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[6,1,2,5,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,1,8,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,1,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,3,7,5,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,3,8,7,5,6,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,7,1,5,3,6,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,6,4,2,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,1,7,5,6,8,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,7,2,8,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,7,6,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,5,7,3,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,5,8,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,6,8,2,4,7,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[2,6,8,5,3,1,4,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,1,4,7,3,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,6,7,3,8,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,2,8,1,4,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,7,5,2,1,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[4,5,6,7,2,8,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[4,5,7,6,1,8,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[1,5,8,6,2,7,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,8,3,2,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,6,5,7,1,2,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[4,7,5,6,3,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,1,6,3,4,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,7,1,4,2,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,6,4,3,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,3,4,5,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,4,1,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,5,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,3,4,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,1,4,2,7,6,8,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[1,6,2,4,7,8,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,7,2,4,1,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,1,4,2,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,5,8,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,8,7,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,7,2,6,5,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,8,2,1,5,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,7,8,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,1,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,4,7,8,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[3,1,7,4,5,6,8,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,1,6,3,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,7,5,6,8,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,8,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,2,5,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,6,5,2,4,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,1,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,3,7,8,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,2,8,7,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,6,8,7,5,2,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,6,7,8,5,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,7,6,8,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,6,4,2,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,1,8,6,2,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,8,6,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,8,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,6,5,3,4,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,1,6,4,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,1,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,7,5,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,1,2,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,2,7,1,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,3,7,1,2,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,6,2,7,1,4,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[5,3,6,7,1,2,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[6,3,7,4,1,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,7,1,5,2,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,5,1,2,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,3,8,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,4,2,3,8,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,7,6,1,4,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,7,2,6,1,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,4,7,5,2,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,8,2,6,3,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,6,1,2,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,4,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,3,7,1,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,3,7,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,5,7,1,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,5,7,1,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,2,7,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,3,7,5,8,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[2,7,6,4,8,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,8,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,6,5,8,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,7,4,8,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,4,6,7,2,8,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[4,6,3,7,1,8,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,7,1,4,8,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,2,4,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,4,7,3,8,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,1,7,8,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[6,5,3,7,1,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,5,1,2,7,8,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,3,6,4,7,8,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[6,3,7,4,8,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,7,1,5,8,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,2,8,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,4,7,8,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,3,7,8,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,6,8,2,7,1,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,4,8,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,8,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,8,7,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,5,8,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,8,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,6,8,2,7,1,3,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,1,8,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,8,4,7,5,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,6,1,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,6,1,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,3,1,4,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[3,8,7,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,4,5,8,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,1,7,8,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,7,3,8,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,7,8,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,3,1,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,3,8,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,3,5,6,7,8,9,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,2,1]=>[5,4,3,2,2,1]=>14
[2,4,5,6,7,8,9,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,1]=>[5,4,3,2,1,1]=>14
[3,4,5,6,7,8,9,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[1,4,5,6,7,8,9,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,1,1]=>[5,4,3,2,1,1,1]=>18
[3,6,4,5,7,2,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[5,3,2,7,4,6,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[6,3,2,5,1,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,7,3,4,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[3,6,2,7,4,5,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[4,2,5,7,3,6,8,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[5,4,7,6,2,3,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,7,3,5,2,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[3,7,6,2,4,5,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,4,5,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,3,1,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,6,3,2,8,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,7,3,1,2,8,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,6,2,3,1,8,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[4,2,6,5,1,8,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[5,4,8,6,2,7,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,5,2,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,1,7,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,6,3,7,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,3,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,1,7,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,5,7,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,8,3,7,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,7,5,8,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,7,3,8,2,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,5,7,1,8,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,6,2,7,1,8,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[6,3,7,1,2,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,4,1,3,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,3,5,1,6,8,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[5,4,6,3,8,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[3,6,4,5,8,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,5,3,4,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,2,8,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,1,8,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,8,3,7,2,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,1,7,2,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,7,8,2,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,7,3,8,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,4,7,8,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,5,8,7,1,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,6,2,8,7,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,7,8,1,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,3,8,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,1,8,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,8,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,8,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,5,8,7,2,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,4,8,7,6,1,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,7,5,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,3,8,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,3,1,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,3,8,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,3,7,2,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,4,3,2,8,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,3,2,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,5,3,8,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,8,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,1,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,5,3,1,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,3,1,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,3,2,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[6,5,3,1,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,4,1,8,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,3,1,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,3,1,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,3,8,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,1,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,3,1,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,7,8,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,4,3,7,2,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,4,3,7,2,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,4,8,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,2,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,4,3,7,2,1,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,3,7,1,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,4,7,1,8,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,5,3,7,8,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,4,3,7,2,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,4,3,2,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,4,3,2,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,6,2,1,3,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[5,8,2,7,4,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,7,8,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,1,7,8,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,6,8,3,1,4,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,1,8,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,7,4,2,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,2,1,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,2,8,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,4,7,1,8,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[1,8,2,4,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,4,3,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,4,3,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,2,5,3,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,7,2,5,3,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,5,3,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,6,3,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,3,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,3,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,8,3,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,8,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,2,8,3,6,4,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,2,8,3,6,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,3,2,8,4,6,5,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,2,3,8,4,6,5,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,5,2,7,3,6,4,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,2,7,3,5,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,2,6,3,5,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,6,3,5,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,5,3,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,5,3,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,5,3,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,2,4,3,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,2,4,3,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,4,3,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,3,4,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,3,4,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,3,4,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,4,3,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,4,3,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,4,3,8,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,2,5,3,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,2,5,3,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,5,3,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,6,3,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,3,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,3,8,4,7,5,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,3,2,8,4,7,5,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,4,2,8,3,7,5,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,2,8,3,7,4,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,2,8,3,7,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,2,8,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,3,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,3,7,2,5,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,6,3,7,5,2,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,6,3,8,5,1,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,3,8,5,1,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,6,8,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,8,3,4,1,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,2,7,5,3,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[5,6,7,2,4,3,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[5,6,8,4,3,1,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,8,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,8,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,4,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,6,8,4,2,1,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,8,2,4,1,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,2,8,5,1,7,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,2,6,8,5,1,7,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,2,6,8,5,1,4,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,6,2,8,5,1,3,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,6,8,2,4,1,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,8,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,8,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,7,8,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,8,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,2,8,1,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,2,7,8,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,8,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,7,2,8,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,8,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,7,8,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,8,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,2,8,1,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,2,7,8,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,8,4,1,7,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,6,2,8,3,1,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,6,8,3,2,1,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,8,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,3,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,3,8,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,8,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,8,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,6,3,8,2,1,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,5,3,2,8,1,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,5,2,3,8,1,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,2,5,4,8,1,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[4,5,3,2,8,1,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,6,3,8,2,1,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,3,8,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,8,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,8,1,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,8,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,3,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,6,8,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,2,7,8,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[5,7,8,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,7,8,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,2,4,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,8,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,2,7,8,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,7,8,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,3,7,5,2,6,4,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,5,4,2,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,8,5,4,3,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,5,6,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,5,7,3,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,5,3,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,5,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,3,7,5,2,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,2,3,8,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,2,8,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,5,1,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,7,5,2,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,3,7,5,1,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,7,1,5,6,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,6,1,7,5,2,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[3,6,5,7,1,4,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[6,5,2,7,4,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,5,2,6,4,8,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[5,3,1,8,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,6,1,8,7,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,3,5,8,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,8,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,5,8,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,5,7,3,4,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,2,7,4,6,3,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,2,1,8,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,3,4,8,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,7,3,5,8,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,4,7,8,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[5,2,4,7,1,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,3,6,4,1,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,3,6,1,4,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[6,3,5,1,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,1,5,8,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,7,6,5,8,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,1,6,3,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,1,4,7,2,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,6,4,7,8,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,1,4,6,8,5,7,2]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[6,3,4,5,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,5,4,6,1,7,8,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]=>[5,3,1,1,1]=>7
[6,7,3,2,5,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,8,3,2,5,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,5,2,3,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,3,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,4,3,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,7,4,3,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,4,7,5,1,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,3,7,1,5,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,1,7,5,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,2,1,8,5,4,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[2,3,8,1,5,4,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,8,5,1,3,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,8,4,3,1,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,8,4,3,7,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,8,4,3,6,5,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,5,7,3,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,8,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,8,6,1,7,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,2,1,8,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,2,1,7,6,8,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,3,7,1,6,8,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,4,7,6,1,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,5,7,6,8,1,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,6,7,5,8,3,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[1,8,6,5,7,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,7,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,5,6,8,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,6,5,7,8,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,4,6,7,1,8,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,3,6,1,7,8,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,2,1,6,7,8,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[6,2,1,5,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,5,1,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,5,7,1,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,4,7,2,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,6,4,7,2,8,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[1,8,4,6,2,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,2,6,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,2,6,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,6,3,2,7,8,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[6,5,3,2,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,3,2,1,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,1,4,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,2,1,4,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,4,1,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,6,3,2,8,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,7,3,2,8,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,8,3,2,7,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,7,2,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,4,8,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,8,2,7,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,5,4,8,2,1,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,4,5,8,1,2,7,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[4,3,5,1,8,2,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,2,1,5,8,3,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,2,1,6,8,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,3,6,1,8,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,4,6,8,1,7,2,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,5,6,8,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[3,6,5,8,7,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,7,5,8,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,8,5,7,6,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,7,8,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,5,7,8,6,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,4,7,8,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[4,2,1,7,8,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[2,3,8,1,7,6,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,8,7,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,8,7,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,8,7,5,4,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[10,3,2,5,4,7,6,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,3,2,5,4,9,8,7,6,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,3,2,7,6,5,4,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,3,2,9,6,5,8,7,4,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,3,2,9,8,7,6,5,4,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,5,4,3,2,7,6,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,5,4,3,2,9,8,7,6,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,7,4,3,6,5,2,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,4,3,6,5,8,7,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,4,3,8,7,6,5,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,7,6,5,4,3,2,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,6,5,4,3,8,7,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,8,5,4,7,6,3,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,8,7,6,5,4,3,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[4,8,3,1,7,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,2,1,7,5,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[1,4,6,2,7,5,8,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,7,5,2,6,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,4,3,1,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,8,4,1,7,5,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,5,1,8,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[3,4,6,5,7,1,8,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]=>[4,2,2,1]=>5
[4,7,5,6,1,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,7,5,1,8,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,8,4,1,7,5,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,5,3,1,8,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,8,4,2,6,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,2,1,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[2,5,3,1,7,6,8,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,8,4,1,6,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,1,6,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,6,1,7,5,8,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[4,7,1,6,5,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,2,6,5,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,1,2,7,5,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[5,3,1,2,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,5,1,2,7,6,8,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[6,7,1,5,8,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,7,6,1,5,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,5,1,7,6,8,4]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]=>[4,4,2,2,1]=>8
[3,6,7,1,5,8,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[5,2,3,1,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,5,2,1,7,6,8,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[1,7,6,2,5,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,4,1,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,2,5,1,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,1,5,2,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,8,3,5,7,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,1,3,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[6,1,4,2,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[3,6,8,2,5,7,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,1,3,2,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[2,5,1,3,7,6,8,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,8,3,5,7,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,3,5,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,1,3,5,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,1,2,3,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[2,7,8,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,8,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,2,1,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,7,8,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,7,8,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,2,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,8,4,5,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,3,6,7,4,5,8,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,5,2,4,8,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,5,4,2,8,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[4,6,5,8,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,4,5,1,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,2,4,1,3,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[2,6,4,8,3,7,5,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,8,7,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,2,5,1,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,2,1,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,5,6,7,8,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,4,6,7,3,8,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[4,2,6,7,3,1,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[4,7,8,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,7,8,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,6,4,8,1,7,2,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,3,8,1,2,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,2,5,3,7,1,6,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[4,3,6,7,2,1,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,4,6,7,2,8,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[3,4,5,2,7,8,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]=>[4,4,2,1]=>5
[3,4,2,5,6,8,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]=>[5,4,3,1]=>6
[5,2,7,8,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,1,2,7,8,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,7,1,8,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,1,2,8,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,6,8,1,2,7,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,8,7,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,2,8,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[1,7,3,4,8,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,7,1,8,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[6,8,2,7,1,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,2,4,8,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,8,3,7,4,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,3,4,7,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,4,8,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,7,2,3,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,1,7,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,2,7,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,7,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,4,7,2,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,7,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,4,3,7,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,8,7,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,1,7,3,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,7,1,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,1,7,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,1,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,5,7,1,6,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,7,1,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,1,7,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,1,3,7,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,8,1,7,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[1,6,4,8,3,7,5,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,7,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,5,7,2,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,2,7,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,7,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,1,5,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,4,2,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,4,2,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,2,5,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,4,3,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,4,1,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,1,8,5,3,7,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,7,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,4,7,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,5,6,2,1,8,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[1,6,5,2,7,4,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,4,2,1,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,4,2,7,5,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,3,2,1,8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[2,5,3,1,7,8,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,6,4,1,7,8,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,5,1,7,8,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,5,7,1,6,8,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[6,5,1,2,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,1,2,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,2,8,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,1,2,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,1,2,5,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,1,5,7,8,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,2,3,1,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,5,2,1,6,8,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[1,6,2,5,7,3,4,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,2,1,5,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,4,1,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,5,1,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,1,4,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,2,4,7,3,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,2,1,3,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,6,7,1,4,8,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[4,2,1,3,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[2,6,1,4,7,8,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,1,2,4,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,3,1,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[6,3,5,2,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,1,6,3,5,2,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[5,2,6,3,4,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,2,7,3,4,1,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,2,8,6,7,3,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,5,7,3,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,7,3,4,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,1,7,3,5,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,1,7,4,5,2,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,5,3,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,8,6,7,4,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,8,6,7,3,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,5,7,3,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,8,5,7,4,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,7,3,6,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,1,7,3,6,2,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,2,7,3,5,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,8,4,7,3,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,5,1,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,2,4,1,7,3,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[6,2,4,1,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[3,1,4,2,8,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,1,5,2,8,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[2,1,6,3,8,5,7,4]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[3,1,6,2,8,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,2,8,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,1,6,2,8,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,2,7,3,8,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,1,8,4,6,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,5,6,2,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,5,6,2,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,4,8,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,7,3,8,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,3,8,4,7,2,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,6,1,4,7,2,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[4,6,1,2,5,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[1,4,8,2,5,7,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,8,4,3,2,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,6,1,4,3,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[2,6,4,8,3,7,1,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,4,6,8,3,7,5,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[2,4,8,5,3,1,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,8,1,4,7,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,8,4,7,6,1,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,6,2,4,7,3,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,6,2,1,4,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[4,6,2,5,3,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,7,5,1,3,6,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,3,6,1,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,3,6,7,2,1,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[6,1,7,5,2,4,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,3,1,2,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[1,4,7,2,5,3,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,6,7,8,3,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,6,1,8,4,2,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,6,7,5,8,2,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,5,6,7,8,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[3,6,5,7,8,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[5,2,7,6,1,4,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[2,5,7,6,8,1,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,7,5,6,8,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,6,8,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,7,1,8,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,8,5,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,3,8,5,6,7,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,1,6,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,5,4,6,7,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,4,5,6,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,4,2,8,6,1,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,4,7,1,5,2,6,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,3,7,8,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[1,7,3,8,5,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,8,3,6,2,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,7,8,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,6,4,3,8,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,6,5,4,1,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[2,4,5,1,7,8,6,3]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]=>[4,4,2,1,1]=>8
[2,6,3,4,5,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,4,1,8,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,5,2,7,1,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,6,2,7,3,1,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,6,7,4,2,8,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,7,6,4,1,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,7,1,5,2,8,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,7,5,2,4,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,2,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,5,3,8,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[1,6,5,4,2,3,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[6,7,5,4,3,1,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,8,1,4,2,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,4,2,5,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,3,7,5,4,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,8,1,3,7,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,1,2,3,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,7,2,3,8,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,8,2,3,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,3,7,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,8,1,3,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,4,1,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,1,2,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,4,1,5,7,3,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,3,5,7,1,4,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,5,1,7,8,3,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,3,6,8,4,7,1]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,1,4,7,8,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,4,7,6,8,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,7,6,1,8,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,7,8,1,4,6,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,7,4,1,6,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[5,3,4,1,8,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,8,4,6,1,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,1,8,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,8,6,5,3,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,5,7,6,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,4,2,7,5,8,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,1,8,6,7,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,8,7,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,7,6,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,8,3,1,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,2,8,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,8,7,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,3,7,1,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,3,8,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,3,7,8,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,6,4,2,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,7,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,8,1,2,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,5,1,2,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,2,4,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,3,1,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,5,1,2,7,6,3,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[4,5,1,2,6,8,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[3,5,6,1,8,4,7,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,5,7,1,2,8,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,6,2,7,5,1,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[4,2,6,1,7,3,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,6,3,1,2,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,5,3,1,7,6,2,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[4,2,5,7,1,6,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[3,5,2,7,8,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[3,4,6,5,8,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,1,4,5,8,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[3,4,6,8,5,2,7,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,5,6,2,8,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[4,2,5,6,1,8,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[4,5,3,1,6,8,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[2,1,7,5,8,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,7,5,3,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,1,2,7,3,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[6,4,1,7,5,2,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,1,3,7,5,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,1,2,6,8,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[3,7,1,2,5,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,2,4,8,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,4,1,7,8,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,4,7,5,1,8,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,7,4,1,5,8,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,7,1,5,8,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,2,8,1,3,7,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,1,6,8,3,4,7,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,8,3,1,5,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,8,6,4,1,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,4,8,5,1,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,3,7,4,5,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[2,6,3,7,5,8,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,2,1,7,8,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,7,2,3,6,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,2,7,3,6,8,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,7,4,6,2,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,3,4,6,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,3,8,4,6,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,8,3,6,7,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,1,7,3,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,3,1,7,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,8,4,7,1,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,7,3,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,8,3,1,7,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,3,8,2,7,1,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,1,8,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,8,1,2,6,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,7,4,1,6,2,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,1,8,4,2,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,6,2,8,5,3,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,8,5,3,1,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,3,7,1,2,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[1,6,3,7,2,8,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,3,2,7,8,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,5,7,8,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,7,2,5,8,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,8,2,4,6,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,6,8,2,7,1,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,6,8,1,7,3]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[4,8,3,5,6,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,2,3,7,8,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,8,7,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,7,1,5,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,7,2,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,8,7,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,7,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,7,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,8,7,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,3,7,5,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,7,5,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,7,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,8,7,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,5,8,7,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,7,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,8,2,7,6,4,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,5,8,1,7,6,4,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,8,1,7,6,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,8,7,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,8,7,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,8,4,7,1,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,7,2,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,7,2,6,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,8,7,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,2,7,6,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,8,3,7,6,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,2,8,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,3,8,2,7,6,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,8,3,2,7,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,1,7,5,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,1,7,6,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,4,1,8,7,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[4,3,1,8,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,1,8,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,8,2,1,7,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,7,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,8,7,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,1,7,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,1,7,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,2,7,6,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,2,7,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,1,7,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,7,1,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,2,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,3,7,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,8,3,7,6,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,3,7,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,7,2,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,7,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,7,2,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,2,7,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,1,8,2,7,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,2,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[4,1,3,8,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,4,8,7,6,5,2]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,8,3,7,6,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,1,3,7,5,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,3,7,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,7,6,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,4,3,6,8,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[3,1,6,2,5,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,5,1,8,2,4,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[1,4,5,2,8,3,7,6]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[3,1,6,5,8,2,4,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[1,6,4,2,5,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,2,6,4,8,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[4,1,2,6,3,8,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[1,4,7,5,2,8,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,5,2,8,7,3,6]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[1,6,4,2,8,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,4,2,8,3,7,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,2,8,6,5,3,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,5,2,8,6,3,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,4,2,8,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,2,1,8,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,7,6,4,2,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,6,3,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,7,5,3,8,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,2,7,6,5,3,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,5,2,6,3,8,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,5,2,7,6,3,8,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,5,2,7,3,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,7,4,2,8,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,1,2,8,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,8,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,3,7,1,8,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,8,7,3,2,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,2,8,7,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,7,4,2,8,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,5,2,7,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,6,4,2,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,2,6,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,7,3,8,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,8,5,3,7,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,6,3,8,7,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,7,6,3,8,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,6,2,7,3,8,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,2,8,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,2,8,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,3,2,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,2,8,7,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,2,8,7,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,6,3,7,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,3,8,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,1,7,3,6,5,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,1,8,7,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,7,8,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,1,6,2,4,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,4,1,5,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,1,4,5,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,4,5,3,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,1,7,8,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,1,4,8,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,5,7,2,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,3,5,8,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,5,7,2,1,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,5,8,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,7,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,8,6,3,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,1,8,2,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,8,1,6,2,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,5,8,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,3,4,1,8,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[4,4,4,2,1]=>7
[2,3,8,5,1,4,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,6,1,5,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,6,7,1,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,5,6,1,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,7,6,5,1,3,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,8,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,5,8,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,1,8,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,1,3,8,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,7,1,3,6,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,8,4,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,8,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,4,3,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,1,8,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,3,8,6,4,1,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,6,7,4,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,4,1,8,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[4,4,4,2,1]=>7
[2,8,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,1,6,4,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,1,4,5,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,6,1,4,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,3,4,5,6,9,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[7,1,2,3,4,5,6,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[2,1,9,3,4,5,6,7,8]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,8,1,3,4,5,6,7,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,10,1,3,4,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,7,6,5,4,2,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,5,2,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,4,2,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,2,4,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,6,5,1,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,6,5,1,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,1,7,6,4,5,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[4,1,3,7,6,2,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[5,1,7,3,6,2,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,1,7,5,3,2,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,2,7,6,3,4,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,3,7,4,5,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,8,2,4,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,8,3,2,7,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,3,8,2,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,1,8,4,7,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,8,7,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,2,7,1,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,7,2,6,5,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,8,3,2,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,4,2,7,3,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,4,8,2,7,3,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[6,4,3,1,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,5,1,4,3,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,6,1,3,4,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[4,6,2,1,5,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[3,2,7,1,4,6,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[4,7,2,1,3,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,1,3,2,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,7,1,2,4,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[1,7,2,3,6,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,1,2,4,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,3,2,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,1,3,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,1,4,5,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,3,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]=>[6,5,4]=>3
[5,1,2,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[6,1,2,3,5,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,7,3,8,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,5,1,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,4,7,6,8,1,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,7,8,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,8,4,5,7,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,5,6,7,1,8,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[3,5,6,2,7,4,8,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,1,7,8,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[2,5,6,1,8,7,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,5,6,8,1,7,3,4]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,4,8,6,2,3,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,6,8,2,3,7,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,5,6,2,8,4,7,3]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[2,5,6,3,4,7,8,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[1,4,2,6,8,5,7,3]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[2,8,3,1,5,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,1,6,8,7,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[3,4,1,6,7,8,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]=>[4,3,3,1]=>5
[4,3,1,7,6,8,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[5,2,7,8,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,7,2,6,4,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,7,3,1,5,8,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,2,1,8,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,2,8,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,8,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,1,2,8,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,1,3,4,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,2,7,3,4,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,1,7,3,4,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,1,7,8,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,1,8,7,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,1,2,7,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,3,7,5,8,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,1,4,5,7,8,6,2]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]=>[4,4,3,2]=>5
[2,1,8,3,4,7,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,8,2,3,4,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,4,6,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,1,6,5,8,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[5,2,6,1,4,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,2,6,4,1,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,2,7,4,8,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,2,7,4,8,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,7,2,3,8,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,2,3,8,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,2,3,1,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,6,2,1,3,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,1,6,4,2,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,6,1,3,2,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,6,3,1,2,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,6,3,2,1,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,7,3,2,8,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,3,2,8,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,3,8,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,3,8,1,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,7,3,1,8,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,1,3,8,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,1,7,4,8,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,5,7,4,8,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,4,8,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,7,4,8,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,7,1,3,8,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,3,1,8,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,3,8,1,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,3,8,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,8,3,1,4,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,1,8,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,1,7,8,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,6,7,8,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,8,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,8,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,1,8,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,7,2,1,8,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,2,8,1,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,2,8,3,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,2,8,3,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,2,7,8,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,2,7,8,4,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,2,7,8,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,7,1,8,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,1,7,8,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[4,1,2,7,8,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[6,2,7,8,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,2,7,8,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,2,7,8,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,2,8,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,7,2,1,8,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,1,2,8,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,1,7,2,8,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,5,7,3,8,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,7,8,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,8,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,1,8,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,8,2,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,1,8,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,1,7,8,5,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,6,7,8,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,8,5,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,1,8,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,8,4,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,3,8,5,2,7,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,2,8,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,4,5,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,8,4,7,5,2,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,1,4,7,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,1,4,8,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[3,6,4,8,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,1,4,8,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,4,7,1,8,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[6,3,8,4,2,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,7,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,3,7,1,6,8,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,8,5,6,7,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,8,1,7,6,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,1,2,7,8,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,6,4,2,8,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,3,7,5,2,8,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,2,7,4,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,7,1,4,8,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,8,1,4,6,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,7,4,2,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,3,8,7,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,6,1,8,7,3,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,4,2,7,3,6,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[6,4,1,5,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,7,4,3,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,7,3,6,4,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,7,6,4,5,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,5,3,4,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,4,3,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,6,5,2,8,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,7,4,2,1,8,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,6,5,3,4,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[5,4,6,3,1,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[6,5,8,4,2,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,2,6,4,7,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,6,2,5,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,3,1,7,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,6,3,7,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,7,3,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,1,7,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,3,7,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,8,5,7,3,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,7,6,8,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,7,1,5,8,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,7,3,1,8,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[1,7,3,8,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,8,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,1,5,8,3,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[5,4,2,7,1,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,4,3,1,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,7,5,6,8,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,5,4,8,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,2,8,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,1,8,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,8,3,7,6,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,1,7,2,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,8,2,4,7,5,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,7,3,8,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,6,8,2,7,3,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,2,6,8,7,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,7,2,8,6,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,8,1,7,2,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,3,8,7,4,5,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,1,8,7,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,8,7,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,7,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,8,3,7,6,2,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,6,8,7,4,2,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,8,4,7,5,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,7,3,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,6,7,4,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,7,4,5,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,7,4,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,5,7,4,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,7,3,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,3,7,4,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,7,4,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,4,8,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,8,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,2,8,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,1,8,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,7,1,8,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,8,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,8,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,8,5,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,7,4,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,7,4,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,1,7,4,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,7,4,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,4,8,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,6,1,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,5,6,2,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,4,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,1,7,3,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,7,3,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,7,3,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,7,3,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,7,3,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,7,3,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,3,8,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,2,8,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,8,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,8,4,7,3,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,4,7,3,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,7,2,6,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,7,2,6,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,5,7,2,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,5,7,3,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,5,7,3,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,3,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,6,7,3,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,7,2,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,6,7,2,5,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,7,2,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,7,1,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,7,1,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,6,7,1,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,8,6,7,3,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,5,1,8,6,7,3,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,1,8,5,7,3,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,6,2,8,5,7,3,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,8,5,7,1,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,7,1,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,7,1,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,3,7,1,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,7,1,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,2,8,4,7,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,1,8,4,7,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,7,2,6,1,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,6,2,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,6,2,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,6,2,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,5,1,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,6,1,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,6,1,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,3,6,2,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,3,6,1,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,4,8,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,5,2,8,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,7,4,6,2,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,4,6,3,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,4,8,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,8,4,5,3,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,6,3,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,4,8,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,3,7,2,4,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,6,3,7,2,8,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,3,8,2,7,1,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,4,8,2,7,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,8,4,6,2,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,5,2,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,5,2,3,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,6,2,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,4,8,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,3,8,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,3,4,2,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[4,6,3,5,2,7,1,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,6,3,5,2,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,6,3,8,2,5,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,8,3,6,2,5,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,6,2,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,5,2,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,6,2,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,6,2,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,3,8,2,7,1,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,3,7,2,8,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,7,3,6,2,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,3,6,2,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,3,8,2,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,4,8,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,3,6,2,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,3,6,2,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,7,3,5,2,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,5,2,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,4,8,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,5,8,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,8,5,7,2,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,4,8,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,3,8,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,3,4,2,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,7,3,4,2,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,4,2,8,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,4,8,2,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,8,4,7,2,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,7,2,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,7,2,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,7,2,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,7,2,5,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,3,8,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,5,2,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,3,5,2,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,5,3,7,2,6,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,5,3,7,2,8,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,5,3,8,2,7,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,8,3,5,2,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,4,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,4,2,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,4,2,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,5,2,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,3,8,2,6,1,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,3,6,2,8,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[4,7,5,2,1,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,5,2,1,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,5,2,1,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[5,6,4,2,3,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[6,4,5,3,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,4,6,1,3,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[4,6,8,1,7,3,2,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,8,1,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,4,8,1,3,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,7,1,3,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,4,8,1,7,5,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,8,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,3,2,8,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,1,6,8,7,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,7,8,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,7,8,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,7,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,2,3,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,2,6,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,2,7,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,6,1,8,7,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,7,1,8,6,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,6,7,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,6,8,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,2,8,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,7,4,2,8,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,8,4,2,7,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,8,6,7,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,5,8,1,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,1,7,6,8,3,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,5,7,8,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,8,7,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,6,2,5,4,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,2,7,5,4,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,1,5,4,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,8,3,4,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,2,4,5,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,2,7,5,1,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,8,2,4,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,2,8,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,6,2,1,4,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[3,6,1,8,5,2,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,4,1,2,8,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[5,8,1,6,3,2,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,8,5,2,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,2,6,1,5,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,7,2,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,6,3,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,2,3,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,5,7,3,2,4,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,2,7,3,1,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,8,2,4,1,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,6,3,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,8,6,4,2,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,5,8,7,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,1,3,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[2,5,8,3,1,7,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,8,1,3,6,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,3,4,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,1,8,3,2,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[7,8,9,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,4,2,7,8,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,6,2,4,8,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,2,4,7,5,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,3,8,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,2,8,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,5,7,8,6,1,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[6,2,1,8,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,8,3,5,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,4,8,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,3,6,4,8,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[6,2,4,7,5,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,2,1,3,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,7,2,3,1,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[1,7,5,3,4,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,6,3,1,8,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[1,2,8,4,3,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,4,2,3,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,7,4,3,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,8,2,4,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,3,8,1,2,7,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,3,2,6,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,7,3,1,2,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,7,5,4,2,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,2,4,6,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,4,2,7,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,6,2,8,3,7,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[5,3,1,6,7,2,4,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[5,3,6,1,2,8,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[1,6,3,2,7,8,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,4,5,3,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,4,1,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,1,4,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[1,8,3,2,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,5,2,6,8,1,7,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,2,5,6,7,8,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[5,2,3,6,7,1,8,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[6,2,3,4,1,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[3,7,5,1,8,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,1,5,2,8,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[1,7,5,4,2,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,4,8,2,7,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,4,6,8,2,7,3,5]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,4,7,6,2,8,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,1,4,7,2,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[1,7,4,5,2,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,1,2,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,7,2,8,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,2,8,7,1,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,5,8,2,7,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[1,4,6,2,8,7,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,4,2,8,6,7,3,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[2,1,7,6,3,4,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,4,7,2,6,8,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,1,4,2,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,4,2,7,6,8,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,2,6,8,7,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[3,1,2,8,4,6,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,3,7,1,8,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,7,4,3,2,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,7,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,7,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,7,8,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[1,4,2,7,8,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[5,2,8,1,3,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,1,8,6,3,4,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,4,2,6,8,3,7,5]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[1,4,2,7,3,8,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[3,1,7,2,8,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,1,7,8,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,3,8,7,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[8,1,2,3,4,5,6,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[7,1,2,3,4,5,10,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,6,6]=>[6,6]=>0
[6,1,2,3,4,10,9,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[4,1,2,10,9,3,5,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[3,1,10,9,2,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,9,10,1,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[4,7,8,5,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,8,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,7,8,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,8,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,7,8,4,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,8,4,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,7,8,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,8,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,6,3,8,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,6,4,8,2,5,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,4,8,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,4,7,3,5,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,6,4,7,2,5,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[4,6,3,7,2,1,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[5,6,3,7,2,1,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[6,4,3,2,1,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[4,5,3,2,7,1,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[3,5,4,2,8,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[6,4,3,2,1,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,3,2,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,6,3,8,2,1,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,5,4,2,8,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,5,8,7,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,6,5,7,8,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,5,4,2,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,6,3,7,2,1,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[4,6,3,7,2,1,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,6,4,7,2,8,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[2,6,4,7,3,8,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,5,4,2,7,8,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[4,5,3,2,7,1,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[6,4,3,2,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[3,5,4,2,6,8,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[5,6,3,4,1,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[2,1,7,8,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,8,3,7,5,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,8,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,2,6,4,8,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[3,2,5,8,4,6,1,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,5,2,3,7,1,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[4,2,5,3,8,1,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,2,5,8,3,1,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,1,5,3,8,2,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,1,5,8,3,2,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,3,8,5,2,1,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,3,5,2,1,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,3,2,7,5,1,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,3,6,2,5,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,6,3,2,5,1,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[4,6,7,1,3,2,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[4,5,1,7,3,2,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,5,1,3,7,2,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[5,2,1,4,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,3,1,4,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[4,3,1,7,5,2,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,3,6,1,5,2,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,6,3,1,5,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[5,3,6,4,1,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[4,3,6,1,7,2,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[6,3,4,1,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,2,4,1,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[3,6,4,1,2,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[4,6,3,1,7,2,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[5,3,6,2,1,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,6,2,7,1,3,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[4,5,2,7,3,1,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,6,7,2,3,1,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[4,6,2,1,7,3,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[3,6,2,1,4,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,6,7,2,4,5,1,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[3,5,2,7,4,6,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,7,2,4,8,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,1,5,7,4,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[6,3,2,1,5,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,2,1,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,2,6,1,5,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,2,1,7,5,3,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[6,2,5,1,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,5,1,2,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,5,1,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,2,6,4,1,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[4,6,5,1,7,2,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[3,6,5,1,2,7,4,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[6,5,2,1,4,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,3,1,4,7,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[2,3,1,8,5,4,7,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,4,1,5,8,3,7,6]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[3,4,5,1,8,2,7,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[1,8,4,5,3,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,4,8,5,3,1,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,5,8,2,1,7,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,2,8,1,7,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[3,4,6,2,1,7,8,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[3,4,6,2,1,7,5,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,2,2,1]=>5
[3,5,6,2,7,1,4,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,2,7,1,8,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,2,7,8,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[3,4,6,2,8,7,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,4,6,8,2,7,1,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,4,8,6,3,7,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,8,4,6,3,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,6,3,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,6,8,2,7,5,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,4,6,2,8,7,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,5,6,2,7,8,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,2,7,4,1,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[4,2,1,1]=>5
[4,5,6,7,2,8,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[3,5,6,8,7,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,5,8,6,7,3,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,8,5,6,7,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,7,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,6,7,3,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,6,8,7,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[4,5,6,7,2,1,8,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[3,4,6,1,8,7,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[2,4,1,6,8,7,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,3,1,8,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[1,8,3,2,6,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,1,6,7,8,4,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,5,1,6,7,4,8,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,5,1,6,7,4,3,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[4,3,1,1,1]=>7
[3,5,6,1,7,4,2,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,1,7,4,8,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[3,4,6,1,8,7,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,4,6,8,1,7,5,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[2,4,8,6,1,7,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,8,4,6,2,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,7,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,6,7,1,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,6,8,7,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[4,5,6,7,8,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[4,5,6,7,1,3,8,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[4,5,6,7,1,3,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[3,2,1]=>3
[4,5,6,7,3,1,8,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[3,5,6,8,7,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,5,8,6,7,4,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,8,5,6,7,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,6,7,4,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,8,2,4,3,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,5,6,1,8,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[4,2,5,6,1,7,3,8]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]=>[5,3,2]=>3
[6,1,5,7,3,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,1,5,8,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,8,2,4,7,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,2,4,7,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,3,5,6,7,1,8,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]=>[4,3,2]=>3
[3,7,1,5,6,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,5,8,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,2,5,1,8,4,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,2,5,1,7,8,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[6,1,5,7,8,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,2,5,6,1,7,8,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]=>[5,3,2]=>3
[5,7,6,1,8,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,8,6,1,7,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,5,8,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,2,5,1,8,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,2,4,1,8,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,2,5,1,6,8,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]=>[5,4,2,2]=>5
[3,8,6,5,1,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,5,1,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[6,5,1,7,8,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,2,5,1,6,7,8,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]=>[5,4,2,2]=>5
[3,2,4,1,8,5,6,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,2,4,1,8,5,7,6]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,2,5,1,8,4,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[6,5,1,7,4,2,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,1,8,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,6,1,8,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,2,6,1,8,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,6,1,8,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[3,2,5,1,8,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[4,2,6,1,8,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,6,8,5,1,7,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,2,5,1,8,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,2,4,1,8,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,2,5,1,7,8,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[3,8,5,1,7,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,1,8,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,2,5,1,8,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[6,5,7,3,1,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[4,6,3,7,1,8,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,6,3,7,5,1,8,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[4,2,6,1,7,5,3,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[2,5,7,4,1,6,3,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,7,4,1,6,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,4,7,3,6,1,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,4,7,8,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,7,5,1,8,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[6,4,3,8,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,4,3,6,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,8,3,6,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,3,6,7,1,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[3,2,5,8,1,6,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,5,4,6,8,1,7,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[5,2,8,4,1,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,2,1,8,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,1,7,5,8,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,1,7,5,3,8,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,6,4,1,8,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,4,8,2,1,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,8,4,1,6,3,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,2,5,6,1,8,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[4,8,3,2,6,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,2,8,1,6,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,2,1,6,8,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[3,2,7,1,5,4,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,1,5,8,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[3,8,2,5,1,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,3,2,6,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,2,6,7,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,2,6,7,8,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[4,3,2,6,7,1,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[4,3,7,2,6,8,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,3,7,8,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,5,7,4,8,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,2,5,7,8,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[3,2,5,7,1,6,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,2,5,7,1,6,4,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[6,3,2,7,1,5,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,3,2,7,1,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,3,2,7,8,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,2,6,1,7,8,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[6,5,2,1,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[2,1,7,5,3,8,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,2,1,8,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,2,7,1,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,3,2,1,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,2,1,4,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[3,5,2,1,7,4,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[3,5,2,1,7,8,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[5,8,4,2,1,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,2,1,8,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,1,7,3,8,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,2,7,1,4,8,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[3,5,8,2,1,7,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,8,3,7,2,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,7,2,8,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,7,2,1,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,8,3,2,7,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,2,8,1,7,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[6,3,2,8,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,2,1,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,8,3,2,1,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,2,1,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,9,8,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,5,7,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,11,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[6,2,3,1,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,5,3,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,1,5,2,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,5,1,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,1,5,3,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,5,1,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,1,8,4,5,3,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,4,7,5,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,3,7,4,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,2,3,1,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,1,3,2,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[2,1,8,6,7,3,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,3,7,5,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,7,3,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,4,8,3,6,1,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,5,8,1,3,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,8,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,5,8,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,8,7,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,7,2,8,4,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,2,8,4,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,6,2,8,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,1,8,4,5,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,8,4,6,1,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,1,8,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,1,6,8,4,5,7,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,3,6,8,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[6,3,7,8,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,3,7,8,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,7,8,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,7,8,2,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,6,7,8,4,2,5,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[5,6,8,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,8,3,7,1,6,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,2,8,7,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,7,8,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[5,2,7,8,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[1,2,7,8,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,1,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,2,8,5,4,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,3,5,4,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,5,3,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,8,5,2,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,1,2,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[3,4,2,1,8,5,6,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[2,7,6,8,4,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,1,8,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,7,5,8,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,8,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,6,8,5,1,3,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,4,8,3,6,5,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,8,4,1,5,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,8,3,5,6,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,6,8,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,8,1,5,3,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[1,6,8,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,3,8,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,1,8,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,8,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,8,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,8,7,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,3,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,8,4,2,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,3,2,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,4,8,2,5,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,4,3,5,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,4,5,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,8,4,5,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,3,1,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,1,3,2,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[2,8,1,5,3,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,4,5,3,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,4,2,8,5,3,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,8,4,2,5,3,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,5,2,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,1,4,8,2,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[1,5,2,8,4,3,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,8,5,4,3,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,4,8,5,3,7,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,7,4,8,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,5,2,7,8,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,2,7,4,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[2,8,1,5,4,7,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,5,7,4,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,4,8,7,5,3,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[2,8,1,4,3,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,2,8,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,2,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,6,4,8,1,7,2,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,6,7,2,8,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,7,1,4,2,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,3,7,1,4,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,7,8,1,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,7,2,8,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,2,7,8,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[6,1,2,8,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,2,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,1,3,2,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,2,7,3,5,8,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,5,8,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,8,1,3,7,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,2,5,8,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,5,8,3,7,4,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[2,8,1,7,3,5,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,8,1,7,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,8,1,7,4,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,4,7,5,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,7,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,8,1,7,5,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,1,4,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,8,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,7,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,2,8,1,7,6,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,8,1,7,6,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,3,4,1,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,3,4,1,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,7,3,4,1,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,8,3,4,1,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,4,1,6,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,4,1,5,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,3,4,1,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,7,3,4,1,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,6,2,8,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,2,7,3,4,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[4,6,2,8,3,5,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,3,5,1,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,8,3,5,1,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,5,1,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,3,5,1,8,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,6,2,3,1,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[5,6,2,4,1,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,6,2,4,1,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[4,6,2,5,1,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,6,2,5,1,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,5,1,8,3,7,2,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,1,7,3,8,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,6,2,7,3,8,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[5,6,2,7,3,8,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,2,7,4,8,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,3,8,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,2,8,4,7,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,2,8,3,7,1,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,6,2,8,3,7,1,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,5,1,7,3,6,2,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,5,1,8,3,6,2,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[6,5,3,2,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,6,3,5,2,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,8,2,4,5,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,1,4,5,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[6,3,8,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,7,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,7,4,3,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,6,8,5,7,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[6,8,3,5,1,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,1,8,4,7,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,8,4,7,6,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,3,8,1,5,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,3,5,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,6,1,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,6,1,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,2,5,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,3,6,2,4,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,6,2,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,8,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,1,8,4,5,7,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,3,5,1,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,5,8,3,6,7,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[5,8,3,6,1,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,8,2,5,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,1,5,6,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,2,1,5,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,8,2,5,6,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,8,1,4,7,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,1,6,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,3,8,6,1,7,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,8,5,6,7,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,7,8,9,10,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,1,1,1,1]=>[3,2,1,1,1,1,1]=>11
[3,5,7,9,10,1,2,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[4,5,6,9,10,1,2,3,7,8]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[4,5,8,9,10,1,2,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[4,7,8,9,10,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[5,6,7,8,10,1,2,3,4,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,9,10,1,2,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[5,6,8,9,10,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[5,7,8,9,10,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[4,5,7,6,2,3,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,5,7,2,6,4,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[2,5,7,3,6,4,8,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,7,3,6,8,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,7,2,3,5,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,2,7,3,6,4,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,1,4,7,6,8,5,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[4,1,3,7,6,8,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[5,1,7,3,6,8,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,7,1,3,5,8,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,8,7,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,7,6,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,7,6,1,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,4,7,1,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,1,7,6,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,2,1,7,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,2,8,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,4,1,7,6,8,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[1,4,2,7,8,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,7,2,8,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,7,1,8,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,7,1,6,8,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[6,7,4,5,8,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,4,7,6,8,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,5,7,8,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,7,8,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,8,7,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,4,8,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,3,8,7,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,7,8,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,7,2,8,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,2,7,8,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,8,7,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,8,1,7,6,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,3,8,2,7,6,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,8,3,7,6,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,1,8,3,7,6,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,8,7,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,7,8,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,7,1,8,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,8,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,7,2,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,2,7,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,1,3,7,6,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,3,7,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,10,4,5,6,7,8,1,3,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[8,3,4,5,6,7,1,10,2,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[3,1,10,5,6,7,8,9,2,4]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[6,7,1,8,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,7,1,5,8,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,8,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,1,8,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,6,5,1,8,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[4,6,5,1,8,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,6,4,1,8,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,4,5,1,8,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,6,1,8,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,5,6,1,8,7,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[3,5,6,1,8,2,7,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[2,5,6,1,8,3,7,4]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,4,6,1,3,8,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[3,4,6,1,2,8,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[4,3,6,1,2,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[5,3,6,1,8,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,2,5,1,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,6,1,3,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[2,3,6,1,4,8,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[4,2,5,3,1,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[6,2,4,1,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,4,1,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,3,1,2,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,6,4,1,2,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,6,4,1,3,8,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,7,1,4,3,8,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,1,4,2,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,3,2,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,1,2,3,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,1,2,4,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,4,8,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,1,4,8,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,6,2,1,4,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[5,6,2,1,8,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,5,2,1,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,2,1,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,4,2,3,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[3,5,2,4,1,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[6,3,2,1,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,3,1,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,4,3,6,5,8,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,6,3,5,8,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,6,3,5,8,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[4,2,6,5,3,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,2,6,5,1,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,2,6,5,1,8,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,2,6,5,8,1,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,2,6,5,8,1,3,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,2,6,5,8,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[2,4,6,1,5,8,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,1,6,5,8,3,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,1,6,5,8,7,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,6,1,5,8,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[4,2,6,5,3,8,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,2,6,5,8,3,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[2,6,4,3,8,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,3,8,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,2,6,8,5,3,7,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,4,6,8,1,5,7,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,1,8,5,7,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,1,6,8,5,7,3]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,1,6,8,5,3,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,6,1,8,5,3,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,8,1,5,3,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[4,2,6,8,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,2,6,8,5,1,3,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,2,6,8,5,1,7,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,4,6,8,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,3,5,1,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,3,1,5,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,3,1,8,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,6,3,8,1,5,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,3,8,5,1,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,3,8,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,3,6,8,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,3,6,8,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,3,6,8,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,3,6,1,8,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,3,6,1,8,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,3,6,8,1,7,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[4,6,5,2,8,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,5,2,8,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,2,5,8,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,2,5,8,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,6,3,8,1,7,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,3,1,8,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,1,6,3,8,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]=>[5,3,3,1,1]=>8
[2,4,1,6,8,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,6,1,8,3,7,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,8,1,3,7,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,3,1,7,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[4,6,2,8,5,7,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,2,8,5,7,1,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,2,4,8,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,8,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,4,8,1,7,5,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,4,1,8,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,1,4,8,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,1,6,4,8,7,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,1,6,4,8,7,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,6,1,4,8,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,1,8,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,8,1,7,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,4,2,8,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,4,8,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,4,8,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,4,7,3,8,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,7,4,5,8,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,2,4,7,3,6,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[1,7,6,3,4,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,4,8,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,7,3,4,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,1,7,4,5,8,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,1,4,7,3,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,3,1,7,5,8,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[2,8,6,3,7,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,1,3,7,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,1,7,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,2,1,8,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,1,3,8,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,1,2,4,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,6,1,5,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[2,6,1,4,5,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[6,5,1,3,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,6,2,4,8,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,3,2,8,4,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[6,4,2,1,5,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,3,5,2,1,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[2,6,4,8,7,1,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,6,4,8,7,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,7,8,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,2,8,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,2,4,8,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,3,7,1,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,4,8,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,2,5,1,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,2,5,1,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,2,1,5,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,5,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,4,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,1,4,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,2,7,1,4,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,1,4,6,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,1,4,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,2,1,4,7,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,5,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,5,1,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,2,5,1,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,2,1,5,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,1,4,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,2,1,7,5,8,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[3,2,7,1,6,8,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,6,1,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,3,7,6,8,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,8,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,6,1,7,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,8,1,6,7,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,1,8,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,8,2,1,7,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,8,1,7,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,1,6,4,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,1,6,4,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,6,1,3,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,8,6,1,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,7,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,7,8,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,2,7,8,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,2,6,8,1,3,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,2,6,7,1,3,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[3,2,6,1,8,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[3,7,2,1,8,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,1,8,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,8,5,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,3,7,8,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,7,1,8,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,2,1,6,8,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[3,2,6,1,8,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,2,6,8,1,7,3,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,3,6,8,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,2,6,7,1,8,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,2,6,1,7,8,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[3,4,6,8,7,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[5,3,6,4,8,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[1,4,6,2,7,8,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[3,1,8,5,4,2,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,2,7,5,4,8,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,3,7,5,4,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,8,7,5,4,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,6,7,8,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[4,5,6,3,8,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[3,6,8,5,4,7,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,8,3,5,4,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,2,5,4,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,2,5,7,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,1,5,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,1,6,2,8,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,6,1,8,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[2,3,8,5,4,1,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,8,1,5,2,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,6,4,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,5,7,4,3,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,5,8,6,4,3,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,4,6,1,5,8,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[2,6,1,5,7,3,8,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,6,8,7,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,8,1,7,4,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,1,7,4,3,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,1,7,6,4,3,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,1,7,8,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,7,5,6,3,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,6,7,5,8,2,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[2,8,1,5,4,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,5,6,3,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,2,5,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,2,1,5,6,3,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]=>[6,4,3]=>3
[4,3,6,1,5,7,2,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[5,1,6,3,7,8,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[1,3,6,8,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[2,4,6,3,7,1,8,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,3,6,4,8,7,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[4,1,6,7,3,8,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[5,4,6,1,3,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[6,4,1,5,2,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,1,7,5,2,3,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[2,8,3,5,4,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,6,3,8,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,6,4,7,8,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[1,8,5,7,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,8,7,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,1,8,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,7,1,4,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,8,7,1,4,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,7,8,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,4,7,5,1,3,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,5,6,4,1,8,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[2,6,4,5,1,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[1,6,5,8,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,8,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,8,9,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,9,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,10,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,9,10,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[3,4,6,2,7,1,5,8]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]=>[4,2,2,1]=>5
[3,6,2,5,4,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,2,7,5,4,1,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[4,3,6,2,8,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,1,2,5,4,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,4,5,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,2,8,5,1,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,6,8,1,7,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,3,6,4,1,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[6,2,1,5,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,7,4,8,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,6,3,7,5,8,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[4,6,7,2,5,8,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[2,4,6,1,7,5,3,8]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,7,5,4,1,6,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,3,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,6,3,5,8,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[1,5,8,4,3,6,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,4,6,2,7,8,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,6,3,2,7,1,4,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[5,6,3,2,7,1,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,4,6,2,8,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,4,1,7,8,5,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[5,6,3,2,1,8,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[6,8,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,3,8,2,1,6,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,7,5,8,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,4,7,2,1,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,7,3,2,1,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,3,2,1,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,3,7,2,5,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,7,8,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,2,5,7,8,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,1,5,7,8,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[3,3,2,2,2]=>6
[3,6,7,2,8,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[6,3,7,2,8,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,2,6,1,7,4,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[2,5,8,4,1,3,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,1,7,8,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,7,2,8,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,2,1,7,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,3,8,2,1,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,7,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,3,2,1,5,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[7,8,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[1]=>0
[1,8,9,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[8,9,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[1]=>0
[7,6,8,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,2]=>[2]=>0
[1,7,9,8,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[5,4,1,6,3,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[5,4,1,6,2,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[5,7,1,6,2,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,1,6,2,8,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,7,6,5,1,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,5,1,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,4,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,4,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,5,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,4,1,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,6,3,8,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,6,3,8,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,7,3,6,2,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,7,6,4,1,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,5,1,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,4,8,7,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,5,7,1,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[6,4,3,5,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,1,4,5,8,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]=>[4,4,3,2,2]=>8
[6,4,3,5,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,4,8,7,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,7,5,1,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,7,6,5,4,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,1,5,8,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,1,5,8,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,1,5,8,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,7,1,6,3,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,4,1,5,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,5,7,8,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,3,5,7,8,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,7,6,4,5,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,3,6,1,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,1,4,5,8,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]=>[4,4,3,2,2]=>8
[2,3,4,8,5,6,1,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,7,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,1,7,6,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,1,6,7,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,5,1,7,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[6,3,5,4,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,1,4,5,8,3,7,6]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]=>[4,4,3,2,2]=>8
[6,3,5,4,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,4,8,5,1,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,1,6,5,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,8,1,5,7,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,8,6,7,2,5,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,7,2,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,1,7,2,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,7,1,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,6,7,1,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,7,1,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,7,5,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,7,5,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,4,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,7,4,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,7,1,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,2,7,1,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,7,2,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,4,7,2,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,1,7,5,6,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,4,7,5,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,5,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,7,5,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,7,4,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,3,7,4,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,2,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,7,2,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,1,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,4,6,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,5,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,7,5,6,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,7,5,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,7,5,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,4,7,5,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,7,5,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,7,4,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,7,1,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,7,3,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,1,7,4,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,7,4,2,8,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,3,8,5,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,7,8,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,2,3,8,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,4,8,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,1,4,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,3,7,8,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,3,7,8,4,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,4,7,3,5,6,8,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,7,3,6,8,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,7,8,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,1,5,4,7,8,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[5,3,1,4,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,4,8,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,3,8,4,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,2,3,6,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,3,5,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,4,7,8,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,8,1,3,6,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,2,4,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,3,8,1,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,2,8,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,8,2,5,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,1,4,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,1,3,6,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,7,4,2,6,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,1,4,2,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,1,2,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,1,2,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,1,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,3,1,6,4,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,2,6,4,1,7,3,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[4,6,1,7,5,2,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[4,5,1,7,2,6,3,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[3,5,6,1,2,8,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[3,5,7,1,8,6,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[3,6,2,7,5,1,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[4,2,5,7,1,8,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,4,7,2,8,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,4,5,8,2,7,1,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[3,4,6,2,8,1,5,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,5,2,6,8,1,7,4]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[4,2,5,6,1,3,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,3,2]=>3
[5,3,6,8,4,7,2,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,7,2,5,4,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,7,2,5,8,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,2,6,8,4,3,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,1,6,5,4,8,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[4,1,6,5,8,3,2,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,1,6,8,4,3,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,7,1,8,4,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,7,1,5,4,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,4,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,8,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,6,8,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,2,8,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,7,8,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[4,7,6,2,8,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,6,2,4,8,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,7,3,8,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,3,5,8,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,6,8,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,6,5,8,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,6,5,1,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,9,2,3,4,5,6,7,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,9,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,2,3,4,5,6,7,8,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,11,2,3,4,5,6,7,8,9,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[3,6,4,8,7,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,6,4,3,8,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[1,6,2,4,7,8,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,6,2,4,8,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,4,7,2,8,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[1,4,7,2,5,8,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,5,6,4,8,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[4,6,8,5,3,7,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,8,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,5,4,2,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,5,2,7,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,7,5,1,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[1,3,6,4,8,2,5,7]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[4,1,7,5,3,2,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[6,5,1,3,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,8,5,3,1,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,6,1,4,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,8,6,4,1,3,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,6,2,5,8,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[3,6,2,5,8,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,6,8,7,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,8,2,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,2,8,3,6,5,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,3,2,7,5,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,6,3,8,5,7,2,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,4,1,7,5,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,8,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,4,3,7,2,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,6,3,4,8,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,8,3,5,4,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,6,3,8,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,2,6,4,7,8,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[2,8,5,7,4,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,3,8,7,1,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,3,8,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,7,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,5,7,8,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[1,4,7,5,3,8,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,6,7,3,1,8,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,6,4,5,3,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,6,5,8,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,6,8,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,8,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,4,2,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,8,6,5,3,2,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,7,5,8,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[1,7,5,8,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,5,7,6,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,3,8,5,7,1,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,5,2,1,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,2,5,6,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,1,5,6,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,5,7,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,8,6,2,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,8,6,1,7,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,8,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,7,6,8,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,1,3,7,8,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,2,8,5,7,6,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,2,8,6,1,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,2,8,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,3,5,4,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,1,5,3,4,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[3,5,8,6,2,7,1,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,1,6,3,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,5,6,3,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,5,4,2,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,6,1,4,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,1,7,3,5,6,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[2,7,4,1,5,6,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,4,1,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,7,6,1,5,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[1,7,6,4,5,2,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,5,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,6,5,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,5,4,3,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,1,4,3,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,1,3,4,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,7,3,6,8,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[3,4,7,8,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,2,5,1,6,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[1,4,7,2,5,8,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,6,2,4,7,1,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[6,8,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,3,6,7,5,8,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[6,3,7,5,8,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,2,7,6,5,1,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[1,2,7,6,5,8,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,8,2,6,1,5,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,3,8,6,4,1,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,6,2,5,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,1,6,2,5,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[6,1,2,5,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,1,8,6,4,7,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,8,3,6,7,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,8,7,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,5,7,4,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,1,6,4,7,2,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[2,4,7,5,1,8,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,5,7,1,4,2,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,6,8,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,8,5,1,3,4,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,3,4,5,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,4,3,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,2,8,3,1,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,3,7,4,8,2,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,3,7,4,1,6,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[2,4,7,3,6,1,8,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,8,7,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,7,1,6,5,3,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,2,7,8,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,3,1,2,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,8,1,4,5,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,6,1,8,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,4,6,1,5,8,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[5,8,1,6,3,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,1,8,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,1,7,5,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,1,7,4,8,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[3,6,1,5,7,4,2,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[2,5,6,1,7,4,8,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]=>[4,2,1,1,1]=>7
[3,1,7,5,6,4,8,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[5,1,7,6,4,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,1,7,8,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,6,5,7,3,4,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,6,4,7,5,8,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,7,4,6,8,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,7,5,6,3,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[1,7,6,5,4,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,6,8,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,7,5,3,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,1,7,5,6,8,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,4,1,7,6,8,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,8,5,6,2,7,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,6,4,2,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,3,7,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,4,1,7,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,4,7,1,8,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,7,4,1,8,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,4,8,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,7,1,8,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,2,8,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,1,4,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,6,2,5,8,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,4,2,8,3,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[6,4,3,1,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,7,6,8,4,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,8,5,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,8,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,6,7,5,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,8,6,7,3,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,8,5,6,7,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,3,5,8,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,3,8,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,2,8,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,5,8,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,2,8,5,7,4,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,3,8,7,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,1,8,7,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,8,5,7,6,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,5,8,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,8,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,8,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,2,1,4,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,2,1,4,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,4,1,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,4,1,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,2,6,1,3,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[2,1,6,4,3,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]=>[6,2,2,2,2]=>4
[2,6,1,4,3,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,4,1,3,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,6,2,1,3,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,4,2,1,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,2,1,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,2,1,8,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,6,1,4,3,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,1,8,4,3,6,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,1,4,3,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,1,3,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,2,1,3,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,1,6,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,1,4,6,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,4,6,3,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,4,8,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,6,1,4,8,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,1,8,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,8,1,3,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,6,2,8,1,3,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,2,6,1,3,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,2,6,1,8,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,2,4,1,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,1,4,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,1,6,8,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,2,1,6,3,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,2,1,3,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,2,1,8,3,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,1,8,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,2,1,8,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,8,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,1,6,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,1,3,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,1,3,6,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,1,8,3,6,5,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,1,4,8,3,6,5,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,4,8,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,4,8,1,6,3,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,8,6,1,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,2,8,4,1,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,6,8,4,1,3,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,1,4,3,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,1,8,4,3,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,1,6,8,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,8,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,1,6,4,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,4,1,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,2,1,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,4,3,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,2,4,1,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,3,6,1,5,2,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,3,5,2,8,1,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,3,7,2,6,5,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,8,2,6,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,1,7,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,1,5,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,8,3,4,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,1,3,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,7,6,8,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,7,6,8,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,7,1,8,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,6,5,8,1,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,3,5,4,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,5,4,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,1,8,4,6,3,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,2,8,4,6,1,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,1,5,4,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,6,8,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,1,8,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,5,8,1,7,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[6,5,7,2,4,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,5,8,2,4,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,7,3,8,5,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,2,7,4,5,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,7,2,6,3,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,4,8,2,6,1,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,8,1,7,2,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,6,5,8,3,7,4]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[6,5,7,4,8,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,5,7,1,8,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,1,7,4,8,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,4,7,1,8,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,6,3,8,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,8,3,1,5,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,3,4,7,1,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,4,8,3,5,7,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,5,3,1,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[4,2,1,8,5,3,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,4,1,3,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,4,8,3,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,8,4,3,2,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,8,5,4,3,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,3,8,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,3,8,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,4,7,8,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,8,1,5,7,3,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,7,6,5,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,8,5,3,7,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,8,1,7,4,3,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,8,1,7,3,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,7,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,5,6,3,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,1,7,8,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[2,7,4,6,3,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,4,3,7,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,4,8,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,7,3,1,4,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,1,8,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,3,5,8,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,8,7,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,5,2,6,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,1,8,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,8,5,7,6,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,8,5,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,5,2,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,3,5,7,2,8,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,5,3,6,1,2,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1]=>3
[5,7,4,6,3,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,8,4,6,3,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,5,7,4,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,5,3,7,1,8,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,5,1,4,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,4,7,5,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,1,4,6,8,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,7,1,3,5,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,3,7,1,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,6,4,1,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,2,5,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,7,4,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,6,8,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,3,7,8,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,7,6,2,1,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,3,6,2,8,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,7,8,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,6,7,5,4,8,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,1,7,4,5,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,7,3,5,1,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,1,6,7,5,8,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[3,2,2,2,2]=>4
[5,7,3,6,1,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,1,7,2,5,6,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[2,4,7,1,6,5,8,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,6,2,1,8,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,4,6,2,7,8,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[4,6,1,2,5,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,6,1,4,8,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,3,1,8,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[3,5,6,4,7,1,8,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[4,2,1,1]=>5
[3,4,6,1,5,7,8,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[3,4,1,5,7,6,8,2]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1]=>[4,4,3,1]=>5
[3,8,2,7,1,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,6,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,6,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,2,6,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,2,6,5,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,2,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,2,6,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,6,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,6,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,2,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,4,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,5,2,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,4,5,7,3,2,8,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,4,6,7,3,8,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[6,4,5,7,3,1,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,5,7,1,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,3,5,1,7,4,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,2,1,5,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,4,6,7,3,8,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,4,6,7,3,8,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,5,6,7,8,3,4,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[2,5,6,7,8,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[3,2,1,6,7,8,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]=>[4,3,3,3]=>3
[5,2,1,6,7,8,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[5,3,6,1,7,8,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,4,6,7,1,8,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[1,5,6,7,8,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[6,4,5,7,2,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,4,6,7,2,8,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,3,6,2,7,8,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,3,6,2,7,8,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[6,3,5,2,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,4,2,1,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,3,4,1,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[4,3,6,2,7,8,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,3,6,2,7,8,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[1,3,6,2,7,8,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,4,6,7,2,8,5,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[3,4,6,7,2,8,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[3,4,5,7,2,1,8,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[4,2,1,5,7,3,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[4,2,1,6,7,8,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[4,3,6,1,7,8,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[1,5,6,7,8,2,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,5,6,7,8,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[3,4,6,7,1,8,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[4,3,6,1,7,8,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,2,1,6,7,8,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[2,3,6,1,7,8,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,4,6,7,1,8,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,5,6,7,8,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[7,1,2,3,4,5,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[1,4,3,7,6,8,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,3,7,5,8,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,3,7,4,8,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,4,8,2,6,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,4,8,3,7,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[6,8,2,4,5,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,8,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,3,6,1,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,1,6,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,4,7,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,3,8,5,2,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,1,3,8,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,2,8,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,5,2,3,8,4,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,1,2,3,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,3,8,1,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,4,1,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,1,4,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,1,6,4,2,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[2,6,3,8,7,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,3,8,5,1,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,1,8,3,4,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,1,3,8,4,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[1,2,4,8,3,7,6,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[2,4,8,1,3,7,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,3,7,1,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,3,7,6,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,8,1,7,4,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,1,5,4,8,2,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[5,3,1,4,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,3,8,4,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,2,3,7,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,3,7,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,2,3,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,4,8,2,3,7,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,8,3,7,2,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,3,8,1,5,2,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,8,1,2,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,3,8,2,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,3,8,2,4,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,4,8,2,7,6,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,4,8,2,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,8,1,2,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,1,2,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,6,4,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[5,1,6,2,8,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,1,5,8,2,7,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,1,2,5,8,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,5,1,2,8,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,6,2,8,7,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,2,6,1,8,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,1,5,8,2,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,5,2,8,7,1,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,4,8,7,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,7,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,1,7,2,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,3,4,8,7,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,3,4,8,2,7,6,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,4,8,1,2,7,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,2,7,1,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,2,7,6,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,2,5,8,1,7,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[2,3,5,1,8,7,6,4]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[6,4,1,2,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[2,3,7,5,4,1,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,3,1,5,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,1,5,4,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,3,6,1,4,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,3,6,2,4,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[6,4,2,1,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,3,7,5,8,6,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,2,7,1,8,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,7,4,8,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[3,1,6,7,4,8,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[1,7,6,5,3,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,6,5,3,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,2,4,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,6,5,3,1,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,4,8,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,4,8,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,7,6,3,8,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,1,6,2,4,8,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[4,7,6,5,2,1,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,6,5,2,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,6,5,1,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[1,7,6,5,2,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,5,3,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,6,5,1,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,6,5,3,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,1,3,5,4,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,2,6,3,4,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,1,6,2,4,7,8,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[1,7,2,4,8,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,4,2,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,1,8,2,6,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,2,1,5,3,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,1,6,2,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[1,7,2,6,8,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,6,7,4,8,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[3,1,6,7,4,2,8,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]=>[3,2,2,2]=>3
[3,2,8,5,4,6,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,7,6,3,5,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,1,2,5,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,6,5,2,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,5,1,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,5,2,1,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,7,6,5,8,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,6,5,8,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,5,1,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,1,6,8,4,2,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,7,6,8,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,7,6,5,1,4,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,5,8,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,5,8,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,2,1,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,2,1,7,3,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,7,2,1,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[6,3,7,4,2,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,7,2,5,3,1,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,7,5,4,1,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,2,1,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,3,2,8,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,7,4,3,2,8,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,7,6,2,4,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,3,6,4,8,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,7,5,3,8,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,8,1,6,2,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,6,2,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,3,2,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,3,2,7,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,5,7,4,3,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,7,2,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,6,1,7,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,4,6,7,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,7,5,8,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,7,2,6,8,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,8,1,4,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,5,8,4,1,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,5,4,8,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,5,8,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,3,6,8,2,1,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,3,5,1,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,2,5,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,1,6,8,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,5,2,1,7,8,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,7,4,8,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,7,2,5,8,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,3,1,8,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,8,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,8,1,7,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,1,7,3,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,8,2,1,7,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,1,4,7,5,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,7,3,8,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,4,7,8,1,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,3,7,8,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,5,8,7,1,3,6,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,3,8,7,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,8,7,6,2,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,7,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,5,8,7,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,7,3,8,6,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,8,7,3,6,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,6,2,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,6,5,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,7,8,1,2,3,4,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1]=>[3,2,1]=>3
[6,2,7,8,9,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[6,7,3,4,8,1,2,5,9]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1]=>[4,1]=>1
[6,4,7,2,5,1,3,8,9]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2]=>[7,2]=>1
[6,5,4,3,2,1,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[7,8,5,6,3,4,1,2,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[1]=>0
[7,5,3,8,2,6,1,4,9]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,3]=>[3]=>0
[7,5,4,3,2,8,1,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]=>[5]=>0
[7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[7,8,3,4,9,10,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,9,4,5,6,1,2,3,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1]=>[2,1]=>1
[7,6,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7]=>[8,7]=>1
[8,5,9,10,2,6,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,6,9,4,7,2,5,1,3,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[2]=>0
[8,6,4,3,9,2,7,1,5,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[9,4]=>[4]=>0
[8,6,5,4,3,2,9,1,7,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,6]=>[6]=>0
[8,7,6,5,4,3,2,1,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[8]=>0
[3,6,5,1,2,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,7,5,8,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,7,2,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,7,8,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,1,2,6,4,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,1,2,5,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,1,2,4,6,3,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[4,1,5,7,8,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[4,1,5,8,7,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,7,1,8,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,1,7,8,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,1,7,4,8,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,1,5,8,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[5,1,8,4,7,2,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,7,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,1,6,3,2,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,1,2,3,7,5,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,8,1,4,3,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,7,3,4,8,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,7,1,4,3,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,8,2,7,3,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,2,8,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,8,7,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,1,4,2,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,5,7,8,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,6,7,1,4,2,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[5,8,3,7,1,4,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,1,7,3,4,6,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,7,3,2,4,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,1,2,3,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,3,7,8,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,1,2,3,8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,2,3,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,1,2,3,5,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,2,3,5,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,1,2,3,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[1,4,8,2,7,3,5,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,8,5,4,7,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,5,4,2,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,3,6,8,4,7,1,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,3,6,8,4,7,5,2]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[2,4,8,1,7,3,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,8,5,7,6,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,6,8,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,8,1,4,7,2,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,4,2,8,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,3,8,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,8,1,7,3,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,1,2,7,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,2,3,8,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,8,2,7,6,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,8,2,7,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,7,6,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,8,1,7,3,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,2,1,7,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,4,1,2,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,1,6,3,8,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,5,1,8,7,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,3,8,7,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,4,8,7,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,8,7,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,8,4,1,7,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,8,7,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,3,8,4,1,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,8,7,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,1,8,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,3,7,6,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,3,8,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,3,8,7,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,8,4,7,2,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,8,4,7,2,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,7,4,6,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,1,2,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,3,1,2,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[5,6,2,4,3,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[5,6,1,2,4,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[4,5,8,1,7,2,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,1,7,2,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,1,8,7,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,5,1,8,7,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,3,6,1,2,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,5,8,3,1,7,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,2,8,7,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,2,5,8,7,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,4,8,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,1,4,8,7,6,2,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,4,8,7,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,3,4,8,7,6,2,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,4,8,7,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,2,5,8,7,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,5,8,3,1,7,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,2,7,5,8,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,8,1,3,7,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,8,1,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,8,2,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,3,7,8,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,7,8,1,3,6,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,6,7,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,3,7,1,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,8,6,4,7,1,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,3,4,1,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,7,4,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,8,3,7,5,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,8,1,6,7,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,8,3,7,2,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,8,7,1,3,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,4,6,8,2,7,5,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,6,5,8,2,7,4,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,6,2,8,1,7,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[1,8,4,5,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,7,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,8,3,7,5,2,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,3,8,2,7,5,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,4,2,7,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,4,5,7,1,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,7,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,3,2,8,5,4,7,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[4,2,8,5,3,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,1,8,4,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,4,3,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,4,8,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,1,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,5,4,2,8,1,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[4,5,3,2,8,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[6,4,3,2,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,2,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,6,3,2,7,8,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[4,1,6,3,2,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,6,4,2,7,8,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,7,4,1,3,6,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,4,2,6,1,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,1,7,3,2,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,7,3,2,6,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,7,3,2,5,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[4,7,5,6,2,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,1,7,5,6,2,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[2,7,5,6,1,3,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,7,1,3,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,6,5,7,2,8,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[5,6,4,7,2,8,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[6,5,4,1,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,5,7,1,8,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,4,6,1,7,8,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[3,4,6,8,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[4,3,1,6,8,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,3,6,8,7,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,3,5,1,8,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,8,5,1,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,1,8,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,3,2,8,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[2,3,8,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,7,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,2,8,7,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,8,7,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,7,8,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,7,8,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,1,7,8,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,4,7,8,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,5,7,6,8,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[4,5,7,6,8,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[5,4,1,7,6,8,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,4,7,5,8,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,5,1,7,4,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,6,7,5,3,8,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,6,7,5,1,4,8,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,7,6,1,5,4,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,5,1,4,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,5,3,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,3,1,7,2,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,1,4,2,3,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,4,2,7,3,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,7,8,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,1,7,3,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,2,8,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,2,4,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,1,8,4,6,7,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,6,4,8,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[6,1,2,7,8,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,2,7,4,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,1,6,4,7,8,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[5,7,1,3,8,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,1,8,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,3,1,5,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,7,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,2,8,4,7,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,1,2,8,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,1,7,2,6,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[5,8,1,7,2,4,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,3,4,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,1,8,6,4,7,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,2,8,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,1,7,8,4,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,7,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,6,2,5,4,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,5,2,8,4,7,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,4,7,3,2,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,4,8,3,2,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,5,3,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,3,2,6,4,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[4,5,8,3,2,7,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,7,6,3,8,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,8,6,3,7,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,3,2,7,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,4,3,2,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,2,8,4,7,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,1,5,8,4,7,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[5,3,2,7,4,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,7,4,3,2,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,7,5,3,2,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,8,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,6,8,3,7,5,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,1,8,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,7,2,6,8,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,6,7,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,5,4,7,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,8,6,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,8,7,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,4,7,3,8,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,4,8,3,7,5,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,7,5,4,8,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,8,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,3,7,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,2,8,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,2,7,8,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,7,4,3,8,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,6,8,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,8,1,2,4,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,8,2,4,7,1,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,5,7,3,6,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,5,2,8,3,1,6,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,2,5,8,3,7,1,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[2,1,6,8,4,7,3,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[1,2,5,8,3,6,7,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[5,3,6,8,4,7,1,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[1,6,5,8,2,4,7,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,1,2,6,8,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[1,4,3,8,2,6,7,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[5,4,8,3,2,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,3,7,2,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,3,6,2,7,5,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,6,3,2,1,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,1,7,3,2,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,1,7,8,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,5,1,2,7,8,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[5,4,7,3,8,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,8,4,7,6,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,1,7,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,4,3,5,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,3,1,5,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,7,3,6,5,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,3,7,6,4,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[1,6,3,4,2,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,3,6,2,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,7,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,4,8,7,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,6,2,8,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,2,1,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,2,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,2,6,3,7,4,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[2,8,5,3,1,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,3,8,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,6,2,3,7,8,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,7,2,8,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,7,1,8,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,1,2,7,8,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[2,4,1,7,8,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[4,2,1,7,3,8,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[6,2,8,4,3,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,8,7,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,8,1,7,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,8,3,7,5,4,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,1,7,5,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,1,8,6,4,3,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,7,2,6,4,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,2,7,5,4,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[2,1,8,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,7,5,4,3,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,2,4,3,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,8,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,4,3,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,6,3,2,7,5,1,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[5,7,4,1,8,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,4,3,1,8,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,8,7,2,5,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,3,7,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,1,8,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,4,8,6,3,5,2,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,5,6,8,4,2,7]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[4,3,2,2,1,1]=>13
[3,5,4,8,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,1,4,6,8,7,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[1,6,3,8,7,2,5,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,2,4,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,3,7,2,6,8,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,6,5,2,8,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,6,5,7,2,4,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[4,2,6,3,8,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,2,6,7,3,5,1,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[3,6,2,4,7,5,1,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[3,6,2,4,1,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,8,7,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,1,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,2,1,5,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,4,8,1,6,5,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,8,1,5,7,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,6,2,8,7,3,5,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,2,4,6,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,4,7,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,5,8,6,4,3,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[1,2,5,7,8,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,7,4,8,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,8,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,7,6,3,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,4,5,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,1,7,4,3,6,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,1,4,7,8,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[3,5,1,4,8,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,6,2,4,7,8,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[5,6,2,4,8,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,3,8,2,4,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,7,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,7,8,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,3,4,2,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,4,7,2,5,8,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[4,6,8,1,3,5,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,3,8,1,2,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,6,4,1,7,2,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[2,8,3,1,5,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,1,7,6,8,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,4,1,7,5,6,8,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[3,7,4,1,6,2,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,7,8,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,8,6,1,5,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,5,2,1,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,7,5,2,8,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,6,4,3,1,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,2,8,3,6,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,8,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,5,2,7,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,3,5,2,1,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,8,5,3,1,4,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,5,4,2,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[1,6,4,7,2,5,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,4,8,2,5,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,5,8,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,8,2,4,3,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,2,4,3,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,6,2,4,7,8,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,5,8,2,4,7,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,2,4,8,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,7,2,4,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,7,2,4,3,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,6,7,2,4,8,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,5,8,2,4,6,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,2,4,6,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,8,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,3,2,4,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,6,2,4,8,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,7,6,2,8,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,4,2,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,4,3,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,6,2,4,8,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,5,8,7,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,2,3,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,4,2,8,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,5,2,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,5,2,3,8,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,5,2,8,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,6,2,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,6,2,4,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,3,2,4,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,2,3,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,5,2,3,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,8,4,2,3,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,4,6,2,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,5,2,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,5,2,3,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,4,2,3,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,4,2,3,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,8,6,2,4,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,3,2,4,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,7,3,4,2,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,2,8,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,4,2,3,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,4,2,3,8,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,6,4,2,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,8,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,2,3,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[3,7,5,6,1,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,4,2,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[1,6,7,4,3,5,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,7,1,4,3,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[3,5,4,1,6,7,8,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[4,7,1,6,3,5,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,1,4,7,6,5,8,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[6,1,7,4,3,5,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[1,7,6,4,3,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,3,8,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,7,3,1,2,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,8,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,8,1,4,2,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,1,3,7,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,4,3,7,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,4,7,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,8,4,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,6,8,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,4,3,7,8,6,1,5]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,4,7,3,8,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,7,6,8,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,5,3,4,8,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[3,7,5,4,8,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,1,4,3,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,1,7,3,8,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,2,3,7,8,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,2,3,4,8,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[2,7,5,6,3,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,2,6,3,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,2,6,8,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,2,3,8,5,6,1,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,2,3,8,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,8,3,7,2,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,8,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,8,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,7,4,8,5,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,4,3,8,5,6,1,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,4,8,3,6,2,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,5,8,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,5,3,8,7,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,7,5,8,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,8,7,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,8,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,7,6,8,4,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,7,6,8,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,7,4,6,5,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,4,6,5,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,5,4,8,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,8,4,6,5,7,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,7,5,8,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[1,6,2,7,5,8,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,4,8,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,4,6,5,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,4,8,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,8,2,6,5,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,8,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,5,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,7,6,8,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,7,6,8,2,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,8,4,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,6,8,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,8,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,6,8,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,2,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,6,5,8,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,4,6,5,7,8,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[3,4,5,6,1,7,8,9,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1]=>[6,5,3,2,1]=>10
[3,4,5,6,7,1,8,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1]=>[6,4,3,2,1]=>10
[3,4,5,6,7,8,1,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1]=>[5,4,3,2,1]=>10
[3,4,5,6,7,1,2,9,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,7,4,3,2,1]=>[7,4,3,2,1]=>10
[3,4,5,6,7,8,1,2,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1]=>[5,4,3,2,1]=>10
[1,6,2,3,8,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,4,3,2,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,6,2,5,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,6,5,3,7,8,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]=>[5,2,2,2,2,1]=>9
[1,3,7,5,2,6,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,4,2,6,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,6,4,3,7,8,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]=>[5,2,2,2,2,1]=>9
[1,4,7,3,2,5,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,5,3,2,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,5,4,8,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,8,1,4,3,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,5,4,3,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,9,6,5,4,3,2,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[8,10,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,6,5,4,9,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[4,6,5,8,3,1,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,8,5,1,3,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,2,4,3,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,9,1,5,4,3,2,8,6]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,5,4,7,2,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,9,6,5,4,3,8,1,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,10,7,6,5,4,3,2,9,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[9,11,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,6,5,9,3,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,6,3,4,8,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,4,5,8,3,7,6,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[6,8,5,4,1,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,5,2,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,9,6,1,4,3,2,8,5]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,4,3,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,3,4,7,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,2,5,4,3,8,7,6]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[8,10,1,6,5,4,3,2,9,7]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,5,7,3,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,9,6,5,4,8,2,1,7]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,10,7,6,5,4,3,9,1,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,11,8,7,6,5,4,3,2,10,9]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[10,12,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,1,7,6,8,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,4,8,5,2,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,8,6,7,4,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,6,8,2,1,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,4,5,8,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,8,7,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,5,1,8,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,8,7,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,6,7,4,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,5,2,4,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[5,2,3,6,4,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,1,4,5,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[3,8,7,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,1,2,4,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,3,7,6,8,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,3,6,8,1,7,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,2,6,8,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[6,3,7,2,4,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,5,3,7,4,1,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,6,4,7,5,1,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[4,2,8,7,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,4,1,5,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,5,8,7,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,1,5,8,7,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[4,2,7,1,8,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,1,7,2,8,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[2,4,8,7,3,5,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,7,8,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,4,7,2,8,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,7,1,4,8,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,1,8,5,2,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,7,4,5,8,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,3,6,7,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,6,3,5,8,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,5,2,7,6,1,8,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[5,1,6,8,4,7,2,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,6,8,7,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,6,4,8,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,2,5,8,4,1,7,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,8,7,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,4,8,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,7,8,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,2,7,3,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,8,7,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,1,7,2,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,8,7,1,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,4,6,7,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,8,2,7,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,8,4,2,1,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,3,7,1,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,1,3,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,3,8,6,2,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,5,2,8,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,3,7,5,1,8,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[6,8,5,2,7,4,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,8,1,4,5,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,8,1,2,4,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,6,1,2,5,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,1,6,2,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,6,5,8,2,3,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,8,6,2,5,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,6,8,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,7,5,4,3,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,8,7,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,4,3,7,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,4,3,8,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,6,1,7,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,5,7,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,6,8,2,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,1,8,7,4,3,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,8,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,8,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,1,3,8,5,6,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,5,8,4,3,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,5,2,8,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[1,8,5,2,3,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,2,5,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,1,5,6,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,3,2,5,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,1,8,3,5,6,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,4,8,2,3,6,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,1,2,7,8,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[3,5,8,1,2,4,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,5,8,1,2,3,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,2,7,1,8,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,8,4,1,2,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,4,8,2,3,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,3,6,7,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,3,7,1,8,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,4,7,3,2,8,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,7,1,4,3,8,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,1,8,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[6,8,5,1,7,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,5,8,7,3,6,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,2,8,6,1,7,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,6,1,8,3,7,5,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,7,1,6,2,8,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,1,5,3,8,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,8,6,3,7,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,8,5,1,2,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,5,2,4,8,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,4,8,2,6,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,2,5,1,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,8,5,2,6,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,2,1,8,5,6,7,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,5,4,8,2,6,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,8,4,5,1,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,8,3,7,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,5,8,6,2,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[6,3,4,8,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,8,1,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,4,8,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,8,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,1,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,4,7,1,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,4,7,8,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,5,3,7,1,4,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,3,1,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,7,1,4,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,3,1,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,3,1,2,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,5,3,8,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,1,2,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,4,3,1,5,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,3,1,5,7,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,3,1,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,7,3,8,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,5,1,8,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[4,7,5,6,2,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,5,6,1,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,5,6,3,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,5,8,4,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,5,3,8,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,8,3,6,5,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,4,7,1,8,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,1,7,3,8,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,1,8,2,7,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,1,8,4,7,2,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,8,1,6,5,7,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,1,8,6,7,2,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,8,2,3,1,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,2,8,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,3,4,1,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[3,6,4,5,2,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,6,4,5,1,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,6,4,8,1,5,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,8,3,6,1,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,4,1,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,3,8,6,7,2,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,8,3,6,2,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,8,2,7,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,4,7,3,5,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,7,3,6,4,5,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,6,4,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,8,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,8,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,8,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,6,3,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,5,6,3,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,2,5,3,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,1,5,3,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,5,8,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,8,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,2,3,1,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,2,8,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,4,2,7,5,6,1,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[3,3,3,1]=>3
[3,4,1,7,5,8,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[2,7,5,8,1,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,1,8,4,7,5,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,8,6,7,1,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,4,3,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,2,5,4,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,5,2,7,3,6,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,5,1,8,2,7,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,1,8,2,7,5,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,4,1,8,6,7,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,4,2,8,1,6,5,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,8,2,5,1,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,2,8,1,6,3,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,3,6,1,8,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[6,8,7,3,4,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,5,8,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,3,6,4,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,8,6,4,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,6,3,5,1,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,4,1,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,4,1,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,8,5,6,7,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,5,8,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,5,7,8,6,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,8,5,7,6,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,3,2,1,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,2,1,5,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,8,1,3,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,3,6,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,4,2,8,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,2,6,8,5,7,3,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,4,2,7,3,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,1,5,8,7,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[6,4,7,8,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,1,3,7,6,2,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[6,3,7,1,5,2,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[3,2,6,8,4,7,5,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,2,8,6,7,3,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,5,8,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,4,3,2,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,2,5,1,6,7,8,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[5,4,2]=>3
[2,4,8,5,7,1,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,7,1,4,6,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,4,3,8,7,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,6,7,3,5,1,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,5,7,2,8,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,4,8,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,7,6,1,4,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,8,2,1,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,6,3,5,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[6,2,5,8,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,1,6,5,8,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[2,1,6,8,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[4,1,8,5,6,2,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,6,4,8,7,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,2,8,4,3,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,2,7,6,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,8,2,7,5,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,1,2,6,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,4,3,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,2,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,1,8,4,3,7,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,3,8,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,4,2,3,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,4,3,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,3,1,6,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,4,8,2,6,3,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,7,3,5,4,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,8,4,5,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,8,3,4,5,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,2,6,4,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,7,2,3,6,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,7,2,3,5,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,2,4,5,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,3,8,4,6,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,8,2,3,5,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,8,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,8,2,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,6,4,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,2,3,6,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,5,4,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,8,3,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,5,2,7,8,3,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,3,2,8,4,6,7,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,8,2,3,4,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,4,3,6,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,3,1,5,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,8,3,1,5,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,5,1,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,4,5,1,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,5,4,1,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,8,6,4,1,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,6,4,1,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,6,7,4,1,8,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[6,5,7,4,1,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,4,7,5,1,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,1,7,5,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,3,8,1,5,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,5,1,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,4,1,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,8,4,1,7,2,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,8,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,5,8,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,4,8,6,1,7,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,1,6,7,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,1,8,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,1,7,6,8,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,4,7,6,1,8,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,5,7,6,8,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,6,7,5,8,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,8,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,6,7,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,5,6,8,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,6,5,7,8,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,7,4,6,1,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,8,4,6,1,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,1,6,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,3,1,6,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,6,3,1,7,8,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[6,2,1,4,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,8,3,1,7,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,4,8,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,2,1,6,8,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,6,8,1,7,2,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,5,6,8,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[4,7,5,8,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,8,5,7,6,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,5,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,6,8,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,6,7,8,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,5,7,8,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[5,4,7,8,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,7,1,8,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,2,1,7,8,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,8,1,7,6,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,7,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,8,7,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,8,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,7,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,5,4,7,3,6,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,4,6,3,7,5,1,8]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]=>[4,2,2,1,1]=>8
[4,2,7,3,6,5,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,2,6,3,1,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[2,5,3,7,6,4,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,5,3,7,4,1,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,2,7,6,3,5,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[2,7,5,3,6,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,7,5,4,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,7,5,2,3,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,1,8,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,5,3,1,8,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[4,2,8,3,1,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,6,8,2,1,4,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,5,2,8,3,4,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,6,3,8,7,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,8,3,6,4,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,6,3,4,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,1,3,8,7,5,4,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[1,2,3,8,6,4,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,7,6,3,8,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,7,6,4,8,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,6,3,1,8,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,1,3,8,5,4,7,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,8,4,3,5,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,2,6,3,1,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[5,4,2,8,3,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,5,8,2,4,1,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,4,8,3,1,6,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[4,2,1,8,3,5,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,8,7,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,8,7,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,7,3,6,4,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,6,3,7,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,3,8,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,8,4,7,6,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,7,3,4,8,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,6,3,8,4,7,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,5,2,3,8,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,2,1,8,3,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,8,4,2,7,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,6,3,4,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,3,8,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,8,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,5,3,8,1,6,4,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,4,7,1,5,3,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,7,1,4,3,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,8,5,7,1,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,7,2,6,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,5,7,1,4,8,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,8,1,5,7,6,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,3,8,1,6,5,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,8,1,7,5,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,1,6,5,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,8,1,3,5,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,5,7,6,1,2,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,6,2,4,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[4,8,6,7,2,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,1,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,8,6,1,5,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,8,5,7,1,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,8,5,6,1,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,5,7,2,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,6,2,1,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,7,6,2,1,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[4,8,6,7,2,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,7,2,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,1,7,5,2,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,2,8,5,1,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,8,5,1,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,6,7,1,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,2,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,3,8,5,1,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,8,5,1,7,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,4,2,8,5,6,1,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,2,4,8,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,2,5,7,6,1,4,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[4,8,6,7,1,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,2,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,5,2,6,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,5,1,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,6,7,5,1,3,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[3,8,5,7,1,4,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,7,1,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,2,8,4,6,1,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,5,1,7,4,6,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,8,4,7,2,5,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,3,8,5,2,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,2,6,7,5,3,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[4,2,6,7,5,3,8,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[4,8,6,7,3,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,3,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,5,7,6,2,4,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[3,4,1,7,5,6,2,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[3,3,3,1]=>3
[4,1,7,5,2,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,1,6,7,5,2,3,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[4,8,6,7,2,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,3,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,7,3,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,6,7,5,3,8,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[4,1,7,5,3,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,8,5,3,1,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,1,6,7,5,3,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[4,8,6,7,3,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,7,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,8,3,6,7,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,7,8,5,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,4,7,1,5,8,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,6,1,4,7,8,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[1,6,8,4,7,5,2,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,8,1,3,5,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,1,6,5,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,3,7,5,8,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[6,1,7,3,8,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,1,7,6,5,8,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[4,8,1,6,7,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,3,8,6,2,7,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,1,3,2,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[1,8,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,2,6,8,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,8,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,7,4,1,6,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,2,4,5,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,8,6,4,5,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,4,6,5,1,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,4,1,7,5,2,6,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[3,3,3,1]=>3
[5,6,8,7,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,5,4,3,6,8,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[3,8,5,4,6,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,1,3,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,1,2,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,1,8,3,6,7,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,7,8,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,4,8,2,7,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,2,7,3,6,5,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,8,7,6,3,4,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,6,3,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,7,5,8,6,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,1,7,8,4,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,3,8,1,4,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,4,5,6,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,8,7,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,7,2,4,8,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[1,5,2,7,4,3,8,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,8,5,6,4,3,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,2,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,1,8,5,7,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,1,2,8,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,4,7,2,8,5,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,3,5,8,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,8,1,5,7,2,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,4,6,5,8,1,7,2]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[6,8,1,5,7,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,2,5,8,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,8,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,5,8,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,7,1,8,5,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,7,5,8,3,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,2,1,8,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,2,7,6,8,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,7,6,8,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,7,4,1,8,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,4,3,1,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,7,4,1,6,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,7,6,8,1,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,1,7,6,8,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,7,6,8,1,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,6,8,2,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,4,2,6,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,8,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,8,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,7,1,8,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,7,6,8,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,6,8,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,3,1,8,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,1,8,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[4,7,8,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,6,5,8,7,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,6,4,8,1,2,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,4,5,1,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,6,7,1,2,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[4,3,6,7,2,1,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[5,3,6,7,1,4,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[5,2,6,7,1,4,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[4,2,6,7,3,1,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[6,2,4,1,5,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,4,1,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,3,4,2,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,3,5,2,7,1,6,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[5,6,3,8,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,7,8,2,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,6,2,8,1,4,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,5,2,1,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,2,3,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[6,2,3,1,5,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,3,4,8,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,4,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,2,3,8,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,3,7,8,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,2,6,3,8,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,3,2,5,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,2,8,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,3,8,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,3,7,8,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,2,4,1,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,3,2,7,4,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,2,5,7,8,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,7,2,3,6,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,8,2,3,6,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,8,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,5,6,8,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[4,6,8,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,1,4,2,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[5,6,8,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,1,4,2,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[5,2,8,3,4,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,5,8,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,5,6,3,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[6,2,3,4,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,1,4,3,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,1,4,3,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,1,4,3,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,6,2,4,1,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[5,6,2,4,1,8,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,7,2,4,1,8,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,1,4,2,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,4,2,7,8,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,8,2,4,1,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,7,4,1,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,4,1,3,7,2,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,1,4,3,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,8,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,4,2,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,6,3,4,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[4,8,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,6,3,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,7,8,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,4,8,7,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,8,7,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,7,8,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,7,6,8,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,8,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,1,3,4,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,1,8,4,2,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,7,4,2,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,8,1,3,4,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,6,3,7,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,3,6,7,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,1,6,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,1,6,2,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,4,8,7,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,3,8,7,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,8,4,3,7,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,4,7,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,7,4,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,4,7,3,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,3,8,2,7,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,4,8,3,7,5,6,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,3,8,2,6,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,3,2,8,1,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,3,8,2,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,8,3,7,5,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,7,3,5,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,8,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,1,6,2,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,7,2,5,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,2,7,5,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,2,4,8,3,6,5,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[3,4,2,1,8,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[3,4,1,8,2,6,5,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,6,7,8,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[4,1,7,8,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,1,2,8,3,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,3,1,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[3,7,6,8,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,8,5,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,6,8,7,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,7,8,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,2,3,8,1,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,8,2,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,4,7,8,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,3,7,8,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,7,2,8,4,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,6,3,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,6,8,4,7,3,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,4,8,6,3,1,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,7,3,8,4,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,4,8,2,6,5,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,2,4,8,1,6,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,4,8,3,6,1,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,2,8,7,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,3,4,2,8,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]=>[4,4,4,2,1,1]=>11
[3,1,4,2,8,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[4,4,4,2]=>3
[3,1,4,8,2,6,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,7,4,8,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,7,2,8,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,3,1,4,8,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]=>[4,4,4,3,1]=>7
[4,8,3,6,2,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,8,2,6,1,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,6,5,8,2,4,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,3,8,7,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,4,5,7,3,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,5,7,3,8,1,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]=>[3,3,2,1,1]=>8
[6,2,4,5,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,8,1,2,5,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,1,6,3,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[6,2,5,1,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,6,1,5,8,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,1,4,5,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,4,8,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,5,4,3,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,7,2,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,8,4,3,7,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,8,3,7,2,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,8,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,3,4,1,2,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,3,8,1,6,7,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,8,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,3,8,6,7,4,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,3,8,6,4,7,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,7,3,2,6,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,7,3,2,5,8,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,2,6,8,5,7,4,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[5,8,2,3,6,7,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,4,7,2,3,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,1,7,5,2,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,5,7,4,1,8,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,2,6,1,7,8,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,2,7,6,3,8,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[6,4,8,7,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,6,8,7,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,2,7,4,1,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[6,3,2,1,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[3,7,1,8,4,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,8,7,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,8,7,2,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,7,8,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[6,8,2,4,7,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,1,8,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,8,3,1,7,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,6,7,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,8,1,5,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,7,8,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,2,7,8,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,7,1,8,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,3,8,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,4,3,2,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,7,3,2,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,7,3,2,1,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,5,3,7,2,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,8,3,6,2,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,7,8,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,7,6,2,1,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,8,7,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,4,2,6,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,2,6,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,2,5,1,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,7,2,5,1,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,8,7,2,5,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,2,7,5,1,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,3,2,7,5,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,3,2,6,7,1,4,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[3,8,2,6,5,1,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,7,8,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,2,7,6,8,1,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,7,6,5,1,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[2,8,7,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,4,3,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,4,7,3,1,5,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,7,3,1,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,4,3,7,1,5,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,4,3,6,1,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[6,3,7,8,1,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,7,6,1,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,3,7,6,1,5,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,8,7,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,4,2,1,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,7,2,1,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,8,7,2,1,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,2,1,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,2,1,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,7,2,1,4,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,8,7,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,2,7,1,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,8,2,6,1,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,2,7,1,5,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,4,2,6,1,8,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[6,2,7,8,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,2,7,6,1,5,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,2,7,6,1,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[6,5,4,1,8,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,8,4,1,6,7,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,7,1,5,8,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,4,7,1,6,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,8,7,1,5,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,3,1,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,8,3,1,5,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,2,1,6,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,2,1,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,3,2,1,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[3,8,2,1,5,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,7,1,5,4,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,2,7,1,6,4,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[4,2,7,1,5,6,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,2,7,1,5,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[2,8,7,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,1,7,8,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,8,1,6,7,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,1,7,5,8,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,4,1,6,7,8,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[4,8,1,6,5,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,3,1,7,5,4,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,3,1,6,7,4,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[4,3,1,6,5,7,8,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[3,8,1,6,5,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,1,6,7,4,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[2,8,1,6,5,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,7,8,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,1,7,6,5,8,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,7,6,5,4,8,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[4,5,8,1,2,6,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,7,3,5,6,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,8,1,7,2,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,4,5,6,8,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[4,5,8,2,6,7,1,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,7,2,3,5,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,1,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,5,7,8,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,5,8,1,7,6,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,7,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,6,8,7,2,1,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,3,6,7,8,1,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,6,8,1,2,5,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,7,2,6,5,4,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,3,2,5,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,8,1,7,5,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,7,8,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,6,3,7,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,5,4,3,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,4,5,3,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,8,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,5,7,6,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,4,8,5,7,3,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[6,4,1,5,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,3,7,4,6,8,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,8,3,7,6,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,4,8,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,6,3,8,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,6,3,2,7,8,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,8,2,4,7,5,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,7,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,8,2,1,7,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,8,1,5,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,3,1,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,6,1,4,3,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[5,7,1,8,3,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,8,1,4,5,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,1,5,4,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,7,1,3,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,8,1,6,3,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,5,4,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,6,3,5,1,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,7,8,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,4,6,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,3,6,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,4,7,2,8,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[4,3,2,5,7,1,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[4,2,3,5,8,1,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,2,8,4,7,1,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,4,7,1,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,4,6,5,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,4,6,7,1,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,3,5,8,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[3,2,4,5,6,8,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]=>[5,4,3,2]=>6
[5,6,8,1,4,2,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,5,7,8,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,5,7,8,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[3,5,7,8,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,5,1,6,8,2,7,4]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[3,1,5,6,8,2,7,4]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[2,3,5,6,8,1,7,4]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]=>[4,3,2,2,1]=>9
[5,6,4,8,2,1,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,1,6,3,8,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,5,1,6,8,3,7,4]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[5,1,2,6,8,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,7,1,8,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[1,5,2,7,8,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,7,5,2,8,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,5,2,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,6,7,5,1,8,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,7,2,8,6,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,7,8,6,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[5,1,7,8,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,1,3,7,8,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,2,7,8,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,2,5,7,8,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[6,2,7,5,1,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,2,6,7,5,8,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,2,7,5,4,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,7,5,2,4,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,2,5,3,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,4,5,2,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,1,7,8,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,5,7,8,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,1,7,8,6,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,3,7,5,1,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,6,7,5,3,8,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,5,4,2,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,7,5,1,4,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,7,8,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,1,7,2,6,5,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[2,4,7,1,5,6,8,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,7,4,1,5,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,6,7,4,5,2,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,3,7,5,8,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,3,1,7,5,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,5,3,7,8,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,7,5,4,2,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,3,2,7,5,8,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,7,4,2,5,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,2,7,4,5,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,3,7,5,8,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,5,1,6,3,2,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1]=>3
[2,7,6,1,3,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,3,8,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,5,1,8,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,1,5,8,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,4,1,8,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,1,6,7,3,8,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,7,4,1,8,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,1,5,8,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,6,5,1,8,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,6,5,1,8,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,7,5,4,8,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,4,8,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,6,1,5,8,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,1,5,8,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,1,5,8,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,1,5,8,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,7,1,5,8,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,3,4,7,8,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[6,8,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,3,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,4,3,1,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,5,6,2,1,8,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[3,5,2,6,8,4,1,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[2,4,5,7,3,8,6,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,2,5,6,8,3,1,7]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[4,2,8,1,5,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,5,6,1,8,4,3,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[5,3,6,8,1,4,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,5,6,8,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[1,4,5,6,8,3,2,7]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[4,5,6,3,8,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[4,5,3,7,2,8,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[6,4,7,3,2,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,1,4,7,3,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,7,8,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,7,3,8,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,5,1,7,4,3,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,7,4,1,8,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,3,7,1,4,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,4,3,1,7,8,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,4,1,7,3,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,6,3,7,8,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,1,6,3,7,8,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,6,1,3,7,8,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,6,1,7,8,3,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[1,6,3,7,4,8,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,7,2,4,1,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,2,1,4,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,7,3,1,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,6,3,1,2,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[5,6,1,3,2,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[5,6,3,2,1,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[2,5,6,3,7,8,4,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,5,6,3,1,7,8,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,6,4,7,3,1,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,7,2,8,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,7,2,8,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,2,7,1,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,7,2,1,3,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[1,3,7,8,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,7,3,8,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,3,7,8,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,6,2,7,8,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[4,6,2,1,7,8,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[2,5,1,7,3,8,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,7,2,1,3,8,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,1,6,7,8,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[6,3,7,1,8,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,2,1,7,3,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,2,7,1,8,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,1,7,8,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,1,3,6,8,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,2,3,6,8,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,3,2,1,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,6,5,8,2,1,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,5,2,1,3,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[3,2,6,4,5,8,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[2,4,6,5,8,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[1,6,2,4,5,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[5,3,2,1,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[6,2,4,5,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,3,4,5,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[3,4,1,8,5,2,7,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,8,4,1,7,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,3,2,8,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,7,6,4,5,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,4,2,5,8,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[4,1,3,5,6,8,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[2,4,8,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,6,2,8,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,7,4,8,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,3,5,8,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[3,2,5,6,8,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[2,1,8,5,6,7,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,2,8,3,5,6,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,3,7,1,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[3,2,6,4,8,1,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,7,8,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,3,8,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,5,3,1,2,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,8,3,1,2,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,2,7,4,1,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[2,8,4,7,1,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,2,3,6,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,2,7,6,1,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[1,6,3,2,5,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[5,8,3,2,1,6,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,7,4,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,4,2,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,7,6,5,8,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,3,7,1,6,2,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,2,6,8,7,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,3,2,1,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,7,5,4,1,8,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,5,6,8,7,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[1,8,4,2,5,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,4,1,5,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,5,6,7,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,4,7,1,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,3,4,7,1,8,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,6,5,2,1,8,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[1,3,4,8,5,7,2,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[5,8,4,7,6,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,5,1,3,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[4,7,1,6,5,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,4,8,7,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,5,1,4,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,1,5,8,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,1,3,5,8,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[6,5,3,8,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,1,6,8,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[6,8,4,3,2,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,4,7,8,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[5,1,3,2,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,1,2,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,3,1,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,3,2,1,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,1,3,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[2,4,7,3,8,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,3,8,2,7,4,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,1,7,8,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[2,7,4,5,8,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,3,7,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,8,7,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,4,7,8,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,4,3,8,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,8,7,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,7,2,4,8,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,6,1,8,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[6,1,3,8,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,3,2,6,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,5,3,6,2,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,1,5,4,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,8,7,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,1,7,6,4,5,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,7,2,4,6,5,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,1,7,6,8,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[5,8,2,6,1,3,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,5,8,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,5,7,8,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,2,8,1,5,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,5,2,6,8,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[3,4,5,1,6,8,7,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1]=>[5,4,2,1]=>6
[4,2,8,5,1,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,5,2,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,7,1,8,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,6,2,1,3,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,3,5,8,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[1,7,8,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,5,1,8,6,7,2]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[3,8,1,4,5,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,5,7,8,2,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[3,4,6,2,8,5,1,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,4,6,8,1,5,2,7]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,4,7,2,1,8,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,8,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,2,1,5,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,2,7,8,4,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[3,5,6,2,8,4,1,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,5,6,8,4,1,2,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[3,5,7,2,4,8,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,8,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,8,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,6,2,1,7,8,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[3,6,2,1,8,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,6,7,2,8,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,6,8,2,4,5,1,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,7,2,1,4,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,8,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,4,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,5,6,7,8,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[4,1,5,7,3,8,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[4,1,6,3,7,8,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,1,6,3,8,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,1,6,7,3,8,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[4,1,6,7,8,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[4,1,6,8,3,5,2,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,1,7,3,2,8,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,1,8,3,2,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,5,2,6,8,1,3,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,5,7,3,8,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,5,8,3,2,1,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,2,3,7,8,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,6,2,3,8,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,2,7,8,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[4,6,7,3,2,8,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[4,7,8,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,2,3,1,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,2,6,8,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,1,2,7,4,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,1,2,8,4,3,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,6,3,8,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,1,6,7,4,8,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,6,2,3,8,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,2,7,8,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,8,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,2,3,4,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,8,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,2,3,4,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,2,3,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,1,2,3,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,2,7,8,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,7,3,8,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,1,7,8,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,1,8,3,4,5,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,2,3,8,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,2,8,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,4,1,8,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,1,2,4,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,5,8,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,1,6,8,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,6,2,8,1,5,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,1,3,8,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,7,5,2,3,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,5,1,3,8,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,7,5,3,2,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,5,1,2,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,7,3,6,5,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,9,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,9,8,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,9,8,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,9,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,9,8,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,9,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[8,10,9,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,9,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,10,9,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,5,7,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,9,8,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,10,9,8,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,5,4,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,6,7,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,9,8,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,9,8,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,6,4,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,9,8,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,10,9,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,6,3,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,9,8,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,10,9,8,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,8,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,3,2,8,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,5,4,3,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,4,1,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,1,5,3,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,6,1,8,5,2,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,4,1,2,8,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[6,8,3,5,4,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,5,6,3,4,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,4,2,6,3,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,2,3,1,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[5,2,8,4,1,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,4,5,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,3,2,5,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,3,7,1,5,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,5,1,8,4,3,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,2,5,4,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,3,1,6,5,8,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[6,1,3,4,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,7,3,2,5,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,1,5,8,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[5,4,6,8,1,2,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,4,7,2,3,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,8,4,1,3,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,4,7,8,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[4,1,3,5,7,8,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[6,5,1,8,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,1,8,4,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,7,3,2,8,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,3,1,4,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,4,7,3,8,5,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,8,6,1,5,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,3,4,2,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,2,4,1,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[2,8,3,4,7,1,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,3,6,7,8,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[1,7,6,3,2,5,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,5,6,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,4,8,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,6,4,5,2,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,3,6,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,2,1,7,5,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,5,4,1,8,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[4,7,2,6,5,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,8,1,4,2,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,4,7,1,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,4,7,8,2,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[1,8,2,4,5,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,4,1,6,8,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[3,2,5,7,6,1,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[4,3,5,6,1,8,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[5,3,4,1,7,6,8,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,1,4,6,5,7,8,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2]=>[5,3,3,2]=>5
[1,4,7,3,5,6,8,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,1,3,6,4,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[1,4,2,7,8,5,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[5,1,2,6,8,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,1,2,6,8,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[1,5,2,4,8,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,6,4,8,7,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,7,4,8,6,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,2,8,5,7,4,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,5,2,4,8,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,6,4,8,7,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,7,8,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,6,8,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,5,6,8,2,7,3,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,3,8,2,6,7,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,7,2,8,6,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,7,8,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,2,6,8,3,7,5,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,5,7,8,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,2,7,8,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,7,2,8,3,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,7,3,4,8,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,3,7,4,8,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,8,4,1,5,3,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,1,5,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,4,2,8,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,4,2,7,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,8,4,7,3,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,4,8,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,6,4,8,3,7,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,5,2,4,8,3,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,8,4,5,7,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,5,2,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,5,1,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,3,8,6,2,7,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,8,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,6,8,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,2,6,8,5,3,7,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,7,8,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,5,8,7,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,6,8,7,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,7,8,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,6,7,8,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,7,8,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,7,6,8,2,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,7,6,2,8,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,3,8,7,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,8,4,7,6,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,5,8,7,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,6,8,7,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,7,8,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,2,6,7,3,4,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,2,4,7,6,3,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,6,2,1,7,8,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,6,2,1,4,8,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[2,6,1,4,5,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[5,4,2,7,6,3,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[2,3,7,6,4,5,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,6,1,7,5,8,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,1,7,4,8,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,1,2,7,8,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[2,6,1,7,4,8,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,6,4,1,7,8,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[5,4,6,1,3,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[3,6,4,1,5,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,6,1,5,4,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,1,4,7,8,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,1,2,4,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,2,4,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,2,4,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,2,3,8,5,4,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[4,3,1,2,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[1,2,3,8,5,6,4,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,5,4,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,6,1,5,4,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[5,1,2,4,8,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,2,4,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,6,3,1,4,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,4,6,3,1,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[3,6,4,5,1,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,6,5,4,1,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[5,2,6,1,7,8,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,1,6,2,8,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,1,3,7,8,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,7,8,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]=>[3,3,3,3,2]=>4
[5,2,4,1,7,8,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,3,1,2,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,1,4,2,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,2,3,8,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[1,2,3,8,5,7,4,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[5,4,1,2,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,1,6,2,8,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[1,2,9,3,4,5,6,7,8]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[1,2,8,4,5,3,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,3,4,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,9,4,3,5,6,7,8]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[1,8,4,3,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,3,2,4,5,6,7,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,2,10,3,4,5,6,7,8,9]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,1]=>7
[6,8,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,1,4,2,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,4,3,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,5,1,4,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,5,3,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,5,4,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,5,4,7,6,8,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,3,7,6,8,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,1,4,3,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,5,8,1,4,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,1,5,3,7,4,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,3,7,4,8,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,4,7,5,8,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,8,3,6,4,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,6,4,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,6,3,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,5,3,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,5,2,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,7,1,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,3,7,1,4,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,3,2,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,1,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,7,1,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,7,1,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,8,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,6,8,1,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,5,8,1,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,1,3,2,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,7,1,4,2,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,8,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,8,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,8,2,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,8,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,5,8,3,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,5,8,2,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,7,5,8,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,8,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,8,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,5,2,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,6,1,5,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,6,5,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,6,5,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,8,4,7,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,5,8,4,7,1,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,8,3,7,1,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,3,7,1,5,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,8,4,3,7,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,4,3,5,1,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,3,5,4,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,8,3,7,5,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,7,4,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,3,5,8,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,7,8,3,6,2,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,3,6,7,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,4,8,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,8,4,7,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,4,1,7,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,7,4,1,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,3,4,7,5,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,5,7,8,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,7,3,6,8,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,8,3,7,2,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,7,3,4,1,8,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[4,6,7,8,3,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,6,8,3,5,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,3,5,6,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,3,5,8,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,3,4,7,8,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,8,2,4,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,4,8,2,6,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,3,6,2,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,5,7,2,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,5,6,7,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,7,8,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,3,6,7,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,7,2,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,4,8,2,7,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,8,2,4,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,4,1,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,2,5,1,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,3,5,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,5,8,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,3,7,2,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,3,4,8,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,8,4,2,3,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,2,3,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,5,3,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,8,5,3,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,3,8,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,8,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,7,3,1,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,3,7,8,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,4,5,3,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,7,4,2,3,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,6,3,7,1,8,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,3,4,7,1,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,6,3,4,8,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,3,5,7,4,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,5,4,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,4,3,5,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,2,5,1,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,3,7,2,4,1,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,4,7,2,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,7,3,6,2,5,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,3,6,8,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,6,7,3,5,8,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[4,5,7,8,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,5,8,3,6,7,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,3,7,2,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,3,4,6,8,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,3,6,8,2,1,4,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,3,6,7,1,8,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,3,4,6,7,1,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[4,6,3,5,7,8,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,5,7,3,6,8,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[4,5,6,8,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[5,7,4,8,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,2,6,5,1,8,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,5,6,7,2,8,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[7,6,9,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,4,9,8,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,8,5,9,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,7,8,9,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,4,3,2,9,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,8,4,3,9,7,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,4,7,6,9,8,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,7,8,4,9,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[5,6,7,8,9,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[4,8,3,2,1,9,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,7,8,3,2,9,6,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[4,5,6,7,8,9,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[3,6,7,8,2,1,9,5,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[3,5,6,7,8,2,9,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,4,5,6,7,8,9,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[8,7,10,9,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[8,9,10,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,6,5,10,9,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[7,9,6,10,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[7,8,9,10,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,5,4,3,10,9,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[5,6,7,8,9,10,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[4,7,8,9,3,2,10,6,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[4,6,7,8,9,3,10,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,2,1,1]=>[4,3,2,1,1]=>9
[4,5,6,7,8,9,10,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[1,6,2,5,3,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,3,8,2,4,6,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,2,3,6,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,2,5,3,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,2,5,3,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,3,6,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,5,4,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,2,7,3,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,2,3,7,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,8,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,3,6,1,2,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[2,1,7,5,8,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,4,1,7,2,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,7,1,8,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,8,1,7,4,2,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,7,8,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,1,2,3,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,8,1,4,2,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,1,2,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,3,1,2,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,1,4,2,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,3,6,8,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,1,2,5,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,2,8,5,4,1,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,4,8,5,1,3,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,5,6,1,8,4,2,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[1,3,6,8,7,4,2,5]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,2,8,5,7,3,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,6,1,5,8,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,7,1,6,8,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,8,1,2,5,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,4,7,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,4,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,4,8,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,6,5,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,1,5,8,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,6,8,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,8,6,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,1,6,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,2,7,4,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,5,2,8,7,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,4,2,7,8,1,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[4,1,3,7,5,6,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[6,3,8,1,7,4,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,7,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,7,3,8,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,6,1,4,5,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[1,6,7,4,5,3,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,3,5,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,3,1,2,5,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,4,7,2,8,5,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,6,8,7,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,8,5,7,1,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,4,1,7,5,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,1,5,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,2,4,8,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[2,7,8,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,2,5,7,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,6,8,5,3,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,2,6,4,8,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,7,1,3,4,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,7,3,2,4,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,4,2,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,3,8,7,5,2,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,8,7,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,4,5,2,8,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[5,3,8,6,1,2,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,6,3,4,8,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,5,3,6,8,7,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[4,8,7,3,5,2,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,3,5,4,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,3,8,6,1,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,6,2,5,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[1,8,5,3,6,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,7,2,4,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[1,5,3,4,8,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,4,1,3,8,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,1,8,6,3,4,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,2,8,3,7,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[5,8,2,4,7,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,5,3,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,7,4,8,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,3,1,4,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,1,3,8,2,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[2,8,3,6,7,5,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,7,2,8,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,6,1,4,7,2,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[1,5,8,4,7,2,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,2,7,4,5,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,1,8,4,5,7,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,8,5,7,3,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,8,5,4,3,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,4,1,5,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,4,6,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,5,6,8,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,8,5,4,1,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,7,4,2,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,8,6,5,1,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,3,4,8,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[4,1,8,6,5,3,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,5,2,7,3,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,8,4,3,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,7,4,3,6,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,7,5,1,2,8,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,2,6,8,3,4,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,6,8,4,7,2,5,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,6,3,8,4,7,5,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,2,7,5,8,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[2,8,3,6,4,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,5,6,8,3,7,4]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,3,2,2,2]=>7
[5,8,1,2,6,4,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,8,3,2,7,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,5,7,2,8,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,4,8,3,6,2,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,7,4,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,5,8,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,7,3,6,4,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,5,6,4,8,2,7,3]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[3,1,5,6,4,8,7,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[3,5,1,6,4,7,8,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[3,6,1,4,2,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,4,6,3,1,7,8,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,3,5,1,8,4,7,6]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,6,1,8,5,4,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,7,4,6,8,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,7,5,1,8,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,7,2,5,3,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,1,7,5,4,8,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[1,2,7,6,4,8,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,3,6,8,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,6,1,8,5,7,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[3,1,5,4,8,7,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[1,2,5,8,4,7,3,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,6,8,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,3,6,8,5,2,7,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[3,5,7,4,8,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,8,3,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,4,6,8,3,5,2,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,3,6,8,5,2,4,7]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,2,6,8,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,5,8,4,3,7,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,3,5,8,2,4,7,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,6,8,2,5,4,7]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,4,6,8,3,2,5,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[3,5,7,4,8,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[4,6,1,7,5,8,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[2,3,6,7,5,8,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,3,7,5,6,8,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,3,6,5,8,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[3,4,6,2,8,1,7,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[3,5,4,6,8,2,1,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[3,5,4,6,8,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[1,2,6,7,4,8,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[3,6,4,7,1,8,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[1,2,6,7,3,8,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[3,1,5,7,6,8,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[3,5,4,6,8,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[4,2,6,1,8,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,6,5,8,7,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,3,6,5,8,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,2,7,4,6,8,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,5,6,8,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,1,6,7,5,8,4,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[4,6,2,7,5,8,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[3,5,7,4,8,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,8,3,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,4,6,8,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,3,6,8,2,5,7,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,3,5,8,2,7,4,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,2,5,8,4,7,6,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,4,8,7,3,6,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,5,8,7,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,3,5,8,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[2,3,7,6,8,5,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,7,1,2,8,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,1,7,6,8,5,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[1,2,6,8,5,7,4,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,5,8,7,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,4,8,7,6,3,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[6,4,5,7,2,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,3,4,7,2,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,2,7,4,6,8,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[5,3,6,2,7,1,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[2,6,3,4,7,1,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,7,3,4,5,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,4,5,6,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,5,7,3,6,8,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,7,6,2,3,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,5,2,3,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,3,1,2,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,5,2,3,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,2,1,7,3,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,2,1,8,3,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,2,8,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,3,8,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,1,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,7,5,8,2,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,5,8,3,6,7,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[2,5,7,1,8,3,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,2,7,1,8,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,7,1,3,8,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,6,2,8,4,5,7,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,1,3,6,8,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,3,4,6,8,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,6,3,8,7,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,4,5,8,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,8,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,8,7,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,7,2,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,3,7,6,1,2,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[1,8,3,7,2,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,7,2,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,2,3,5,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,8,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,2,8,7,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,7,1,4,5,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,3,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,2,3,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,5,8,7,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,6,2,4,7,1,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[3,4,7,2,5,1,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,1,6,4,8,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[4,1,8,5,3,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,6,2,5,7,1,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[1,2,8,3,7,5,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,3,2,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,1,2,8,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[1,6,3,8,7,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,3,8,1,2,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[7,8,10,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[7,8,10,9,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[7,8,10,9,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[7,8,10,9,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,8,10,6,9,4,7,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[1,6,7,10,9,4,8,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,2,1,1,1,1,1]=>[3,3,2,1,1,1,1,1]=>17
[1,8,10,4,5,9,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[7,8,10,9,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,8,10,6,9,2,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[1,6,7,10,9,2,3,8,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,2,1,1,1,1,1]=>[3,3,2,1,1,1,1,1]=>17
[1,8,10,2,5,9,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[1,8,10,2,3,4,9,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[3,6,8,7,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,2,8,5,4,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,7,2,4,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,4,1,6,5,8,7,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[5,3,3,1]=>5
[3,5,1,2,4,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[3,7,5,2,1,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,2,7,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,8,4,7,3,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,7,4,1,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[4,3,5,1,2,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[3,1,4,6,2,8,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[1,4,6,5,2,8,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[3,4,5,6,1,8,7,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]=>[5,3,2,1]=>6
[3,4,5,8,7,2,1,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[1,4,7,2,6,3,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,5,7,3,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,5,1,7,4,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,1,4,8,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,8,1,6,3,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,8,6,3,7,2,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,4,7,6,3,8,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,6,3,7,5,8,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,1,3,5,8,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[5,7,4,3,8,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[1,4,8,3,7,6,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,3,8,2,1,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,4,2,7,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,6,7,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,6,8,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,5,3,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,7,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,1,4,2,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,4,1,8,5,7,6,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,6,5,1,2,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,8,5,6,7,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,5,7,2,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,8,6,5,7,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,3,6,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,5,8,7,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[1,2,5,8,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[4,2,1,5,8,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[5,2,4,6,1,7,3,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[1,5,3,6,8,7,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[3,5,4,6,1,8,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[3,1,5,7,6,8,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[1,4,5,6,8,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[1,4,6,3,7,2,8,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,7,3,6,5,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,2,6,5,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,7,5,2,6,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,2,6,4,7,5,1,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[6,2,3,7,5,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[2,8,3,6,1,7,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,2,6,5,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,2,6,1,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,1,3,7,2,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[6,1,3,7,5,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,1,8,6,2,7,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,7,8,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,6,1,8,2,7,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,2,7,8,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,8,6,1,7,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,8,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,1,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,7,8,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,3,8,4,1,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,4,8,6,5,1,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,4,8,6,2,7,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,6,4,7,8,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[3,4,6,5,1,2,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]=>[6,2,2,1]=>5
[1,4,6,2,3,8,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[4,5,2,1,7,3,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[5,6,7,1,2,8,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[4,7,5,1,2,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,1,6,2,8,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,8,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,8,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,6,2,7,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,1,2,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,8,1,2,7,4,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,2,7,3,6,8,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,3,6,4,2,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[4,1,5,3,8,2,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[5,2,6,4,7,3,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[2,6,3,4,7,5,1,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,3,5,4,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,7,4,3,5,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,3,1,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,5,4,2,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,4,1,7,2,6,3,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,4,1,8,3,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,2,8,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,4,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,5,3,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,3,1,8,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,8,4,2,7,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,6,8,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,8,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,7,4,2,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,2,7,3,4,6,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,8,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,8,3,5,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,1,7,3,5,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,1,5,8,4,2,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,3,1,6,8,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,7,4,8,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,8,2,7,3,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,7,3,4,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,7,5,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,8,3,7,6,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,3,2,6,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,4,7,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,8,2,7,3,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,6,8,7,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,8,1,7,2,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,7,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,3,5,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,5,2,4,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,7,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,3,7,6,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,5,2,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,7,8,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,3,8,1,5,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,1,8,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,3,1,7,5,4,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,5,7,4,1,3,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,6,8,4,3,7,1]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,4,7,5,8,1,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,4,7,1,8,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,2,1,8,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,5,7,6,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,7,5,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,5,4,8,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,4,7,2,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,7,4,8,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,3,2,8,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,3,2,7,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,1,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[3,5,7,4,2,6,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,6,4,5,1,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,3,5,1,7,6,2,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[3,5,4,7,1,6,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,4,7,5,6,1,2,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[3,4,5,8,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[3,5,4,6,1,8,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[4,3,5,1,6,8,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[4,2,1,5,6,8,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[7,3,2,1,6,5,4,10,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,7,7]=>[7,7]=>0
[8,3,2,1,7,5,4,10,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[8,5,2,1,7,4,3,10,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[6,3,2,1,10,5,4,9,7,8]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[7,3,2,1,10,5,4,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,5,2,1,10,4,3,9,7,8]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[7,5,2,1,10,4,3,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[8,3,2,1,7,6,4,10,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[8,4,2,1,7,6,3,10,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[5,3,2,1,10,7,4,9,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[7,3,2,1,10,6,4,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,2,1,10,7,3,9,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[7,4,2,1,10,6,3,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[7,6,2,1,10,5,3,9,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[8,4,3,1,7,6,2,10,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[5,4,3,1,10,7,2,9,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[7,4,3,1,10,6,2,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[7,6,3,1,10,5,2,9,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[7,6,5,4,3,2,9,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[6,5,4,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,3,8,2,7,1,6,9]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3]=>[3,3,3]=>0
[4,8,3,7,2,6,1,5,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1]=>[1,1,1,1]=>0
[3,6,9,2,5,8,1,4,7]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[8,7,6,5,4,3,2,10,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[5,10,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,3,8,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,8,2,7,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,7,2,8,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,1,7,2,8,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,1,8,2,7,3,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,2,4,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,8,2,4,3,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,2,5,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,2,7,3,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,7,2,8,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,1,7,2,5,3,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,1,7,2,4,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,1,6,2,4,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[1,8,2,7,5,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,4,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,4,7,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,2,6,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,7,2,6,3,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,1,7,4,3,6,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[1,8,5,4,3,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,3,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,2,5,3,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,2,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,7,3,2,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,1,7,2,6,8,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[5,1,7,4,2,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,1,6,3,2,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[6,5,4,3,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,5,1,7,3,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,2,8,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,3,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,4,3,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,8,1,7,5,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,3,1,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,8,2,1,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,2,8,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,1,7,8,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,4,1,7,8,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,2,1,6,7,3,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[5,4,2,7,3,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,1,5,3,2,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[3,1,6,2,8,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[6,3,1,7,8,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,5,4,1,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,4,3,1,6,7,2,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[6,5,4,2,7,8,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,4,2,6,3,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[5,4,2,1,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[5,4,3,1,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[6,3,8,1,2,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,7,1,2,5,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[5,2,3,7,1,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[2,5,3,6,1,8,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]=>[5,3,1,1,1]=>7
[2,6,7,3,1,8,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,1,3,5,4,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,8,3,1,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,5,7,1,8,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[4,3,1,2,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[5,1,2,7,3,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,1,4,7,8,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,4,7,8,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,5,4,6,8,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[1,5,4,6,8,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,6,7,3,2,4,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,1,3,7,2,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,2,4,7,8,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,2,5,7,6,1,8,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[4,5,2,8,6,1,7,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[5,3,1,8,2,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,8,3,2,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,5,7,6,8,1,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[4,1,5,7,6,2,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,5,1,8,6,2,3,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[5,2,1,8,3,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,4,2,1,8,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[7,8,9,10,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,5,2,3,6,10,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1]=>[2,1]=>1
[7,8,4,5,9,10,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,9,10,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,4,5,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,5,2,6,10,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,2,1]=>[2,1]=>1
[7,8,4,5,9,10,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,9,10,4,5,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,5,2,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1]=>[2,1]=>1
[7,8,4,5,9,10,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,9,10,4,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,2,5,6,10,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,2,1]=>[2,1]=>1
[7,8,4,9,10,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,9,10,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,2,5,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1]=>[2,1]=>1
[7,8,4,9,10,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,4,9,2,5,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1]=>[3,1]=>1
[7,8,4,2,5,9,10,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[6,5,1]=>[5,1]=>1
[7,4,8,9,10,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,4,8,9,10,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,4,8,9,2,5,1,3,6,10]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2]=>[3,2]=>1
[4,6,7,2,5,1,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[3,6,7,2,1,4,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[5,2,3,6,1,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[2,6,7,3,1,4,5,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,7,1,5,2,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[4,6,7,3,5,8,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[6,4,7,1,5,2,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,2,7,3,1,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,1,4,6,7,2,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[3,5,4,6,7,8,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[1,6,7,3,2,4,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,1,3,6,2,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,2,4,6,7,1,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[2,5,4,6,7,1,3,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[4,3,1,1,1]=>7
[2,6,7,4,5,1,3,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,7,4,5,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,2,5,6,7,1,3,8]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]=>[4,3,2]=>3
[4,5,2,6,7,1,3,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]=>[4,3,1]=>3
[5,3,1,6,2,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[6,1,7,3,2,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,1,7,4,5,2,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,3,7,4,5,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,4,1,6,7,2,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[5,2,1,6,3,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[1,3,6,7,5,2,8,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,3,6,7,2,5,8,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,7,4,6,2,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,1,7,2,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[5,6,1,4,7,3,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,3,2,1,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[6,3,4,5,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,4,5,1,6,8,7,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]=>[5,4,2,1,1]=>9
[4,3,2,5,6,8,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[3,7,5,4,6,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,1,4,6,5,8,2,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[2,3,4,5,8,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[2,3,4,5,8,1,7,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,1,4,6,5,8,7,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[3,7,5,4,6,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,6,1,4,7,2,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[4,3,1,7,5,6,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,3,1,7,6,5,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,1,4,6,7,8,5,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]=>[4,3,3,2]=>5
[3,7,5,2,6,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,2,6,8,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,6,1,2,7,4,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[6,3,5,2,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,3,2,1,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,3,1,4,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,3,1,2,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[1,7,4,6,5,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,4,6,1,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,6,1,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,6,7,1,5,8,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,3,6,7,5,1,8,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[4,3,2,6,7,1,8,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,3,3]=>2
[2,7,4,6,5,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,4,5,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,4,5,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,7,4,6,5,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,4,6,1,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,3,4,5,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,6,1,8,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,8,6,1,7,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,4,7,1,8,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[8,10,7,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,6,9,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,10,7,9,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,6,9,4,8,3,5,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,10,5,9,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,5,9,4,8,3,6,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,10,5,9,4,8,3,7,1,2]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[8,10,7,9,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,6,9,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,10,7,9,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,6,9,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,10,5,9,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,5,9,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,10,5,9,4,8,2,7,1,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[8,10,7,9,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,6,9,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,10,5,9,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,5,9,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,10,5,9,3,8,2,7,1,4]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[8,10,4,9,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,4,9,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,10,4,9,3,8,2,7,1,5]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[10,12,9,11,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,7,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,6,9,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,6,9,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,7,8,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,7,9,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,6,8,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,6,9,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,6,9,4,8,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,5,8,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,5,9,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,5,9,4,8,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,6,11,5,9,4,8,3,7,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,7,8,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,7,9,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,6,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,6,9,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,6,9,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,7,8,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,7,9,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,6,8,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,6,9,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,6,9,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,5,8,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,5,9,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,5,9,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,6,11,5,9,4,8,2,7,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,7,8,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,7,9,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,6,8,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,6,9,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,6,9,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,5,8,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,5,9,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,5,9,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,6,11,5,9,3,8,2,7,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,9,11,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,8,11,4,9,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,7,11,4,9,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,6,11,4,9,3,8,2,7,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[10,12,5,11,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,2,1,7,3,5,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[2,1,8,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,3,5,8,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,3,1,5,4,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,1,4,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[4,2,1,8,3,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[2,1,8,6,3,5,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,2,1,7,3,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[2,7,3,1,4,8,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,3,6,8,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,3,1,5,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,7,5,1,6,8,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,7,5,6,1,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,6,8,5,1,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,6,1,8,3,5,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,1,6,8,3,7,4,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,8,3,5,7,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,3,6,4,5,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,8,4,7,5,1,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,6,1,8,3,5,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,7,3,1,5,6,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,7,5,1,6,3,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,8,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,7,1,8,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,5,1,6,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,2,1,7,3,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,2,1,7,8,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,7,1,8,3,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,3,6,4,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,2,1,7,4,5,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,6,8,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[2,1,8,3,7,4,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,3,6,7,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,4,8,5,1,6,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,8,5,6,1,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,1,8,4,5,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[1,6,8,3,7,2,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,8,1,5,7,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,2,6,8,4,7,3,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,1,5,8,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,2,4,8,3,6,7,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[4,1,2,7,8,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,5,7,4,8,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[5,3,8,4,7,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,1,2,3,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,2,8,4,3,5,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,2,8,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,2,6,3,8,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,2,8,5,3,6,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,3,8,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,1,2,7,8,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[1,6,2,8,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,4,2,7,3,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,8,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,2,8,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,7,8,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[1,8,7,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,2,8,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,8,3,2,6,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,3,2,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,4,3,7,5,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,3,8,7,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,6,4,7,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,8,2,7,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,2,7,5,3,6,4,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,3,7,5,4,8,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[3,7,4,8,6,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,8,2,7,6,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,3,1,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,3,6,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,6,5,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,4,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,2,1,4,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,1,7,2,4,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,4,7,1,5,2,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,6,7,4,1,5,8,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[4,3,2,7,1,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,1,2,8,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,4,8,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,6,8,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,8,2,7,4,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,8,2,3,7,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,5,3,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,7,8,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,4,8,1,6,3,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,1,2,8,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,3,2,6,4,8,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[4,1,6,3,5,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[2,4,5,3,8,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[1,8,5,3,2,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,5,2,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,2,7,6,5,8,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[2,4,1,6,7,8,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1]=>8
[1,8,4,3,6,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,7,3,2,8,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[2,5,7,3,6,8,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,3,2,1,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,1,4,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[3,4,7,8,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,6,7,8,1,4,5,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,6,2,8,1,5,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,3,6,8,5,1,4,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,1,6,4,8,2,5,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[1,8,5,2,4,6,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,2,3,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,2,8,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,4,8,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,4,8,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,6,8,3,4,1,7]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,5,6,8,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,5,7,8,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,5,7,8,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,3,2,6,8,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,5,6,8,2,4,1,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[3,5,6,8,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,6,7,8,1,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,6,7,8,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,5,7,8,2,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,6,7,8,1,4,3,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,5,7,8,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,5,7,8,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,7,3,8,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,4,7,3,8,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,4,7,3,8,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,2,5,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,5,2,3,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,5,3,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,4,6,3,8,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,4,7,3,8,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,5,7,8,3,1,6,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,5,7,8,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,5,6,8,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[5,4,6,2,8,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,3,2,6,8,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,7,2,8,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,5,7,8,2,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,6,7,8,1,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,6,7,8,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[2,6,7,8,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,8,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,7,8,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,6,7,8,1,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,5,7,8,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[5,4,7,2,8,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,2,7,8,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,3,2,7,8,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,5,7,8,2,1,6,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,6,7,8,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,8,1,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,8,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,6,7,8,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,4,5,6,7,8,1,3,9]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,1]=>[5,4,3,2,1,1]=>14
[1,4,5,6,7,8,2,9,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,1,1]=>[5,4,3,2,1,1,1]=>18
[4,2,7,1,5,3,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,8,6,1,5,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,6,7,5,1,4,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[2,7,1,3,5,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,2,1,5,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[1,3,4,8,2,7,5,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,1,4,8,2,6,7,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[4,8,6,2,1,5,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,6,5,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,7,3,5,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,4,7,5,1,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,6,1,7,5,8,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[4,7,3,5,6,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,4,6,8,5,1,7,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[4,6,8,2,1,5,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,8,2,1,3,5,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,2,3,5,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,3,6,1,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,1,3,5,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[4,7,5,2,6,1,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,6,2,8,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,5,6,2,7,1,3,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]=>[4,2,1]=>3
[1,6,2,7,4,8,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,2,1,7,8,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,7,3,8,4,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,7,8,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,8,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,5,6,1,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,3,6,7,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,3,7,6,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,2,8,3,7,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,6,4,8,1,5,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,2,6,3,7,1,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[2,6,4,8,1,3,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,6,4,8,1,7,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,4,5,1,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,5,6,4,1,2,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[6,2,1,1]=>5
[3,5,6,4,1,2,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[6,2,1,1]=>5
[2,6,4,3,1,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,4,3,1,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,4,3,1,8,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,5,8,4,1,2,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,5,8,4,1,2,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,5,8,4,1,6,2,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,8,3,6,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,5,8,4,1,6,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,8,4,1,7,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,6,4,2,1,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[3,6,4,2,1,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,5,6,4,1,8,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[2,6,4,5,1,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[3,6,4,5,1,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[2,5,6,4,1,7,8,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,5,6,4,1,7,3,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]=>[5,2,1,1,1]=>7
[3,6,4,5,1,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[4,1,7,6,2,8,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,7,6,1,2,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,6,5,3,1,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,6,1,5,3,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[3,6,1,4,2,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[2,6,4,5,7,8,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,1,3,4,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,4,5,6,1,8,7,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]=>[5,3,2,1,1]=>9
[2,8,3,4,7,5,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,7,4,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,8,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,6,1,7,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,5,1,7,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,7,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,5,1,8,7,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,7,1,8,4,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,2,3,8,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,3,5,8,6,7,4,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[4,6,7,2,5,8,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[6,2,1,3,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,4,2,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,1,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,1,4,3,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,6,2,8,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,4,5,1,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,2,3,1,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[3,4,2,1,8,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[2,7,6,8,1,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,5,8,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,6,8,1,5,2,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,2,8,7,4,5,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,3,8,5,7,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,4,8,7,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,1,6,8,3,7,5,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,6,8,2,4,1,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,2,8,1,7,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,5,4,8,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,5,3,4,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,8,1,5,3,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,8,2,6,4,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,2,8,3,7,5,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,1,5,8,3,6,4,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,8,5,3,6,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,4,1,6,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,3,5,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,4,5,6,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[7,9,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,5,9,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,8,7,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[7,9,6,8,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,8,4,7,1,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,4,2,5,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[4,2,7,5,6,3,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,4,7,5,6,2,1,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,7,3,5,6,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,7,2,5,6,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,6,8,5,2,7,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,8,5,1,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,4,8,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,2,7,8,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,8,4,1,2,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,8,5,6,3,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,8,2,5,6,4,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,8,5,3,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,1,5,2,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,5,2,4,6,7,8,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]=>[5,4,1,1,1,1]=>9
[4,1,5,3,6,7,8,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[5,4,2]=>3
[3,2,6,4,1,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[4,5,3,1,6,7,8,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[5,4,1]=>3
[3,5,2,1,6,7,8,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[5,2,3,1,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[1,5,3,2,6,7,8,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]=>[5,4,1,1,1,1]=>9
[3,2,5,6,1,7,8,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]=>[5,3,2,2]=>5
[3,2,8,7,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,8,4,7,2,1,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,7,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,6,5,1,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,4,6,2,3,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,4,6,1,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,2,4,3,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,5,4,2,7,1,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[6,7,4,1,5,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,7,4,2,3,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,5,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,1,5,4,7,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,1,5,6,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,1,2,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,2,8,1,6,5,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,1,5,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[3,5,1,4,6,7,8,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[5,2,1,4,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[5,4,1,3,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[5,1,3,4,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[3,1,8,2,5,7,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,1,6,4,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,1,3,8,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,5,7,1,3,8,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,8,1,5,7,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,1,5,8,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,6,4,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,6,5,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,8,7,3,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,7,2,8,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,7,1,8,6,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,1,4,2,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,1,4,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,5,1,4,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,8,4,5,2,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,8,5,1,7,3,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,5,1,3,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,6,1,5,3,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,1,7,6,3,8,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,1,7,6,4,2,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,1,8,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,6,3,2,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,1,7,4,8,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[4,1,8,6,3,7,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,4,6,8,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[5,4,8,2,7,3,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,7,3,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,3,8,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,7,2,4,8,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,6,8,4,2,7,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,4,2,8,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,5,2,7,1,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,7,3,1,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,7,4,3,8,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,5,4,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6]=>[6,6]=>0
[5,4,3,2,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[7,6,5,4,3,2,1,10,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,7,7]=>[7,7]=>0
[5,6,3,7,4,2,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[6,4,8,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,7,6,5,3,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,7,2,4,6,5,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,6,8,4,2,5,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,8,4,1,5,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,4,8,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,2,7,8,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,1,5,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,4,8,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,4,8,5,2,6,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,1,8,4,3,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,7,1,4,2,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,1,5,3,6,8,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[6,1,8,5,3,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,6,4,1,8,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,5,2,1,8,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[1,5,3,2,8,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,4,2,1,7,8,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,7,3,6,2,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,3,4,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[6,7,3,1,5,4,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,8,3,1,2,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,1,5,6,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,1,2,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,2,8,1,6,5,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,2,1,4,7,6,3,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[4,5,8,2,1,3,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,8,2,3,1,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,1,3,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,1,3,4,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[6,8,2,4,5,1,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,7,2,5,1,4,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[4,6,7,3,1,5,2,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[5,8,1,2,4,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,3,5,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,1,4,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,8,2,3,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,8,4,2,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,4,6,3,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,3,5,7,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,4,7,2,6,1,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[4,5,7,3,2,6,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,5,7,2,3,6,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[2,6,3,4,7,5,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,6,4,2,7,5,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[4,5,2,7,1,6,8,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[3,4,1,6,5,8,2,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[5,3,3,1]=>5
[4,1,2,8,5,7,3,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,1,4,8,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,6,3,1,7,4,2,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[6,4,2,8,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,3,7,5,1,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,3,7,8,2,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,2,6,7,1,8,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[4,6,3,1,7,8,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[5,3,1,6,7,8,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[4,1,6,2,7,8,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,5,6,7,8,9,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[4,5,6,7,8,9,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[5,6,7,8,9,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[5,6,7,8,9,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[5,6,7,8,9,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[4,5,6,7,8,9,10,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[4,5,6,7,8,9,10,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[5,6,7,8,9,10,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,10,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,10,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,10,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[7,8,9,10,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,9,10,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,7,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[4,8,3,7,6,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,3,8,7,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,8,7,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,2,8,7,6,1,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,7,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,8,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,2,8,7,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,1,7,6,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,2,7,6,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,8,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,1,7,6,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,1,8,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,1,7,5,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,1,7,5,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,1,8,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,3,1,8,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,3,1,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,1,8,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,2,1,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,3,2,1,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[8,7,5,3,1,10,9,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,5,3,1,10,9,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,7,4,3,1,10,9,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,4,3,1,10,9,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,5,4,3,1,10,9,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[6,5,4,3,1,10,9,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[8,7,5,2,1,10,9,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,5,2,1,10,9,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,7,4,2,1,10,9,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,4,2,1,10,9,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,5,4,2,1,10,9,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[6,5,4,2,1,10,9,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[8,7,3,2,1,10,9,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,3,2,1,10,9,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,5,3,2,1,10,9,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[6,5,3,2,1,10,9,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[8,4,3,2,1,10,9,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[6,4,3,2,1,10,9,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[6,1,4,2,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,8,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,8,2,3,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,2,3,8,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,6,2,3,8,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,8,2,3,6,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,2,3,8,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,3,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,4,3,8,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,8,4,3,6,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,8,4,1,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,8,4,2,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,3,8,1,4,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,8,3,6,1,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,6,4,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,1,3,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,8,2,4,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,4,3,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,6,4,7,8,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[1,6,4,2,7,5,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,6,4,2,7,1,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[1,4,7,2,5,6,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,4,8,5,3,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,5,4,2,7,8,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,5,2,4,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,4,6,2,8,5,7,3]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[3,4,8,5,2,1,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,8,5,3,1,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,3,5,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,8,7,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,2,8,5,7,3,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,6,8,7,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,8,2,5,4,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,5,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,3,2,5,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,6,2,1,7,5,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[1,6,3,7,8,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,6,2,3,7,8,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,6,3,7,1,2,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[4,2,1,3,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]=>[5,5,4]=>2
[3,8,2,5,4,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,6,3,8,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,8,2,7,4,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,3,8,5,1,7,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,6,8,1,2,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,4,3,5,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,3,8,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,7,2,8,3,9,4,10,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2]=>[6,4,2]=>3
[6,1,7,8,9,10,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[6,7,1,8,2,9,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,1]=>[5,3,1]=>3
[6,7,1,8,9,10,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[6,7,8,1,9,10,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[6,7,8,9,1,2,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[8,3,2,1]=>[3,2,1]=>3
[6,7,8,9,1,2,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[6,7,8,9,1,10,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[3,8,1,7,5,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,6,7,5,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,7,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,4,1,8,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,3,6,5,8,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[2,6,1,3,5,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[4,6,1,3,5,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[6,1,4,3,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,1,3,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,1,3,5,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,1,8,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,1,3,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,4,3,8,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,4,3,8,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,2,1,4,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[1,8,4,6,3,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,8,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,4,1,8,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,1,3,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,1,3,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,1,3,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,6,8,1,3,5,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,8,1,3,5,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,1,8,3,5,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,1,6,8,3,5,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[1,4,6,3,8,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[4,6,1,3,8,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,1,8,3,5,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,1,6,8,3,5,7,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[4,1,3,6,8,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[1,4,3,6,8,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[4,1,3,8,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[2,1,8,3,6,5,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,6,1,4,3,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,8,1,4,3,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,6,3,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,1,3,6,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,4,8,3,6,5,7,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,8,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,8,6,3,5,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,6,3,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,1,3,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,6,1,3,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,1,3,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,4,1,3,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,6,2,1,3,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[6,8,1,4,3,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,8,4,3,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,4,1,8,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,4,2,8,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,4,2,7,3,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[5,7,1,4,6,3,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,8,1,4,6,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,7,4,5,8,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[3,5,7,4,6,8,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[6,8,4,1,7,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,6,1,7,8,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,6,4,1,8,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[3,5,8,4,6,7,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,6,8,4,5,7,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,7,8,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,8,1,4,5,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,1,4,5,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[3,7,1,5,4,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,5,4,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,5,4,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,4,5,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,7,1,4,6,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,6,4,2,7,3,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,4,7,2,8,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,7,2,8,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,6,4,2,8,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,8,1,4,6,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,1,5,4,6,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,5,4,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,6,1,5,4,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[6,8,3,1,4,2,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,3,1,4,2,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[3,6,1,5,4,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[6,8,3,1,4,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,7,2,8,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,8,1,4,7,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,1,5,4,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,5,4,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,6,1,5,4,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[6,7,3,1,4,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,8,3,1,4,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,8,7,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,3,1,4,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[3,7,1,5,4,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,5,4,2,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,1,4,7,3,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,2,7,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,7,2,8,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,7,1,4,8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,8,3,1,4,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,1,5,4,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,4,1,2,8,5,7,6]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[4,4,4,1]=>3
[3,7,1,5,4,2,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[6,7,3,1,4,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,8,3,1,4,5,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,1,5,4,2,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,8,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,2,7,3,1,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,8,2,6,3,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,7,8,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,1,7,2,5,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[1,6,2,5,8,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,1,8,7,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,5,8,6,2,3,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,4,8,3,1,6,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,2,7,1,8,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,6,1,3,8,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,5,2,8,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,3,5,1,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,3,8,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,8,6,5,1,7,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,2,8,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,3,4,1,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,2,8,3,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,8,4,3,1,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,3,1,7,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,4,1,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,6,1,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,8,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,7,8,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,8,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,4,7,8,3,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,5,8,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,8,3,1,5,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,3,2,4,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,8,4,1,6,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,5,1,6,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,4,8,7,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,4,8,7,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,4,8,6,1,5,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,8,6,1,4,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,6,8,7,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,6,8,5,1,3,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,4,1,3,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,8,3,1,4,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,6,8,7,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,3,6,4,8,1,5,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,8,4,6,3,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,8,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,3,6,8,1,5,4,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,5,6,1,4,7,8,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,5,6,1,4,7,3,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]=>[5,2,1,1,1]=>7
[2,7,6,1,8,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,8,1,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,8,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,7,6,1,8,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,5,1,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[2,3,4,7,6,1,5,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]=>[3,3,3,2,1]=>7
[1,8,4,5,2,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,5,2,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,6,4,8,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,5,4,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,5,4,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[3,4,1,5,6,8,7,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]=>[5,4,3,1]=>6
[3,7,1,6,8,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,3,1,8,6,4,7,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[1,8,4,3,6,2,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,1,8,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[3,7,1,6,8,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,3,5,4,7,2,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[2,7,6,4,8,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,5,2,6,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,8,5,3,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,3,4,6,5,8,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]=>[5,3,3,2,1]=>9
[2,3,4,7,5,1,8,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,5,1,6,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,1,6,5,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,7,1,6,8,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,4,6,1,8,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]=>[5,3,3,2,1]=>9
[6,3,5,8,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,4,5,2,3,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,5,8,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,6,8,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[1,5,7,4,6,3,2,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,2,8,4,6,3,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,5,4,6,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,5,7,4,6,3,8,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,4,1,7,8,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,4,2,7,8,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,1,4,6,8,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,1,8,4,6,3,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,7,6,2,4,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,3,4,5,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,5,4,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,2,4,7,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,2,4,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,4,8,7,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,2,8,6,1,5,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,7,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,3,6,2,4,8,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[3,5,2,8,6,1,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,7,2,5,1,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,1,8,6,2,3,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,4,1,8,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[3,7,6,1,8,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,8,2,6,3,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,5,8,3,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,3,7,2,5,8,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,2,3,5,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,3,7,1,4,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,3,8,1,4,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,3,1,8,5,4,6,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[3,4,7,6,1,8,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,5,2,6,7,1,8,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[3,2,8,4,7,5,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,1,6,5,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,2,8,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,3,1,7,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,2,5,6,1,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,2,5,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,5,3,8,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,6,4,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,3,5,7,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,3,2,5,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,1,7,4,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,6,1,7,3,5,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[5,6,1,7,3,4,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[6,1,7,3,4,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,1,7,4,2,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[2,8,1,7,6,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,8,6,5,1,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,4,2,8,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,6,4,2,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[4,2,3,8,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,8,7,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,3,8,1,6,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,3,7,1,6,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[4,2,3,7,8,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,1,6,4,2,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[6,4,7,8,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,5,7,8,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,7,8,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,2,4,7,8,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[3,2,4,8,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[4,8,7,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,6,7,4,2,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[6,7,4,8,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,5,3,7,1,6,4,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,1,6,8,4,2,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,3,7,5,1,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[3,7,5,8,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,4,7,1,5,8,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,7,6,8,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,8,7,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,8,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,8,7,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,4,6,7,1,5,8,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[6,7,8,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[3,1,7,5,4,2,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,1,8,5,4,6,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,8,5,2,3,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,4,1,3,6,7,2,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[3,2,7,1,5,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[6,3,7,1,5,4,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,5,1,3,6,8,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[3,6,8,1,5,4,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,8,3,1,5,4,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,2,1,5,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[4,8,2,1,7,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,3,8,1,5,7,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,7,1,2,6,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,7,8,1,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,2,1,5,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[4,7,2,1,8,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,7,8,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,7,4,1,6,5,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,1,4,5,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,5,1,4,7,6,8,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[2,6,4,1,7,5,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,6,8,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,8,5,7,1,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,7,8,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,2,8,1,6,5,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,2,4,1,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,4,8,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,8,1,6,4,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,1,8,4,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,1,4,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,6,1,5,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,7,1,4,5,3,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,5,1,7,4,6,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[2,7,6,1,4,5,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,8,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,3,1,6,5,8,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[5,3,1,2,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,6,2,1,8,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,3,7,2,1,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,7,2,8,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,2,4,5,1,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,6,4,5,2,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[3,7,4,5,1,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,5,8,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,7,4,2,6,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,7,1,8,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,7,4,1,6,3,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,7,4,8,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,4,8,6,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,8,3,5,6,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,3,5,6,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,1,5,6,7,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,3,5,6,7,2,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]=>[5,4,3]=>3
[5,8,4,3,6,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,8,4,1,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,5,8,4,6,7,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,8,3,6,7,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,3,8,2,1,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,4,2,6,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,2,5,6,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,5,6,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,5,6,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,1,8,5,7,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,6,8,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[6,3,1,8,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,5,8,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,4,5,8,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,6,5,8,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,3,6,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,8,5,6,7,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,2,8,5,6,7,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,1,5,6,7,3,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]=>[5,4,3]=>3
[1,5,3,8,6,7,4,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,5,8,6,7,3,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[4,3,5,8,1,7,2,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,5,4,8,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[1,4,8,5,6,7,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,4,8,5,6,7,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,7,1,5,6,3,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,4,3,6,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,7,2,5,6,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[2,6,3,1,4,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[3,7,1,4,2,6,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,5,6,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,5,6,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,3,2,5,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,3,4,6,2,8,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[5,3,7,4,2,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,4,7,2,3,8,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,7,2,8,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,3,7,2,4,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[2,6,5,1,8,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,7,3,4,2,1,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,7,4,2,3,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,5,3,1,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,5,4,1,8,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,10,1,2,3,4,6,7,8,9]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[8,10,1,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,11,1,3,4,5,6,7,8,9,10]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,3,10,1,4,5,6,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[4,3,1,10,2,5,6,7,8,9]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[5,4,1,2,10,3,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[7,6,1,2,3,4,10,5,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,6,6]=>[6,6]=>0
[8,7,1,2,3,4,5,10,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[8,11,1,2,3,4,5,6,7,9,10]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,9,1,2,3,4,5,6,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[6,2,4,3,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,7,1,3,4,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[2,6,5,7,3,1,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,7,3,1,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,1,4,7,8,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,8,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,1,8,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,3,2,4,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,2,4,7,5,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,2,1,6,3,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[2,7,6,8,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,1,7,3,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[4,2,1,3,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[5,8,1,7,4,3,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,7,4,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,8,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,2,1,8,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,2,1,6,3,8,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,2,1,7,3,5,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[3,6,7,5,2,1,4,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,5,2,1,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[4,8,6,2,7,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,6,7,5,2,4,8,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[3,6,7,5,2,4,1,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[4,2,1,7,3,6,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,2,1,7,3,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,7,6,8,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,8,1,7,4,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,8,6,2,4,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,2,1,3,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,8,1,7,3,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,2,1,8,3,7,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[2,6,1,5,4,7,8,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[4,6,3,5,8,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[3,5,6,1,4,8,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[2,7,5,1,8,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,5,2,1,3,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,5,6,2,4,1,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[6,2,1,1]=>5
[2,5,6,1,4,8,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[6,7,8,4,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,4,6,8,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,8,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,8,4,6,7,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,8,4,7,5,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,8,6,1,7,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,8,5,1,6,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,7,1,4,2,3,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[4,8,5,2,1,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,8,4,2,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,8,4,6,2,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[3,1,8,2,5,6,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,5,1,8,2,6,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,5,1,2,8,4,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[2,3,5,8,6,1,7,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[3,2,8,5,7,1,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,6,2,8,5,1,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,2,1,8,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,7,1,4,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,5,1,6,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[2,7,3,6,5,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,6,4,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,2,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,3,6,4,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,6,2,8,4,3,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,8,7,2,4,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,8,3,7,2,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,8,1,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,1,3,8,4,6,7,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,4,7,5,6,8,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,7,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,8,4,7,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,8,5,7,3,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,5,2,7,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,7,3,4,8,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,7,8,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,3,4,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,7,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,1,7,2,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,7,2,3,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,7,1,8,2,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,1,7,8,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,5,8,2,7,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[6,3,5,8,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,2,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,7,1,2,3,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[3,6,8,1,2,7,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,8,6,1,2,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,5,2,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,4,8,7,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[4,3,6,8,7,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,4,1,8,2,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,1,8,2,7,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,1,2,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,3,1,4,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,6,3,8,7,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,4,1,6,8,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,7,1,2,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,7,4,1,2,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,5,1,2,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,1,2,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,1,2,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,7,4,1,2,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[1,8,3,4,2,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,4,1,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,2,4,6,1,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,2,3,1,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,1,4,3,7,2,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,1,3,5,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[2,1,8,3,7,5,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,1,5,8,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,2,8,1,6,7,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[6,2,5,8,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,2,8,5,1,6,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,3,8,2,5,7,4,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,8,7,1,6,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,5,6,1,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,4,8,6,2,7,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,5,6,8,4,1,7,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[6,2,3,1,5,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[2,6,1,4,5,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[3,6,4,1,5,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,5,6,1,3,2,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]=>[6,2,1]=>3
[4,5,7,1,2,6,3,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[3,7,4,1,2,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,4,2,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[2,7,1,3,5,6,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,3,4,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,1,2,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,3,2,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,5,3,8,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,5,7,2,3,8,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,8,2,6,5,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,4,8,2,5,7,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,5,7,6,2,3,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,3,8,2,6,4,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,8,3,2,5,7,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,8,3,5,7,6,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,4,8,3,5,7,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,3,8,4,2,6,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,8,2,3,5,7,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,5,7,3,8,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,2,6,7,5,8,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[6,7,5,2,1,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[3,4,8,7,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,7,5,2,8,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,8,3,1,7,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,1,4,8,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,4,7,1,8,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,4,6,8,2,1,5,7]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,8,2,5,6,1,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,2,8,6,4,1,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,2,5,7,3,8,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,1,2,8,5,6,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,2,1,6,8,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,2,6,8,4,1,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[1,5,6,8,3,4,2,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[4,5,8,1,6,3,2,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,1,6,8,3,2,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,5,7,3,8,2,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[6,4,3,7,8,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,4,3,1,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,5,3,1,7,8,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[5,7,3,8,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[1,4,5,7,3,8,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[4,6,3,7,8,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,3,6,7,8,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[1,5,3,6,7,8,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[4,6,1,7,3,8,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[6,3,7,1,8,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,2,4,8,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,6,1,4,7,3,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,2,5,6,7,8,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]=>[4,3,2,2]=>5
[5,2,3,6,7,8,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[6,7,1,3,2,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,2,7,1,3,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,2,1,7,3,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,4,2,7,1,8,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,2,6,3,7,8,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,2,6,3,7,8,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[6,7,3,8,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,6,2,7,4,1,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[6,7,3,2,1,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[3,5,7,2,1,8,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[6,7,8,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,3,7,8,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,6,7,4,8,5,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,4,7,1,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,6,2,7,1,8,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[1,7,4,8,5,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,7,8,5,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,5,7,8,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,3,7,1,8,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,6,4,7,8,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,5,6,1,7,8,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]=>[4,2,1,1,1]=>7
[5,6,1,2,7,8,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[6,7,2,1,8,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,2,8,5,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[1,6,7,4,8,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,2,4,6,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,7,4,6,2,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,7,4,3,6,2,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,8,4,5,3,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,3,4,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,4,6,3,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,5,4,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,2,7,1,4,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[6,3,8,1,2,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,3,7,4,6,2,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,7,5,2,6,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,5,2,7,1,3,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,5,2,3,6,1,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[6,4,1]=>3
[4,6,5,3,7,1,8,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[2,5,4,7,1,6,8,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[4,2,3,8,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,2,4,8,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,4,8,1,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,5,4,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,3,5,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,3,4,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,5,2,4,7,1,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[5,3,4,8,1,6,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,5,3,7,1,6,2,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[6,2,4,8,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,4,3,7,8,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,2,6,7,3,8,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[1,5,7,4,2,8,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,7,2,8,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,3,7,8,6,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,3,6,8,2,7,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[4,5,2,7,1,8,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,3,6,5,7,8,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,2,3,5,6,8,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[5,2,6,4,7,8,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[4,2,6,7,3,8,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,2,5,6,8,1,7,4]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[6,4,5,2,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,5,2,3,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,4,2,5,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,2,5,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,2,5,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,2,5,3,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,6,5,2,3,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[6,8,7,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,6,7,5,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,4,7,5,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,7,4,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,4,7,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,2,6,7,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,4,6,7,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,7,4,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,4,5,8,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,8,7,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,6,2,8,7,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,2,4,8,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,6,8,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,2,6,5,8,7,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,2,4,5,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,5,2,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,3,6,8,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[6,4,5,8,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,7,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,7,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,7,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,7,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,5,8,7,2,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,1,6,8,7,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,6,8,7,4,5,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,4,8,6,7,5,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,8,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,2,8,4,7,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,2,7,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,2,7,5,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,6,8,4,7,5,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,8,7,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,5,8,2,7,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,1,6,8,4,7,5,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,1,8,6,4,7,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,8,7,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,6,4,7,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,2,7,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,9,4,8,3,7,1,2,6]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,9,3,5,8,1,2,4,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,9,5,8,1,2,3,4,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,9,1,2,3,4,6,8]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[7,9,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,10,5,9,2,4,8,1,3,7]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,10,5,9,4,8,1,2,3,7]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[7,10,2,4,6,9,1,3,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,10,4,6,9,1,2,3,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,10,6,9,1,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,10,1,2,3,4,5,7,9]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,2,5,6,3,8,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[6,2,5,7,4,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,7,3,2,5,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[3,2,6,4,8,1,5,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[2,3,6,4,7,8,5,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]=>[4,2,2,2,1]=>7
[5,7,8,2,6,3,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,3,1,7,8,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,3,6,7,4,1,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[1,6,3,5,2,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[3,4,8,2,7,5,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,3,2,8,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,8,4,7,2,5,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,8,1,5,3,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,8,1,6,2,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,8,4,6,7,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,6,8,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,8,1,6,5,7,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,8,2,5,3,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,2,3,7,6,1,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,2,3,7,4,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,2,6,8,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,7,5,1,8,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,7,8,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,4,3,8,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,8,1,6,3,5,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,8,2,4,5,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,6,8,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[4,3,2,8,5,7,1,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,6,4,2,8,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[4,7,3,2,5,1,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,2,4,7,5,8,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[4,2,3,8,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,8,1,4,6,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,7,8,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,8,4,7,2,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,1,6,8,4,7,2,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,1,6,8,3,2,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,6,1,8,3,2,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,8,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,7,8,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,7,8,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,8,2,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,6,1,8,2,3,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,1,6,8,2,3,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,5,1,2,8,3,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,5,2,1,8,3,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,6,2,8,1,3,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,6,2,8,4,7,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,3,6,8,4,7,5,1]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,2,6,8,4,7,1,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,2,6,8,3,1,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,2,5,1,8,3,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,1,2,5,8,3,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[5,1,2,4,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,4,1,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,2,5,3,8,1,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,2,5,4,8,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,5,2,4,8,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[5,4,2,1,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,4,2,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,4,1,3,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,4,3,1,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,5,3,1,8,2,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,5,1,3,8,2,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,1,5,4,8,7,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,5,1,4,8,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,5,4,1,8,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,6,5,8,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,6,8,7,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[3,4,5,1,8,7,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[3,4,1,5,8,7,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[4,1,3,5,8,2,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,3,6,8,2,1,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,4,6,8,3,7,5,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[3,4,5,2,8,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[5,3,1,4,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,3,4,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,3,2,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,2,1,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,3,2,5,8,1,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,4,2,5,8,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[3,2,4,5,8,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[4,2,3,5,8,1,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[5,2,3,1,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,1,3,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,2,3,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[6,5,7,4,2,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,7,5,3,8,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,2,3,7,8,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,5,6,7,3,4,8,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[6,7,8,2,1,4,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,3,8,4,7,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,1,7,8,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,5,8,2,7,1,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[6,2,8,5,3,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,4,2,8,5,1,7,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,8,6,5,2,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,7,2,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,1,8,2,6,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[6,8,3,4,1,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,1,7,6,2,8,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,8,2,5,7,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,5,6,7,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,7,6,3,1,8,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,2,8,3,1,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,5,7,3,8,4,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,2,7,1,8,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,2,1,8,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,3,7,5,8,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,7,8,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,7,4,5,8,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,7,1,4,8,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[1,6,5,3,8,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,7,4,8,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,8,6,1,3,5,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,3,2,4,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,4,8,2,5,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,3,7,2,5,8,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,4,7,8,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[2,6,4,3,8,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,8,2,1,6,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,6,8,3,2,1,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,2,6,8,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,2,5,3,8,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,8,2,6,5,3,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,8,5,4,1,3,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,1,8,6,5,4,2,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,4,8,7,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,8,3,7,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,7,3,6,2,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,4,3,7,1,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,4,8,7,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,1,5,7,4,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,7,3,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,4,8,3,7,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,8,3,6,7,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,6,1,3,8,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[6,8,2,1,7,4,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,1,6,4,2,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,2,7,5,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[3,7,6,2,5,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,5,8,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[4,7,2,6,3,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,3,2,4,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,7,2,4,6,1,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,3,7,2,8,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,3,2,8,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,7,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,5,4,8,1,7,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,2,8,1,7,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,1,3,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,6,1,8,7,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,6,1,2,8,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[2,7,6,8,1,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,7,1,6,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,6,5,4,3,2,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[6,5,4,8,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,6,5,4,3,9,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[5]=>0
[8,7,6,5,4,3,2,10,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[6,7,4,2,5,1,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,7,2,4,6,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,7,5,1,6,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,4,6,3,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,4,7,1,3,8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,4,2,7,3,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,5,1,2,7,6,8,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[5,4,6,8,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,4,8,1,3,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,1,3,8,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[1,3,8,4,5,7,2,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,6,7,4,5,3,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,3,7,4,2,8,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,6,1,3,7,2,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[2,8,1,3,6,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,4,2,6,8,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[6,8,3,2,7,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,5,6,3,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,1,2,4,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,5,3,4,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,3,5,6,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,4,2,1,5,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,4,6,2,8,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[4,2,1,7,5,8,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[4,7,2,6,5,1,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,7,4,1,2,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,6,5,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,3,6,5,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,3,7,1,6,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,2,1,7,5,6,8,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,2,4,8,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[4,2,6,8,7,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,4,6,1,8,5,2,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[4,1,6,7,5,8,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[4,3,6,7,5,1,2,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[4,3,7,1,6,8,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,3,7,5,6,8,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,1,7,3,6,5,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[2,8,7,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,1,4,2,6,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,7,3,6,2,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,8,7,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,2,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,7,2,6,8,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,2,7,3,6,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,7,3,6,5,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,8,2,4,5,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,4,1,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,2,4,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,5,3,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,5,1,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,4,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,5,4,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,7,5,6,3,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,7,5,6,1,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,6,7,5,3,1,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[2,8,7,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,1,2,4,6,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,7,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,7,5,6,2,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,8,1,5,2,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,5,3,4,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,7,5,6,3,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,8,7,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,2,3,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,1,7,2,4,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,5,7,1,2,6,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[5,4,1,7,3,6,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[3,6,4,7,5,2,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[3,4,7,6,2,5,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[4,7,5,6,1,3,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,6,4,3,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,6,3,1,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,7,1,3,8,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,6,5,2,7,8,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[3,2,8,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,3,6,5,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,2,3,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,8,5,1,2,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,7,5,1,8,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,1,7,8,2,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,5,2,8,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,7,6,4,2,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,1,3,7,8,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,1,4,3,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,5,7,6,8,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[5,7,6,8,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,1,6,8,4,2,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,6,8,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,4,7,8,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,6,4,8,5,1,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,7,4,8,1,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,1,4,8,2,5,7,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[4,8,5,2,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,6,3,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,3,7,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,1,6,3,5,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,5,4,3,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,4,5,3,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,1,5,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[6,3,2,1,5,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[3,7,1,6,2,5,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,4,5,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,1,5,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[2,3,6,1,5,4,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]=>[6,2,2,2,1]=>7
[6,3,4,1,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,4,1,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[2,6,4,1,5,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,5,1,3,7,4,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[6,2,5,1,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,5,2,1,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,7,1,2,8,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,1,2,5,4,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,6,2,1,3,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[5,2,6,1,3,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[4,7,1,3,5,2,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,1,5,3,2,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,7,1,4,2,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,1,6,2,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,6,3,1,2,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[4,2,5,3,1,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]=>[6,5,2]=>3
[5,3,6,1,2,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[6,5,1,8,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,5,2,3,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,8,7,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,5,1,2,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,7,6,1,5,3,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,6,4,1,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,1,7,5,3,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,6,2,4,7,8,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[3,4,6,1,7,8,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[3,4,8,6,7,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,8,5,6,7,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,4,1,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,1,7,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,7,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,2,5,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,5,2,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,8,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,5,2,7,8,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,7,8,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,3,4,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,5,3,6,8,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[5,6,3,4,8,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,6,7,8,5,1,3,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[5,1,8,6,3,4,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,8,1,5,3,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,4,5,8,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,6,4,8,7,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,5,8,1,3,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,8,3,1,2,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,1,8,3,5,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,8,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[3,4,8,1,2,6,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,8,2,4,3,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,3,1,6,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,3,5,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,4,8,6,1,3,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,7,1,8,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,7,8,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,3,8,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,4,1,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,1,7,6,3,8,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,8,2,5,7,6,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,6,5,1,8,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[2,6,5,3,4,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,6,1,5,2,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,2,3,5,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,6,7,5,1,8,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,5,1,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,3,5,1,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,4,7,6,5,8,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,1,4,8,7,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[3,2,8,7,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,5,1,6,7,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,5,1,6,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,6,7,2,8,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[2,5,1,8,6,7,4,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,5,1,8,6,7,4,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,2,3,8,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,3,8,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,5,8,6,7,4,1]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[6,2,1,5,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,6,3,2,8,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,7,6,8,3,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,7,5,8,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,4,8,7,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,3,8,1,4,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,5,7,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,4,8,7,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[3,6,8,2,4,1,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,5,8,2,6,7,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,2,8,1,6,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,8,4,6,7,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,8,3,4,6,7,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,8,1,6,7,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,1,6,7,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,1,8,2,6,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,4,8,7,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,8,5,7,4,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,4,1,6,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,1,4,6,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,7,3,8,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,3,2,8,4,6,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,8,3,2,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,5,8,2,4,6,1,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[6,4,7,8,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,8,3,6,4,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,2,5,3,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,4,3,2,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,3,2,8,4,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,7,4,3,1,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[2,8,7,3,5,1,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,2,7,3,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,1,7,4,3,8,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,1,4,3,8,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,3,2,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,8,4,2,7,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,2,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,4,8,3,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,1,6,8,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[6,1,5,7,8,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,7,6,1,2,5,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,7,6,1,5,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,8,3,2,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,4,7,1,3,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,7,4,8,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,6,8,2,5,1,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[1,2,6,3,8,5,7,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,5,2,6,8,4,7,3]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[5,7,2,3,8,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,4,7,5,8,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,8,3,6,1,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,4,8,7,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,3,1,2,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,1,2,5,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,8,4,1,2,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,1,7,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,1,8,2,4,7,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,3,8,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,4,1,8,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,5,1,8,7,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,6,1,8,3,7,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,1,2,8,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,8,4,1,7,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,8,7,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,7,6,2,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,7,6,5,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,6,4,5,2,3,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,7,4,5,2,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,5,2,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,2,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,3,4,2,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,7,3,4,2,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,7,3,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,7,3,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,4,2,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,8,4,7,3,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,2,8,5,7,3,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,7,3,5,2,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,7,3,5,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,6,2,5,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,6,2,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,6,2,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,2,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,2,4,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,2,8,5,6,4,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,4,2,8,5,6,3,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,2,8,4,6,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,2,8,4,5,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[7,8,9,10,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[1,6,4,7,2,8,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,7,3,5,8,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,4,8,2,3,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,6,2,4,5,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,6,2,3,5,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,5,3,4,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,4,8,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,7,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,3,4,1,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,7,2,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,3,7,4,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,1,7,3,5,8,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[1,8,5,7,2,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,8,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,7,3,8,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,1,5,7,8,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,8,7,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,1,2,4,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,1,2,3,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[1,6,5,8,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,5,8,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,7,4,8,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,7,2,8,6,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,1,8,2,3,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,4,8,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,8,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,5,1,8,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,7,1,3,8,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,1,8,2,7,3,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,8,7,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,8,7,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,8,7,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,8,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,7,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,8,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[6,4,2,3,8,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,2,7,5,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,4,1,7,5,8,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[6,4,2,7,5,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,4,7,2,6,8,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,1,6,8,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,1,6,8,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,4,1,7,8,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[6,4,2,3,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,2,7,5,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,4,2,7,5,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,4,7,2,6,8,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[5,4,7,3,6,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[3,4,7,2,6,5,1,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,8,3,2,5,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,3,5,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,1,3,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,1,2,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,7,1,6,2,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,1,6,2,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,2,6,5,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[4,8,3,1,2,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,6,3,4,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,1,3,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,1,3,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,4,2,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,7,3,6,2,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,4,7,2,6,1,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,4,3,7,5,1,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,4,3,7,5,1,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,2,4,3,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[3,8,7,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,7,3,6,1,5,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,8,3,2,1,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,7,3,6,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,5,2,8,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,3,2,8,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,8,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,5,8,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,3,7,8,5,1,2,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,3,7,8,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,2,5,8,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,4,8,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,8,4,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,8,7,4,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,2,8,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,5,3,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,8,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,7,3,5,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,8,3,7,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,8,3,7,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,4,7,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,7,3,8,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,4,7,3,8,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,6,3,8,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,3,6,2,4,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,3,6,1,4,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,3,7,2,4,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,3,1,5,6,8,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[4,2,1,5,8,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,2,1,5,8,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,2,1,5,8,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,3,1,5,7,8,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[4,3,1,7,5,8,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[6,7,3,1,4,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,3,7,1,4,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,3,1,5,7,8,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[3,2,1,8,5,4,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,5,7,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,2,7,1,8,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,7,2,1,8,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,2,1,8,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,2,1,8,5,6,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[4,3,1,6,7,8,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[4,2,1,6,8,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,2,1,6,8,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,2,1,6,8,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,2,6,1,8,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,6,1,8,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,6,1,8,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,6,1,8,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,2,1,6,8,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,3,1,6,7,8,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[6,7,3,1,5,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[4,2,1,7,8,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,2,1,8,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,4,6,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,4,6,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,4,7,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,1,8,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[4,2,1,7,8,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,2,7,1,8,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,7,2,1,8,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,2,7,1,8,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,1,7,8,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[3,2,1,8,4,5,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[6,3,8,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,2,5,7,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,3,8,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,7,8,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,6,7,3,8,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,4,7,2,6,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,8,2,4,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,8,2,4,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,7,4,2,6,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,4,8,2,7,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,3,1,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,7,4,2,6,1,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,6,4,2,3,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,6,3,7,8,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,3,8,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,3,7,2,4,5,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,3,7,2,5,8,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,3,6,8,2,4,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,4,6,2,3,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,3,6,7,8,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[3,6,4,2,1,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,5,8,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,3,4,2,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[6,3,4,2,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,6,4,2,1,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[2,5,4,1,7,8,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,7,8,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,1,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,8,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,8,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,1,5,7,8,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[2,7,8,6,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,8,5,7,6,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,8,5,6,4,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,2,1,8,5,6,3,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[2,5,6,3,8,4,1,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[6,3,4,2,1,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,7,8,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,4,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,2,1,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,8,6,4,2,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,8,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,4,2,1,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,7,8,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,7,6,2,3,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,6,1,8,4,3,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,1,7,5,8,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,8,5,7,6,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,6,2,1,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,7,5,8,4,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,6,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,7,8,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[7,6,5,8,4,3,2,1,9]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,3]=>[3]=>0
[7,6,5,4,9,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[7,6,5,4,3,8,2,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]=>[5]=>0
[7,6,5,4,3,2,8,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]=>[6]=>0
[6,9,8,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,7,9,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[2]=>0
[7,5,8,9,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,7,6,9,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[9,3]=>[3]=>0
[6,4,3,7,5,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[7,6,4,8,9,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]=>[3]=>0
[8,7,6,5,10,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,2,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[7,6,5,3,9,8,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,7,6,5,4,9,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,5]=>[5]=>0
[6,5,2,7,8,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[8,7,6,5,4,3,9,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,6]=>[6]=>0
[7,6,5,4,3,1,8,9,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[7,10,9,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[9,8,10,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2]=>[2]=>0
[6,5,8,7,4,3,2,1,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2]=>[2,2]=>0
[8,6,9,10,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[7,5,4,8,6,3,2,1,9]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,3]=>[3]=>0
[5,9,8,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,3,2,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[7,6,4,3,9,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[7,4,8,9,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,7,6,4,10,9,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,7,2,5,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[7,6,5,3,2,8,4,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]=>[5]=>0
[7,6,3,8,9,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]=>[3]=>0
[7,6,5,4,2,1,8,3,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]=>[6]=>0
[6,3,2,7,5,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[7,6,5,2,9,8,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,7,6,5,4,3,1,10,9,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[1,5,3,7,4,2,8,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,7,3,4,2,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,6,3,4,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,3,2,5,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,2,3,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,2,3,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,6,3,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,6,4,1,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,3,7,5,2,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[5,1,7,3,4,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[1,2,7,4,3,6,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,8,2,4,5,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,8,3,2,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,8,7,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,2,7,1,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,8,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,8,2,3,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,3,2,5,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,3,8,2,6,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[6,4,2,8,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,2,3,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,6,1,3,4,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[4,6,2,1,5,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,7,2,1,3,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,1,3,2,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,7,1,2,4,5,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,8,2,3,5,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,1,3,2,6,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,1,3,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,3,2,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]=>[5,5,4]=>2
[5,1,2,4,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,4,8,1,2,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,7,6,3,2,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,8,3,2,7,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,2,7,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,4,7,3,6,2,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,3,2,8,1,7,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,8,3,7,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,7,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,8,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,4,7,6,2,1,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,4,2,7,1,6,8,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[2,3,6,7,4,1,8,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,6,3,4,7,8,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,7,8,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,1,7,8,4,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,1,3,2,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[3,7,8,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,2,3,8,1,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,1,8,2,5,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,7,8,4,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,2,8,6,3,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,2,4,8,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,2,7,4,8,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,2,4,7,1,8,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[3,7,4,2,6,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,6,2,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,5,8,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,6,4,8,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,1,7,4,8,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,6,7,3,8,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,3,6,4,7,1,8,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]=>[4,2,2,2,1]=>7
[3,4,6,7,8,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[3,1,7,5,4,2,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[6,3,8,5,4,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,2,5,4,7,8,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,2,5,6,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,6,4,8,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[4,8,1,5,2,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,1,8,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,1,8,6,4,3,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,6,3,8,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,1,2,5,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,8,7,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,2,7,5,8,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,1,6,3,7,5,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[1,3,6,7,8,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[4,1,6,3,7,8,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,1,6,4,8,2,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,3,8,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,5,1,7,4,3,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[4,1,8,5,2,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,6,8,3,7,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,4,6,1,3,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[6,5,8,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,3,5,7,6,8,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,4,8,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,4,8,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,8,4,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,8,4,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,2,8,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,7,8,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,6,3,2,7,4,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,5,1,6,2,8,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[1,3,7,2,5,4,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,6,1,7,4,3,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,4,7,3,5,2,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,7,5,2,4,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,5,7,4,3,8,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,3,7,4,8,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,4,7,2,3,8,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,7,3,1,8,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,4,6,3,8,2,7,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,4,7,3,8,2,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,5,1,7,8,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,2,6,7,8,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[4,3,6,7,8,2,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,5,2,7,8,4,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[1,5,7,4,8,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,1,6,8,4,7,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[4,6,2,1,7,8,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[5,3,6,4,7,8,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[3,5,2,6,8,4,7,1]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[2,5,4,6,8,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,3,6,2,8,7,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,4,6,3,8,7,2,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[2,5,7,4,3,8,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,7,2,4,8,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,6,3,7,2,8,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,3,6,7,8,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[1,4,7,3,8,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,5,4,7,8,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,2,6,7,8,5,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[1,3,7,2,8,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,1,6,8,2,4,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,3,7,8,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,4,7,8,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,3,1,5,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,3,4,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,2,4,3,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,2,4,8,1,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,2,4,6,8,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[4,6,7,8,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[5,3,8,7,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,4,8,7,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,6,8,7,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,4,8,7,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,7,4,2,8,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,4,1,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,7,6,8,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,6,8,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,3,7,8,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,7,4,8,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,3,7,4,1,6,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,7,8,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,4,7,3,1,5,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,3,1,7,4,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,1,7,6,4,2,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[4,8,7,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,7,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,3,6,1,5,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,3,6,5,1,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,6,3,5,1,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,6,3,1,5,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,1,6,5,3,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,6,1,5,3,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[2,6,5,3,1,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,5,1,8,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,5,8,1,7,3,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,8,1,3,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,8,3,1,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,3,8,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,6,1,5,8,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,1,6,5,8,3,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[1,4,6,5,8,3,7,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[4,1,6,5,8,7,3,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[2,6,5,3,8,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,4,3,8,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,3,7,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,8,5,3,7,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,8,1,5,7,3,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,1,8,5,7,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,1,6,8,5,7,3,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[1,4,6,8,5,7,3,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,4,6,8,5,3,7,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,6,1,8,5,3,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,6,8,5,3,1,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,5,1,7,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,8,3,5,1,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,8,3,1,5,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,3,1,8,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,3,8,1,5,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,3,8,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,3,6,8,1,5,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,3,6,1,8,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,1,6,8,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,1,3,6,8,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,3,6,1,8,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,6,8,1,7,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,5,2,8,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,2,8,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,5,8,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,5,8,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,6,3,8,1,7,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,3,1,8,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,1,6,3,8,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[1,4,6,3,8,7,5,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[4,1,6,8,3,7,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,6,1,8,3,7,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,8,1,3,7,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,2,8,5,7,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,5,7,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,8,7,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,8,7,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,4,1,8,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,4,8,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,4,8,7,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,4,1,8,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,8,7,5,1,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,7,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,3,4,7,8,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[2,3,7,1,4,8,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,6,1,3,7,8,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,7,3,4,8,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,7,3,2,8,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,2,5,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,2,4,3,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,2,5,3,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,4,7,6,2,3,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,6,4,8,2,1,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,6,2,8,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,6,2,3,7,5,1,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,7,2,3,6,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,2,3,5,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,3,2,7,4,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,3,2,6,4,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[4,6,2,3,5,7,1,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[3,5,2,1,6,8,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[1,5,2,6,8,4,3,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,5,7,2,8,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,2,1,8,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,6,8,4,2,1,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,3,2,6,1,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[1,5,8,2,7,4,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,7,2,3,4,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,2,3,4,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,8,2,3,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,1,8,4,5,7,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[6,1,2,3,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,8,2,3,4,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,3,5,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,2,1,5,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,6,5,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,4,6,2,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,2,4,1,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[2,4,7,8,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,8,7,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,8,2,7,4,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,7,2,8,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,1,2,8,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,2,1,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,7,8,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,1,3,4,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,8,1,3,4,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,2,3,4,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,3,4,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,7,2,3,4,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,3,4,8,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,8,7,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,5,3,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,2,1,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,1,2,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,7,2,6,1,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,2,8,1,6,3,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,1,4,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,5,1,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,5,2,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,2,4,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,8,3,6,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,7,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,4,5,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,3,6,5,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,7,2,6,5,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,1,6,5,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[6,1,2,8,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,1,8,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,1,8,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,1,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,1,3,8,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,3,7,1,6,8,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,3,7,2,6,8,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,2,6,7,5,8,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[1,2,7,5,6,3,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,8,7,6,4,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,6,1,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,6,2,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,6,1,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,6,4,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,3,7,5,6,8,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,8,7,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,4,6,8,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[1,7,6,3,5,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,7,2,6,5,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,4,6,1,5,7,2,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,2,2,1]=>5
[1,6,8,5,7,3,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,4,1,5,8,6,3,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[4,6,1,2,5,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,6,7,2,1,4,8,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[1,3,6,5,7,8,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[6,8,5,2,4,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,8,3,4,6,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,3,8,1,6,5,4,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,4,7,8,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,6,2,7,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,8,2,1,6,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,2,8,6,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,1,2,7,5,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[2,7,8,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,4,5,7,2,6,8,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[2,8,6,4,3,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,8,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,2,8,7,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,8,7,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,5,8,7,1,2,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,5,8,7,3,2,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,5,8,7,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,6,8,1,7,5,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,6,8,4,7,2,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,5,8,3,7,6,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,2,8,4,7,6,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,5,8,3,7,2,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,8,4,7,2,1,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,6,8,2,3,7,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,6,8,4,2,7,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,8,4,2,7,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,2,3,7,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,1,8,4,3,7,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,5,8,4,3,7,1,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,6,8,4,1,2,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,8,1,3,2,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,6,8,4,3,2,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,6,8,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,6,2,8,7,5,4,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,4,8,7,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,6,4,8,7,2,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,2,5,8,7,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,2,4,8,7,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,1,5,8,7,2,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,1,4,8,7,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[1,6,4,8,2,7,5,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,5,8,2,7,6,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[2,4,5,8,3,7,1,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,6,5,8,1,2,7,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[1,6,4,8,3,2,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,5,8,3,2,7,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[2,6,5,1,8,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,3,5,4,8,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[1,6,5,4,8,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,5,3,8,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,3,4,8,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,6,5,4,8,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,6,5,4,3,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,4,2,6,7,8,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]=>[4,3,3,1]=>5
[2,6,7,3,5,4,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,8,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,7,1,2,8,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,8,1,2,7,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,1,3,6,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,3,2,8,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,4,1,5,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[4,7,5,1,6,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,5,3,1,7,6,8,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[4,6,1,2,7,5,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[2,7,1,3,6,5,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,8,2,6,5,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,6,1,2,8,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,5,3,1,8,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,8,5,6,3,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,3,4,8,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,4,3,8,1,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,2,1,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,3,2,5,1,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,8,3,2,5,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,6,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,1,3,4,7,6,8,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[6,1,4,2,7,5,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,4,3,7,1,6,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[6,7,5,4,1,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,10,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[3,9,8,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,8,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,7,6,5,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,7,6,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,7,8,1,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,1,6,7,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,6,1,8,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,2,5,1,8,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,5,7,1,8,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,3,8,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,8,1,7,3,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,8,1,7,2,3,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,5,8,1,2,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,7,8,3,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,8,1,7,3,2,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,8,7,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,8,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,2,6,8,1,4,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[3,5,2,4,6,8,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[2,4,5,7,3,6,8,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,4,5,3,6,8,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]=>[5,4,2,1,1]=>9
[5,2,4,6,8,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,1,3,4,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,3,5,2,6,8,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[4,3,5,7,2,8,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[4,3,5,7,2,6,8,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[4,6,3,7,2,5,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[4,6,3,1,7,8,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,3,5,1,7,8,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[5,7,1,3,4,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,1,3,4,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,5,7,1,3,6,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,3,6,7,1,5,8,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[4,6,3,5,1,7,8,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[4,6,3,5,7,2,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,5,6,4,1,7,8,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[3,1,5,6,7,4,8,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]=>[4,3,2,2]=>5
[5,1,6,7,3,4,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[6,4,7,1,3,5,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[1,6,7,3,4,5,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,6,7,4,5,8,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,4,8,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,3,6,1,2,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[3,5,2,6,1,7,8,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[3,5,2,6,7,4,8,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[5,2,3,6,7,4,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[5,2,3,6,1,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[5,2,6,1,3,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[4,2,6,7,3,5,8,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[6,3,7,2,4,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[3,5,7,2,8,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[3,7,2,4,8,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,4,6,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,5,7,2,6,8,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[6,3,7,2,5,8,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,3,5,7,2,8,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,5,7,2,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,2,4,5,7,3,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,2,4,5,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,7,1,2,5,6,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,6,7,5,8,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,7,1,2,5,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[5,6,2,4,7,3,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,4,2,6,7,3,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[5,4,2,6,1,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[5,6,4,1,2,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[6,4,5,1,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,3,5,1,7,8,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,5,7,2,8,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,5,7,1,3,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,6,4,7,1,3,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,4,6,3,1,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,6,3,7,4,1,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,7,3,1,4,8,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[6,7,3,4,1,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,7,4,2,1,5,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,6,7,3,1,8,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,3,7,8,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,3,7,2,4,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,7,2,3,8,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[6,7,3,2,4,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,3,2,5,1,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,5,3,2,7,8,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,5,3,2,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,5,2,7,3,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,5,2,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,7,3,5,1,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,6,7,4,1,2,8,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,7,2,4,1,8,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,4,2,7,8,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[6,5,7,2,1,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,7,2,1,4,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,6,7,3,1,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,7,8,3,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,7,8,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,8,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,8,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,8,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,7,3,8,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,5,7,8,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[1,5,7,8,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,8,3,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,7,8,1,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,8,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,1,7,8,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,1,7,8,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[1,3,7,8,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,7,5,8,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[5,1,7,3,8,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,7,1,8,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,5,7,1,8,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[1,7,5,3,8,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,1,8,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,3,8,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,7,5,8,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,8,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,8,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[5,7,8,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,1,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,7,8,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,3,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,1,8,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,7,1,8,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,1,8,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,1,3,8,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,7,1,5,8,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,7,3,5,8,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,3,7,8,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,5,1,7,8,6,4,2]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[5,3,1,7,8,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,1,5,7,8,6,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[5,7,3,4,6,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,3,4,8,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,3,4,8,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,3,4,1,8,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,3,4,1,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,3,4,6,1,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,1,4,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,1,4,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,3,1,4,8,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,3,1,4,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,3,7,4,1,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,3,7,4,1,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,7,1,4,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,7,1,4,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,7,5,1,2,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,1,2,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,1,2,6,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[6,1,4,3,5,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,5,7,3,8,4,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,4,7,8,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,7,2,5,8,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,2,4,5,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,1,4,6,3,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[3,5,6,2,4,1,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[6,2,1,1]=>5
[3,8,6,7,5,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,7,8,3,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,5,3,4,8,1,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[5,1,8,2,3,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,7,6,2,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[3,7,8,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[5,8,7,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,6,1,8,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,7,2,6,3,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,1,8,4,6,7,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,7,8,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,8,1,5,6,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,7,2,4,8,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,8,3,6,7,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,4,5,8,1,7,6]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[4,7,3,2,1,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,4,7,5,2,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,4,8,1,7,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,7,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,3,1,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,7,5,2,3,1,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,7,2,6,5,1,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,4,2,1,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,8,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[2,1,7,3,6,8,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,5,7,8,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,5,7,8,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,4,1,5,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,2,7,8,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[6,1,7,4,3,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,8,3,4,2,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,2,6,1,5,7,8,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[2,4,6,7,3,5,8,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[3,2,2,1,1]=>8
[6,5,8,3,7,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,7,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,6,3,1,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,8,2,5,7,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,7,2,8,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,5,7,4,8,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,3,7,5,1,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,4,8,7,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,7,2,8,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,6,2,5,8,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[5,2,8,4,7,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,4,8,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,4,5,8,7,6,1,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,2,7,3,8,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[2,5,1,4,7,3,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[6,1,3,8,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,1,5,6,2,8,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[4,1,5,2,8,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,1,5,3,2,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[3,4,5,1,8,7,6,2]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[4,4,2,1]=>5
[1,4,5,2,8,7,6,3]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[1,6,4,2,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,6,3,1,8,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,3,6,2,8,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,6,2,7,5,1,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[1,5,3,6,2,8,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,5,8,3,2,7,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,5,8,2,1,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,6,2,5,1,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[5,2,8,4,1,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,4,8,7,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,8,2,4,7,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,5,2,1,7,4,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[6,3,1,7,2,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,5,2,3,8,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,5,1,2,8,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[6,4,1,2,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,1,7,2,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,2,8,1,3,7,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,7,5,6,8,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,6,3,7,5,8,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,7,4,5,8,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,8,4,7,5,3,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,7,5,6,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,6,4,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,5,2,8,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,7,6,3,1,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,6,4,5,1,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,2,6,4,1,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,1,3,7,5,8,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,1,7,3,6,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[2,1,7,4,8,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,8,6,3,7,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,3,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,3,8,4,7,5,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[5,3,1,6,8,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,2,8,7,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,8,3,1,5,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,2,7,1,5,6,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[3,3,3,1]=>3
[4,7,3,8,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,2,7,3,1,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[1,3,7,2,8,4,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,5,3,8,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,4,5,7,1,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,4,6,2,7,1,3,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[1,7,5,8,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,1,2,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,8,4,1,3,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,7,1,3,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,8,3,1,7,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,3,8,7,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,8,7,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,1,8,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,4,1,8,5,7,3,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[5,8,2,1,7,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,7,1,8,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,1,8,7,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,8,9,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,7,8,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,5,8,7,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,2,7,1,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,3,8,5,2,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,3,7,5,2,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,5,7,8,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[5,6,2,4,1,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[4,8,3,7,5,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,3,4,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,2,3,4,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,3,4,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[4,2,8,5,7,6,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,6,4,5,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,4,5,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,6,5,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,3,7,5,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,7,5,8,6,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,8,1,7,3,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,7,8,4,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,2,8,3,7,6,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,2,5,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,3,8,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,2,3,4,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,2,3,4,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,4,1,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,3,4,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,8,3,1,5,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,2,8,5,3,4,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,4,2,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,6,7,5,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,8,5,1,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,5,7,1,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,2,5,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,4,8,5,2,7,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,8,7,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,8,7,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,3,8,5,7,1,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,8,7,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,8,7,1,6,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,3,8,6,7,5,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,2,8,6,7,5,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,8,6,2,7,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,3,8,6,7,5,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,7,1,8,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,8,7,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,8,4,7,5,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,8,5,7,2,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,8,3,7,2,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,1,3,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,1,8,2,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,2,8,6,7,5,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,3,6,1,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,1,7,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,1,8,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,2,8,6,7,1,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,8,3,6,7,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,2,6,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,7,6,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,2,8,6,7,4,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,8,6,7,5,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,3,6,7,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,6,7,3,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,3,6,7,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,7,4,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,5,7,4,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,5,8,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,1,7,6,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,7,6,2,3,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,7,1,8,6,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,1,7,6,4,5,2,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,5,8,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,8,7,5,2,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[6,3,8,7,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,2,5,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,5,8,1,3,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,1,5,3,8,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,8,1,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,1,3,4,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,1,4,2,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,8,1,3,2,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,1,3,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,8,7,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,7,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,7,2,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,6,8,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,7,4,2,8,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,4,7,2,1,8,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,3,4,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,8,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,3,7,1,5,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,4,2,8,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,7,8,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,3,7,2,8,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,8,2,6,7,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,8,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,2,1,5,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,3,1,8,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,7,8,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,7,8,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,3,7,6,8,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,7,8,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,4,3,6,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,8,6,2,7,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,7,5,8,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,8,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,3,8,7,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,8,7,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,6,7,2,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,7,8,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,7,6,4,8,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,8,4,6,7,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,2,8,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,2,4,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,6,2,8,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,6,3,8,7,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,7,4,3,1,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,7,4,3,6,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,3,8,6,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,5,8,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,8,5,7,3,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,3,7,2,4,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,4,6,8,2,7,1,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,7,8,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,6,8,5,7,1,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,7,4,8,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,2,5,7,8,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[5,2,7,4,6,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,6,7,1,8,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[4,2,5,6,7,1,8,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]=>[4,3,2]=>3
[6,1,3,8,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,4,1,8,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,7,5,2,8,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,4,1,8,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,6,3,1,7,8,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[3,6,4,8,1,5,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,5,8,4,2,6,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,7,4,1,6,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,1,2,6,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[4,5,1,8,2,3,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,7,1,8,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,2,6,1,3,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[6,7,1,3,2,5,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,1,4,3,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,6,1,4,2,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[6,7,2,4,1,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,2,4,3,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,2,3,1,5,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,3,5,4,8,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[3,6,5,7,4,8,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[5,6,2,4,3,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[4,5,2,6,1,7,3,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[5,3,1]=>3
[4,5,1,6,3,7,2,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[5,3,1]=>3
[4,5,3,6,1,7,2,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[5,3,1]=>3
[5,6,3,4,1,7,2,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[5,6,1,4,3,7,2,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[5,6,1,3,2,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[5,6,4,7,1,3,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[6,7,4,5,1,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,7,5,8,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[4,6,5,7,1,3,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,6,1,3,2,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,5,3,7,6,8,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[4,6,5,7,3,8,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,6,5,7,2,3,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[3,5,4,6,1,7,2,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[3,5,1,6,4,7,2,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[3,5,2,6,1,7,4,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[3,5,2,6,4,7,1,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[4,6,2,3,1,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,6,2,7,3,5,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,6,2,7,5,4,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[4,6,1,7,3,8,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[2,4,7,1,3,8,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,2,6,7,4,3,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[3,5,2,7,6,4,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[1,5,7,4,3,8,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,7,3,1,8,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,7,2,8,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,7,3,1,8,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,7,3,4,8,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,2,6,7,1,8,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[1,3,7,2,8,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,1,5,6,8,4,3,7]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,3,2,2,2]=>7
[2,4,7,3,1,8,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,7,2,8,5,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,6,2,7,1,8,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[1,6,4,5,7,8,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,5,1,7,8,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,3,6,2,8,7,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[2,1,5,6,8,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,3,2,2,2]=>7
[2,4,1,7,8,5,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,6,2,8,4,7,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[2,1,5,6,8,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,3,2,2,2]=>7
[3,6,5,2,7,8,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[6,2,4,7,5,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,5,7,8,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,7,4,1,8,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,4,6,8,5,7,2,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[4,2,5,7,3,1,8,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[4,5,6,2,8,7,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[2,5,6,8,1,7,4,3]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[4,5,6,1,8,7,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[4,5,6,3,1,8,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[4,3,6,2,1,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[4,6,3,2,1,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[4,6,3,1,7,5,2,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,5,3,7,6,1,8,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,5,1,7,3,8,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[2,5,7,1,4,3,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,3,5,7,6,1,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[4,3,6,1,7,5,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[5,3,2,1,6,4,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,3,1,6,2,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,1,6,3,2,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[2,6,1,4,7,5,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,6,1,7,4,2,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[4,6,1,7,5,3,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[5,1,6,3,7,4,2,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[5,3,6,4,2,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,3,2,6,4,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,2,1,6,3,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,2,6,3,1,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[4,2,6,3,1,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,6,2,1,7,4,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[3,6,2,7,4,1,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[3,5,7,2,8,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,1,3,6,5,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,6,1,3,7,5,4,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,6,1,7,5,2,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[5,1,6,2,7,4,3,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[5,2,6,4,3,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,2,1,6,4,3,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,4,2,1,6,3,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,4,2,6,3,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,4,1,6,2,7,3,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,1,6,4,2,7,3,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[3,6,1,7,5,4,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,6,1,5,4,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[5,1,6,4,3,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,4,1,6,3,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,4,3,1,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[4,2,7,6,5,8,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,8,2,6,5,4,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,7,6,8,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,2,8,7,6,5,9,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,8,7,2,5,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,9,2,7,6,5,4,1,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,11,10,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[5,3,2,6,7,4,1,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[5,2,8,7,6,9,4,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,3,7,2,5,6,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[3,9,8,2,6,5,4,1,7]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,10,2,8,7,6,5,4,1,9]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,12,11,10,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[6,7,1,4,3,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[3,7,1,6,5,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,5,6,2,4,7,1,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,2,1,1]=>5
[3,5,8,7,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,7,8,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,6,4,7,1,3,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]=>[4,2,1,1,1]=>7
[4,7,1,6,3,5,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,5,3,8,7,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[1,4,8,2,7,6,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,7,3,5,1,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,5,8,7,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,4,2,1,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,7,8,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,7,6,2,1,8,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[1,4,6,7,3,5,8,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[2,3,1,8,4,7,6,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,7,4,8,6,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,7,2,8,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,6,3,8,2,7,5,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,5,3,8,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,7,4,1,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,7,5,1,3,8,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,4,3,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,2,4,8,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,4,2,8,7,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[5,1,4,3,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[3,7,8,5,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,2,4,1,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,6,8,2,5,7,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,7,2,5,8,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,2,7,8,4,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,1,7,8,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[2,7,6,4,1,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,7,6,3,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[6,3,1,7,5,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,2,7,5,3,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[1,5,8,2,7,4,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,7,2,8,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,3,1,8,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[2,6,8,5,7,4,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,5,2,1,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,7,4,6,2,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,6,4,8,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,7,1,8,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,6,2,7,1,8,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[6,7,2,4,3,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,4,3,8,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,8,2,7,4,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,4,8,3,6,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,3,1,8,5,6,4,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[3,8,5,6,4,7,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,3,6,4,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,2,3,1,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,2,4,3,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,6,2,7,1,5,3,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,7,1,6,2,5,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,1,5,3,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,6,3,5,1,7,2,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[6,7,3,5,1,4,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,6,3,7,1,4,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[5,7,1,6,3,4,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,8,5,6,3,4,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,6,4,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,1,6,4,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,5,8,1,7,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,7,1,4,2,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,5,1,4,2,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[4,6,5,8,3,7,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,5,8,2,3,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,4,2,6,5,8,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[5,3,3,1]=>5
[3,5,4,6,2,8,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[1,8,3,5,4,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,2,7,1,8,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[4,7,2,3,1,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,4,3,8,1,7,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,5,3,8,4,7,1,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,3,8,1,7,4,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,7,1,8,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,7,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,7,4,8,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,5,1,8,7,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[1,5,2,8,7,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,2,8,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,5,8,7,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[2,3,6,8,7,4,5,1]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,3,7,8,6,4,5,1]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,5,7,8,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,5,6,8,2,7,3,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[5,2,6,8,3,7,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,1,6,8,7,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[6,1,4,8,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,8,4,7,3,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,3,4,7,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,5,7,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,1,7,8,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[5,2,7,8,3,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,6,7,8,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[6,8,4,5,2,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,5,3,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,8,4,2,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,4,7,5,8,6,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,6,7,4,8,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[6,7,4,2,8,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,7,5,2,8,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,7,5,3,8,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,2,8,3,7,4,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,7,8,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,6,8,3,2,7,4,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,6,8,4,2,7,5,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,5,8,2,7,3,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,4,7,2,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,8,1,3,7,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,7,4,8,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,7,2,8,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[1,7,4,8,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,3,7,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,2,3,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,4,5,8,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,7,3,4,8,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,6,4,7,8,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[6,4,2,7,8,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,8,3,4,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,4,2,5,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,4,7,8,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,2,7,4,5,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[2,5,8,3,4,1,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,6,2,7,4,3,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[4,6,7,3,2,5,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[2,6,7,3,8,5,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,1,8,4,5,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,7,8,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,12,1,3,4,5,6,7,8,9,10,11]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[3,6,8,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,6,8,4,7,2,3,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,5,7,8,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[3,4,5,7,8,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,7,6,8,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[3,6,7,4,8,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,4,5,6,8,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[1,4,5,8,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,2,5,8,3,6,4,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,4,5,8,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,6,7,4,8,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,5,6,8,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[1,4,5,8,6,2,7,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,2,5,8,3,4,7,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,6,7,2,3,5,8,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,2,3,5,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,2,3,5,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,4,5,2,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,4,5,2,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,2,3,4,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,2,3,7,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,5,7,6,2,8,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,6,7,2,3,8,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,4,3,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,2,6,3,5,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,6,2,1,5,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,6,5,2,1,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,8,2,1,6,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,2,1,4,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,4,3,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,8,4,6,5,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,6,4,8,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[4,6,5,2,8,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,6,4,5,8,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,4,2,8,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,4,8,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,6,3,5,8,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,2,6,3,8,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,2,4,3,8,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,1,4,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,1,8,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,1,8,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,5,2,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,7,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,1,4,8,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,6,8,7,4,5,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,4,8,6,7,5,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,8,6,5,7,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,6,8,7,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,5,8,2,1,7,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,1,6,8,4,3,7,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[6,8,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,6,4,7,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,2,1,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,5,3,1,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,8,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,8,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,3,8,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,3,8,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[1,7,8,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,3,1,8,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,3,8,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,1,4,8,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,4,1,3,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,6,7,8,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,7,1,8,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,2,7,8,4,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,2,7,8,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,6,7,4,8,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,4,8,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,2,7,8,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,6,7,1,8,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,8,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,8,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,7,8,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,7,2,8,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,8,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,3,7,8,1,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,1,2,8,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[1,6,7,8,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,2,4,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,7,5,3,6,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,2,6,7,4,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[4,1,5,7,3,2,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,6,1,7,3,2,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,6,1,8,3,2,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,1,8,3,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,1,7,8,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[1,6,5,7,8,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,5,8,7,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,1,8,7,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,7,3,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,6,3,2,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,1,6,3,2,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[6,1,2,3,7,5,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,8,1,5,3,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,7,3,4,8,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,3,4,7,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,2,4,3,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,2,4,3,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[3,8,1,2,4,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,8,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,3,7,5,8,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,8,1,7,6,4,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,5,7,3,4,6,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,1,2,3,5,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,2,3,5,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,1,2,3,7,6,4,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,1,2,3,8,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,5,6,3,4,7,8,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[5,4,6,3,1,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[4,6,2,3,1,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,7,3,2,8,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,4,5,1,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,6,7,4,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,5,6,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,4,6,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,3,4,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,4,3,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,1,7,6,8,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,7,6,1,8,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,2,3,8,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,2,3,7,8,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,2,3,8,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,3,5,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,8,3,6,7,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,5,1,8,4,6,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,6,1,8,4,5,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,6,8,3,5,2,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,7,8,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,8,2,3,5,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,2,3,1,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,7,4,8,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,7,8,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,2,8,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,3,2,4,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,7,3,1,4,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[3,7,4,1,8,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,3,7,4,8,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,7,4,1,5,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,8,3,2,4,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,3,8,7,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,8,7,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,1,8,6,7,5,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,4,8,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,5,4,8,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,1,6,8,3,4,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,2,5,1,7,4,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,2,1,8,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,6,3,8,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,8,3,4,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,4,3,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,8,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,4,6,3,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,3,8,4,1,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,3,6,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,3,6,5,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,4,7,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,4,6,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,5,1,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,8,2,5,1,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,1,5,2,4,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,1,8,5,2,7,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,5,1,3,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,6,1,5,7,2,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[6,3,1,2,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,1,8,2,3,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,8,7,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,7,3,5,1,4,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,7,5,8,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,7,8,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,4,7,6,2,8,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,7,4,1,6,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,8,4,5,7,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,6,1,7,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,1,4,7,8,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,6,7,2,4,8,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,3,7,4,8,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,3,6,7,4,8,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,3,2,8,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,8,2,6,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,6,2,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,8,5,7,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,5,7,2,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,2,4,7,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,3,8,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,6,3,5,8,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,6,3,2,8,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,6,3,8,2,7,4,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,6,5,8,7,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,3,6,8,2,7,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,7,2,8,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,4,7,2,6,8,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,2,7,6,8,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,7,3,8,5,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,3,2,7,5,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,7,2,5,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,7,5,1,4,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[2,7,8,5,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,7,8,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,5,7,8,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,8,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,7,8,2,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,5,8,4,3,7,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,8,4,7,3,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,7,4,8,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,8,7,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,5,4,8,2,7,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,3,7,5,8,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,5,7,3,8,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,5,6,8,4,7,2,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[6,3,1,8,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,8,1,7,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,1,7,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,2,5,6,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,7,5,6,2,4,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,6,7,4,3,5,2,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,5,2,3,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,5,3,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,8,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,6,7,4,3,2,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,5,7,1,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,4,3,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,7,8,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,5,8,3,4,1,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,5,7,3,4,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,2,5,7,4,1,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,2,5,8,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,8,4,6,1,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,2,8,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,2,8,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,5,7,8,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,6,5,7,3,8,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,6,2,7,5,8,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,2,4,8,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,5,2,1,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,5,3,7,8,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,2,5,3,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,2,3,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,1,2,3,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,4,2,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[1,9,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,1,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[1,2,9,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[3,2,1,9,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[4,3,2,1,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[1,2,10,9,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,1]=>7
[5,2,7,4,1,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[4,7,3,1,5,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,8,3,4,1,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,8,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,4,2,6,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,3,8,5,2,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,2,3,7,1,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,2,3,7,5,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,7,3,4,8,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,3,4,8,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,3,1,9,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,3,1,9,5,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,1,9,8,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,7,2,9,3,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[7,1,9,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,2,1,10,9,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[6,5,4,1,10,9,8,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[7,2,1,10,4,3,6,5,9,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[7,4,1,10,6,2,9,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[7,6,1,10,9,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[8,1,10,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,8,5,3,7,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,1,8,5,3,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,4,8,6,3,1,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,6,8,2,1,7,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,4,1,5,8,2,7,6]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[4,4,3,1]=>5
[3,4,6,2,1,8,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[3,5,6,2,1,7,8,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[3,4,6,2,7,8,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[4,2,2,1]=>5
[3,5,6,2,1,7,4,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,2,1,1]=>5
[3,4,1,6,8,7,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[3,5,6,1,8,7,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[2,1,3,8,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,3,8,6,7,1,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,1,8,6,7,5,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,5,8,6,1,7,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,6,1,8,7,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,4,1,6,8,7,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[3,4,6,8,7,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,5,1,6,7,8,4,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[4,5,6,1,7,8,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[4,5,6,1,7,3,8,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,2,1]=>3
[3,5,1,6,7,4,8,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[3,5,1,6,7,4,2,8]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]=>[4,3,1,1]=>5
[4,5,6,1,7,3,2,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]=>[4,2,1]=>3
[6,5,8,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,2,7,8,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,4,8,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,4,8,7,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,6,2,4,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,1,7,8,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,8,6,3,4,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,5,4,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,5,4,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,3,4,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,1,4,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,7,5,4,8,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,2,7,5,4,8,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,5,8,4,7,3,1,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,3,7,5,4,8,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,8,3,2,4,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,2,5,4,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,1,7,5,4,8,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[1,3,7,5,4,8,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,8,4,7,3,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,8,4,7,3,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,4,7,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,3,7,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,5,4,7,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,5,4,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,7,4,6,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,1,3,2,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4]=>0
[2,7,3,5,4,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,7,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,3,4,6,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,2,1,4,7,8,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]=>[4,4,4,3]=>3
[5,4,2,8,1,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,8,2,6,4,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,2,5,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,5,2,1,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[2,5,8,6,3,1,4,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,3,5,8,1,4,7,6]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,6,8,1,5,7,4]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[6,3,8,5,2,7,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,7,5,2,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[2,5,7,6,3,1,4,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,8,7,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,8,7,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,8,1,6,5,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,8,7,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,6,8,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,7,8,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,6,1,8,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,8,6,3,1,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,8,1,3,7,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,8,1,7,3,6,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,8,1,5,7,3,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,1,4,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,6,8,1,5,7,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,7,1,5,8,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,6,3,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,6,1,8,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,5,8,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,5,1,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,8,5,1,7,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,1,7,6,2,3,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,1,7,6,2,8,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,1,8,7,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,1,8,4,7,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,6,1,8,7,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,8,5,1,7,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,1,8,7,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,8,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,8,4,1,7,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,8,7,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,8,3,7,1,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,4,7,1,2,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,1,2,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,5,1,8,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,1,8,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,1,7,2,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,5,1,7,2,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,7,4,1,8,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,8,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,8,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,7,5,3,6,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[1,8,4,2,3,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,3,4,6,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,1,7,2,3,6,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,6,2,1,5,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[4,5,2,3,1,7,8,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]=>[5,5,1]=>2
[3,2,6,7,4,1,8,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]=>[3,2,2,2]=>3
[5,6,2,7,1,4,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[6,2,3,8,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,8,3,4,7,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,2,7,5,1,3,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[2,6,3,1,8,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,4,3,7,8,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[5,3,2,7,4,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,1,2,7,6,8,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[2,6,3,1,8,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,5,6,4,7,8,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[4,2,1,1]=>5
[5,3,6,4,2,8,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,4,2,3,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,1,8,2,5,7,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,4,7,2,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,2,3,8,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,4,1,5,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[3,2,7,6,4,1,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[2,5,4,1,7,6,8,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[4,4,1,1,1]=>6
[6,2,1,4,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[2,6,5,1,7,8,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,7,5,2,1,6,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,2,3,7,8,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,8,3,1,7,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,1,5,2,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,2,7,1,6,3,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,1,7,4,2,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,8,4,2,1,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,2,1,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,1,4,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,2,5,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,3,1,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,2,1,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,1,7,3,2,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,2,1,8,3,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,8,1,6,2,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,4,7,2,1,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,2,1,7,3,4,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[6,4,3,1,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,3,1,7,2,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,2,1,6,5,8,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,2,1,8,5,7,3,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,3,2,1,7,4,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,4,2,1,7,5,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,1,8,4,2,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,1,8,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,3,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,3,2,7,6,1,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,3,2,8,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,3,2,8,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,8,1,7,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,7,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,5,8,4,7,3,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[4,3,2,5,8,1,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,3,1,7,2,8,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[5,4,1,7,2,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,5,3,1,7,8,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,4,2,1,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,4,2,1,6,7,3,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[5,3,2,1,6,7,4,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[6,4,2,1,7,8,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,3,2,6,8,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[4,3,2,6,1,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[5,3,2,1,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[3,8,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,8,3,7,4,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,5,4,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,6,3,7,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,8,4,3,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,2,7,3,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,4,2,8,3,6,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,3,8,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,8,4,3,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,3,7,4,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,2,7,3,1,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[6,4,3,7,1,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,4,3,8,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,2,7,3,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,3,1,7,8,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,2,7,8,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,4,1,6,3,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[6,5,1,7,8,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,3,1,7,8,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,4,1,7,3,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,3,2,7,8,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,5,4,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,1,3,5,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,3,8,7,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,7,1,8,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,7,6,4,8,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,2,7,1,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,4,7,5,6,1,8,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,4,7,5,6,3,8,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,4,1,7,6,2,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[3,5,6,7,1,4,8,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[2,7,6,1,3,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,2,1,6,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,7,2,5,6,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,7,4,5,3,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,6,5,7,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,4,3,2,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,5,6,2,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,8,1,3,2,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,4,5,2,8,6,7,3]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[2,3,1,7,8,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]=>[3,3,3,3,1]=>4
[3,5,7,6,2,8,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[4,5,6,1,2,8,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[5,4,1,2,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,1,2,6,8,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[5,1,3,2,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,5,4,2,7,8,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,6,7,8,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[5,2,8,6,3,4,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,6,8,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,3,8,1,7,2,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,7,8,4,2,1,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[6,5,1,8,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,8,4,2,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,5,8,3,1,6,7,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,8,1,2,6,7,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,2,8,1,5,6,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,5,8,3,2,6,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,8,6,2,4,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,2,7,8,4,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[5,1,8,3,4,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,7,2,1,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,1,6,3,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,7,2,5,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,4,5,8,3,6,1,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[3,5,8,1,2,6,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,6,1,3,4,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,6,1,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,4,3,6,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[2,6,4,3,7,8,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,2,1,7,8,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,4,6,5,1,7,8,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[1,4,7,5,6,8,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,7,6,5,8,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,7,5,2,4,6,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,6,1,7,4,2,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[3,7,4,8,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,3,5,7,8,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,6,5,7,1,8,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[6,4,7,8,2,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,7,3,8,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,7,8,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,5,8,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,6,7,4,8,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[5,7,3,1,6,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,7,3,1,8,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,1,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,1,2,3,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,5,4,6,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,1,3,5,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,7,2,3,6,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,4,6,7,5,8,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,2,2,1]=>5
[3,4,5,7,6,1,8,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[2,6,4,5,7,8,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,8,5,1,6,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,5,1,3,6,8,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[5,4,6,1,3,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[6,3,5,7,1,4,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,7,6,4,1,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,4,1,5,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,5,8,6,7,4,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,1,6,7,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,2,5,1,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,8,2,1,6,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,2,8,6,3,7,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,6,1,2,5,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[1,4,5,8,2,3,7,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[3,6,1,5,8,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,6,5,1,4,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[5,2,6,1,4,8,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[2,5,1,8,4,7,3,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,7,1,4,3,6,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,3,7,5,8,2,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,5,4,8,1,3,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,7,3,5,8,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,2,6,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,6,8,7,2,4,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,1,7,6,8,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,1,7,2,6,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,1,7,2,3,6,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[2,6,1,7,3,5,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,4,1,2,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,8,3,4,7,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,8,1,2,7,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,6,8,1,2,4,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,1,3,8,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,3,7,4,8,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,6,8,2,3,7,5]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[3,5,8,1,7,2,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,6,8,1,7,3,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,1,5,8,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,3,2,7,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,7,2,8,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,6,7,3,8,1,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,7,2,8,6,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,2,3,8,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,2,4,3,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,7,3,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,7,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,5,1,4,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,4,3,1,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[6,3,4,1,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,8,5,2,7,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,7,5,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,7,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,6,5,8,2,4,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,2,1,8,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,2,7,4,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,6,5,2,7,3,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[6,2,7,1,8,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[2,7,5,4,8,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,1,3,2,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,1,4,7,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,3,8,7,4,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,4,8,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,6,7,8,2,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[5,8,3,2,4,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,6,5,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,1,8,6,4,3,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,6,5,3,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,6,1,3,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,6,1,2,5,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,4,1,7,6,8,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,4,1,7,8,5,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[6,3,5,4,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,1,3,6,7,5,8,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,3,3]=>2
[1,7,5,3,8,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,4,5,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,5,8,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,4,7,8,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,4,7,8,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,7,4,5,8,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,3,1,8,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,4,7,8,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,6,4,7,8,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[4,3,6,7,1,8,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[4,3,6,7,1,8,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,6,4,7,8,1,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[2,3,6,4,1,7,8,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[4,7,2,1,5,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,4,5,2,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,7,2,8,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[5,1,3,4,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[5,4,2,1,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[6,1,7,3,8,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,6,7,3,8,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,4,7,8,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,3,2,1,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,2,7,3,1,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,2,4,7,8,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,6,7,3,1,8,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,4,7,8,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,8,4,7,1,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,6,1,5,3,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,7,4,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,3,8,7,1,6,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,7,8,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,5,8,7,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,8,1,2,7,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,1,2,7,4,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,8,4,1,3,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,5,8,7,3,6,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,8,7,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,7,4,8,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,4,8,7,5,1,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,5,2,4,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,1,8,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,3,8,7,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,3,7,8,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,7,6,8,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,6,7,8,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,4,7,8,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,4,7,8,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,8,3,4,1,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,3,4,1,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,2,7,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,3,1,8,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[4,5,3,2,8,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,5,8,6,1,4,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,8,5,6,1,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,1,5,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,3,7,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,8,5,3,2,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,6,4,8,5,1,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,4,8,6,5,2,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,7,5,6,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,5,1,3,8,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[4,5,1,2,8,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[5,4,8,1,3,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,5,7,2,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,5,7,6,4,1,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[4,7,5,2,1,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,2,3,6,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,2,4,8,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[1,7,2,4,8,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,3,2,1,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,1,7,2,5,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[4,8,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,6,7,4,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,3,1,6,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,1,2,5,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,5,4,2,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,8,7,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,5,3,7,8,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,1,3,8,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,2,7,4,8,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,3,2,6,8,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,1,2,4,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[3,5,4,2,8,1,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[5,1,3,8,4,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,7,3,5,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,7,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,6,8,1,7,3,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,1,6,8,7,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[6,5,8,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,5,8,3,6,7,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,5,8,3,7,4,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,8,2,7,1,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,2,3,6,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,3,4,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,8,7,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,6,8,5,2,7,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,1,7,8,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,7,4,3,5,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,5,7,8,4,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[6,2,7,1,3,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,1,8,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,8,7,1,6,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,7,1,8,5,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,3,2,4,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,3,4,2,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,4,3,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[3,8,6,5,4,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,5,6,3,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,5,7,2,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,7,5,8,3,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,8,5,7,1,4,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,2,7,3,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,5,4,3,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,2,4,5,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,7,2,8,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,1,3,6,4,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[5,1,8,7,4,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,7,5,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,3,4,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,2,1,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,3,1,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,1,4,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,8,3,5,7,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,1,3,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,1,6,4,3,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[2,8,3,6,4,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,1,7,5,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,3,8,7,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,2,1,5,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[7,1,9,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,9,8,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,7,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,9,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,9,8,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[8,1,10,9,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,1,7,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,6,9,8,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,1,10,9,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,9,8,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,8,7,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,9,8,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,10,9,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,2,9,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,1,10,9,8,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[1,6,4,8,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,3,5,6,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,5,6,2,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,8,5,3,7,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,4,8,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,2,5,4,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,4,1,2,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[1,7,4,2,5,3,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,4,2,1,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,3,8,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,4,3,1,5,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,4,2,3,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,5,2,4,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,4,8,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,2,8,6,1,3,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,3,1,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,7,3,1,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[6,5,2,4,7,1,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,7,4,1,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,4,3,1,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,8,1,3,5,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,5,8,1,3,7,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,6,1,8,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,7,3,1,8,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,8,1,4,7,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,5,4,7,6,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,5,8,3,7,6,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,1,5,3,8,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,5,1,8,2,7,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,8,5,3,1,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,2,8,1,7,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,2,1,8,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[5,6,2,7,8,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,6,2,8,7,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,8,6,3,7,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,3,7,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,8,2,7,5,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,2,8,7,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,6,2,7,4,1,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,7,2,3,1,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,7,2,8,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,6,7,2,1,8,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,7,2,1,3,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,1,7,8,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,6,1,7,2,4,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,1,6,7,8,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,1,6,8,7,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,8,6,7,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,6,8,7,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,1,6,7,4,8,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,6,1,7,8,4,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,6,8,1,7,5,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,8,6,1,7,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,7,1,8,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,6,7,1,3,8,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[5,6,7,1,3,2,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,7,3,1,2,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[5,6,7,3,8,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,6,8,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,6,7,3,8,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[1,4,8,6,3,2,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,4,2,5,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,2,5,7,6,3,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,1,5,8,6,3,2,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,7,6,1,8,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[4,7,5,1,6,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,4,8,3,7,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,7,1,8,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,4,1,8,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,2,5,4,7,8,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[5,2,4,3,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[3,1,7,6,5,8,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[1,2,7,5,6,8,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,4,7,2,8,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,2,1,7,6,8,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[3,2,8,6,4,7,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,8,6,5,3,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,5,2,7,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,5,3,1,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,5,3,6,8,1,7,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,5,2,6,1,8,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[1,6,3,5,7,2,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,4,6,7,8,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[5,4,2,6,8,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,5,1,4,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[3,6,4,5,2,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[1,7,8,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,8,3,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,7,8,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,7,8,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[1,3,7,5,8,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,7,5,8,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,5,7,1,8,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,8,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,8,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,7,1,8,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,5,3,7,8,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,3,7,8,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,6,2,1,4,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[4,6,2,5,1,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,4,2,5,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,5,8,1,7,3,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,8,2,7,3,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,3,7,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,8,1,7,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,3,8,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,2,8,3,7,1,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,4,6,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,1,5,8,4,3,6,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[5,8,3,2,7,1,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,3,8,2,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,5,8,2,7,1,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,5,8,2,6,1,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,6,8,3,7,1,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,1,8,3,7,2,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,4,6,2,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,1,6,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,8,1,6,2,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,4,8,1,6,2,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,5,1,6,2,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,4,3,8,1,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,1,8,4,2,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,4,2,1,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,3,8,4,1,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,4,2,8,1,5,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,8,5,2,7,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,2,6,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,1,4,8,5,3,6,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[3,2,8,4,1,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,4,3,1,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,7,5,6,2,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,7,4,3,8,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,4,3,8,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,8,4,2,6,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,1,6,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,7,5,2,8,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,6,4,3,2,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[2,6,7,5,3,8,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,7,4,8,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,1,6,7,5,3,8,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,8,4,2,1,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,4,3,8,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,4,8,1,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,5,8,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,8,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,4,8,1,2,5,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,1,3,4,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,4,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,4,8,2,1,5,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,7,5,8,2,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,5,8,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,4,8,1,5,7,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,5,7,6,1,4,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,7,4,8,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,8,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,6,7,5,1,3,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,3,1,4,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,4,8,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,5,8,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,8,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,4,8,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[1,5,6,3,4,8,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[5,1,7,3,4,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,7,8,2,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,8,6,2,3,7,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,3,4,7,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,3,4,7,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,7,5,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,6,7,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,1,3,8,4,6,5,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[1,3,2,8,5,4,6,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,5,6,8,7,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,4,8,5,7,6,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,8,5,7,3,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,8,6,5,7,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,7,2,8,5,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,2,7,8,6,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,2,8,6,7,3,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,8,7,5,4,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,7,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,1,8,6,7,5,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,7,8,6,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,7,1,8,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,4,8,2,6,1,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,3,8,4,1,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,4,8,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,4,8,5,1,6,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,8,1,4,6,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,4,8,2,6,3,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,3,8,1,4,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,6,8,1,5,3,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,1,7,5,8,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,2,1,8,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,2,7,8,5,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,3,7,8,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,1,5,7,8,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,7,5,6,8,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,8,4,5,6,7,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,1,4,8,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,4,1,8,6,5,3,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[4,2,1,8,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,7,8,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[2,3,7,8,5,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,7,3,8,5,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,2,8,5,1,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,1,2,8,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,4,2,8,7,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,2,6,8,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,5,7,1,8,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,7,6,1,8,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,1,5,8,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,3,8,5,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,7,9,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,7,9,10,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,7,9,10,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,7,9,10,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,7,9,10,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,6,9,3,7,2,1,4,5,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[2]=>0
[8,5,9,4,2,6,7,1,3,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[2]=>0
[8,5,9,3,2,6,1,4,7,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[2]=>0
[8,4,9,3,2,1,5,6,7,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[2]=>0
[1,8,7,5,3,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,4,2,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,5,4,7,1,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,3,7,1,6,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,6,4,2,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[1,5,3,8,7,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,3,6,1,8,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,1,5,3,8,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,8,7,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,1,8,7,5,4,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[5,3,8,7,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,8,6,3,5,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,8,5,2,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,6,4,7,5,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,8,6,3,7,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,7,4,1,8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,1,8,7,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,6,3,2,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,8,7,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,2,8,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,7,5,8,6,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,2,5,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,1,8,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,1,8,7,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,8,6,4,1,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,8,6,3,2,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,1,8,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,5,2,7,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,1,7,4,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,1,7,5,8,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,7,4,6,3,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,5,2,1,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[3,5,6,2,1,4,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[6,2,1,1]=>5
[3,5,7,8,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[4,1,8,5,7,3,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,7,5,8,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[2,1,5,8,7,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,1,5,7,8,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[3,3,2,2,2]=>6
[5,1,7,4,8,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,7,2,8,3,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,6,2,7,3,1,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,7,8,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,4,1,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,8,4,1,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,4,8,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,8,1,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,5,8,1,2,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[1,8,5,4,2,3,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,4,8,1,2,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,5,3,8,1,2,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[6,4,3,8,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,3,8,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,6,3,8,7,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,6,3,8,1,7,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,6,8,4,1,7,3,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,8,7,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,8,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,7,5,8,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,7,8,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,5,6,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,8,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,3,6,8,7,1,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,3,5,8,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,8,6,7,1,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,8,3,2,7,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,8,7,6,1,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,8,7,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,4,7,8,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[1,8,5,7,6,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,7,6,1,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,6,7,8,5,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,6,8,7,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,8,6,7,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,4,8,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,3,8,7,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,7,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,8,7,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,6,1,3,2,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,2,7,6,8,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[2,8,7,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,1,8,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,1,6,3,2,8,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[4,6,1,8,7,3,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,3,1,4,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,3,5,2,8,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,4,2,8,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,7,6,8,1,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,1,8,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,1,7,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,6,3,5,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,1,6,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,8,1,4,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,6,7,4,1,8,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[1,7,4,6,8,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,6,5,4,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,7,2,3,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,3,1,8,4,6,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,8,1,6,7,4,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,4,3,6,8,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,6,1,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,3,8,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,1,7,4,8,5,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,8,6,2,7,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,4,8,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,7,5,1,8,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,7,3,2,8,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,8,4,6,1,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,6,5,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,2,7,6,1,5,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[3,5,1,6,8,4,7,2]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[6,1,5,7,3,8,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,8,4,7,3,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,8,3,7,4,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,8,1,6,4,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,2,6,8,3,1,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,6,5,8,4,1,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,7,3,1,6,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,1,3,2,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,7,1,5,2,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,2,8,7,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,4,1,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,1,7,2,3,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,1,8,2,7,5,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,7,4,3,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,1,7,4,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,1,7,3,2,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[4,7,2,1,6,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,2,1,5,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,3,1,6,2,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[6,1,5,2,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,5,3,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,2,8,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,8,6,1,5,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,6,1,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,7,1,3,8,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,6,7,1,5,2,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[5,6,2,7,1,3,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,2,8,1,3,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,1,8,3,7,5,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,2,7,3,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,1,8,3,7,4,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,1,7,4,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,1,8,4,5,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,2,7,1,6,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[4,5,7,3,1,6,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,5,7,2,8,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,5,1,7,2,6,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[4,5,7,2,8,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,6,7,2,1,5,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[4,6,7,1,3,8,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,6,1,5,7,8,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[4,6,7,1,5,8,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[6,1,3,7,4,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,2,1,7,4,8,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[4,1,5,2,7,6,3,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[3,7,2,1,5,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[6,2,7,1,4,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,7,4,2,1,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,3,2,1,7,6,4,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,3,2,8,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,5,3,8,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,5,3,6,4,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,6,1,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,8,1,4,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,4,1,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,8,3,2,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,1,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[2,5,8,1,4,3,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,6,8,2,1,5,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,7,4,8,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,1,4,8,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[2,7,4,1,8,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,1,8,4,2,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,1,5,7,3,6,2,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,2,5,8,3,1,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[6,1,2,7,8,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,3,1,8,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,1,8,4,7,5,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,8,7,3,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,7,6,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,1,4,7,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,8,1,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,8,7,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,7,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,1,6,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,1,5,4,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,6,1,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,7,5,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,8,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,4,2,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[1,3,7,5,4,2,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,1,3,5,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,1,2,5,4,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,1,6,3,4,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,2,6,3,4,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[3,4,7,5,8,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,4,7,1,5,3,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,3,6,7,4,8,1,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,3,6,7,4,8,5,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[2,7,6,5,3,1,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,2,6,1,4,7,8,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[4,7,6,5,2,1,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,3,6,2,4,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,7,4,2,1,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,3,1,5,4,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,3,6,1,4,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[1,7,4,2,6,3,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,4,1,2,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,4,1,2,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,7,6,3,8,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,6,5,2,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,5,1,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,7,2,6,1,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,7,1,6,8,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,5,8,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,11,10,9,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[3,2,10,9,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[3,9,2,8,7,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,9,8,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,2,8,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,6,2,3,8,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[4,5,3,2,7,8,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[6,5,7,3,8,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,8,7,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,2,7,4,5,8,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[6,8,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,3,4,7,5,8,1,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[6,3,4,7,8,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,3,7,4,8,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,3,7,4,8,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,7,8,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[5,4,3,1,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,7,6,2,8,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,1,7,5,8,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,5,6,8,4,7,3,2]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[4,1,3,7,6,5,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,4,1,7,5,8,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[6,8,5,1,7,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,7,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,1,6,7,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,1,2,7,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,4,7,2,3,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,3,2,1,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,7,4,1,8,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,4,1,3,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[2,7,8,5,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,7,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,1,5,8,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,8,7,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,5,7,3,8,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,2,6,8,3,1,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,7,6,2,4,5,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[2,3,6,5,8,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,3,5,8,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[4,2,3,8,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,4,1,2,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,2,3,7,4,6,8,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[3,2,7,1,4,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[5,8,3,2,4,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,7,1,8,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,1,8,2,7,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,2,7,5,3,8,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,2,7,1,4,8,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[6,2,8,3,7,5,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,3,7,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,4,8,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,5,8,7,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,6,3,8,5,7,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,6,8,3,7,4,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,8,4,3,7,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,3,7,4,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,4,8,7,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,5,3,8,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,6,7,8,4,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,6,8,5,4,7,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,8,5,6,4,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,6,4,7,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,3,7,8,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[4,3,7,8,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,2,8,6,4,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,8,6,5,7,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,8,6,7,4,5,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,8,7,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,8,2,7,4,5,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,8,4,5,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,8,4,6,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,8,5,6,7,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,6,8,5,7,2,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,4,6,8,7,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[1,8,3,5,7,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,5,8,4,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,7,4,6,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,6,5,8,4,7,2,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,6,8,4,5,7,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,2,7,1,3,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,2,5,1,3,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[5,3,6,1,7,2,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[3,7,1,2,5,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,1,2,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[6,4,2,3,7,1,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,7,5,2,8,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,8,5,6,1,2,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,8,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,5,8,1,2,4,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,1,2,5,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,7,2,4,8,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,6,3,8,1,2,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,6,3,7,1,2,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,1,7,8,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,1,2,8,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,8,1,6,2,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,8,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,7,5,2,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,8,1,3,7,4,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,8,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,8,2,7,1,4,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,7,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,4,8,2,7,5,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,1,3,4,7,2,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,1,2,7,5,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,2,8,7,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,1,7,3,6,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,2,1,5,7,4,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,2,3,7,4,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,4,8,7,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[2,3,8,7,4,1,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,7,3,8,6,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,3,7,6,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,7,1,4,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,6,7,5,2,1,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[6,3,1,4,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,3,1,4,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[5,1,2,4,7,6,8,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,7,4,1,2,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,8,1,2,6,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,7,8,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[1,2,8,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,1,8,4,5,7,6,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,5,4,7,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,8,1,5,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,5,7,6,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,2,1,6,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,6,5,2,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,1,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,7,8,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,7,8,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,8,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,8,1,7,4,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,7,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,3,4,6,7,2,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[1,3,4,8,7,5,2,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,6,1,4,2,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[1,6,8,4,3,7,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,1,4,7,8,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[6,1,7,4,3,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,8,7,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,2,3,1,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,2,1,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,4,1,8,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,8,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,3,8,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,7,4,3,6,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,6,4,5,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,6,5,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,3,7,5,8,1,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,4,7,3,6,2,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,3,4,2,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,1,3,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,2,3,8,5,7,1,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[2,8,5,7,3,4,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,6,4,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,3,5,8,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[6,1,8,3,4,2,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,6,4,2,3,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,4,5,6,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,3,5,7,8,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1]=>[4,4,3,1,1]=>8
[3,8,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,3,1,4,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,8,4,2,6,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,4,8,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,1,8,4,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,8,1,5,7,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,1,2,5,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[3,8,4,1,6,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,8,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,7,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,3,7,4,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,3,1,8,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,7,1,4,8,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,5,7,4,8,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,6,7,4,5,8,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,1,7,4,5,8,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,3,7,4,8,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,3,6,8,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,5,3,7,4,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,7,8,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,3,8,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,6,3,8,1,4,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,7,8,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,8,3,1,2,5,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,2,1,5,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[5,4,2,6,1,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[2,5,8,1,7,4,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,8,2,7,4,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,3,7,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,5,1,8,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,2,7,3,1,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,2,3,7,1,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[5,2,7,3,8,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,1,5,8,4,3,7,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[5,8,4,2,6,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,2,4,8,1,5,7,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,4,8,3,1,7,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,3,2,1,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,3,7,2,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[3,4,8,2,1,6,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,8,3,7,2,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,8,1,7,2,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,1,7,4,6,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,7,1,8,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,7,6,3,8,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,6,4,8,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,4,8,7,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,4,3,8,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,4,1,8,6,2,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,8,5,4,2,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,6,5,2,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,8,7,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,2,6,3,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,5,2,1,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,7,2,3,5,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[3,7,6,4,2,8,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,6,4,8,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,1,8,7,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,3,7,2,1,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,7,4,2,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,3,1,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,1,4,8,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,1,7,5,4,8,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,3,7,5,8,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,4,2,6,8,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,5,2,8,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,8,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,3,8,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,4,8,1,5,6,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,8,1,5,2,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,6,8,4,1,2,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,8,1,2,5,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[7,9,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,7,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,9,8,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,9,8,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,6,2,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,9,8,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,6,3,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,9,8,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,2,4,7,6,1,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[3,5,4,7,2,6,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,7,6,1,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,7,6,1,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,4,6,1,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,4,6,1,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,4,6,2,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,2,5,7,4,6,1,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[3,5,2,7,6,4,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,2,6,4,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,6,2,4,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,7,6,1,2,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,3,7,6,1,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,7,6,4,1,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,5,7,2,6,1,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,2,7,6,1,4,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[5,3,7,6,4,1,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,7,5,4,1,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,4,1,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,1,4,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,1,4,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,5,7,1,2,6,8,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,1,6,8,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,2,7,1,6,4,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,2,1,6,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,1,6,2,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,5,7,1,4,6,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,1,4,6,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,1,4,2,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,1,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,2,7,1,4,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,2,5,7,4,1,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[3,5,2,7,4,1,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,4,2,1,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,4,1,2,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,5,4,7,1,6,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,7,1,2,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,7,2,1,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,2,7,1,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[3,5,4,7,2,1,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,7,1,2,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[5,7,6,3,1,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,6,3,1,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,5,7,4,1,2,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,4,2,1,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,2,5,7,4,1,8,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,2,5,7,1,4,8,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,5,2,7,1,4,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,2,1,4,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,1,4,2,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,7,5,2,1,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,5,1,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,2,7,5,1,8,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,5,1,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[3,7,2,5,1,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,5,2,1,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,1,7,5,8,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,3,4,1,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,5,6,8,1,7,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[3,7,6,4,1,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,1,8,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,1,7,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,7,6,1,5,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,8,7,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,7,8,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,2,5,8,1,6,7,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,2,5,8,1,7,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,8,2,4,1,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,2,6,8,1,5,4,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,2,8,6,7,1,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,6,8,7,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,2,6,7,1,5,4,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[3,2,8,5,7,1,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,6,5,7,1,8,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,1,8,7,4,3,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,4,7,6,8,2,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,1,8,2,3,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,8,5,3,4,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,2,4,6,8,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[1,6,8,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,7,4,8,6,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,2,6,7,8,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[6,4,2,7,3,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,5,4,8,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,8,2,3,1,7,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,4,3,8,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,8,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,2,5,7,4,8,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[2,8,5,6,7,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,2,7,8,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,6,8,5,1,4,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,4,2,8,6,5,7,3]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[3,5,1,6,8,7,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[5,7,6,2,1,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[2,5,8,7,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,1,7,5,2,6,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,2,4,8,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,1,5,6,7,8,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[3,4,6,5,1,7,8,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[5,2,2,1]=>5
[5,3,7,2,4,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,7,5,2,4,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[5,7,3,2,4,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,2,1,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,2,4,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[3,7,2,5,4,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[5,1,3,2,4,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[5,1,3,2,7,4,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[1,7,3,2,5,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,3,7,2,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[3,2,7,5,1,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,7,5,1,2,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[5,7,3,1,2,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,5,3,7,2,4,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,3,2,7,4,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,3,2,4,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,3,2,1,4,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[5,3,2,1,7,4,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[1,3,7,2,5,4,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,3,1,2,7,4,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,3,1,2,4,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[1,3,7,5,2,4,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,7,1,3,2,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[3,7,1,5,2,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,2,5,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,1,5,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,2,1,7,5,4,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[3,1,2,7,5,4,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[3,1,7,2,5,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,5,2,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[1,7,5,3,2,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,9,2,4,5,6,7,8]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1]=>[2,2,2,2,2,1,1]=>10
[1,9,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,9,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,2,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[3,9,8,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,10,9,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[4,9,8,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,10,9,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,8,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,9,8,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,10,9,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,8,5,1,7,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,9,8,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,10,9,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[6,8,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,1,2,8,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,10,9,2,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,10,1,9,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[3,10,9,8,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,11,10,9,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[1,9,8,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[4,10,9,8,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,11,10,9,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[1,9,8,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[4,9,8,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,9,8,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,11,10,9,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,8,1,4,7,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,9,8,5,1,7,6,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,9,8,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,10,9,8,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,11,10,9,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[1,9,6,2,8,7,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,7,4,3,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,9,8,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,10,9,1,2,8,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,11,10,9,2,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[1,7,2,9,8,6,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>6
[1,8,5,4,2,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,9,6,2,1,8,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,1,2,9,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,11,10,1,9,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,11,2,10,9,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[1,7,2,3,6,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,6,4,8,2,7,1]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,5,1,4,8,2,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[1,7,5,4,8,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,1,6,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,8,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,4,8,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,4,8,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,1,4,8,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[3,6,4,2,8,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,5,2,4,8,1,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,5,6,4,8,1,2,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[1,5,6,4,8,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[3,6,4,1,8,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,6,4,5,8,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,6,4,3,8,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,4,2,8,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,6,4,3,8,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,3,8,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,5,8,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,6,4,8,3,7,2]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[2,5,6,4,8,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[3,5,6,1,4,7,8,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[1,6,4,5,8,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,4,6,8,7,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[3,5,6,8,2,1,7,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[4,2,5,6,3,1,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,3,2]=>3
[3,5,6,8,1,7,2,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[4,1,5,6,3,2,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,3,2]=>3
[4,5,3,1,7,2,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[2,5,4,7,3,8,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,5,7,1,8,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[4,5,3,7,1,2,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,3,6,1,2,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[5,1,3,2,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[3,6,1,7,4,5,2,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[5,1,3,4,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,3,1,4,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[4,5,2,3,7,1,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[4,2,6,1,3,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[4,6,2,1,3,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[3,6,2,1,7,4,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[3,6,2,7,1,5,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[4,6,2,7,1,3,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[3,5,7,1,8,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[5,1,4,2,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[3,6,1,7,2,5,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[2,6,5,3,4,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,6,1,7,5,4,2,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[5,1,4,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[5,4,1,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]=>[6,5]=>1
[6,4,2,5,3,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,2,3,5,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[6,2,4,5,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,2,3,5,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[2,6,4,1,5,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,8,1,6,7,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,4,5,7,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,6,1,4,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,1,6,4,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,1,4,8,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,4,5,2,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,3,6,1,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,2,3,8,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,4,5,8,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,5,2,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,3,1,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,1,3,6,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,1,8,3,6,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,1,4,8,6,3,7,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[6,4,8,2,5,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,6,8,4,1,5,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,8,1,4,5,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,1,6,8,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[2,8,1,4,6,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,6,2,3,7,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,7,5,3,4,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,5,8,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,5,8,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,3,8,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,4,7,3,5,8,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,7,1,8,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,2,8,3,1,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,2,3,6,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,3,6,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,4,3,6,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,1,3,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,5,3,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,5,3,7,1,2,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,5,1,3,6,2,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[6,4,1]=>3
[4,2,6,5,1,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[4,3,5,7,2,1,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[3,4,7,6,8,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,4,6,2,5,8,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[4,2,5,1,6,8,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[1,8,2,3,6,5,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,8,3,5,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,3,7,2,6,5,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,4,7,3,6,8,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,2,3,8,4,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,6,2,7,3,1,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[1,5,3,7,6,8,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,3,7,8,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,3,7,8,5,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,2,6,5,7,8,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[4,2,6,7,5,8,1,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,2,2]=>2
[3,2,4,7,8,5,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,3,2]=>3
[3,2,6,7,8,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[5,1,8,3,6,4,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,8,5,7,2,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,1,3,8,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,8,5,6,1,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,1,7,6,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,7,6,8,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,7,4,8,5,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,3,6,8,7,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[1,8,4,6,7,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,8,3,7,1,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,6,8,7,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,4,8,3,1,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,5,8,7,1,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,7,4,8,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,6,4,8,2,7,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,8,3,1,7,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,3,8,2,7,5,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,3,8,1,7,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,8,1,3,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,3,8,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,1,3,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,3,4,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,4,3,7,8,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,2,7,8,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,2,8,7,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,7,6,3,1,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[6,3,1,7,5,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,3,1,8,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,7,6,3,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[1,8,2,7,6,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,8,6,3,7,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,8,2,7,5,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,7,4,1,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,2,8,7,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,3,7,6,5,8,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,4,8,7,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,7,5,2,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,3,1,4,7,5,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,3,1,4,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,8,2,5,7,6,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,6,4,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,8,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,7,4,1,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,4,7,5,2,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[1,6,4,7,5,3,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,3,5,2,8,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,5,2,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,5,7,2,6,3,1,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[3,5,8,4,6,1,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,4,7,3,5,2,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,7,4,2,6,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,2,6,3,5,7,1,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[1,4,5,8,2,7,3,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[2,4,5,8,1,6,7,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,2,5,7,8,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[4,1,7,3,5,2,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[6,1,3,7,4,2,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,1,6,8,2,7,4,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[6,1,3,8,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,8,2,3,1,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,6,8,1,5,7,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[5,7,4,2,8,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,3,7,2,8,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[2,7,3,8,1,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,8,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,5,7,2,8,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,5,6,8,3,1,7,2]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[5,6,4,8,3,1,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,4,7,1,2,6,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,8,1,6,2,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,3,1,7,2,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[4,7,3,1,2,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,2,7,1,3,6,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[4,8,3,1,2,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,3,6,5,7,8,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[6,1,3,4,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,2,4,1,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[2,6,5,3,1,7,8,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,7,4,3,6,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,6,3,1,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,6,3,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,5,7,4,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,6,5,7,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,6,2,7,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,5,3,8,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,6,5,8,3,4,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,1,5,3,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,5,8,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,7,2,8,5,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[1,4,8,7,3,5,6,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,6,8,5,7,4,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,7,6,8,5,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,2,8,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,8,7,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,6,4,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,7,2,5,3,1,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[3,6,7,4,8,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,8,5,7,6,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,4,7,8,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,7,8,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,2,6,8,7,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,1,7,8,2,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,1,3,8,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,1,8,4,2,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,7,1,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,3,8,1,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,8,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,8,4,1,7,5,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,5,8,6,3,1,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,7,1,2,8,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,6,1,8,2,7,5,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,7,4,1,2,8,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,3,7,1,2,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,2,1,8,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,7,8,3,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,4,8,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,8,7,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,2,6,7,8,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[2,7,5,8,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,7,8,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,7,8,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,5,8,6,7,4,1,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,6,8,4,7,1,5,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,7,1,3,6,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,6,4,8,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,1,7,5,6,8,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,3,6,5,7,1,8,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]=>[4,2,2,2,1]=>7
[3,7,5,4,2,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,3,6,7,4,2,8,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[3,6,4,8,2,7,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,7,8,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,8,5,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,8,4,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,8,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,2,3,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,2,3,6,5,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,8,4,7,2,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,8,5,4,6,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,5,4,6,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,1,6,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,5,4,6,1,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,5,4,6,3,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,5,4,6,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,8,4,7,3,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,6,4,2,7,8,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[4,5,8,1,7,6,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,8,4,7,1,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,5,8,4,7,3,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,6,4,1,7,8,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[3,6,4,8,7,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[1,6,4,3,7,8,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,4,2,7,8,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,6,4,3,7,1,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,1,7,8,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,4,8,7,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,5,8,4,7,6,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,8,1,6,7,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,1,6,5,8,2,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,1,6,5,8,4,7,2]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[3,2,6,5,8,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,3,7,1,6,5,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,2,6,4,8,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,1,6,4,8,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,1,6,4,8,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,6,4,8,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,3,7,5,8,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,7,5,8,2,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,3,7,4,8,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,7,4,8,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,8,1,6,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,7,2,6,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,7,1,5,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,3,7,1,6,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,4,8,2,6,3,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,1,6,3,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,7,5,2,3,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,1,7,8,6,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,7,2,8,3,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[1,2,6,8,3,7,4,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,8,3,2,1,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,4,1,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,4,7,6,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,2,7,5,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,2,7,3,8,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,5,2,6,8,3,7,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,8,3,2,5,7,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,1,5,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,3,5,1,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,4,3,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,3,8,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,7,3,5,6,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,7,8,4,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[3,1,6,8,4,7,5,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,2,7,5,8,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,5,4,7,8,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,4,6,7,8,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,1,7,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[3,2,7,6,1,8,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[4,3,6,2,1,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,6,4,2,5,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[4,6,2,3,7,5,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[5,8,4,2,3,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,3,4,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,4,2,3,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,8,3,2,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,3,7,2,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,6,4,7,1,8,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,5,4,8,1,6,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,4,7,3,8,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,4,3,2,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,2,6,5,8,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,5,2,8,4,6,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,2,7,4,6,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,2,7,3,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,1,2,8,3,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,6,3,4,8,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,5,3,4,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,1,2,8,3,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,2,7,3,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[5,8,1,2,3,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,8,2,3,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,7,2,3,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[1,6,8,2,4,5,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,3,8,7,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,8,2,7,4,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,3,7,4,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,7,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,2,4,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,4,6,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,7,5,1,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,2,5,8,7,3,6,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[1,8,3,5,7,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,4,6,8,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[2,3,5,7,4,8,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,4,6,3,7,8,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,5,7,1,8,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,3,8,5,2,4,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,6,7,1,8,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,8,3,1,4,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,4,2,6,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,1,8,5,6,3,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,6,2,7,8,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,5,2,6,7,8,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[4,3,1,1]=>5
[4,5,1,6,7,3,8,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,1]=>3
[2,8,4,1,7,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,8,7,1,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,6,8,1,7,4,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,7,3,2,6,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,7,1,2,3,5,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[3,1,6,7,8,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[3,1,4,8,5,6,2,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[1,6,7,8,9,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1,1,1,1]=>[3,2,1,1,1,1,1]=>11
[6,7,8,9,1,2,3,4,5,10]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,1]=>[3,2,1]=>3
[6,7,8,1,2,3,4,5,9]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1]=>[2,1]=>1
[1,7,8,9,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[1,7,8,9,10,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,1,1,1,1,1]=>[3,2,1,1,1,1,1,1]=>13
[5,6,7,1,8,2,3,4,9]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1]=>[4,2,1]=>3
[4,6,7,8,1,2,3,5,9]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,1]=>[3,2,1,1]=>5
[1,6,7,8,2,9,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,1,1,1,1]=>[3,2,1,1,1,1,1]=>11
[1,5,7,8,9,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,1,1,1,1]=>[3,2,2,1,1,1,1]=>14
[1,6,7,8,9,10,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,1,1,1,1]=>[4,3,2,1,1,1,1,1]=>18
[2,6,3,8,7,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,1,3,8,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,6,1,8,7,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,8,1,5,7,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,2,8,7,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,4,8,2,7,6,5,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,7,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,1,8,5,7,6,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,2,4,7,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,3,7,4,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,8,5,7,6,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,2,1,8,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,8,2,7,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,3,7,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,2,1,7,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,8,7,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,1,3,7,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,4,8,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,1,3,7,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,1,7,6,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,8,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,6,3,2,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,5,7,2,4,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,7,1,3,2,8,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,8,1,3,2,7,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,2,5,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,4,8,2,3,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,7,8,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,8,1,5,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,4,3,6,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,6,5,2,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,6,5,1,3,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,4,6,8,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,7,4,2,1,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,3,2,1,8,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,7,6,3,2,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,2,1,7,3,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,5,8,1,7,3,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,3,4,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,2,8,5,3,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,7,4,1,6,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,5,8,2,6,1,7,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,7,6,1,5,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,7,6,2,5,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,5,8,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,6,5,8,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,2,8,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,3,6,8,5,1,2,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[2,7,1,5,8,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,1,8,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,8,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,1,2,5,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,1,2,7,8,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[4,7,3,1,2,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,7,6,1,5,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,4,2,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,6,4,7,8,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[4,2,7,5,8,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,2,7,1,3,8,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,2,1,4,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,6,2,7,3,4,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[6,1,3,8,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,6,8,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,8,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,8,6,4,2,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,5,8,6,4,1,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,6,2,3,5,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[4,7,2,3,1,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,7,3,1,5,4,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,3,8,2,6,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,2,5,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,6,2,5,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[5,1,8,6,4,7,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,5,6,3,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,6,1,5,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[6,7,2,3,1,5,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,5,1,7,6,3,8,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,5,1,6,2,8,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[4,8,3,6,1,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,2,7,8,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[7,2,3,4,5,6,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[6,2,3,4,5,1,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[2,1,7,5,8,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,7,3,8,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,8,7,4,6,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,7,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,8,6,7,5,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,7,6,5,8,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,6,7,8,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,5,3,8,2,7,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,8,5,4,1,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,7,2,5,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,3,8,7,5,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,6,4,1,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[6,8,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,4,8,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,2,5,1,7,8,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[1,4,5,3,8,2,6,7]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[5,1,8,2,4,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,5,4,8,2,3,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,5,1,4,7,8,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[4,8,3,1,6,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,8,2,6,5,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,6,2,4,8,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[4,7,3,2,6,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,7,2,5,8,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[1,5,6,8,3,7,2,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[6,1,5,8,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,6,8,1,3,4,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,8,5,6,3,4,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,1,3,5,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,2,4,8,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,1,7,8,5,4,6,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[1,6,2,7,4,8,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,7,1,8,4,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,1,8,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,7,6,3,5,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,6,8,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,2,8,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[5,1,6,8,7,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[1,5,7,6,8,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,1,5,7,8,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[3,3,2,2,2]=>6
[4,6,2,5,7,1,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[3,8,6,7,5,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,5,8,6,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[1,6,8,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,6,8,1,5,4,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,5,4,7,6,2,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,3,7,6,5,1,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,1,5,8,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,7,5,3,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[2,7,6,4,8,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,2,5,3,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,8,4,1,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,4,8,3,7,1,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,2,8,4,1,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,7,5,1,8,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,1,3,2,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,2,7,6,3,5,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,7,8,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,1,6,8,3,7,4,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,6,2,7,4,3,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[3,7,8,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,7,3,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,6,5,1,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,5,1,2,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,5,1,7,6,8,2]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]=>[4,4,2,1]=>5
[3,8,7,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,2,6,1,8,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,2,6,1,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,8,2,6,1,4,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,7,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,7,2,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,3,4,5,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,2,1,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,2,5,4,3,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,7,3,4,8,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,1,8,7,5,6,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,5,8,7,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,4,1,3,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,1,7,4,6,8,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,7,2,4,6,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,2,7,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,6,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,8,3,5,7,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[3,5,8,1,7,6,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,8,1,3,6,7,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,3,2,8,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,4,3,8,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,8,4,3,1,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,7,2,4,6,10,1,3,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[2,10,7,9,4,6,8,1,3,5]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[8,7,6,5,2,4,10,1,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]=>[6]=>0
[6,10,5,9,8,7,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,10,3,9,2,6,8,1,5,7]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,10,7,9,2,6,8,1,5]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[8,7,3,6,2,5,4,10,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[7,6,3,5,10,2,4,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,10,4,9,3,8,2,7,6,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,9,8,7,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,12,9,11,4,6,8,10,1,3,5,7]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[2,12,5,11,8,10,7,9,4,6,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[2,12,7,11,6,10,5,9,4,8,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[2,12,6,9,5,8,7,11,4,10,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[4,2,8,1,5,7,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,7,2,5,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,4,7,3,2,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,7,2,6,3,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,7,5,4,6,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[6,8,3,2,1,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,1,7,5,3,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,3,7,2,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,6,5,7,2,8,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[4,6,5,3,8,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,6,5,8,7,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,8,4,1,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,8,7,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,4,2,8,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,8,7,5,3,1,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,6,3,1,4,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[6,2,1,1,1]=>7
[2,4,7,8,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,5,3,2,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,8,7,3,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,4,7,8,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[3,3,3,2,2]=>6
[6,1,4,3,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,1,2,7,5,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,7,3,1,4,6,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,1,6,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,5,6,7,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,1,2,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,5,8,1,4,6,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,1,8,7,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,7,2,8,6,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,5,2,3,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,4,7,5,2,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,5,2,3,7,8,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,6,3,8,7,5,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,8,4,1,5,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,2,5,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,4,1,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,8,3,7,1,6,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,8,5,2,4,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,6,2,8,7,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[2,4,6,1,8,7,5,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,8,4,5,1,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,8,2,7,6,1,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,1,6,8,7,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[1,8,2,4,5,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,5,7,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,2,5,7,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,3,8,1,5,7,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,6,1,8,7,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,6,2,8,7,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,3,8,7,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,3,8,7,5,1,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,2,8,1,5,7,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,2,5,7,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,1,4,5,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,6,8,7,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,1,6,8,7,2,5,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,8,4,5,1,6,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,4,5,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,3,8,6,2,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,1,4,5,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,8,4,6,2,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,6,8,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,4,8,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,8,1,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[1,6,5,8,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,7,1,6,2,4,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,1,2,7,6,8,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,1,7,2,5,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,7,6,5,8,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,5,2,7,8,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[1,6,3,8,7,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,3,2,4,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,2,7,8,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[5,1,2,6,8,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[1,8,6,2,5,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,8,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,7,1,2,8,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,5,8,7,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,9,3,4,5,6,7,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,4,5,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,3,4,5,6,7,8,9,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,10,9,4,5,6,7,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,7,4,8,2,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,6,1,4,2,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,4,1,7,2,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[6,4,7,3,2,5,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,4,5,7,8,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,7,4,1,6,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,1,2,7,6,8,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[6,3,2,8,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,8,3,5,4,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,5,2,4,6,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,4,8,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,4,8,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,8,2,5,3,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,4,5,2,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,8,6,5,3,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,7,8,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,3,2,8,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,8,1,2,7,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,3,6,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,1,3,2,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[2,5,1,3,7,8,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[4,3,7,2,1,8,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,6,7,2,1,3,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[4,6,2,3,1,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[3,6,4,2,5,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,1,6,4,7,5,2,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[3,6,2,7,5,4,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[2,4,7,5,3,6,1,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,7,3,4,1,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,3,5,8,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,4,7,3,8,6,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,2,7,5,8,6,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[3,3,3,1]=>3
[3,1,5,4,7,8,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[4,5,7,2,3,1,8,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,7,8,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,5,8,7,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,4,7,5,3,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,2,4,7,1,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,4,7,1,3,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,1,4,7,5,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,1,8,4,7,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,7,3,6,1,2,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,2,1,7,4,3,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,7,6,2,3,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,3,6,1,8,7,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,6,8,7,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,4,1,7,5,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,7,8,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,8,7,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,7,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,7,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,3,7,5,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,7,3,1,8,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,6,7,5,3,4,8,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,4,5,7,3,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,1,4,5,8,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,8,5,3,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,1,5,6,8,3,7,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[6,4,1,8,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,7,2,6,8,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[8,1,2,3,4,5,6,7,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[1,3,8,5,2,7,4,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,8,3,7,6,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,3,8,7,6,2,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,2,6,7,8,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,5,6,8,1,2,7,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[3,5,8,6,1,2,7,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,6,8,7,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[1,4,6,8,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,5,3,8,1,7,2,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,5,8,4,1,7,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,6,5,7,8,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,6,4,8,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,5,4,8,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,7,5,2,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[2,5,7,4,6,1,3,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,1,7,4,5,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[2,6,4,8,3,1,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,1,6,5,7,8,2,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[6,1,3,7,4,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,7,2,4,1,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,3,8,2,5,6,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,8,6,7,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,3,8,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,6,7,5,2,8,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[5,4,6,7,8,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,3,6,7,8,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,3,7,6,8,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,4,8,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,8,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,7,3,6,2,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,5,6,3,8,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[5,4,8,7,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,4,7,8,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,3,6,4,8,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,3,7,4,6,2,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,5,6,2,7,3,8,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,2,1]=>3
[5,4,6,2,8,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,2,1,6,3,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[4,5,6,3,7,1,8,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,2,1]=>3
[6,3,2,8,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,8,4,1,5,2,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,5,4,3,8,1,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,5,7,4,3,1,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,3,4,2,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[3,7,5,4,1,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,2,5,1,3,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[5,3,4,1,7,2,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[4,1,6,3,5,2,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,2,1,8,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,7,2,5,6,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,7,5,4,2,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,4,1,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[2,8,6,1,7,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,2,7,5,6,3,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[2,8,5,1,6,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,4,5,3,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,4,1,5,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,1,8,6,3,7,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,3,1,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,3,8,7,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,2,6,8,7,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,3,8,5,7,2,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,8,5,4,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,4,5,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,3,1,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,4,1,3,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,3,4,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,1,4,3,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[4,2,7,3,8,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,7,3,2,8,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,3,7,2,8,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,3,1,2,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,4,3,1,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,3,4,1,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,3,4,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,1,7,3,4,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,8,7,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,3,4,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,2,8,1,6,7,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,1,7,8,2,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,2,3,7,4,1,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,3,7,4,1,2,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[3,7,2,8,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,7,5,1,2,4,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[2,1,4,8,3,7,5,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[1,2,7,8,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,8,1,4,3,2,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,3,5,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,7,8,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,3,7,8,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,5,6,4,8,1,7,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,5,4,6,7,1,8,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[4,3,1,1]=>5
[1,5,2,6,4,8,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,6,2,5,3,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,3,5,4,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,6,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,4,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,4,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,3,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,7,4,8,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,2,8,5,7,6,3]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,8,1,3,2,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,5,3,8,4,7,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,8,4,7,3,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,3,8,1,5,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,8,7,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,7,3,5,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,3,8,7,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,3,8,7,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,8,5,3,1,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,7,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,4,1,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,5,8,7,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,8,7,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,3,8,7,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,8,7,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,8,6,4,2,7,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[6,8,4,1,5,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,1,7,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,4,6,1,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,8,6,5,1,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,2,1,8,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,5,8,3,1,6,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,7,2,8,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,7,3,2,4,8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,2,7,8,4,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,7,8,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,7,4,8,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,8,5,1,7,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,8,3,7,4,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,1,6,3,4,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[3,5,2,6,4,8,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[3,5,2,4,8,1,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[6,3,8,2,4,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,3,8,7,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,3,8,7,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,4,2,1,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,6,4,3,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[6,5,3,1,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,1,7,8,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,8,1,7,6,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,8,2,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,2,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,5,6,3,8,2,4,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[2,6,7,4,3,8,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,2,4,7,3,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[1,5,8,7,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,8,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,7,2,8,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,2,6,1,5,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[1,7,8,3,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,8,3,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,4,8,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,4,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,7,4,5,6,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,3,4,5,6,8,1,2,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]=>[5]=>0
[1,8,4,5,6,7,9,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,6,4,2,3,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,8,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,7,2,3,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,5,6,2,3,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,2,8,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,7,5,8,2,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,5,2,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,5,8,6,3,7,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[2,5,8,4,6,1,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,3,8,6,1,7,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,3,5,8,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,3,2,5,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,2,8,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,8,4,6,1,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,8,6,1,4,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,6,5,4,8,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,4,6,8,5,3,7,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,8,1,7,6,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,8,1,5,7,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,4,1,5,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,6,8,5,2,7,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,6,8,5,4,2,7,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,6,4,8,5,2,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,6,4,1,8,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,6,4,1,5,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[4,8,6,5,1,3,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,3,5,6,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,2,4,7,1,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[2,7,5,4,6,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,7,4,6,1,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,6,7,4,1,3,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,5,7,4,1,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[2,4,6,3,5,7,8,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[5,2,2,1,1]=>8
[4,1,6,3,5,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,6,4,2,5,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[2,3,6,1,5,7,8,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]=>[5,2,2,2,1]=>7
[4,3,6,2,5,7,8,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[4,6,1,2,5,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[2,6,4,1,5,7,8,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,4,1,6,5,7,8,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1]=>[5,3,3,1,1]=>8
[4,7,3,1,8,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,6,4,2,7,1,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[4,2,7,5,3,1,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,3,6,4,8,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,6,3,8,7,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,6,3,8,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,7,3,8,6,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,3,2,6,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,3,2,6,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[2,7,5,3,1,8,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,7,5,8,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,7,5,2,6,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,3,5,2,8,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,5,3,6,8,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[1,2,9,4,5,6,7,8,3]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[1,2,8,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,5,3,4,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,9,5,4,6,7,8,3]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[1,9,4,3,5,6,7,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,2,10,4,5,6,7,8,9,3]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,1]=>7
[3,5,6,7,8,9,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,2,6,4,1,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[2,8,6,5,3,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,8,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,8,7,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,4,7,6,8,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,4,2,8,7,5,1,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[6,4,1,8,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,5,4,2,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,6,1,5,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,8,2,7,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,4,7,1,3,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,1,3,8,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,8,5,2,4,7,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,1,4,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,9,1,2,3,5,6,7,8]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,9,1,2,4,5,6,7,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,3,4,5,6,7,9]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,4,5,8,6,3,2,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[4,5,2,6,7,3,1,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]=>[4,3,1]=>3
[5,2,8,3,6,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,6,3,1,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[4,3,5,1,6,7,8,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[5,4,2]=>3
[5,7,6,1,2,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,6,7,5,1,2,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[1,7,6,8,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,6,8,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,6,3,7,1,4,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[5,3,2,1,8,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,8,6,4,5,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,9,8,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,9,8,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,9,8,5,7,6,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,10,9,8,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,11,10,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2,2]=>0
[1,8,7,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,7,6,5,4,3,2,10]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,1,8,7,6,5,4,3,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[1,8,5,4,6,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,8,3,7,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,4,3,2,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,3,8,2,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,4,8,3,2,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,4,3,2,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,8,3,1,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,6,7,3,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,3,2,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,3,8,2,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,8,4,3,2,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,3,8,2,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,5,6,7,8,1,2,9,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1]=>[4,3,2,1]=>6
[4,5,6,7,1,2,8,9,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1]=>[6,3,2,1]=>6
[4,5,6,1,2,7,8,9,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1]=>[6,5,2,1]=>6
[4,5,1,2,6,7,8,9,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1]=>[6,5,4,1]=>6
[6,4,2,3,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,2,3,6,1,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[5,2,3,8,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,3,7,4,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,8,6,4,7,2,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,1,8,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,8,2,5,7,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,3,4,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,4,7,8,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,8,5,1,4,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,1,3,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,8,5,2,7,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,7,8,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,7,4,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,2,3,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,5,8,3,7,2,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,7,2,8,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,5,1,8,4,6,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,2,1,5,6,8,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[5,4,3]=>3
[4,1,2,6,5,8,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,1,8,3,2,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,7,5,8,1,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,6,2,7,8,3,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[4,6,1,3,8,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,3,6,2,1,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,7,4,5,1,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,5,8,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,1,4,5,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,5,4,8,6,3,2,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,8,7,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,2,6,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,1,8,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,8,5,6,7,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,7,4,8,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,3,6,8,2,7,1,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,3,7,4,8,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,3,6,1,4,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[4,3,6,8,2,7,1,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,3,7,4,8,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,8,4,1,6,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,1,4,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,1,6,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,8,3,6,7,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,8,2,5,6,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,8,1,5,7,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,8,1,2,3,4,5,9,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1]=>0
[2,8,9,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,9,10,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[7,1,8,2,9,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[4,2]=>[2]=>0
[6,1,7,2,8,3,9,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2]=>[4,2]=>1
[5,1,6,2,7,3,8,4,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2]=>[6,4,2]=>3
[8,1,9,2,10,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[5,1,3,7,4,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,1,3,4,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[2,5,8,7,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,1,7,8,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,5,4,8,3,7,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,6,8,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,3,5,7,4,6,8,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]=>[3,3,2,2,1]=>8
[4,5,2,3,8,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,7,4,5,8,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[5,8,2,1,6,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,3,7,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,4,7,8,5,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,3,1,4,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[4,3,8,5,1,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,7,5,8,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,3,5,8,2,1,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,8,5,3,7,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,5,7,3,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,5,1,3,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,8,5,1,3,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,8,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,4,7,5,8,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[1,8,5,7,2,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,4,2,3,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,6,8,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,6,3,8,2,7,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,2,7,5,8,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,8,2,3,6,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,6,8,2,7,5,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,6,5,4,3,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,3,4,5,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,2,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,5,8,3,6,2,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,2,7,8,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,2,8,7,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,4,3,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,8,4,3,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,7,3,2,6,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,7,3,6,2,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,6,2,7,1,5,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[1,4,3,6,8,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[1,5,3,7,6,8,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,4,5,7,8,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,2,6,5,7,8,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,2,2]=>2
[3,2,5,7,6,8,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[3,2,4,6,8,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[5,3,2,6,8,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[3,1,8,6,4,7,2,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,8,5,4,2,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[5,3,2,8,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,8,2,7,6,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,4,8,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,8,5,1,3,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,7,2,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,7,5,1,8,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,5,6,2,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,5,8,7,3,1,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,4,5,8,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,1,5,8,6,7,2,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,3,7,6,1,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,7,5,6,1,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,3,7,5,6,2,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,5,1,8,6,7,3,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,5,8,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[2,1,5,8,6,7,4,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[3,4,5,8,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[4,7,1,5,6,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,6,4,7,1,3,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,3,8,6,4,7,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,1,5,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[3,6,4,7,2,1,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[3,8,4,6,1,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,4,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,5,6,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,5,2,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,5,1,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,1,7,3,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,1,4,6,7,2,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[6,5,4,7,1,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,1,4,7,2,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,6,2,5,4,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[4,1,2,7,5,8,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[6,1,3,5,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,4,3,1,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[6,2,3,5,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,2,3,8,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,2,1,3,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,7,4,1,8,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,1,7,5,8,3,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[6,7,1,3,8,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[1,6,7,4,3,8,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,4,2,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,1,6,7,4,3,8,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]=>[3,2,2,2,2]=>4
[6,7,3,2,1,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,5,7,3,1,4,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,7,3,2,8,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,7,1,8,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,8,1,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,1,8,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,4,5,8,3,1,6,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,7,4,6,1,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,3,8,5,1,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,5,6,7,3,8,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,6,5,4,8,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,3,5,8,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,7,2,4,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,6,4,8,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,8,7,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,8,7,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,7,6,5,4,2,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[4,7,1,6,5,3,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,8,1,6,5,3,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,1,8,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,1,7,6,3,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,4,1,8,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,7,6,1,4,3,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,8,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,5,1,4,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[1,8,6,3,4,2,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,6,4,5,8,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[3,1,6,4,5,8,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[4,6,8,7,2,5,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,2,7,8,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,6,3,8,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,2,3,4,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,2,3,7,1,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,2,3,4,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,4,7,8,5,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,2,6,7,4,1,5,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[5,8,3,7,6,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,1,7,2,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,6,7,1,4,2,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[4,7,5,8,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,5,1,8,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,8,7,5,3,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,5,1,4,6,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,1,4,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,8,1,7,5,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,5,7,1,4,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[5,2,6,7,4,8,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[1,7,5,2,6,4,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,5,7,8,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[6,7,4,1,3,2,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,7,2,8,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,7,8,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,3,4,7,8,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,2,1,5,7,8,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[5,4,1,6,7,8,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[5,1,4,6,7,8,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[4,1,5,3,7,8,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[6,7,4,1,8,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,2,4,3,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,1,5,4,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,2,8,7,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,2,1,7,5,8,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[1,3,6,4,7,8,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[4,5,1,3,7,8,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[5,2,3,1,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,6,4,3,7,8,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,6,3,7,8,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[7,1,2,3,4,5,8,9,10,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6]=>[7,6]=>1
[6,7,1,2,3,4,8,9,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1]=>[6,1]=>1
[6,8,3,5,7,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,3,8,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[7,8,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1]=>0
[2,3,8,4,7,5,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,7,2,8,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,3,7,5,8,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,3,7,8,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,8,1,7,5,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,7,8,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,5,1,7,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,8,3,5,1,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,5,3,8,2,1,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,8,3,2,5,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,7,1,3,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,5,6,7,8,9,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,7,4,6,8,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,2,8,6,5,3,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,4,8,5,2,6,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,5,3,2,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,1,3,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,2,3,7,8,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,2,8,6,3,1,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,3,5,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,4,5,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,2,5,3,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,5,7,8,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[1,2,8,4,3,6,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,3,2,4,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,5,3,4,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,4,5,3,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,3,2,6,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,1,7,8,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,7,8,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,5,8,6,1,4,2,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,8,4,2,7,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,4,1,8,7,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,5,1,7,8,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[5,4,7,8,2,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,6,1,8,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,3,8,7,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,7,1,5,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[3,4,6,2,1,8,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[4,5,7,2,1,6,3,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[5,6,4,8,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,7,4,8,2,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,7,5,8,2,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,4,2,6,3,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,4,1,6,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,5,1,6,7,8,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[4,5,2,6,1,3,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1]=>3
[3,4,6,7,2,5,8,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[6,7,1,2,4,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,6,3,4,7,8,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,3,6,4,7,5,8,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,8,2,6,7,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,3,2,8,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,8,7,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,8,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,7,6,2,4,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,3,7,2,8,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[6,1,2,7,4,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,1,2,6,3,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[5,1,2,7,3,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,1,2,7,3,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,2,1,5,3,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]=>[6,5,3]=>3
[7,5,4,3,2,1,8,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]=>[6]=>0
[7,5,3,2,1,8,6,4,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]=>[5]=>0
[7,4,3,2,1,8,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,5]=>[5]=>0
[6,4,3,2,1,7,5,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5]=>[7,5]=>1
[7,5,3,1,8,6,4,2,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,4]=>[4]=>0
[5,3,2,1,6,4,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4]=>[7,6,4]=>3
[6,2,1,7,3,8,4,9,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3]=>[5,3]=>1
[8,6,5,4,3,2,1,9,7,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,7]=>[7]=>0
[8,6,4,3,2,1,9,7,5,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,6]=>[6]=>0
[8,6,4,2,1,9,7,5,3,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,5]=>[5]=>0
[6,2,5,4,1,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,3,2,1,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[6,5,3,2,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,5,8,4,7,6,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,2,7,4,8,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[6,8,3,7,5,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,8,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,4,3,8,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,3,2,8,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,2,5,4,8,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[3,2,8,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,8,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,8,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,1,4,8,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[5,8,1,3,7,2,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,5,1,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,3,2,1,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,1,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,4,7,1,8,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,1,7,5,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,2,8,1,7,5,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,4,1,5,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,8,6,1,2,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,1,4,3,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,1,4,3,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[4,7,1,5,3,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,8,1,2,4,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,4,1,3,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,4,3,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[1,8,3,6,7,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,7,4,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,9,2,3,4,5,6,7,8,10]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[4,6,7,2,1,8,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,7,1,8,2,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,6,1,3,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,6,2,7,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,7,1,5,3,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[4,6,7,2,1,8,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[4,2,5,6,7,8,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[4,1,3,5,6,7,8,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[3,7,8,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,6,8,3,2,7,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,8,2,3,7,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,8,1,7,4,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,3,7,1,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,7,8,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,5,7,8,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[3,8,2,5,4,7,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,5,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,6,2,1,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,6,1,2,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,8,5,2,7,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,7,8,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,5,4,1,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,6,8,5,3,1,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,1,3,7,6,4,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,6,5,2,7,8,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[1,6,5,2,3,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[4,6,5,1,7,3,8,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[5,7,3,1,2,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,3,2,5,1,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,1,2,4,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,1,7,2,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,7,2,8,5,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,2,4,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,6,5,8,1,7,2,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,2,7,3,4,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[1,3,5,8,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,3,5,8,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[6,1,7,4,8,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,7,4,1,3,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,1,7,6,3,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,2,7,3,8,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,2,7,5,3,4,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,2,7,8,3,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,7,8,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,8,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,2,8,7,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,8,1,5,7,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,5,7,8,3,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,4,3,1,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,1,3,7,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,5,7,4,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,6,8,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[4,5,1,3,8,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[1,2,6,8,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[5,6,8,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,7,5,3,8,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,2,3,4,7,1,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,8,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,8,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,1,4,2,6,8,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[6,3,2,4,7,1,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,5,6,8,4,2,3,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,7,8,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,5,8,6,2,4,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,3,7,2,6,8,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,8,6,2,4,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,6,3,7,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,2,4,8,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,7,6,3,8,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,6,8,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,8,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,6,4,3,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,6,3,4,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,6,2,8,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[1,7,2,3,5,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,2,3,5,1,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[2,8,3,7,5,1,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,8,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,4,3,6,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,8,2,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,1,2,8,5,3,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,8,4,2,5,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,5,6,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,5,6,4,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,5,7,6,8,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[2,7,1,4,5,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,2,7,4,3,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,1,3,8,4,6,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,8,7,1,3,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,7,3,5,1,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,8,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[1,7,2,5,6,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,4,8,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,4,5,3,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,3,2,8,4,5,7,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,6,8,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,2,5,3,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,2,8,3,6,7,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,2,5,3,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[8,3,4,5,6,7,1,9,10,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[7,3,4,5,6,1,8,9,10,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6]=>[7,6]=>1
[4,1,3,7,2,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[6,2,7,5,1,3,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[1,7,5,6,2,3,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,6,1,2,4,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,7,4,3,8,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,3,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,6,7,5,2,8,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[5,8,1,3,6,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,4,3,7,1,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,6,7,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,3,8,4,7,1,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,4,7,8,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[1,6,4,7,8,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,2,3,6,7,8,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[6,2,7,3,8,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,3,7,8,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,5,8,4,7,1,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,5,8,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,1,8,5,7,2,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,8,7,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,5,4,1,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[6,2,5,1,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,4,1,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,3,5,4,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,3,8,7,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,8,4,5,1,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,1,8,5,7,6,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,8,4,2,3,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,2,8,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[2,8,3,7,4,1,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,1,8,7,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[4,2,8,7,3,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,3,4,8,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,4,8,2,6,7,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,6,8,2,5,1,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,8,2,5,7,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,8,5,4,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,5,4,1,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,1,5,7,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,2,7,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,4,7,3,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,7,6,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,8,1,7,4,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,3,1,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[3,2,1,9,8,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[2,3,4,7,6,8,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[3,8,1,2,5,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,2,5,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,6,5,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,6,3,8,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,5,2,6,7,1,8,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,1]=>3
[2,8,6,4,7,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,6,5,2,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,2,4,1,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,3,2,4,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,3,2,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,2,4,6,1,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[6,8,3,4,7,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,1,3,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,5,7,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,8,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,6,8,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,5,2,8,1,7,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,7,5,2,8,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,2,6,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,8,6,1,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,7,6,4,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,3,8,4,7,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,6,1,4,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,7,2,1,4,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,4,2,5,8,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,1,7,5,8,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,4,8,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,5,8,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,3,5,8,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[4,8,5,3,7,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,8,7,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,7,4,8,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,8,2,3,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,6,3,8,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[3,6,5,1,4,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[6,5,1,8,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,3,5,8,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,5,6,8,1,4,2,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[4,3,5,8,2,1,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[6,4,7,2,3,1,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,8,1,5,4,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,8,4,7,2,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,4,3,7,1,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[6,5,3,7,2,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[5,6,2,8,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,1,2,6,8,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[5,7,4,3,6,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,6,2,7,8,3,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,1,2,4,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,6,3,5,2,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,6,3,4,8,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,2,6,4,1,7,8,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,8,4,6,3,2,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,3,8,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,7,8,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,6,2,4,8,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,4,7,8,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,7,5,2,4,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,7,5,2,3,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,4,7,3,2,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,7,3,2,8,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,3,7,2,8,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,7,2,5,8,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,7,3,2,5,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,3,2,6,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,7,6,2,8,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,7,6,2,3,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,10,4,5,6,7,8,9,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,9,5,6,7,8,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,11,4,5,6,7,8,9,10,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,10,4,9,6,7,8,1,3,5]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,8,5,6,7,1,9,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,11,10,5,6,7,8,9,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,12,4,5,6,7,8,9,10,11,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[6,3,8,5,4,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,6,3,8,7,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,1,8,7,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,3,6,8,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,4,6,3,8,7,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,5,8,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,8,5,7,3,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,3,7,1,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,1,7,3,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,5,1,8,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,6,5,8,3,7,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,5,8,1,7,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,8,5,1,7,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,7,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,7,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,5,1,3,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,5,1,8,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,6,5,3,8,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,2,2,1,1]=>8
[2,4,6,5,8,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,8,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,7,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,8,7,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[3,2,2,1,1]=>8
[4,8,7,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,4,7,5,8,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,8,6,5,3,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,8,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,6,1,7,8,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[6,1,2,7,8,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,3,2,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,6,3,1,7,4,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[4,8,3,7,1,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,3,2,1,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,3,8,1,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,3,8,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,3,8,2,7,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,2,7,6,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,6,2,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,3,7,2,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,7,6,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,2,7,6,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,4,2,5,3,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,8,6,2,7,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,2,4,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,8,6,2,3,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,8,6,3,4,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,3,6,8,2,7,4,5]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,4,3,8,2,5,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,7,2,3,8,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,4,2,5,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,6,2,8,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,2,3,8,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,3,8,2,7,4,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,8,2,5,6,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,7,3,2,8,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,2,7,3,6,8,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,2,3,6,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,3,2,5,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,2,5,8,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,2,3,4,5,6,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[6,2,3,4,5,9,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,3,4,9,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,2,3,9,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,9,4,5,6,7,8,1]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,9,3,4,5,6,7,8,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,3,4,5,1,8,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,6]=>[6,6]=>0
[8,2,3,4,5,6,7,10,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[7,2,3,4,5,6,10,8,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,6,6]=>[6,6]=>0
[6,2,3,5,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,3,4,5,10,7,8,9,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[5,2,4,8,1,6,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,3,4,10,6,7,8,9,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[2,1,4,9,5,6,7,8,3]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,2]=>[3,3,3,3,2,2]=>8
[4,2,3,10,5,6,7,8,9,1]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[1,3,9,4,5,6,7,8,2]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1]=>[2,2,2,2,2,1,1]=>10
[3,2,10,4,5,6,7,8,9,1]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,10,3,4,5,6,7,8,9,1]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,6,4,5,7,3,1,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,5,6,3,4,7,1,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]=>[5,2,1,1,1]=>7
[1,3,7,5,6,8,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,6,7,4,5,8,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,7,5,6,8,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,6,3,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,7,5,2,8,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,2,5,8,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,3,7,4,6,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,3,7,6,4,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,6,3,7,4,2,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,5,7,6,3,4,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,3,6,4,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,7,2,5,6,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,5,6,2,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,5,7,4,1,3,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,7,3,1,8,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,3,1,5,8,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,3,5,8,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,3,6,4,1,8,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[4,7,5,2,1,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,5,7,3,1,2,8,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,5,1,8,3,2,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[5,7,4,6,3,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[3,6,1,2,4,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,5,3,8,4,1,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,3,1,2,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,7,5,2,3,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,6,8,4,5,1,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,2,3,7,6,4,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,2,7,3,5,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,2,8,4,5,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,3,1,7,8,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]=>[3,3,3,3,1]=>4
[6,8,7,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,5,3,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,8,5,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,3,1,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,6,2,3,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,5,4,2,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,3,8,2,1,6,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,7,4,1,8,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,1,7,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,2,1,8,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,1,7,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,7,8,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[4,5,3,7,8,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[1,5,4,7,3,6,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,7,3,6,8,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,8,2,7,3,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,6,3,5,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,5,7,8,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,7,5,6,2,1,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[6,2,1,7,4,5,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[2,6,8,4,7,5,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,7,5,1,4,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,8,2,7,3,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,5,7,3,8,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,6,8,4,2,7,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[6,4,1,8,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,7,4,3,8,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,4,2,7,8,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[2,4,7,8,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,7,8,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,5,2,7,8,6,3,1]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[4,6,2,5,3,1,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[2,6,7,5,4,1,3,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,1,6,7,5,3,2,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[3,2,2]=>2
[6,7,4,3,1,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[1,7,5,6,4,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,7,8,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,5,7,3,8,6,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[6,8,5,3,7,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,1,5,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,6,2,1,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,8,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,8,1,6,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,6,5,7,8,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]=>[4,2,2,2,1]=>7
[4,8,2,3,5,7,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,2,3,8,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[6,7,4,8,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[4,3,5,6,1,7,8,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]=>[5,3,2]=>3
[3,5,2,6,4,7,8,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[4,1,2,8,5,7,6,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,5,6,4,7,8,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]=>[5,3,2,2]=>5
[3,1,4,6,7,5,8,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2]=>[4,3,3,2]=>5
[2,6,4,5,8,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,4,1,3,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,4,1,7,2,6,8,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[3,3,3,1]=>3
[2,4,7,5,8,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,1,6,4,8,7,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[3,7,6,2,1,5,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,2,6,1,3,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[2,8,4,6,7,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,1,4,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,8,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[5,6,2,8,7,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,6,7,2,8,1,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[2,6,7,1,3,5,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,6,7,1,8,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,4,1,8,7,2,6,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,1,5,7,2,8,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[3,8,1,4,7,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,3,2,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,8,3,2,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,1,2,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,2,1,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,4,2,7,1,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,4,3,7,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,2,4,7,1,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,4,8,7,1,6,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[3,2,5,7,1,8,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[4,2,8,3,1,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,2,1,3,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,8,1,3,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,4,6,8,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[5,6,4,7,1,2,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[4,6,7,5,8,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[4,5,7,1,6,8,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,2,7,6,8,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,5,1,7,6,8,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[6,7,2,8,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,2,7,8,4,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,3,7,8,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,4,1,7,8,5,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[4,1,3,7,8,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[4,3,1,8,5,2,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,8,5,4,2,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,5,1,3,2,7,8,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]=>[5,5,1]=>2
[5,1,3,2,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[2,3,7,8,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,5,8,1,2,6,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,3,6,7,8,2,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[1,3,4,8,6,2,7,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,8,2,5,4,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,6,8,2,3,7,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,5,7,2,3,6,1,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[2,7,3,4,1,5,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,2,3,4,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[3,5,2,4,6,7,8,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,4,1,1]=>5
[4,2,6,3,5,7,8,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[1,4,8,5,6,2,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,8,5,6,1,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,3,5,8,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,7,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,3,8,5,2,6,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,2,3,5,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[1,6,4,3,2,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,5,2,3,6,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,5,3,8,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,2,6,8,3,7,1,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,2,5,8,6,7,1,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,8,6,3,4,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,2,4,1,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,4,7,8,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,3,8,4,1,6,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,1,7,4,5,6,2,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[2,4,8,3,5,7,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,3,8,2,4,7,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,7,2,4,6,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,3,2,4,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,4,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,4,3,5,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,8,7,4,1,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,2,1,7,4,6,5,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[3,2,6,5,1,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[5,3,2,6,7,1,8,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[3,2,8,6,7,4,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,3,8,6,7,2,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,6,2,8,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,8,4,7,6,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,7,8,6,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,5,6,8,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[5,7,8,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,5,4,2,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,2,1,7,6,3,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[4,1,6,5,2,7,8,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[5,4,1,6,7,2,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[6,8,5,3,1,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,6,3,8,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[1,8,3,6,7,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,2,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,5,7,3,2,6,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,3,7,2,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,1,4,8,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,4,8,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,7,1,5,2,4,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,6,7,3,5,4,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,3,5,6,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,3,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,4,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,7,6,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,7,5,6,8,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,6,7,4,3,1,8,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[2,1]=>1
[6,7,8,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,6,3,2,5,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,6,8,2,5,4,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,2,7,5,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,4,3,2,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,4,7,2,6,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,3,7,6,2,8,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,6,2,8,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,8,4,3,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,2,8,4,3,6,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,5,6,3,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,3,5,2,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,2,5,8,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,8,3,2,7,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,5,8,2,6,3,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,7,6,4,8,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,6,5,2,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,8,2,6,5,4,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,6,3,8,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,7,6,4,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,3,8,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,3,8,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,5,4,2,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,2,4,8,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,5,3,2,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,3,2,8,7,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[1,2,8,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,8,3,1,2,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,1,7,5,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,7,5,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,1,5,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,1,5,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,8,7,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,2,7,5,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,1,5,3,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,1,7,8,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,3,1,7,6,4,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[1,8,6,4,2,9,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,6,4,3,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,7,5,3,2,8,6,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,7,6,4,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,8,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,8,6,4,2,9,7,5,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,4,8,6,7,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,3,6,8,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,7,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,7,4,5,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,2,6,4,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,6,4,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,5,4,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,7,2,8,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,5,7,2,8,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,2,7,5,8,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,2,5,8,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,7,3,8,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,7,4,8,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,7,4,8,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,2,7,4,8,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,5,1,4,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[2,7,6,8,3,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,7,6,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,8,7,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,5,1,2,4,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[2,4,8,7,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,6,8,7,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,5,1,4,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[6,5,1,2,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,6,5,3,1,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,8,7,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,8,7,5,3,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,8,7,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,4,8,7,3,6,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[4,8,7,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,7,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,8,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,7,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,3,4,1,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,8,7,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,8,7,3,1,4,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,6,3,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,3,1,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,7,5,1,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,8,7,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,4,8,7,3,6,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,7,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,9,2,3,4,5,6,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,2,3,4,5,7,6,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,2,3,4,5,6,7,9,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[4,7,3,6,5,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[3,1,6,8,5,7,2,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[5,7,2,1,8,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,3,8,7,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,3,7,4,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,7,3,5,8,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,4,8,1,3,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,2,1,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,8,3,5,7,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,3,6,8,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,7,3,6,8,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[1,8,2,7,5,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,6,1,7,3,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,1,2,8,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,1,3,8,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[1,3,2,8,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[2,5,7,1,8,4,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,7,1,6,8,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[5,4,7,6,8,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[2,4,8,6,7,3,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,3,8,7,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,6,8,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,6,9,8,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]=>10
[1,4,9,8,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1]=>[2,2,2,2,1,1,1]=>12
[1,3,9,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1]=>[2,2,2,2,2,1,1]=>10
[1,8,10,9,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[6,7,9,1,8,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,7,10,9,8,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]=>12
[5,6,9,8,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,1,8,7,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,6,8,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,5,10,9,8,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1,1]=>[2,2,2,2,1,1,1,1]=>16
[4,5,8,7,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,9,8,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,4,10,9,8,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1,1]=>[2,2,2,2,2,1,1,1]=>15
[2,3,9,8,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,9,11,10,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>8
[1,7,6,9,8,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>6
[7,8,10,1,9,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,8,11,10,9,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1,1]=>14
[1,6,9,5,8,7,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]=>10
[6,7,10,9,1,8,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,1,8,4,7,6,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,7,9,5,1,8,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,6,11,10,9,8,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1,1,1]=>[2,2,2,2,1,1,1,1,1]=>20
[1,4,9,8,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1]=>[2,2,2,2,1,1,1]=>12
[5,6,9,8,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,10,9,8,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,5,11,10,9,8,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1,1,1]=>[2,2,2,2,2,1,1,1,1]=>20
[1,3,9,8,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1]=>[2,2,2,2,2,1,1]=>10
[1,5,8,4,3,7,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,4,10,9,8,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,4,9,8,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,2,10,9,8,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,7,1,5,4,8,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,1,6,7,5,8,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1]=>[4,3,3,1,1]=>8
[2,5,1,7,8,6,4,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,5,6,2,8,7,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[3,4,5,6,2,8,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]=>[5,3,2,1]=>6
[3,7,4,2,8,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,6,3,1,4,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,7,4,2,5,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,6,8,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,3,8,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,1,6,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,2,1,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,8,5,7,2,6,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,6,1,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,4,7,6,1,2,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[4,5,8,7,6,1,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,4,7,2,1,5,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,4,7,3,1,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,5,3,7,4,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,6,3,8,4,2,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,7,2,5,3,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[1,8,3,4,5,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,4,2,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,7,5,3,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,4,8,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,8,5,3,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,4,2,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[1,2,7,4,3,5,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,8,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,2,5,1,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,5,2,1,6,8,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[1,7,8,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,5,6,2,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,4,1,5,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,2,8,1,6,4,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,2,1,3,7,6,4,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,4,1,2,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,8,4,1,2,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,7,3,2,8,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,6,3,2,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,3,7,2,8,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,4,6,2,8,5,3,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,5,6,2,8,4,3,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[3,4,8,6,5,7,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,8,6,1,7,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,3,6,8,1,7,4,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,3,7,1,8,6,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,6,1,7,8,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,4,8,5,6,7,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,4,8,5,6,7,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,2,1,6,8,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[4,8,3,1,6,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,8,5,4,2,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,5,8,4,2,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,8,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,7,4,5,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,3,5,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[3,6,4,2,5,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[2,1,5,8,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[4,2,8,5,6,3,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,7,2,6,8,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,7,2,3,4,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[1,8,7,3,2,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,1,2,3,8,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,1,8,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,6,4,2,5,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,2,1,8,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[2,8,1,6,5,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,6,4,3,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[5,4,6,8,1,3,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,7,1,6,4,5,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,3,8,7,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,10,9,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1,1]=>[2,2,2,2,2,2,1,1]=>12
[6,7,3,4,8,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,1,7,2,5,6,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[4,1,5,7,3,2,8,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[6,4,1,7,2,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[4,8,2,5,3,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,3,4,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,1,4,5,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,4,7,1,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,8,3,5,6,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,5,1,6,8,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[5,4,2,7,8,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[6,8,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,6,8,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,3,8,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,7,5,1,8,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,2,1,5,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,3,2,8,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,8,3,2,7,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,1,7,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,7,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,7,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,8,2,1,7,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,7,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,4,2,8,1,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,8,4,2,1,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,4,7,1,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,8,3,1,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,7,4,1,2,5,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,6,7,4,2,5,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,6,7,5,8,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[1,6,7,5,8,3,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,8,6,5,7,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,1,6,8,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,5,8,7,4,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,7,5,8,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[4,7,5,3,8,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,7,5,3,6,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,5,3,1,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[2,7,5,3,6,4,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,5,3,8,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,7,5,8,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,6,8,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,6,8,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,5,3,6,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,7,5,6,3,8,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,3,6,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,3,1,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,5,3,4,8,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,2,8,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,1,6,3,2,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,7,6,1,8,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[3,8,7,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,7,2,8,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,8,5,6,7,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,6,2,8,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,1,7,3,8,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[2,7,8,3,1,5,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,5,6,7,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,2,7,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,6,7,8,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,7,8,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[4,7,6,2,8,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,8,7,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,5,8,7,3,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,5,1,2,8,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[5,6,1,2,8,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,8,7,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,1,4,8,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,7,6,1,3,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,7,1,4,2,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,1,6,4,8,3,7,5]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[1,5,7,8,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,5,7,8,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,5,7,8,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,8,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,4,7,3,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,4,2,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,4,6,3,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,8,5,3,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,6,1,4,2,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[6,2,1,1]=>5
[1,6,3,8,4,2,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,5,7,8,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,1,8,2,6,7,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,6,7,8,2,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,5,7,1,6,3,4,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,2,8,3,6,5,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,8,7,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,5,6,3,4,8,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[5,2,4,7,8,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[2,4,5,7,1,8,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]=>[3,3,2,1,1]=>8
[6,1,4,2,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,1,2,3,7,8,9,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[1,6,7,2,4,3,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,3,4,5,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,4,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,2,5,6,3,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,4,8,6,7,2,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,2,5,1,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,7,2,5,8,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,6,7,8,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,1,5,3,6,8,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[5,4,2]=>3
[3,7,5,1,6,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,8,7,4,6,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,8,1,5,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,3,5,2,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,4,7,8,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,1,7,8,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,6,3,8,5,1,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,1,5,8,6,7,3,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,5,8,2,6,3,1,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,3,4,7,6,1,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[2,8,5,4,1,3,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,8,7,1,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,4,6,3,1,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[5,2]=>1
[4,3,6,5,1,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[1,5,6,8,7,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,4,8,3,6,5,2,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,8,6,4,7,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,8,6,4,3,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,5,1,8,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,7,6,8,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,8,4,7,6,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,7,4,5,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,3,7,4,8,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,6,1,7,8,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,2,6,7,8,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[6,5,8,1,2,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,1,8,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,4,3,7,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,2,8,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,1,7,6,2,8,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[1,5,2,7,6,3,4,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,8,1,7,6,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,8,7,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,5,1,8,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,8,7,6,1,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,10,1,9,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,8,1,3,4,5,6,7,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,11,10,1,3,4,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[4,5,3,1,8,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[3,4,8,1,5,2,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,5,8,6,2,7,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,1,8,5,7,2,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,8,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,5,8,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,6,7,1,8,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[3,4,6,7,8,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[3,2,6,7,8,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[6,2,7,4,8,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,1,3,8,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,1,8,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[1,2,6,7,8,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,6,7,4,8,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,6,7,8,3,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[6,1,2,4,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,1,2,4,5,3,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[5,7,1,6,2,4,3,8,9]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,1]=>[7,1,1]=>2
[7,3,4,6,1,2,5,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[6,1,2,9,4,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,8,5,1,7,2,3,4,9]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[1,1]=>0
[5,7,1,9,2,8,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[7,9,4,6,1,8,2,3,5]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,1,2,3,5,6,7,4,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[8]=>0
[8,1,7,3,2,6,4,5,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[8]=>0
[7,3,4,6,1,2,5,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7]=>[8,7]=>1
[8,3,4,5,7,1,2,6,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[8]=>0
[7,9,4,6,1,8,2,3,5,10]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1]=>[1,1]=>0
[6,8,10,1,7,2,9,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[8,10,4,5,7,1,9,2,3,6]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,7,4,8,6,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,8,7,2,3,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,2,7,1,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,8,6,1,4,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,2,5,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,1,2,3,4,5,6,7,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[8]=>0
[7,1,2,3,4,5,6,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7]=>[8,7]=>1
[3,2,6,4,8,7,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,7,2,8,6,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,1,8,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,7,4,8,3,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,3,8,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,3,6,8,7,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,3,8,2,5,7,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,2,6,8,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,1,6,4,8,7,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,1,6,8,7,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[3,8,1,4,5,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,1,4,2,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,8,3,5,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,1,2,5,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,3,6,8,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,2,8,3,5,1,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,8,3,5,7,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,2,4,5,7,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,5,1,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,5,7,1,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,1,5,2,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,3,5,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,2,1,5,8,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,3,6,1,5,8,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[3,4,7,1,5,6,8,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,6,7,4,1,2,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[4,3,2,7,1,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[2,6,8,1,5,3,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,8,2,1,5,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,2,5,3,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,8,2,3,6,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[2,4,8,5,3,6,7,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,3,2,6,4,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[2,4,5,3,8,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[4,3,5,2,8,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,8,5,3,2,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,4,2,8,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[4,1,2,7,5,6,8,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[5,6,7,4,2,8,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[2,5,7,4,6,8,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,8,1,2,5,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,1,8,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,1,8,5,4,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,3,2,6,8,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[3,7,6,4,8,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,1,6,8,5,4,7,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,3,5,8,4,6,7,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[3,5,2,8,4,6,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,4,5,8,2,6,7,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[5,4,2,8,3,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,4,8,2,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,5,4,8,3,6,7,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,3,2,5,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,8,3,5,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,8,3,2,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,3,4,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,1,7,8,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,5,7,6,3,2,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,1,7,8,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,2,8,5,1,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,7,8,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,8,2,5,1,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,4,2,1,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,7,4,1,3,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,2,7,5,1,8,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,1,6,5,3,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[1,5,4,6,3,8,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,8,6,4,7,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,8,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,4,8,1,7,3,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,8,6,2,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,5,4,8,7,3,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,4,2,8,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,6,8,1,7,4,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,8,6,1,7,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,8,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,7,6,2,8,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,2,7,8,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,7,8,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,7,8,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,8,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[4,7,8,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,1,4,7,2,5,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,7,8,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,3,2,7,4,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[2,6,4,3,7,5,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,4,6,5,7,1,2,8]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]=>[4,2,2,1]=>5
[2,3,6,7,8,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[5,7,4,1,6,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,5,1,2,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,8,1,3,7,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,7,4,8,6,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,6,8,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,8,1,6,7,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,7,4,3,8,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,7,8,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,6,8,7,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,1,4,6,7,3,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[4,7,2,8,5,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,5,2,8,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,4,7,5,8,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,1,8,3,4,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,8,6,3,5,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,6,8,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,6,5,2,8,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,4,8,7,5,2,6,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,7,3,6,8,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,8,7,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,1,5,2,7,8,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,4,2,2]=>4
[1,8,7,3,2,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,4,8,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[1,2,7,6,8,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,6,3,2,5,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,3,4,2,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,8,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,6,3,2,8,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,2,5,8,4,6,3,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,5,3,2,7,8,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,1,8,6,2,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,7,6,4,3,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,7,6,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,3,6,8,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,3,5,7,8,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,6,3,2,7,8,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,2,7,6,8,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,4,7,5,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,5,2,1,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,2,6,8,4,3,7,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[5,3,7,2,6,4,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,8,2,6,1,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,3,2,8,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,3,7,2,8,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,5,7,3,8,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,7,8,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,1,3,4,2,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[1,5,3,7,8,4,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,3,8,2,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,7,5,8,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,7,5,8,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,3,4,7,8,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,7,6,8,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,1,2,7,5,8,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[3,3,3,3]=>0
[3,7,1,2,8,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,3,1,7,4,6,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[2,4,7,3,5,6,1,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,7,6,4,2,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,8,2,4,6,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,4,8,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,4,5,8,1,6,7,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[6,8,7,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,8,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[3,1,6,8,5,2,7,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,3,8,1,5,6,4,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,4,8,1,2,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,2,4,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,8,2,3,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,3,8,1,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,3,8,2,4,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,7,1,8,6,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,1,3,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,5,4,6,1,7,8,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,1,1]=>5
[2,7,1,5,6,4,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,7,2,8,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,5,6,4,1,7,2,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,2,1,1]=>5
[2,5,6,1,7,4,3,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,7,1,8,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,1,8,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[8,6,4,2,1,10,3,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,4,2,9,1,3,5,7,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[9,4]=>[4]=>0
[6,2,8,3,1,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,7,8,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,3,2,8,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,8,5,3,2,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,6,7,3,2,8,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,7,5,2,3,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,4,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,8,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,8,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,8,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,8,6,3,5,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,8,4,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,6,7,4,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,8,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,7,8,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,4,2,3,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,5,6,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,4,6,3,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,8,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,4,5,6,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,8,2,7,3,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,7,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,7,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,1,6,7,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,1,3,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,8,3,6,7,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,8,4,6,2,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,8,7,6,4,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,8,7,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,7,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,3,7,5,6,8,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,2,4,7,5,8,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[3,3,3,2]=>3
[2,8,7,6,4,5,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,2,4,7,6,8,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[5,3,2,6,4,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[5,3,2,6,7,4,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[4,3]=>1
[5,3,2,7,6,4,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[3,5,2,7,4,6,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,2,5,7,4,6,8,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,2,7,5,4,8,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[3,7,5,2,4,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,3,7,5,4,8,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,4,7,6,8,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[5,2,8,4,1,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,5,2,1,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,8,6,3,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,2,9,3,4,5,6,8,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[7,1,2,3,4,8,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,5]=>[5]=>0
[6,9,1,2,3,4,8,5,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,2,10,3,4,5,6,7,9,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,1]=>7
[1,11,2,3,4,5,6,7,8,10,9]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>0
[7,10,1,2,3,4,5,9,6,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,2,3,7,4,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4]=>[6,4]=>1
[5,7,1,2,6,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,9,1,2,6,3,4,8,7]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,9,5,2,3,6,8,7]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,5,7,4,1,8,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,8,4,3,1,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,1,2,8,5,7,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[6,1,2,3,4,5,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6]=>[6,6]=>0
[4,1,2,3,9,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[2,1,3,8,5,7,4,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,9,4,6,8,3,5,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[1,8,2,4,6,9,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[5,4,1,6,3,7,8,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[4,5,1,3,6,7,8,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[5,4,1]=>3
[5,1,7,6,3,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,1,7,5,4,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,7,2,1,6,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[1,5,8,2,4,7,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,1,6,4,7,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,6,5,7,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,1,4,7,3,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,8,2,7,4,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,7,2,1,8,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,1,6,8,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,2,1,8,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,4,1,7,3,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,2,4,7,8,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,4,3,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,7,4,8,6,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,8,6,5,7,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,7,8,6,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,2,8,4,7,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,7,3,6,8,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,4,7,8,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[1,4,7,2,6,8,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,3,7,6,5,1,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,2,7,6,4,1,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[6,2,3,5,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,2,8,5,1,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,5,8,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,2,4,5,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,4,1,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[2,3,8,4,1,6,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,5,7,3,1,6,2,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[2,3,1,4,8,5,7,6]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]=>[4,4,4,3,1]=>7
[4,2,6,1,5,8,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[3,1,8,5,7,6,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,1,8,7,4,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,4,8,7,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,5,7,6,1,8,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,6,2,8,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[1,5,3,2,8,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[6,1,4,3,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,1,8,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,6,2,8,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,3,5,2,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,8,4,1,3,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,1,4,7,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,3,8,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,3,5,8,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[3,4,7,5,8,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,7,8,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,3,6,2,8,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,4,3,7,1,8,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,6,5,7,3,8,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,8,2,7,4,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,7,8,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,6,5,4,7,1,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,8,3,4,6,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,7,4,2,5,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,8,7,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,3,1,5,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,2,7,1,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,7,1,5,2,6,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,8,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,7,1,6,8,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,2,6,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,2,7,1,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[6,8,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,1,6,5,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,4,7,1,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,4,8,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,4,5,2,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,3,7,6,5,8,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,5,6,7,8,9,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[6,7,8,5,4,3,2,1,9]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1]=>[2,1]=>1
[6,5,7,8,4,3,2,1,9]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2]=>[3,2]=>1
[6,5,4,3,7,8,2,1,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4]=>[5,4]=>1
[7,8,9,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1]=>[2,1]=>1
[6,7,8,9,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,6,8,9,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2]=>[3,2]=>1
[6,5,7,8,9,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[6,5,4,7,8,9,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3]=>[4,3]=>1
[6,5,4,3,2,7,8,9,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[3,5,7,6,8,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[4,2,5,3,7,6,1,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,2]=>2
[6,2,4,3,7,5,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,2,5,3,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[4,2,6,3,7,5,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[5,2,7,3,6,4,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,3,8,2,5,4,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,8,3,6,4,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,8,4,6,5,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,4,7,3,6,5,2,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,8,3,7,5,2,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,2,1,4,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,1,4,8,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,8,3,7,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,2,8,3,7,4,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,3,7,4,8,5,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,2,7,3,8,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,2,7,4,8,5,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[5,2,6,3,8,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[6,2,5,3,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,3,6,4,8,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[6,2,4,3,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,4,3,8,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,5,3,8,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[6,2,4,3,1,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,2,5,3,1,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[4,2,6,3,1,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[3,2,7,4,1,6,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,3,1,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,2,7,3,1,6,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,2,7,3,1,5,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,5,2,4,8,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[6,2,1,5,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[3,2,8,5,1,6,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,2,8,4,1,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,5,2,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,5,2,8,7,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,7,2,8,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,8,2,7,1,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,3,1,5,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,1,5,7,8,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[6,7,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1]=>[7,1]=>1
[3,2,1,7,8,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[1,7,6,3,2,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,6,4,7,8,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[4,2,2,2,2]=>4
[1,6,3,2,4,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,5,3,2,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,8,1,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,6,7,1,8,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[1,3,7,6,2,4,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,7,3,8,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,2,7,8,3,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[6,4,8,1,5,7,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,7,4,1,3,6,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,1,4,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,8,7,9,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,8,7,6,9,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,8,7,6,5,9,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,6,5,4,9,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,6,5,4,3,9,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,1,5,4,7,3,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,3,6,8,4,1,7,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[1,7,2,8,6,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,2,4,8,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,4,6,7,8,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]=>[4,3,3,2]=>5
[5,2,6,8,1,3,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,8,1,6,3,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,5,6,2,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,7,6,1,8,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,6,5,2,1,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[6,7,2,4,3,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,5,3,7,2,1,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,3,8,2,1,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,2,8,1,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,5,8,3,2,7,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,8,5,2,7,3,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,7,8,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,3,8,2,1,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,9,2,4,5,6,7,8,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[3,6,7,4,5,2,8,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[3,5,7,4,6,2,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[5,3,7,6,2,4,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,6,7,2,5,3,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[6,4,7,8,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,8,1,7,6,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,7,1,8,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[1,5,8,2,6,4,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,4,6,8,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,7,5,6,8,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,6,7,4,8,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[4,8,1,7,2,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,6,7,1,5,4,8,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,2,7,6,5,8,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[1,7,3,4,5,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,4,5,6,9,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,2,7,4,5,8,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[7,9,3,4,5,6,1,8,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,9,3,4,5,6,7,10,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[7,8,3,4,5,2,9,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[6,1]=>[1]=>0
[6,7,3,2,5,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,1,8,4,5,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,8,9,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,9,3,4,5,1,7,8,2]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[8,10,3,4,5,6,7,1,9,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,5,1,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,1,4,6,2,8,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[1,5,8,7,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,7,2,1,3,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,7,2,6,8,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,8,5,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,4,5,7,3,8,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,4,7,8,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,5,8,7,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,5,7,8,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,6,2,1,4,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[6,8,2,7,5,4,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,1,7,6,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,2,3,10,4,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[7,6,1,2,3,4,10,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,6,6]=>[6,6]=>0
[2,10,1,5,3,4,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[4,1,2,10,3,5,6,7,8,9]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[4,1,5,6,7,8,9,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[6,4,3,2,8,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,3,6,1,8,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,3,8,2,6,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,5,7,4,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,2,5,4,8,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,7,6,8,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[6,1,5,8,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,5,7,4,8,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,1,5,7,8,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[4,6,7,3,1,8,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[4,2,6,3,1,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[6,1,4,2,5,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,5,3,8,4,6,2,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,7,6,4,8,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,8,5,7,6,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,5,8,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[6,1,5,8,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,7,5,1,3,2,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,2,6,1,7,3,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[4,2,6,8,3,7,1,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[6,8,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,8,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,3,6,4,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,3,8,1,4,2,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,1,5,6,3,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,2,6,5,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,7,2,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,8,3,7,4,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,4,3,6,2,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,2,6,3,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,4,3,1,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,6,8,5,2,4,7,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,7,8,4,3,2,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,3,8,4,7,2,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,7,1,3,2,8,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,4,3,1,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,7,6,5,8,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,7,4,2,8,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,4,3,7,8,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,8,5,7,6,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,3,6,8,7,2,5,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[5,8,7,1,4,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,3,7,1,4,5,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,7,6,5,3,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,6,5,4,1,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,3,5,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,6,1,5,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,3,9,8,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,8,7,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,3,8,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,6,8,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,4,7,3,8,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,3,5,7,2,6,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[1,7,2,8,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,8,3,6,2,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,2,5,7,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,6,2,7,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,4,2,7,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,8,7,3,4,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,7,8,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,7,5,8,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,6,8,1,5,4,3,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,2,1,7,6,3,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[3,5,8,2,1,4,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[4,2,8,5,3,7,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,7,5,3,8,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[6,4,5,1,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,7,8,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,5,8,1,3,7,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,5,3,6,8,7,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[4,7,2,6,8,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,3,2,8,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,1,5,8,7,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,1,8,6,5,7,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,2,7,6,4,5,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,8,5,6,3,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,4,2,1,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,7,3,2,5,1,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,2,5,3,8,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,5,6,2,7,3,1,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]=>[4,2,1]=>3
[5,3,4,7,1,6,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[3,5,1,4,6,8,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[2,3,7,4,1,8,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,5,1,8,6,3,7]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[6,3,7,1,5,2,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,1,3,7,8,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[1,4,5,3,8,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[4,6,2,7,5,8,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[6,5,2,4,8,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,4,3,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,2,1,4,3,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[6,2,1,5,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,8,7,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,3,8,1,5,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,3,6,7,2,8,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,3,3]=>2
[6,1,3,2,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[3,7,8,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,2,7,3,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,5,8,2,7,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,2,7,3,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,8,2,7,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,5,7,8,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[5,7,3,4,2,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,4,2,3,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,4,7,3,2,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,8,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,4,6,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,3,8,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,8,2,3,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,6,8,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,6,8,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,4,8,5,1,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,7,8,2,3,1,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,4,7,8,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,8,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,1,3,2,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[6,1]=>1
[4,3,8,1,2,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,6,3,2,8,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,3,7,2,1,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,4,8,3,7,2,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,8,5,2,1,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,1,5,4,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,4,8,3,2,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,4,3,7,2,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,4,3,7,8,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,4,5,6,7,8,2,9,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1]=>[5,4,3,2,1]=>10
[1,4,8,6,3,2,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,8,6,2,5,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,4,8,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,8,1,7,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,3,1,5,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,9,8,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,3,5,8,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,5,8,7,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[6,8,5,7,3,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,3,6,8,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,1,6,8,4,7,3,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,2,8,3,4,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,1,8,7,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,3,5,8,4,7,2,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[2,3,8,7,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,8,7,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,8,5,1,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,7,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,5,6,8,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[1,7,4,3,5,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,4,3,8,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,2,7,6,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,3,6,2,1,8,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[4,3,8,6,2,7,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,6,8,2,7,5,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[5,3,8,6,7,2,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,7,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,2,8,7,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,7,1,4,6,5,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,1,2,6,5,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,2,5,6,8,7,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[6,5,8,3,7,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,7,6,4,8,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[1,3,7,8,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,7,6,8,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,7,4,6,8,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[6,5,8,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,3,1,5,2,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,2,4,1,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[2,1,7,4,3,8,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,1,5,7,6,3,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[1,4,8,2,3,6,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,6,7,3,5,2,8]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,4,8,2,6,7,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,3,2,4,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,2,4,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,3,2,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[4,2,6,5,3,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[5,2,1,6,8,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[1,3,5,8,6,2,7,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[2,3,8,4,1,7,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,3,8,5,7,4,2,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,2,8,6,3,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[2,8,6,3,5,7,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,8,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,8,6,4,2,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,5,2,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,5,2,1,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,2,1,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,2,4,3,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[3,7,5,2,8,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,1,4,7,3,2,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[2,3,5,4,8,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,4,2,2,1]=>8
[2,3,5,7,4,8,1,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,7,6,1,5,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,7,6,1,2,5,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,7,1,6,8,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,1,8,6,3,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,5,8,6,2,3,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,3,4,6,2,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[5,4,8,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,7,3,4,8,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,6,4,2,7,8,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[6,5,2,3,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,5,2,3,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,3,7,4,1,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,4,7,5,3,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,7,6,4,8,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,7,4,8,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,1,4,7,5,2,8,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[4,3,5,1,8,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[2,5,3,6,1,8,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]=>[5,3,1,1,1]=>7
[2,5,6,8,3,1,7,4]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,7,2,4,5,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,5,3,2,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,7,3,5,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,5,6,4,8,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[1,6,4,7,5,2,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,5,4,7,8,3,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,4,5,8,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,2,6,7,8,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,4,6,7,8,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[4,7,3,8,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,3,2,7,5,8,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[4,8,5,3,2,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,4,5,3,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,3,7,8,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,3,7,8,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,6,3,7,8,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,4,8,5,3,2,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,7,4,3,8,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,7,3,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,2,8,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,5,8,3,6,7,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,8,5,7,1,3,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,4,7,2,1,5,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[4,8,2,7,1,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,5,8,3,6,7,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,1,6,8,3,2,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,1,5,6,8,2,7,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[5,7,8,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,5,2,8,7,3,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,8,5,3,1,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,2,3,1,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,2,3,6,8,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,2,1,7,8,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,2,1,3,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,7,8,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,2,8,6,4,1,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,2,8,4,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,7,8,3,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,7,2,6,4,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,2,3,4,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,2,1,3,7,5,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,8,7,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,2,3,7,8,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,7,6,4,2,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,4,7,2,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,7,5,8,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,2,4,8,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,7,2,4,3,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,3,4,6,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[2,8,3,6,1,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,1,8,5,2,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,8,4,5,6,2,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,5,8,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,5,4,8,6,1,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[2,7,5,1,4,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,1,2,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,3,5,2,8,1,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[1,7,3,8,2,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,4,8,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,3,8,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,1,8,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,6,8,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,6,1,5,8,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[6,4,8,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,8,2,4,1,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,1,2,4,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,5,2,3,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[5,5,2]=>2
[6,3,5,8,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,7,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,5,3,7,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,6,2,8,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,3,8,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,4,3,6,5,2,1,10,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,7,7]=>[7,7]=>0
[1,10,5,4,7,6,9,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,10,5,4,9,8,7,6,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,10,7,6,5,4,9,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,10,9,6,5,8,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,5,7,2,4,3,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,3,2,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,7,2,4,6,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,2,6,5,3,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,6,8,7,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,7,4,3,5,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,6,2,8,7,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,4,2,3,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,2,3,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,8,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,5,2,8,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,3,7,4,2,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,5,2,7,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,7,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,2,5,8,6,3,7,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,5,8,7,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,5,8,7,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,6,8,7,5,3,2,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,2,6,8,7,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[1,5,8,6,3,2,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,8,5,2,6,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,6,3,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,2,8,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,3,8,6,4,2,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,7,4,2,3,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,3,7,5,4,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[3,8,2,7,5,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,4,8,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,7,3,6,8,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,2,8,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,5,8,7,1,4,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,4,6,5,8,2,7,1]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[5,2,4,1,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,2,7,1,6,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,2,8,6,4,7,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,1,3,4,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,3,6,7,2,8,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[5,3,6,7,2,4,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[1,5,8,2,6,7,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,7,5,2,3,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,1,7,5,4,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[2,7,3,6,5,1,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,2,4,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,7,5,6,4,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,8,4,6,1,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,4,7,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,8,6,7,1,4,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,1,5,8,6,2,4,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,5,4,6,8,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[6,5,2,4,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,2,8,3,4,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,4,3,8,7,1,6,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[1,5,8,7,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,4,7,3,8,2,9,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1]=>[5,3,1]=>3
[5,3,4,8,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,4,6,3,7,2,8,1,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2]=>[6,4,2]=>3
[6,5,7,4,8,3,9,2,10,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2]=>[6,4,2]=>3
[3,4,5,8,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[5,6,4,7,3,8,2,9,1,10]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1]=>[7,5,3,1]=>6
[5,4,2,3,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[5,1,7,4,3,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,3,7,6,8,2,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[6,1,8,5,2,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,4,1,3,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[3,1,8,7,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,5,8,7,2,4,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,3,6,5,8,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[3,2,6,8,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,3,7,1,8,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,8,5,6,7,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,7,3,1,8,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,7,8,2,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,3,4,7,8,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,1,2,4,7,8,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,1,7,8,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,1,5,2,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[1,7,3,6,4,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,6,4,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,4,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,2,8,5,6,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[6,3,1,2,7,4,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,1,7,4,2,3,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,7,3,4,6,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,7,2,5,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,1,7,2,6,3,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,1,8,2,6,3,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,6,3,7,4,5,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,4,7,3,5,1,6,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,6,3,5,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,3,7,5,4,1,6,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,4,6,2,1,5,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]=>[6,2,2,1]=>5
[3,4,7,2,1,6,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[2,6,8,3,5,1,4,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,3,6,1,5,8,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[2,3,7,1,6,5,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,4,7,1,3,6,8,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,4,7,8,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,5,7,1,4,6,3,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,7,1,6,3,5,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,3,7,1,6,5,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,5,7,1,4,3,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,7,3,1,4,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,4,7,2,1,6,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[4,6,3,7,1,5,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[5,7,3,2,8,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[2,6,5,7,1,8,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,6,8,5,4,1,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,4,7,8,1,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,5,7,1,4,6,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,4,7,1,6,3,8,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,7,1,6,8,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,8,3,1,7,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,8,3,4,5,6,7,9,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[7,2,3,4,5,6,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[2,1,9,4,5,6,7,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,8,3,4,5,6,7,1,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,1,4,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,8,3,7,4,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,9,1,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,9,8,1,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,2,5,7,3,1,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,3,7,5,2,1,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[1,6,7,4,3,2,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,5,1,4,7,2,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[4,4,1,1]=>4
[2,5,1,4,7,8,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,1,1,1]=>6
[4,3,7,1,5,2,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[6,4,3,1,7,2,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,2,7,4,3,1,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[2,6,4,1,7,3,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,3,2,7,4,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,3,2,5,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[3,2,6,5,7,1,4,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[1,7,3,2,5,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,7,3,5,6,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,6,3,2,5,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[5,6,2,1,4,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[4,6,1,5,2,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[1,6,5,3,7,2,4,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,2,7,6,1,8,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,8,2,6,1,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,8,3,6,2,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,7,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,2,7,8,3,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,8,7,6,2,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,4,5,8,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,1,8,5,4,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,8,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,8,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,4,7,5,8,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,7,4,2,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,1,5,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,6,2,5,7,3,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[4,2,8,5,3,6,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,1,7,8,4,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,4,1,6,2,8,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[6,2,3,1,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[3,1,8,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,5,1,8,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[4,5,3,7,1,6,8,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[4,2,8,5,3,6,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,8,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,2,8,6,4,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,1,4,7,2,6,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[1,8,2,5,6,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,4,8,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,6,1,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,7,6,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,3,7,5,4,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,4,7,1,3,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[2,8,5,1,4,7,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,4,8,5,6,2,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,8,2,3,4,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,3,4,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,3,5,2,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[2,4,5,7,3,6,1,8]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1]=>[3,3,2,1,1]=>8
[6,5,1,3,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,7,4,3,2,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,8,7,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,7,8,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,7,8,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,4,2,1,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,1,4,7,3,6,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,7,6,3,5,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[1,6,5,8,7,4,2,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,1,3,8,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,7,5,6,8,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,7,5,8,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[1,7,4,5,2,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,7,4,2,8,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[4,6,3,2,7,8,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[3,6,2,1,7,5,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[2,6,7,3,1,5,4,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,1,3,8,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,6,3,2,8,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,7,2,8,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[3,1,8,4,6,5,7,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,2,3,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,4,7,5,8,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[5,3,8,6,4,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,10,1,2,3,4,5,9,6,7]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,7,1,2,3,4,5,9,10,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[6,1,2,3,4,5,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[2,10,1,5,6,7,8,9,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,4,7,1,8,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,7,4,2,3,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,8,2,5,1,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,4,2,3,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,5,2,1,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,7,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,6,8,4,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,3,1,7,4,8,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,6,8,3,7,1,2,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,2,8,4,7,1,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[6,4,8,3,7,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,2,8,7,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,8,4,2,7,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,6,7,8,9,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[3,4,7,8,5,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[4,7,3,2,5,6,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,2,7,6,4,5,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[1,7,3,6,8,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,6,5,1,8,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[1,7,8,2,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,4,7,1,2,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[5,7,4,8,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,3,7,8,1,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,2,6,8,7,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,3,7,5,1,8,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,3,1,2,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,2,1,3,8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,5,8,2,4,3,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,3,6,8,1,5,2,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[5,4,6,8,3,1,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,6,8,4,5,1,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,3,7,6,1,8,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,2,7,8,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,2,8,3,1,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,2,8,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[2,1,3,8,7,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,8,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[1,6,8,3,2,4,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,3,2,8,7,6,4,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[2,1,3,8,7,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[1,6,3,7,2,5,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,2,4,6,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,2,8,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,6,2,8,4,1,3,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[2,4,8,3,1,6,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,5,8,4,2,1,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,8,3,1,4,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,8,1,3,5,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,7,8,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,4,8,5,7,1,2,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,6,8,2,5,1,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,6,8,7,2,5,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,4,6,5,8,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[2,4,6,7,8,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[3,2,2,1,1]=>8
[1,4,2,6,8,5,3,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[1,2,6,8,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,6,8,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,8,7,6,3,2,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,7,6,3,2,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,3,2,4,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,3,2,4,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,2,7,6,4,3,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,8,7,5,2,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,4,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,2,5,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,7,5,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,3,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,6,3,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,7,4,2,5,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,3,2,7,5,4,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,4,7,5,2,6,3,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,6,4,8,7,5,2]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,3,7,6,4,2,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,7,5,2,4,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,6,3,2,8,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[1,5,7,6,4,2,3,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,3,2,8,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,3,5,2,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,3,5,2,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,3,7,5,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,7,1,5,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,3,8,2,6,4,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,8,2,6,5,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,6,1,8,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,7,1,4,8,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,5,7,1,4,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,8,3,5,7,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,7,6,1,2,4,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,8,3,5,7,6,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,3,4,2,8,5,7,6]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]=>[4,4,4,2,1,1]=>11
[5,7,6,2,4,8,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,7,5,2,3,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,5,3,8,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,4,1,8,2,6,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,1,8,2,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,7,1,5,2,6,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[6,5,1,4,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[1,8,7,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,9,3,4,5,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,7,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,6,8,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,3,7,8,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,4,5,2,8,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,8,6,2,3,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,2,1,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,2,6,1,5,8,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[6,4,2,3,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,8,6,4,5,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,1,7,4,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,5,1,8,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,4,3,7,2,8,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,8,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,3,1,4,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,7,2,8,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,2,6,7,8,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[1,7,4,6,3,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,4,1,3,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[4,5,3,1,8,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[6,3,4,2,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,2,7,8,1,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,8,4,3,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,8,2,5,6,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[8,5,3,7,2,10,4,9,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,6,3,5,10,2,7,9,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,3,7,4,5,10,2,9,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,5,10,4,7,6,2,9,1,3]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[8,3,4,10,5,6,7,9,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,8,1,6,7,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,2,8,6,1,5,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,7,2,5,8,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[6,7,8,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,2,8,3,5,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,7,4,5,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,8,2,5,3,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,5,2,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,8,7,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,7,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,7,5,3,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,3,8,2,5,4,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,6,2,5,8,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,8,7,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,7,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,2,4,8,3,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,8,3,5,4,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,2,5,4,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,6,7,5,2,4,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,5,6,4,7,2,3,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,7,4,2,5,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,3,7,5,2,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,5,4,7,2,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,3,2,6,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,2,3,6,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,3,2,7,4,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,8,5,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,2,3,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,6,2,4,3,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,8,4,7,3,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,4,2,6,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,4,2,6,5,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,5,8,3,7,4,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,4,8,3,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,3,2,7,5,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,3,6,4,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,4,7,3,2,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,8,7,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,1,3,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,8,7,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,5,3,4,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,5,3,7,8,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,8,7,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,3,4,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,1,7,3,8,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,1,3,2,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,1,3,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[3,4,5,6,8,1,9,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,4,5,6,8,9,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,4,3,2,1]=>[4,4,3,2,1]=>9
[5,6,1,7,8,9,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[3,2,5,8,7,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,2,5,8,7,3,1,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,4,8,5,7,2,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,6,4,8,5,7,2,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,8,4,7,3,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,8,7,3,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,5,8,2,1,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,4,3,8,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,3,2,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[6,1,3,8,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,2,8,4,5,7,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,2,1,8,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,2,5,8,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[5,6,3,8,7,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[2,5,8,4,7,1,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,6,2,4,8,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,1,6,5,8,7,2,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,8,5,3,6,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,5,3,4,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,3,6,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,2,4,8,5,7,1,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[6,4,5,8,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,6,2,8,5,3,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[2,8,3,1,4,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,3,6,5,1,2,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[5,8,3,7,6,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,3,8,7,6,5,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,8,7,2,6,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,7,2,6,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,7,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,2,8,7,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,2,1,8,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,8,7,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,5,3,2,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[2,8,3,4,1,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,3,7,5,4,8,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,5,6,3,1,8,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[5,2,1,4,3,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[1,5,6,3,8,4,2,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[2,6,5,3,8,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,7,3,8,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,3,6,2,8,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,3,6,5,4,8,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[5,2,2,2,1]=>7
[3,7,5,4,8,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[5,3,7,1,2,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[6,3,8,7,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,8,7,6,1,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,4,1,7,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,6,8,1,4,7,5,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,4,8,1,2,7,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,1,6,7,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,1,2,6,7,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,2,1,6,7,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,6,4,8,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[3,6,8,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,8,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,6,1,3,2,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,5,3,6,7,1,8,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,1]=>3
[1,4,7,8,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,6,1,3,5,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[2,5,1,4,8,3,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[6,1,2,5,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,4,5,6,8,3,1,7]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,4,5,8,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[4,5,1,8,6,3,7,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[1,8,2,3,4,5,9,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[3,8,7,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,5,6,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,5,2,3,6,7,8,9,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1]=>[6,5,4,1]=>6
[5,4,3,2,6,7,8,9,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]=>[6,5,4]=>3
[6,7,4,5,2,3,8,9,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1]=>[6,1]=>1
[7,8,4,5,9,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[4,1]=>[1]=>0
[7,4,3,8,9,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]=>[3]=>0
[7,5,8,3,6,2,4,9,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,2]=>[2]=>0
[7,6,5,4,3,2,8,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[6,7,8,9,2,3,4,5,10,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[8,3,2,1]=>[3,2,1]=>3
[7,8,9,10,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,3,8,9,10,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,6,5,4,3,2,8,9,10,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6]=>[7,6]=>1
[8,9,6,7,4,5,2,3,10,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[8,7,6,5,4,3,2,9,10,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[1,5,6,3,8,2,7,4]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[2,6,3,8,4,7,1,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,3,5,7,8,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,5,6,3,7,2,8,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,7,5,3,6,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,7,3,4,2,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,3,4,2,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,5,3,8,2,7,6]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[4,4,2,1,1,1]=>11
[6,5,1,4,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,1,4,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,7,5,4,2,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,6,8,3,7,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,8,5,2,1,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,5,4,8,2,6,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,4,7,1,8,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,4,8,2,6,5,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,2,8,1,7,4,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,8,2,6,7,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,6,8,2,7,4,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[2,6,7,3,4,1,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,6,5,7,8,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,6,7,2,8,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[3,7,6,1,8,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,2,6,4,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,5,8,6,7,3,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,5,8,7,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,7,6,2,8,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,2,5,8,6,7,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,7,5,8,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,5,8,1,2,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,4,7,8,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,5,6,8,1,3,7,4]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[5,3,6,8,1,2,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,6,5,8,3,2,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,5,6,8,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[2,5,8,7,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,7,5,8,3,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,4,7,8,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,6,8,7,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,4,7,8,5,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,8,4,7,5,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,5,6,7,8,3,9,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,4,8,9,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[7,8,9,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,5,7,8,9,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[2,8,7,5,1,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,7,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,3,7,1,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,7,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,3,2,4,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,1,4,3,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]=>[6,5,1,1,1]=>7
[5,3,8,2,4,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,3,2,6,1,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,8,2,1,4,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,5,8,3,6,2,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[4,5,8,3,6,1,2,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,2,7,1,8,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,7,8,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,2,7,8,1,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,7,1,3,8,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,7,8,4,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,8,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[7,1,2,3,4,5,8,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]=>[6]=>0
[6,1,2,3,4,7,5,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5]=>[7,5]=>1
[5,1,2,3,6,4,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4]=>[7,6,4]=>3
[6,2,1,7,4,8,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,7,4,3,2,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,3,6,2,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,8,2,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,2,1,6,3,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[5,1,3,4,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[3,8,4,5,7,2,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,7,5,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,6,3,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,7,6,3,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,5,6,8,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[5,4,1,8,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,8,4,5,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,2,1,8,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[4,7,3,8,2,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,3,1,8,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,2,1,3,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,7,1,2,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,1,4,7,8,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,8,7,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,6,2,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,8,4,2,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[6,8,3,2,5,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,5,6,8,7,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[6,1,2,4,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,5,1,3,7,6,8,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,4,1]=>2
[3,5,4,8,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,6,2,4,5,8,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[2,6,4,8,3,1,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,6,4,1,5,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[3,6,4,5,2,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[3,6,4,1,5,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,6,4,1,5,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[3,1,6,5,2,8,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[1,7,2,4,3,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,7,4,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,2,4,5,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,5,3,6,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,3,1,4,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,3,1,8,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,3,5,6,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,5,7,4,8,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,8,1,3,5,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,2,8,6,4,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,6,8,4,1,2,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,7,8,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,1,5,2,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,1,8,5,4,7,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,4,8,5,2,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[5,1,3,4,2,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,4,2,1,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[4,2,5,1,8,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[6,8,2,7,1,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,4,7,3,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,3,1,4,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,8,3,2,6,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,2,5,3,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[6,8,4,1,3,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,2,6,1,7,8,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[5,4,1,6,7,3,2,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[5,2,1,6,4,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[1,6,2,3,5,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,3,4,8,5,2,6,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,5,7,2,3,6,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,2,5,7,8,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[4,8,1,7,6,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,8,3,1,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,4,8,3,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,1,7,6,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,8,7,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,7,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,4,6,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,4,7,6,1,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,4,8,3,1,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,4,8,2,1,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,7,2,6,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,4,7,6,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,6,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,3,8,7,2,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[5,4,3,1,7,6,2,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[4,1,3,7,5,6,2,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[2,6,8,3,1,7,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,5,4,8,1,7,3,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,6,3,1,4,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[6,1]=>1
[2,6,5,3,4,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,6,1,5,3,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[3,4,7,8,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[3,6,2,4,7,8,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[5,3,6,4,8,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[1,5,4,8,6,2,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,5,2,7,6,3,8,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[3,3,1]=>2
[5,8,3,1,2,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,5,1,2,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,1,3,8,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[2,1,6,7,4,8,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[3,2,2,2,2]=>4
[5,7,8,1,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,7,8,4,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,7,5,8,2,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,8,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,7,8,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,1,4,3,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,1,6,8,3,4,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[5,6,8,1,2,3,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,8,1,2,7,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,1,2,8,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[6,4,7,3,5,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,7,8,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,4,8,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,6,2,5,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,2,2,2]=>3
[1,6,4,5,2,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,4,7,3,2,5,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,2,1,4,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,1,5,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[1,3,5,8,2,6,7,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,4,9,2,5,6,7,8,3]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1]=>[2,2,2,2,1,1,1]=>12
[3,9,1,4,5,6,7,8,2]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,3,7,2,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,4,5,8,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,8,4,3,1,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,6,7,4,2,8,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,8,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,7,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,7,2,3,6,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,1,2,6,7,8,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]=>[4,3,3,3]=>3
[3,8,1,6,4,2,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,6,3,4,7,8,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,1,5,7,6,2,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[6,3,1,4,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[2,4,3,7,6,1,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,1,7,6,5,2,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[1,4,7,6,8,3,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,3,1,8,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,1,5,2,8,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[4,4,2,2]=>4
[1,2,8,4,3,7,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,6,1,8,7,4,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,7,6,3,1,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,3,1,8,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,8,6,3,2,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,5,4,2,8,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,4,2,8,5,3,7,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,7,4,8,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,8,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,6,3,8,1,7,5,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,1,8,6,3,7,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,8,6,4,1,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,4,2,7,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,1,7,2,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,8,1,7,5,3,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,7,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,8,2,6,3,5,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,5,7,1,6,2,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[4,1,8,5,3,6,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,4,2,5,3,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[3,1,5,8,2,7,4,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[6,4,1,5,3,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,2,1,5,4,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[3,1,8,5,4,6,2,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,8,4,5,3,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,2,7,1,6,3,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,3,5,7,1,6,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[4,1,8,5,3,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,8,4,5,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,6,8,5,7,4,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[2,6,1,8,5,7,4,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,8,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,7,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,6,8,5,3,7,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[3,2,2,2,2]=>4
[3,2,6,8,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[4,1,8,5,2,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,6,8,5,2,4,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[6,5,8,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,5,8,7,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,8,4,5,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,4,5,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,7,3,5,8,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,6,2,4,8,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,7,5,4,3,8,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,1,8,4,7,6,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,6,1,8,5,4,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,4,8,3,7,6,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,6,8,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,6,8,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,6,8,2,5,4,7,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,6,8,3,2,5,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,2,8,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,6,1,8,5,7,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[5,2,6,8,4,1,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,6,3,8,7,2,5,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,5,8,2,7,4,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,6,8,5,7,4,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,4,8,7,6,3,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,7,6,3,4,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,3,1,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,8,2,1,7,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,3,8,5,7,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,4,8,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[6,2,8,1,7,5,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,5,1,8,7,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,6,2,7,8,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,7,3,5,6,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,8,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[3,2,5,6,8,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[2,5,6,4,8,3,7,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[5,3,2,4,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,2,5,7,3,8,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[4,7,3,1,6,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,2,7,6,8,1,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,7,4,6,8,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,2,5,6,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[5,4,1,3,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[6,1,5,8,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,3,5,7,8,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[6,1,5,8,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,6,4,1,8,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[4,5,2,1,7,8,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[2,3,7,8,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[7,1,9,3,4,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,10,1,4,5,6,7,8,9,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[8,1,10,3,4,5,6,7,2,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,2,1,9,4,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,9,7,3,4,5,1,2,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,3,1,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,1,2,6,4,8,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[3,8,1,2,9,5,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[9,1,11,3,4,5,6,7,8,2,10]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[8,2,1,10,4,5,6,7,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,10,8,3,4,5,6,1,2,9]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,2,3,1,9,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[5,9,6,3,4,1,7,2,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,2,8,6,1,3,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,4,8,2,5,6,1,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,8,1,4,2,9,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,6,7,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,7,5,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,2,5,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,7,2,8,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,8,3,6,4,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,3,8,5,2,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,8,4,5,1,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,2,5,8,4,7,1,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,5,8,1,3,4,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,5,1,8,7,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,6,1,3,8,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[5,1,7,8,3,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,1,7,6,2,8,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[5,3,6,7,4,2,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,4,2,8,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,4,2,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,7,2,6,8,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,6,5,2,7,8,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[5,4,6,2,7,8,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[5,1,8,6,4,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,2,1,8,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,6,2,3,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[6,5,7,8,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[2,1,7,6,8,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,4,7,2,8,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,3,2,7,8,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,4,8,2,7,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[5,6,7,9,1,2,3,8,4]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[1,5,8,9,2,6,7,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,1,1,1,1]=>[2,2,2,1,1,1,1]=>12
[1,5,6,9,2,3,8,7,4]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,1,1,1,1]=>[3,3,2,1,1,1,1]=>14
[1,2,7,9,5,8,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,2,2,2,1]=>[3,2,2,2,2,2,1]=>11
[4,7,9,1,5,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,5,9,1,2,8,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,8,9,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,6,9,4,8,2,7,5,3]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]=>10
[1,4,9,2,8,7,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1]=>[2,2,2,2,1,1,1]=>12
[5,9,3,8,1,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,9,1,8,7,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,9,10,5,6,7,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[7,8,10,4,5,9,1,2,6,3]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,6,10,4,9,2,8,7,5,3]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,1,1,1,1,1]=>[2,2,2,1,1,1,1,1]=>15
[1,4,10,2,9,8,7,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1,1]=>[2,2,2,2,2,1,1,1]=>15
[5,10,3,9,1,8,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,3,1,5,2,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,3,6,5,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,6,3,1,5,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,4,7,3,8,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,7,3,1,8,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,1,7,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,5,2,1,4,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[7,6,8,9,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,4,6,7,8,9,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[1,2,6,8,3,4,7,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,5,6,8,3,2,4,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[1,7,4,8,6,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,3,5,7,4,8,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,5,4,7,2,8,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,8,5,2,6,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,8,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,7,4,2,5,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[6,8,7,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,4,2,8,6,7,5,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,7,8,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,6,1,5,2,7,8,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[6,2,8,4,7,1,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,7,8,4,2,5,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,4,2,8,5,1,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[6,8,2,7,5,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,4,3,7,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,8,7,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,8,4,5,7,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,8,5,7,1,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,4,8,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,8,4,7,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,7,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,8,7,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,7,8,3,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,5,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,8,7,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,7,8,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,1,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,7,8,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[4,5,7,8,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[5,4,6,8,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,5,8,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,7,6,8,2,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,7,6,8,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,4,7,8,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,5,7,8,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[4,5,6,8,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[5,7,3,4,2,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,1,5,3,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,8,6,2,5,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,4,1,7,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,2,7,4,8,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[2,8,5,1,4,3,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,7,5,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,3,6,4,7,2,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[4,2,6,5,7,3,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[5,4,6,2,7,3,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[4,2]=>1
[3,2,6,5,8,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[3,2,6,5,8,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,2,6,5,8,7,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[5,2,6,4,8,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[5,4,7,6,8,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,4,7,5,8,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,2,7,5,8,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,7,5,8,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,3,7,2,8,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[4,3,6,2,8,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[4,3,7,6,8,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,3,7,6,8,2,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[5,3,7,2,8,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,2,6,4,8,7,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,2,7,3,8,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[5,2,7,6,8,3,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[3,2,7,6,8,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,6,8,5,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[6,2,7,5,8,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,7,8,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,3,2,5,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,2,5,3,7,8,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[5,3,6,2,4,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[5,8,2,6,3,7,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,2,3,7,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,5,6,4,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,4,3,7,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,5,7,6,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,8,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,7,5,3,8,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[2,4,8,3,7,5,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,3,7,5,6,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,2,5,8,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,7,3,8,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,5,3,7,1,2,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[6,7,2,8,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,3,2,8,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,7,8,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,5,8,1,3,2,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,7,8,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,7,1,3,8,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,6,7,4,3,8,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,7,6,4,5,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,7,2,8,3,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,7,2,8,5,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,1,5,8,6,4,7,2]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,3,8,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,6,4,7,5,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,6,2,8,7,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,5,6,1,8,7,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[3,6,2,8,4,7,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[2,3,8,5,7,4,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,8,6,7,5,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,7,8,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[3,5,1,8,6,4,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,1,3,8,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,8,3,6,4,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,8,6,3,4,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,7,5,8,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,7,8,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,3,7,8,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,1,2,5,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,1,2,3,5,4,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[6,1,2,5,4,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,1,4,6,7,3,2,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[6,7,3,5,4,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[1,6,4,3,7,2,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,7,8,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,3,6,5,7,8,9,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,2,2,1]=>[5,4,2,2,2,1]=>12
[3,4,5,6,7,1,2,8,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1]=>[7,4,3,2,1]=>10
[2,7,3,1,4,8,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,6,5,7,8,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[4,3,1,5,8,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[4,7,1,3,2,5,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,1,6,7,3,2,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[1,7,2,5,6,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,6,8,3,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,4,8,6,1,7,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,5,4,7,1,8,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[6,1,3,8,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,1,8,7,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,8,6,3,1,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,7,1,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,5,4,1,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,1,5,7,6,3,2,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[6,3,4,2,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,5,1,7,6,3,2,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[5,4,2,1,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,2,1,5,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,5,3,6,7,8,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]=>[4,3,1,1,1]=>7
[1,8,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,2,4,5,7,8,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]=>[4,4,3,2]=>5
[2,3,4,7,5,8,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,1]=>7
[6,5,2,8,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,2,7,8,4,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,8,2,7,5,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,1,7,4,3,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[1,7,8,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,3,7,4,2,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,7,6,4,3,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,3,4,2,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,4,3,8,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,2,7,6,3,5,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,3,7,2,8,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,7,5,6,1,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,6,8,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[3,2,6,4,8,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[4,2,2,2]=>3
[4,2,8,3,6,5,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,2,8,5,7,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,5,7,1,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,3,4,1,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[6,5,7,3,4,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[5,2,7,6,8,1,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[1,7,5,8,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,7,1,2,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[3,7,5,6,8,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[3,6,5,2,4,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[6,8,5,2,4,3,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,4,2,8,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[3,7,1,6,2,5,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,6,7,2,5,1,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,6,2,5,1,7,8,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[3,4,2,7,8,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[3,8,5,2,4,7,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,1,4,3,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,2,3,8,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,7,6,3,1,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,6,8,2,1,3,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1,1]=>[2,2,1,1]=>4
[4,6,2,7,8,1,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[4,6,2,7,9,1,3,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[6,2,3,7,1,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[4,2,5,7,9,1,3,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[6,4,2,8,1,3,5,7,9]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,3]=>[3,3]=>0
[4,6,8,9,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[4,6,7,8,2,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[6,2,3,7,9,1,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,3,4,1,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[7,8,5,9,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[7,8,5,3,9,6,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[4,1]=>[1]=>0
[7,4,8,5,9,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,8,4,9,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[7,8,5,3,1,9,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[5,1]=>[1]=>0
[6,7,8,4,2,9,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>[2,1]=>1
[6,7,3,8,4,9,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,6,7,8,3,9,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[6,7,3,8,4,1,9,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1]=>[3,1]=>1
[5,6,7,8,3,1,9,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[6,2,7,3,8,4,9,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2]=>[4,2]=>1
[4,5,6,7,8,2,9,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[5,6,1,7,2,8,3,9,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1]=>[5,3,1]=>3
[8,9,6,10,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,6,4,10,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,5,9,6,10,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[8,9,6,4,2,10,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[7,8,4,9,5,10,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1]=>[3,1]=>1
[6,7,8,9,4,10,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[6,7,8,9,4,2,10,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,3,2,1]=>[3,2,1]=>3
[5,6,7,8,9,3,10,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,3,1,10,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[7,4,3,2,1]=>[4,3,2,1]=>6
[6,7,2,8,3,9,4,10,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,1]=>[5,3,1]=>3
[4,5,6,7,8,9,2,10,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,5,4,3,2,1]=>[5,4,3,2,1]=>10
[6,1,3,4,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,1,3,6,2,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[6,3]=>1
[1,5,7,6,8,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,7,1,3,8,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[2,6,1,4,3,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,6,2,4,3,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[5,3,7,6,1,8,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[1,5,6,3,7,8,4,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,5,7,6,3,8,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,3,7,8,5,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,7,8,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,5,6,1,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,6,2,8,4,7,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,7,6,3,4,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,7,5,4,6,1,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[5,3,4,7,6,8,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,3,7,4,6,1,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,7,6,3,4,1,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,6,1,3,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,3,4,1,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[5,7,6,1,3,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,6,3,8,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[5,1,3,7,6,2,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[1,6,3,7,2,4,5,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,3,2,4,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,8,5,3,2,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,6,2,7,1,3,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,4,6,5,1,8,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[3,5,1,4,7,2,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[4,4,1,1]=>4
[5,1,4,8,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,3,4,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,2,3,7,8,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[1,5,3,8,4,2,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,4,2,1,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,1,7,4,2,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,1,6,8,4,2,7,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[1,5,2,8,3,6,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,3,4,9,5,6,7,8,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,4,5,6,7,8,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,4,9,6,5,7,8,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,4,6,7,8,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,9,4,3,5,6,7,8,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,10,4,5,6,7,8,9,1]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[5,6,2,3,7,4,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[6,2,4,7,3,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,4,8,5,3,6,7,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,5,6,3,1,8,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[4,5,1,2,7,8,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,4,1]=>2
[4,8,5,1,2,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,6,7,5,1,2,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[6,1,4,7,3,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[2,8,4,6,3,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,4,1,5,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,1,7,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,7,5,1,3,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,5,6,3,8,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[5,6,1,3,7,2,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[5,6,1,8,2,3,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,6,1,2,8,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[3,7,8,1,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,7,8,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,6,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,5,6,4,2,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,5,8,6,4,2,7]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[1,5,7,8,6,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,8,2,6,5,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,1,2,3,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,6,2,5,8,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,2,7,3,4,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,2,1,6,5,7,8,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[2,7,5,4,1,3,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,6,5,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,6,3,5,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,5,8,7,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,7,8,5,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,4,8,5,7,3,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,8,5,2,7,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,3,4,8,5,2,7,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,5,8,7,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[6,5,3,7,4,1,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,1,5,4,6,8,7,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]=>[5,4,2,2]=>5
[3,6,1,4,5,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[1,8,4,7,2,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,8,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,4,2,3,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[3,8,1,6,4,2,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,3,7,4,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,7,8,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,8,1,2,6,5,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,1,8,3,7,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[2,8,1,6,5,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,2,5,7,6,8,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[4,3,5,1,7,8,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,2]=>2
[1,8,5,2,3,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,6,2,3,4,5,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,5,8,2,3,4,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,2,7,8,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,3,8,7,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,4,8,2,7,6,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,2,5,6,4,8,1,7]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,3,2,2]=>5
[2,3,7,1,5,8,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,3,6,1,7,5,8,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]=>[4,2,2,2,1]=>7
[3,6,4,2,1,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,3,2,6,5,8,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,6,5,2,1,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[4,6,1,7,5,8,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,2,6,5,1,7,8,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[4,1,5,7,6,8,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[3,5,6,2,1,4,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[6,2,1,1]=>5
[4,2,5,7,6,8,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[4,3,6,5,2,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,3,6,5,1,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[3,6,4,5,2,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,5,6,4,2,8,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,2,1,1]=>5
[4,6,5,3,1,7,8,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[5,8,1,4,2,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,8,2,3,1,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,4,8,1,7,2,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,3,6,8,1,4,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[3,5,1,8,6,4,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[4,7,2,8,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,3,8,4,6,2,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,5,6,8,7,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,3,2]=>3
[1,5,6,8,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,6,8,1,2,4,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,8,1,4,5,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,3,5,1,8,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[1,3,5,6,8,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[4,3,2,2,1,1]=>13
[5,6,8,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,5,1,2,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,8,7,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,7,2,8,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,1,5,3,4,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,8,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,2,1,7,8,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[1,5,6,4,2,8,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[3,2,8,1,7,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,7,8,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[6,8,1,7,3,4,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,5,6,7,8,9,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1,1]=>[4,3,2,1,1,1,1]=>15
[4,6,5,3,8,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,5,6,3,8,1,7,2]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,2,1]=>3
[6,3,7,5,2,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,2,4,5,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,3,7,5,1,4,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,3,8,2,4,6,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,1,7,3,4,2,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[3,1,7,2,5,8,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,8,7,6,3,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,1,5,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,6,2,8,1,7,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[5,3,1,8,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,1,4,6,8,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,3,2]=>5
[4,1,5,7,3,8,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[3,3,2]=>2
[6,2,5,8,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,5,7,8,4,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,6,5,7,4,1,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[3,1,1,1]=>3
[1,6,5,7,4,2,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,4,7,5,2,1,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[3,6,7,5,8,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,4,7,2,5,6,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,1]=>3
[2,5,3,7,8,6,4,1]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,2,3,8,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,4,3,1,2,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]=>[7,6]=>1
[7,6,5,4,3,1,2,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7]=>[8,7]=>1
[6,8,7,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,6,1,4,5,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,8,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,1,8,4,6,5,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[2,3,1,8,4,6,7,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[6,2,3,4,5,1,9,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6]=>[6,6]=>0
[2,3,4,9,6,7,1,8,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,6,1,7,8,4]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,9,5,1,7,4,8,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,3,10,5,6,1,8,9,4,7]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,5,6,1,8,4,9,7]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,5,6,1,8,4,7,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,5,6,1,4,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,5,1,7,4,9,6,8]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,5,1,7,4,6,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,5,1,4,6,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,10,4,1,6,3,8,5,9,7]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,4,1,6,3,8,5,7,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,4,1,6,3,5,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,4,1,3,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[5,8,7,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,5,1,7,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,2,7,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,2,8,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,8,7,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,3,8,7,6,2,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,7,6,1,4,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,1,6,2,7,5,3,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,3,1,7,6,2,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,5,3,1,2,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[5,7,6,2,3,1,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,1,3,7,5,2,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,1,6,3,2,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[2,4,8,5,6,3,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,7,4,1,3,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,7,4,1,3,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[2,6,8,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,2,3,7,4,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,5,1,6,3,2,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]=>[6,3,1]=>3
[5,1,6,3,2,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,1,6,2,4,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,3,4,8,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,8,2,6,7,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,4,7,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,8,5,2,7,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,4,7,2,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,8,4,3,1,5,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,4,5,8,3,2,6,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[1,5,2,4,7,8,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,2,7,4,3,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[2,7,3,4,8,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,6,8,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,4,5,3,8,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,3,7,4,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,6,3,2,7,5,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,4,2,7,1,5,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[2,5,3,6,4,7,8,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]=>[5,3,1,1,1]=>7
[4,2,5,3,6,7,8,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[5,4,2]=>3
[1,6,5,2,4,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,7,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,4,2,8,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,6,8,3,5,2,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,6,2,3,5,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,8,3,6,5,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,3,8,6,5,2,4,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,7,3,2,8,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,6,5,2,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,5,3,2,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,2,8,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,5,2,8,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,8,3,7,2,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,4,2,8,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,8,5,2,7,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,5,1,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,8,2,7,4,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,1,7,5,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,6,4,8,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,5,6,2,8,7,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[1,6,5,3,4,7,8,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[4,2,6,7,8,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[4,6,5,1,3,7,8,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[5,1,7,2,6,4,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,1,7,6,5,8,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[5,2,1,7,6,4,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,2,3,6,7,8,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[4,7,2,1,6,5,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,7,6,4,1,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,3,6,7,8,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1]=>8
[6,5,1,3,7,8,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,1,2,4,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,1,4,8,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,8,5,7,2,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,7,5,8,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,7,5,8,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,1,4,7,8,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,8,6,1,2,4,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,8,7,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,1,8,7,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,1,2,4,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,7,1,4,2,3,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,1,7,4,8,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,7,8,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,7,6,5,4,3,2,9,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,7]=>[7]=>0
[3,1,5,6,7,8,9,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,2]=>[5,4,3,2,2]=>9
[4,3,8,5,6,2,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,3,8,6,7,2,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,3,8,1,7,2,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,5,4,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,5,4,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,7,1,8,5,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,8,2,3,5,1,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,8,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,1,6,4,8,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,1,1]=>5
[3,5,8,6,2,1,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,4,8,5,6,1,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,8,2,5,6,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,4,2,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,5,3,1,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,8,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,1,2,8,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,8,2,7,5,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,7,4,6,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,7,2,6,5,8,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,8,5,7,4,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[6,7,5,2,4,8,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,7,5,4,8,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,5,8,1,3,4,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,4,5,1,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,8,7,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,7,1,4,3,2,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,8,1,3,4,2,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,6,3,2,8,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[5,2,1,1,1,1]=>9
[1,3,7,6,8,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,6,7,3,2,8,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,2,7,6,8,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[1,3,8,5,2,7,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,4,1,5,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,1,6,5,7,2,4,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[2,6,1,5,7,4,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,5,7,1,6,3,8,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,1,5,7,4,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,6,5,1,4,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,6,5,1,7,2,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[4,1,1,1]=>3
[3,6,5,2,1,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[5,4,3,6,1,7,2,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[4,5,2,7,6,1,3,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,6,5,3,1,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[5,4,1,6,3,7,2,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,4,2,6,3,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[3,6,5,7,1,4,2,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[3,6,5,1,4,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[4,3,6,5,7,1,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,2,6,5,1,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,1,6,5,3,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[4,2,5,7,6,1,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[3,4,7,6,1,2,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,2,5,7,6,3,8,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[4,1,6,5,2,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[3,6,5,7,2,1,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[3,5,7,6,2,4,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[5,4,2,6,3,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[4,6,5,2,7,3,1,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,6,5,2,1,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[3,5,8,2,1,4,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[3,5,8,2,4,6,7,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,3,8,2,1,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,1,8,2,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,3,8,2,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,5,8,4,2,3,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,2,1,4,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,4,1,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,4,6,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,2,4,3,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,1,4,6,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,8,4,6,7,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,1,8,4,6,7,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,4,6,3,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,4,6,7,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,6,7,2,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,8,1,6,2,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,1,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,4,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,7,2,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,4,6,7,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,6,3,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,5,8,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,6,8,5,1,7,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,1,5,8,7,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[3,3,2,2,2]=>6
[4,3,1,7,8,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
[5,6,8,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[2,8,5,3,6,4,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,6,4,7,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,3,2,7,8,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,2,7,8,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,8,3,7,1,4,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,2,7,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,3,2,7,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,2,4,8,7,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,6,8,1,5,3,4,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,2,5,6,8,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[3,8,1,6,4,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,2,4,8,6,3,7,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[5,7,2,3,1,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[1,8,6,4,7,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,5,8,7,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,3,8,7,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,8,5,1,7,4,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,6,4,7,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,4,6,3,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,6,4,7,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,4,5,6,7,9,1,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,1]=>[5,4,3,2,1]=>10
[3,4,5,7,8,9,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,3,2,1]=>[4,3,3,2,1]=>9
[3,5,6,7,8,9,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,4,5,6,9,1,2,7,8]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[4,1,8,6,3,7,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,3,1,6,2,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[3,5,4,1,7,8,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[6,4,2,1,5,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[3,1,5,8,7,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[3,2,5,7,8,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[5,3,7,4,2,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,3,7,4,2,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,3,8,4,2,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,8,4,3,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,1,8,4,3,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,7,4,3,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,2,7,4,3,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,3,7,4,1,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,1,5,7,8,4,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[3,1,5,7,8,4,2,6]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[3,3,2,2]=>4
[5,2,7,4,1,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,2,3,7,4,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,2,3,7,4,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,2,3,7,4,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,1,3,7,4,5,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,2,8,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,1,3,7,4,5,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,8,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,1,8,5,3,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,5,7,8,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[2,5,7,8,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,8,2,7,5,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,4,1,8,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[5,6,8,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,1,5,3,8,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,8,7,1,4,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,7,8,2,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[5,3,2,1,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[5,3,2,4,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,2,4,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[4,8,1,7,3,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,2,4,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[2,7,6,3,1,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,4,5,6,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,6,8,3,7,1,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,3,5,8,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[1,7,6,4,2,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,7,2,5,1,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,6,5,7,1,4,8,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[3,5,1,7,8,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[3,4,1,8,6,7,5,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[4,3,8,5,1,7,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,1,3,2,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,7,4,2,5,8,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,3,8,4,7,5,2,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,3,7,1,4,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,7,2,6,1,4,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,8,5,7,6,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,4,7,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,7,4,6,8,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[4,8,6,3,7,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,3,1,7,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,6,4,8,1,7,3]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[5,7,2,1,6,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,7,8,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,5,2,1,6,7,8,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[5,4,1]=>3
[4,5,6,3,1,7,8,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[5,2,1]=>3
[3,5,6,7,4,1,8,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[3,5,1,4,2,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[1,3,8,4,6,2,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,8,4,2,3,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,3,2,7,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,7,6,5,2,4,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,2,8,6,7,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,5,4,3,2,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[8,9,10,1,5,6,7,3,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,7,1,3,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,5,6,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,1,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,3,4,7,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,6,10,1,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,5,6,10,3,4,7,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,10,1,5,6,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,7,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,5,6,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,1,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,6,10,1,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,5,6,10,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,10,1,5,6,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,1,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,3,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,6,10,1,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,5,6,10,3,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,5,6,10,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,10,1,5,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,10,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,5,10,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,10,1,5,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,1,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,10,1,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,5,10,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,5,10,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,5,3,6,10,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[8,9,5,3,6,10,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[8,5,9,10,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,5,9,10,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,5,9,10,1,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,5,9,10,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,5,9,10,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,8,5,7,4,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,7,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,5,2,4,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,2,7,8,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,6,3,7,5,8,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[4,2,5,7,8,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,6,8,4,5,2,1,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,2,5,8,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[6,7,2,4,5,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[5,2,7,8,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,4,7,8,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,2,8,3,1,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,8,6,2,7,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,4,8,2,1,7,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,8,4,2,1,7,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,4,6,8,2,5,7,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[3,6,2,4,8,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[1,5,2,6,8,3,7,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[4,5,3,1,8,2,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[5,1,7,8,3,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,1,7,3,2,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,2,1,7,3,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,8,2,1,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,5,1,8,3,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[6,7,8,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,6,2,7,8,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[8,1,9,10,7,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,1,10,9,6,7,8,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[3,1,9,10,8,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[3,1,8,9,10,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,2,2,2,2]=>[3,2,2,2,2,2]=>5
[4,7,6,3,5,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,7,6,5,2,4,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,4,7,8,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,7,8,3,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,8,2,3,5,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,1,4,6,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,3,1,4,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,5,7,1,8,6,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[4,3,8,6,5,2,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,3,8,6,5,1,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,4,7,3,1,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,2,5,6,8,4,1,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[4,3,2,2]=>5
[3,7,5,6,2,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,4,5,6,7,1,9,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,6,4,3,2,1]=>[6,4,3,2,1]=>10
[5,3,4,2,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[5,6,8,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,5,2,1,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,4,3,5,6,8,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1]=>[5,4,3,1,1]=>9
[6,3,2,4,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,3,1,2,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[2,5,6,3,8,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[6,8,4,2,3,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,7,6,2,8,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,1,3,8,5,2,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,8,5,4,7,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,4,3,8,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,1,4,5,8,6,2,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[1,8,3,2,5,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,7,3,2,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,7,8,1,3,2,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,7,4,8,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,8,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,1,2,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,1,2,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,2,5,7,8,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[3,4,5,8,1,7,2,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[6,3,4,2,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,6,3,7,8,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[4,3,8,6,7,5,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,5,6,2,7,8,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[4,2,1]=>3
[4,5,6,2,7,1,8,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,2,1]=>3
[4,5,6,2,1,7,8,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[5,2,1]=>3
[4,5,6,2,1,7,3,8]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]=>[5,2,1]=>3
[6,8,7,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,5,1,6,7,3,2,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]=>[4,3,1]=>3
[2,5,1,8,3,7,4,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,7,2,1,3,8,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[3,7,5,4,1,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[7,6,5,4,3,1,2,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[9,8,7,6,5,4,3,2,1,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,9]=>[9]=>0
[8,7,6,5,4,3,1,2,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[7,6,5,4,2,1,3,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[7,6,5,4,1,3,2,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[2,7,4,5,6,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,4,6,8,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[2,8,4,5,6,7,9,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,5,8,1,6,7,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,4,7,5,6,8,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,7,6,5,2,8,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,3,5,8,6,7,9,2,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,3,3,2]=>[3,3,3,2]=>3
[2,5,4,8,6,7,3,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,7,3,6,4,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,5,1,4,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[6,3,5,4,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,3,7,6,4,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[3,7,6,4,2,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[5,1,4,7,6,8,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,8,1,4,3,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,4,3,8,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[1,6,4,3,8,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,7,4,1,3,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[4,3,1,8,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,2,7,5,1,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[5,2,3,7,4,1,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[2,1,7,4,3,6,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,7,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,3,1,4,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,2,5,4,6,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,3,8,1,6,7,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,6,4,2,5,7,8,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[6,5,3,4,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,6,3,4,1,7,8,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[6,8,2,3,1,5,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,3,1,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[6,4,3,7,5,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[5,2,4,7,8,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,4,8,7,2,3,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,2,1,7,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,7,2,1,8,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,5,4,7,3,8,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,6,8,4,1,7,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,1,8,4,7,6,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,5,6,8,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,2,4,7,8,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[1,6,2,7,4,5,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,7,8,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[7,9,6,8,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,7,5,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,9,5,8,4,7,2,3,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,9,4,8,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,7,1,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,9,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,6,9,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,10,9,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,2,5,1,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,4,3,2,7,1,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5]=>[7,5]=>1
[5,4,3,2,6,1,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4]=>[7,6,4]=>3
[2,5,3,7,6,4,8,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,1,5,7,6,4,2,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[3,3,2,2]=>4
[2,5,6,8,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[3,6,2,4,5,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,6,2,5,4,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,5,1,7,6,4,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[3,3,1,1]=>4
[3,6,1,4,5,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[4,6,1,3,5,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[3,6,4,2,5,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[4,2,6,3,5,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[3,4,7,6,5,1,2,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,5,2,7,1,3,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,6,1,2,5,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[5,8,4,7,1,3,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,7,1,3,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,8,1,3,5,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,3,2,7,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,3,1,5,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,1,2,5,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,8,3,4,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,7,1,6,4,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,5,2,6,1,3,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]=>[6,3,1]=>3
[4,3,5,8,6,1,7,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[5,1,3,6,7,4,2,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[4,3]=>1
[4,2,8,3,6,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,8,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[6,2,1,7,5,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[3,7,1,8,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,6,7,1,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,1,2,4,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,3,1,6,4,7,2,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[1,5,2,3,7,8,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[4,2,8,1,6,5,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,6,4,1,7,2,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[7,8,9,3,2,1,4,5,10,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1]=>[2,1]=>1
[5,2,6,3,7,8,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[2,6,1,5,7,8,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,1,6,4,7,8,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,2]=>1
[4,7,6,8,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[5,7,4,8,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[3,6,7,5,8,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[2,1,1,1]=>3
[3,7,5,6,8,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,6,8,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,4,7,2,6,3,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[2,4,5,8,3,1,7,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[1,4,7,5,8,3,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,6,8,7,3,5,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,7,8,6,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,8,7,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,6,3,5,4,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,8,1,6,5,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,8,7,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,2,5,1,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[2,6,5,1,3,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,6,5,1,2,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[5,6,4,1,2,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[6,4,5,1,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,4,6,1,3,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[5,7,1,4,3,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[2,6,4,1,3,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[5,1,1,1,1]=>4
[1,2,6,7,8,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[6,1,4,8,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,3,7,1,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,4,1,7,3,2,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[1,5,6,7,4,8,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[6,3,2,5,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,7,3,8,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[4,5,2,7,6,3,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[3,3,1]=>2
[4,5,2,1,7,6,3,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[2,6,7,8,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,3,2,5,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,6,3,7,8,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[5,6,7,1,8,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[1,7,8,4,6,5,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,2,8,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,1,2,8,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[2,7,8,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,2,7,6,3,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,4,7,6,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,4,7,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,4,6,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,1,8,4,7,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,4,2,8,1,7,6,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[2,4,5,8,1,7,6,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[3,1,8,2,6,7,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,6,8,1,4,3,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,1,8,2,6,7,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,6,5,2,8,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,6,1,5,8,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,8,4,5,3,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,5,3,2,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[6,2,5,3,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,2,4,5,3,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,5,4,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,8,5,4,7,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,8,4,2,5,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,2,8,3,5,7,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,6,2,4,8,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,8,5,4,2,6,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,2,8,6,4,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,6,5,2,7,4,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,1,6,7,4,2,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[1,5,4,2,8,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,8,5,4,6,2,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,4,6,2,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,4,1,6,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,5,1,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[4,8,1,3,7,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,3,1,2,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[6,4,2,3,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,2,1,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,7,8,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,7,6,8,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,6,4,2,1,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,5,7,4,1,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,6,1,8,3,5,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,7,1,8,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,8,3,6,1,5,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,8,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,2,8,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,6,8,7,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,1,2,6,8,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[4,3,3,3]=>3
[5,7,4,2,1,8,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[6,4,8,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,8,2,5,7,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[6,4,8,2,5,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,2,4,5,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,8,2,4,7,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,2,7,1,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,2,4,1,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,2,5,7,1,6,8,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[2,4,8,5,6,7,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,5,2,3,8,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[2,5,4,7,6,1,3,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,2,3,7,6,1,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,2,3,7,6,1,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,2,7,3,5,1,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,6,2,3,8,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,2,3,1,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[5,7,2,3,4,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,2,7,3,5,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,5,2,3,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,5,2,3,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,3,4,2,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,2,4,5,6,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,2,5,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,8,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,3,1,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,3,1,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,2,1,4,6,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,2,7,1,5,6,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,2,3,8,1,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,1,3,8,4,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,3,2,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[5,1,3,4,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[6,1,3,4,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,8,7,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,2,8,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,2,3,7,4,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[2,5,3,7,4,6,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,6,7,3,4,5,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,7,3,4,5,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[3,8,4,5,2,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,3,4,5,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,7,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,10,3,4,5,6,7,8,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[4,5,7,2,8,3,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[7,2,8,3,9,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[4,2]=>[2]=>0
[5,8,3,7,2,9,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,5,6,9,3,8,2,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[4,5,6,8,2,9,3,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[7,4,5,6,3,9,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[5]=>0
[8,4,7,3,10,6,2,9,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,3,10,5,7,2,9,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[8,2,9,3,10,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[5,2,1,3,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[1,6,5,7,2,8,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,1,5,2,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[1,6,5,7,2,8,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,4,6,2,8,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,5,4,6,2,8,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[5,3,1,1,1,1]=>9
[1,5,6,4,8,2,3,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[6,2,1,5,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,5,3,7,8,1,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[3,4,2,8,1,6,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[4,3,7,5,1,6,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,2,6,1,4,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[6,2]=>1
[3,5,2,8,6,7,4,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[5,3,7,4,2,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,6,2,8,7,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,6,3,5,2,7,8,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[4,1,6,3,5,7,2,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[3,1,5,7,4,6,8,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[4,3,6,1,5,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[5,3,1,4,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[5,4]=>1
[4,6,7,1,3,5,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[5,6,1,3,4,7,2,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[2,5,3,7,8,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[3,3,1,1,1]=>6
[4,6,2,1,3,7,8,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[3,6,2,4,1,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[3,2,6,7,4,8,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[6,3,2,7,5,8,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,2,7,1,4,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,2,6,1,5,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[2,5,4,1,3,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]=>[6,5,1,1,1]=>7
[5,4,1,2,6,7,3,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[5,4]=>1
[6,5,2,7,4,1,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,7,3,1,4,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,7,4,3,1,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,2,5,6,7,8,9,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[3,1,6,7,8,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[3,2,2,2]=>3
[6,4,5,2,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[3,7,5,6,2,1,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,7,6,3,8,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,1,2,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,4,1,3,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[5,1,8,3,4,6,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,2,3,7,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,8,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,7,2,5,1,6,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,5,4,7,2,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,2,4,6,5,8,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[3,5,4,8,7,1,6,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[6,3,1,7,4,2,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,8,5,3,7,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,2,6,3,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,6,4,2,1,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[6,8,1,3,2,7,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,3,6,4,1,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[2,4,3,5,8,1,6,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,4,3,1,1]=>8
[5,8,2,6,7,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,5,3,8,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,1,2,4,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,5,8,2,7,3,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,7,6,8,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,5,3,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,1,2,4,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[4,6,1,3,7,8,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[1,5,6,3,8,7,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[5,3,2,6,8,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[6,3,5,2,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,3,8,7,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,5,3,1,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,8,6,1,5,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,4,7,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,4,1,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[6,4]=>1
[2,7,1,4,6,3,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,1,4,5,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,1,5,8,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[8,1,2,7,4,10,6,5,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,1,7,3,2,10,6,4,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[7,1,2,3,10,5,6,9,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[8,1,2,3,10,5,9,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,1,2,10,4,3,9,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,1,2,10,4,9,5,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[8,1,10,3,2,5,9,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,1,10,3,2,9,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,1,2,3,10,9,5,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,1,2,10,3,9,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,1,2,10,9,4,6,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[8,1,10,2,4,9,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,1,10,2,9,3,6,4,5,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,10,1,3,4,9,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,10,1,3,9,2,6,4,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,3,8,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,4,6,5,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,2,8,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,1,2,6,3,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[6,4]=>1
[6,5,1,4,7,3,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[2,7,8,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,6,5,7,8,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,6,7,5,8,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[3,2,2,1,1]=>8
[2,4,6,3,7,8,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[4,2,2,1,1]=>8
[2,4,5,6,8,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,4,5,6,8,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[4,3,2,1,1]=>9
[2,4,5,6,3,8,1,7]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]=>[5,3,2,1,1]=>9
[2,3,4,6,8,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,3,3,2,1]=>9
[5,2,8,3,4,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,4,1,2,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[4,1,7,3,8,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,5,2,7,6,8,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,7,6,8,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,8,2,7,6,5,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,5,8,2,7,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,4,8,5,7,3,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,1,4,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,4,8,5,2,1,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[4,8,7,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,7,4,6,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,4,1,8,7,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,3,3,1]=>3
[1,3,5,6,8,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[4,3,2,2,1,1]=>13
[2,8,7,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,7,3,4,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,1,3,2,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[2,6,5,8,3,1,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,7,8,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[3,2,8,4,5,7,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,1,8,2,4,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,3,8,4,7,6,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,6,4,7,8,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,4,3,7,6,1,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[3,1,2,8,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[2,3,8,4,1,7,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,6,1,3,2,7,8,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[6,7,2,5,8,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,1,7,8,2,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,4,6,7,1,5,8,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[3,4,5,7,8,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[3,3,2,1]=>5
[1,8,7,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,4,5,8,1,3,7,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,7,8,6,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,3,1,5,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,8,3,5,6,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,7,5,8,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,2,8,5,6,1,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,7,5,8,1,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,7,5,8,1,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[3,4,7,5,2,8,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[4,3,2,5,7,8,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,3]=>2
[2,4,7,5,8,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,5,4,7,3,8,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,7,8,4,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,5,4,8,7,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,2,4,5,8,1,6,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[3,6,8,4,2,7,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[1,4,7,6,3,8,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,6,5,1,7,2,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[1,3,6,8,2,4,7,5]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[1,6,7,4,3,8,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,7,2,8,5,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,1,3,8,7,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[1,6,4,7,3,8,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[3,4,5,6,7,8,2,1,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1]=>[5,4,3,2,1]=>10
[4,8,1,6,3,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,6,2,4,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,2,4,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,6,8,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,8,4,6,3,5,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,8,3,6,4,5,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,1,4,6,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,7,5,4,1,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,1,8,5,3,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[3,8,5,2,1,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,4,8,2,6,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,5,8,1,3,7,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[1,4,7,8,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,8,6,1,2,5,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,2,1,8,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,3,7,6,1,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[6,8,1,5,4,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,2,5,4,8,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[4,6,8,7,3,1,2,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,5,2,6,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,5,6,2,8,1,4,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1]=>5
[8,9,10,4,5,6,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,5,6,10,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[8,9,10,4,5,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,5,10,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,4,5,2,3,6,10,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[7,1]=>[1]=>0
[8,9,10,4,5,6,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,5,6,10,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[8,9,10,4,5,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,5,10,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,4,5,2,6,10,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[6,1]=>[1]=>0
[8,9,10,4,5,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,5,10,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,9,4,5,2,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[8,9,4,5,2,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[8,9,10,4,2,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,10,2,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,4,2,5,6,10,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[6,1]=>[1]=>0
[8,4,9,10,2,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[8,9,10,4,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,4,10,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,9,4,2,5,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[8,9,4,2,5,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[8,4,9,10,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,2,4,3,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[6,1,8,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,8,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,4,8,7,1,2,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,6,4,3,8,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[4,6,3,8,5,2,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,1,3,8,5,6,2,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[5,2,8,3,1,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,7,8,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,2,4,5,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,2,8,1,5,7,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,4,6,7,2,1,5,8]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]=>[3,2,2,1]=>5
[2,6,7,1,4,3,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,7,6,2,1,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,2,5,3,8,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,2,7,4,8,5,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[7,8,9,10,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[2,8,9,10,3,6,7,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[7,8,9,10,4,5,6,1,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,3,5,6,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[3,8,9,10,4,6,7,1,5,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,6,9,10,4,7,8,1,5,2]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[7,8,9,10,1,5,6,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[1,8,9,10,2,6,7,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[7,8,9,10,3,4,6,1,5,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,8,9,10,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[3,8,9,10,4,5,7,1,6,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,7,9,10,3,4,8,1,5,2]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[7,8,9,10,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,8,9,10,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[1,8,9,10,2,5,7,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>7
[6,7,9,10,1,4,8,2,5,3]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,1]=>[2,2,1]=>2
[1,7,9,10,2,5,8,3,6,4]=>[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]=>12
[1,7,8,10,2,5,9,3,6,4]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,3,2,1,1,1,1,1,1]=>[3,2,1,1,1,1,1,1]=>13
[5,8,2,7,4,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,2,8,3,7,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,8,3,1,2,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,8,3,2,1,7,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,8,3,5,1,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,5,2,6,8,7,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[1,7,6,3,8,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,7,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,2,8,7,4,5,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,2,4,3,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,4,2,5,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[3,8,2,1,5,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,3,2,8,7,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[3,3,3,3,1,1]=>8
[5,4,2,7,3,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,6,3,7,8,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[6,2,5,4,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,1,5,6,3,8,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[6,8,7,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,5,1,3,7,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,5,8,3,7,6,1]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[5,6,4,1,8,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[6,4,5,1,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,3,5,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[1,3,8,7,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,5,4,1,8,3,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[5,1,4,8,3,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,8,3,2,7,6,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,7,3,4,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,5,3,1,2,4,6,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[8,7,5,3,1,2,4,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[5,3,1,2,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[7,5,3,1,2,4,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[3,1,2,8,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[5,3,1,2,4,9,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[1,4,3,8,5,7,2,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[6,7,1,5,2,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[1,5,3,7,6,4,8,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,8,1,3,6,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,7,3,4,8,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,4,7,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,1,6,5,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,3,8,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,5,7,4,8,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,8,5,6,7,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,7,1,2,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[2,7,6,4,3,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,2,7,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,8,1,6,2,5,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,4,2,5,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,3,1,2,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,4,8,5,2,3,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,8,5,2,3,7,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,8,7,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,5,4,2,8,3,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,8,7,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[6,7,4,2,8,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,1,6,8,7,2,3,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,7,5,6,2,8,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,7,5,2,8,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,8,4,3,2,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,9,8,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,10,9,8,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,1,7,3,5,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,3,7,6,4,8,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,6,4,8,7,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,1,8,7,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,1,5,8,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,1,8,5,7,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,7,3,5,8,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,7,3,5,8,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,3,1,6,4,8,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[2,5,6,7,1,4,8,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]=>[3,2,1,1,1]=>7
[4,7,5,3,2,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,7,5,2,8,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,8,6,7,2,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,1,2,7,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,1,8,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,6,3,7,8,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[6,3,1,8,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,5,8,1,4,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,1,8,9,10,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,8,1,2,3,9,10,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[6,5,1]=>[5,1]=>1
[7,8,1,2,9,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,1,9,2,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1]=>[3,1]=>1
[7,8,1,9,10,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,9,1,2,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,2,1]=>[2,1]=>1
[6,8,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,1,8,7,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,7,6,5,4,3,2,9,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1,1,1,1,1]=>[7,1,1,1,1,1,1]=>6
[6,8,4,3,5,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,4,7,3,6,8,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,7,1,4,6,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,4,7,3,6,8,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,7,5,6,1,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,2,8,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,1,3,8,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,4,1,8,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,1,4,2,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,8,2,1,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,3,1,8,7,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[1,5,6,7,2,4,3,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[6,8,3,7,1,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,6,4,1,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,7,3,6,2,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,7,4,5,1,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[1,6,5,3,8,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[5,6,1,2,4,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[4,1,8,7,2,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,2,4,6,1,8,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]=>[5,3,3,2]=>5
[3,6,7,4,1,2,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[2,1,1,1]=>3
[1,4,7,5,8,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,6,8,4,7,3,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,6,7,5,4,8,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[4,5,7,2,6,3,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[2,3,5,7,8,1,6,4]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,5,7,4,2,3,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,4,7,5,3,6,8,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,4,7,8,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,5,3,6,8,2,4,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[4,8,1,2,6,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,2,6,3,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,2,3,7,5,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,1,2,6,5,7,8,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[5,3,3]=>2
[1,8,4,2,7,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,3,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,1,8,3,7,4,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,1,7,6,8,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,3,1,8,2,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,8,3,2,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,1,5,4,6,7,8,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]=>[5,4,2,2]=>5
[2,8,5,7,3,1,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,7,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,1,7,3,8,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,7,5,3,2,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,1,6,5,7,8,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1]=>[5,3,3,1]=>5
[2,8,7,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,6,2,3,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[4,5,7,6,2,8,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,1]=>2
[3,1,8,7,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,5,6,8,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[2,8,3,1,5,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,4,1,5,2,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,1,7,8,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[1,8,6,2,4,3,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,3,1,6,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,3,1,6,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,2,7,1,5,8,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[1,4,5,6,7,8,9,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,1,1]=>[5,4,3,2,1,1,1]=>18
[4,8,5,1,3,2,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,3,1,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[5,5]=>0
[4,1,6,5,2,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,1,6,3,7,2,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,2,2]=>2
[4,6,1,2,8,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[4,1,3,6,7,2,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[2,6,5,1,3,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,7,4,3,1,5,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[2,1,1,1,1]=>4
[2,6,3,1,7,4,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,5,3,7,2,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[2,3,6,7,1,5,4,8]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]=>[3,2,2,2,1]=>7
[2,7,5,8,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,6,7,3,2,4,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[5,6,1,4,7,2,3,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[4,1]=>1
[1,2,5,7,8,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,2,7,8,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,3,8,6,7,1,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,6,8,2,7,4,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,2,7,4,6,1,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,4,8,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,6,8,5,1,2,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,1,3,6,8,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[6,3,5,7,1,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,8,5,3,2,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,7,3,4,2,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,3,4,2,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,7,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,8,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[7,2,8,9,10,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,1,7,8,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[3,8,2,1,6,7,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,8,3,1,7,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[8,9,10,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,10,2,1,4,7,6,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[8,6,9,10,2,1,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[7,8,9,10,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,9,10,3,4,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,5,3,10,2,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[8,6,9,3,10,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[8,9,4,5,10,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[7,8,4,9,10,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,5,8,9,10,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[2,10,4,5,6,7,9,1,3,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,7,4,1,5,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,1,6,4,7,8,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[4,2,2,2,2]=>4
[5,7,8,3,4,2,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[4,7,5,3,8,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[2,6,4,7,8,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,5,1,8,4,6,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,2,8,4,6,7,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,8,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,3,5,8,4,6,7,2]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[3,4,5,8,2,1,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[6,8,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,4,8,2,7,1,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,1,8,3,4,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,3,7,8,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,1,7,6,3,4,5,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,3,5,2,1,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,1,5,3,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,3,6,8,5,1,7,4]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,2,4,8,6,1,7,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,3,2]=>3
[2,1,3,8,4,5,7,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,2,8,5,4,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[2,1,3,7,8,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]=>[3,3,3,3,2]=>4
[2,1,3,8,4,7,6,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[3,1,2,8,4,5,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[1,2,8,7,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,6,7,2,3,8,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,2,6,5,7,8,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,2]=>3
[3,2,7,5,6,8,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[2,2,2,2]=>0
[2,1,8,7,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,1,5,8,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,4,6,8,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[2,8,5,1,6,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,7,1,8,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[6,1,5,4,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[6,4,5,1,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,2,5,3,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,6,5,2,1,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,8,4,3,6,7,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,5,3,8,6,7,4,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[3,2,6,5,1,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[4,5,8,1,6,7,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,1,8,4,6,7,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,3,8,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,6,3,7,8,1,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,3,8,7,2,1,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,3,8,4,7,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,1,6,7,4,5,2,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[5,1,3,2,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[6,4,2,5,7,3,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[5,7,8,4,2,3,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,4,5,2,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,2,4,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,3,4,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,4,5,3,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,6,4,8,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[2,8,3,7,6,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,2,6,8,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[3,7,2,5,8,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,6,5,3,8,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[2,4,8,7,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,2,8,7,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,5,2,7,6,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,5,1,7,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,7,6,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,4,6,2,5,7,1,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,2,2,1]=>5
[1,7,5,2,6,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,1,7,2,4,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,8,2,1,3,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,1,7,6,4,3,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[6,4,8,5,1,7,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,8,1,3,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,3,2,7,4,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[6,2,1,8,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,1,8,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,2,1,7,6,3,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,2,6,8,5,7,1,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[1,3,4,7,8,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[1,5,4,3,8,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,2,5,8,4,3,6,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[3,3,2,2,2,1]=>11
[1,5,8,2,6,4,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[3,5,6,2,4,7,8,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,2,1,1]=>5
[3,5,6,7,2,4,8,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[3,2,1,1]=>5
[3,5,7,6,8,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,2,6,8,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,5,2,7,6,8,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,4,2,6,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[2,2,1,1]=>4
[3,5,4,7,2,6,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[3,4,5,7,2,6,8,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,7,2,8,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]=>[3,3,2,1]=>5
[3,5,4,7,8,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[3,5,4,7,2,8,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,3,1,1]=>4
[3,2,5,7,4,8,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[3,5,7,4,2,8,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,8,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[2,3,5,7,8,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]=>[3,3,2,2,1]=>8
[3,5,2,7,8,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[3,5,7,8,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,5,7,8,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[3,2,5,6,7,8,9,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,2]=>[5,4,3,2,2]=>9
[4,2,5,6,7,3,8,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]=>[4,3,2]=>3
[4,2,5,6,7,8,9,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[6,1,8,4,3,5,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,6,4,8,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,8,4,1,5,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,8,3,5,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,8,2,5,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,5,1,8,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[5,2,4,8,1,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,4,8,6,7,2,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,5,7,3,8,2,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[4,6,8,1,2,5,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,5,6,8,2,1,4,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,4,5,8,6,3,1,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[5,4,8,2,3,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,7,5,8,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,6,7,5,1,8,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[1,7,3,6,5,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,7,5,2,8,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[5,8,7,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,2,8,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,5,7,8,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,1,7,6,8,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[4,6,7,2,1,5,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[1,7,6,2,4,3,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,1,6,2,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,2,5,8,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,6,8,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,5,3,4,8,2,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[2,8,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,6,5,7,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,2,7,4,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,5,2,8,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,7,2,4,1,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[5,1,2,8,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,1,5,7,2,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[4,1,8,2,6,5,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,1,4,7,8,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,1,5,7,8,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[5,6,8,3,7,4,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,6,1,5,7,2,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[2,5,8,4,6,3,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,3,7,1,2,6,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[6,8,1,5,2,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,5,8,2,3,7,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,6,2,7,4,8,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[1,7,3,2,4,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,1,8,2,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,8,1,3,2,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,7,5,3,8,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,3,8,1,4,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[4,2,5,8,1,3,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[2,4,3,8,1,5,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[3,1,7,4,8,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[6,4,5,3,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,7,3,8,5,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,1,8,2,6,5,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,8,4,1,5,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,7,8,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,8,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,1,8,5,3,4,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,8,6,3,1,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,7,2,8,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,5,6,3,8,1,4,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[1,7,8,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,1,7,4,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,2,3,5,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,8,5,6,4,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,8,4,5,1,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,6,5,7,8,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[3,1,1]=>2
[2,5,8,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,3,2,1,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[1,6,5,3,8,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,2,5,3,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,5,3,4,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,6,5,3,4,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[5,3,4,8,1,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,1,3,4,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,5,3,4,8,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[5,1,3,8,4,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,3,8,1,4,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,5,8,1,7,6,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,6,5,4,8,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,6,5,4,8,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,5,2,4,8,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[2,5,3,6,8,4,1,7]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[4,3,1,1,1]=>7
[4,6,2,5,1,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[2,3,6,5,8,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[2,3,8,7,6,4,1,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,8,3,6,4,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,7,4,8,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[2,2,2,2,2]=>0
[4,2,8,1,3,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,5,1,4,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[6,8,7,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,1,2,4,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[2,4,6,5,7,1,8,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,1,1]=>8
[3,2,8,9,10,1,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,2,2,2,2]=>[3,2,2,2,2,2]=>5
[4,2,6,7,8,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[6,2,4,7,8,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[3,5,2,1,7,8,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[4,2,7,8,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[1,2,7,8,6,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[4,8,1,2,6,5,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,8,1,2,3,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,1,4,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,3,8,5,7,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,3,8,5,7,1,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,8,3,1,4,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,5,7,6,1,3,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,7,1,6,5,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,8,5,4,7,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,4,6,8,7,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[4,6,5,1,3,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,4,6,2,1,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2]=>1
[3,2,8,5,1,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,5,4,1,2,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,5,1,1]=>4
[5,3,8,1,4,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,3,8,1,4,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,7,5,8,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,4,5,1,8,3,7,6]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[6,4,5,3,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[2,5,6,7,8,9,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[2,1,6,7,8,9,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2,2,2]=>[4,3,2,2,2,2]=>9
[2,5,6,7,8,9,10,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,1,1]=>[5,4,3,2,1,1,1]=>18
[2,5,6,3,4,1,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[6,2,1,1,1]=>7
[4,6,2,1,5,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,6,7,2,3,8,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[2,3,5,8,7,4,1,6]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[2,3,5,8,7,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[4,5,3,7,8,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[2,3,5,8,1,6,4,7]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[3,3,2,2,1]=>8
[1,7,4,5,8,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,6,3,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,2,6,1,5,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,3,7,8,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[5,2,6,7,8,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[5,6,2,7,8,3,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[2,3,7,5,8,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,7,8,5,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,5,6,7,1,8,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,3,7,8,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,4,7,8,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[1,2,8,7,4,6,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,1,4,8,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,3,1,8,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,3,2,7,6,1,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[1,3,7,6,2,4,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,2,7,4,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,3,2,8,1,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[1,6,5,3,2,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,7,3,5,2,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,3,7,2,5,1,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,1,4,3,2,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[1,6,8,7,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,3,6,1,8,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[1,4,8,7,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,5,7,6,3,1,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,6,7,5,1,3,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[3,6,5,1,4,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[4,6,7,3,1,5,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[5,4,1,8,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,2,4,7,5,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,2,5,1,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,2,6,1,5,8,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,2,2,2]=>3
[4,2,3,6,7,5,1,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[6,2,3,5,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[1,6,3,8,4,7,2,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,4,8,5,6,2,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,2,7,1,8,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[1,3,8,5,6,7,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,2,4,1,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,8,4,1,3,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,7,2,3,8,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[3,2,7,4,8,1,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[5,2,8,1,7,4,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,5,4,7,3,1,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,1,1,1]=>6
[4,6,3,1,2,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[2,5,6,4,8,1,3,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[4,2,1,1,1]=>7
[5,4,1,6,2,3,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[5,4,1,2,7,6,3,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[5,8,7,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,7,8,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,2,8,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,1,2,4,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[3,7,8,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,8,2,7,4,5,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,8,2,4,5,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,3,8,1,7,5,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,1,8,4,2,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,1,4,7,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,2,7,3,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,3,1,9,8,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3,1]=>[3,3,3,3,3,1]=>5
[2,8,1,5,3,7,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,2,4,7,5,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,8,4,7,1,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,8,2,3,5,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,6,2,3,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,6,2,3,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,3,7,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,2,3,7,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,2,8,3,7,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,1,7,8,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,6,1,8,2,7,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,3,5,2,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,3,5,2,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[5,4,8,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,4,5,8,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,5,1,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,6,3,1,5,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,5,4,8,6,3,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,4,8,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,4,5,8,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,3,4,1,2,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[3,5,4,8,2,6,1,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,6,4,5,1,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[4,3,5,1,8,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,2]=>2
[3,5,4,8,1,6,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,4,8,5,6,1,2,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,4,8,5,6,2,1,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,5,4,8,1,6,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[1,7,6,2,5,4,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,1,7,4,3,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,1]=>1
[3,7,2,1,5,6,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,3,7,8,2,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,7,5,6,4,2,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[6,1,4,3,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[3,8,6,4,5,2,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,5,8,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,8,5,3,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,5,7,2,8,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,7,4,5,1,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,6,8,1,2,5,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,8,5,1,3,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,7,4,5,2,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,7,8,4,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,5,7,2,1,6,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,5,1,6,8,3,7,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[1,7,4,5,2,6,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,5,9,6,7,2,8,3]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1,1,1]=>[3,3,3,2,1,1,1]=>15
[2,4,5,9,6,1,7,3,8]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[3,3,3,2,1,1]=>11
[3,1,5,8,4,6,2,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,6,5,8,2,1,3,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[1,4,8,3,5,6,2,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,7,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,9,8,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,3,1,8,5,7,2,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,7,2,4,5,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[3,2,7,4,6,1,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,6,7,2,4,1,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[3,8,6,7,1,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,2,8,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,6,3,2,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[5,7,1,8,4,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,4,8,7,6,2,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,1,5,2,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,7,6,2,5,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,5,3,4,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,2,3,8,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,3,4,1,9,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[4,2,3,1,9,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[3,2,1,9,4,6,7,8,5]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[2,1,9,3,5,6,7,8,4]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[6,5,1,4,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,7,6,2,5,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[6,3,2,4,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[2,6,4,5,8,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,7,4,8,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,8,7,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,7,2,4,5,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,6,8,7,2,5,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[3,2,2,1,1,1]=>11
[1,6,2,7,5,3,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,3,7,2,6,4,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,7,3,2,8,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,5,2,4,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,7,3,8,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,2,4,7,5,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,2,7,4,3,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,5,8,2,3,6,4,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,9,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,8,9,1,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,5,3,6,7,1,4,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[4,3,1,1,1]=>7
[6,4,1,5,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,4,1,5,7,3,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,2,7,3,8,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,5,7,4,3,8,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,7,3,1,4,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,8,3,2,7,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,2,6,8,7,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[3,4,5,6,7,9,1,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,1]=>[5,4,3,2,1]=>10
[3,4,5,6,8,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[4,3,2,1]=>6
[3,4,5,6,7,9,2,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,1]=>[5,4,3,2,1]=>10
[3,4,5,6,7,1,9,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,6,4,3,2,1]=>[6,4,3,2,1]=>10
[1,5,6,7,3,4,2,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[4,6,8,5,2,1,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[1,6,7,8,2,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,7,8,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[5,7,8,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,7,8,2,3,1,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,3,4,2,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[6,5,3,4,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6]=>[6,6]=>0
[7,6,4,5,3,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[4,5,2,7,8,6,1,3]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[1,3,5,8,7,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[6,4,1,8,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,1,3,8,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[3,6,7,2,1,5,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[2,5,6,1,3,8,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[5,2,1,1,1]=>7
[3,8,5,7,2,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,7,1,4,5,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,1,2,5,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,6,3,5,7,1,8,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[4,7,3,5,2,6,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[2,3,5,4,7,1,8,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]=>[4,4,2,2,1]=>8
[6,8,4,1,5,7,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,8,9,6,1,2,3,4,10,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1]=>[2,1]=>1
[2,8,9,10,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[8,9,7,5,6,1,2,3,10,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[2,9,10,8,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[7,8,9,5,1,2,3,4,10,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1]=>[2,1]=>1
[7,8,9,1,6,2,3,4,10,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1]=>[2,1]=>1
[2,8,9,10,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[2,8,9,10,1,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[2,8,3,6,4,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,8,7,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,5,3,4,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[5,4,8,7,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,7,6,8,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,2]=>0
[6,3,7,4,5,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,3,6,5,8,2,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,2,2]=>2
[6,3,8,2,7,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,2,8,4,7,5,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,7,8,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,5,8,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,8,1,7,2,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,5,7,3,8,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,6,4,7,1,8,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[1,6,5,7,3,8,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,8,5,3,7,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,2,3,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,5,1,3,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,4,2,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,5,1,3,7,8,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[5,1,3,2,7,8,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,6,8,2,4,7,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[6,7,4,2,3,8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,8,7,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,3,2,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,7,1,4,6,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,6,2,5,7,3,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,4,3,8,2,5,7,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[1,5,7,3,6,4,2,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,6,7,2,4,8,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,7,2,8,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,3,4,1,7,8,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,7,6,5,8,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,1,8,3,2,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,2,6,8,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[5,8,4,1,3,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,4,7,1,5,6,2,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[2,2,2,1]=>3
[4,8,2,6,5,3,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,8,6,3,5,1,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,2,5,4,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,4,6,5,2,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,2,6,4,1,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[6,2]=>1
[6,8,4,3,2,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,8,5,4,3,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[6,2,8,5,4,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,5,3,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,8,5,4,7,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,5,7,3,4,8,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,2,4,7,8,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[8,9,4,5,10,1,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[1]=>0
[4,8,5,6,1,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,5,6,8,7,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[1,7,8,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,8,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[2,3,7,5,8,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,8,5,1,2,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,3,6,4,8,2,7,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,7,6,2,8,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,6,2,8,1,7,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,8,4,5,1,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,3,8,1,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,6,8,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,2,5,3,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[1,6,5,7,4,2,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,2,7,4,8,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,6,7,4,8,5,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[2,1,1,1,1]=>4
[3,2,7,5,8,4,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,5,8,6,4,3,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,4,2,5,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,7,5,4,6,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,3,4,2,8,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[2,5,7,4,6,8,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[2,5,6,4,1,3,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[6,2,1,1,1]=>7
[4,6,1,3,5,7,2,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[5,1,1]=>2
[3,2,7,5,8,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[4,3,6,8,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,5,3,2,1,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[3,6,5,8,1,7,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,1,6,8,5,2,3,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[3,2,2]=>2
[4,5,2,8,6,7,1,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,5,2,8,6,7,3,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,5,8,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,5,1,6,4,8,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]=>[5,3,1,1,1]=>7
[3,2,4,5,8,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[4,4,3,2]=>5
[4,5,2,1,3,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[4,2,3,6,8,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,5,1,3,2,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[5,5,1]=>2
[3,4,5,8,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[3,4,5,8,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[3,3,2,1]=>5
[6,4,1,3,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,3,1,2,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[1,5,8,2,4,3,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,8,5,7,2,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,7,3,2,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,3,2,8,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,1,6,7,8,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[1,5,6,3,7,2,4,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[1,5,6,7,4,2,3,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,1,6,7,3,4,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[6,8,5,1,7,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,5,2,3,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,8,3,1,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,5,1,7,3,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,2,7,3,8,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,7,8,3,6,5,2,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,7,5,1,8,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[3,5,2,6,8,7,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[4,3,1,1]=>5
[6,4,2,3,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,3,7,5,1,2,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,2,3,8,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,5,8,1,2,7,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,4,3,6,8,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[4,3,3,1,1,1]=>11
[6,8,3,5,4,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,2,5,6,3,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,1,5,6,3,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,5,7,1,6,3,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[2,7,1,4,8,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,5,6,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,1,8,7,4,6,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[4,6,8,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[4,5,7,3,6,1,2,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[4,5,8,2,6,1,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,4,5,7,2,1,6,8]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]=>[3,3,2,1]=>5
[4,5,6,8,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[4,5,7,2,6,1,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[3,9,2,1,4,5,6,7,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,5,7,2,3,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,6,7,2,5,8,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[2,1,1,1]=>3
[5,3,6,7,4,8,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[4,2,7,8,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,2,7,8,5,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,4,3,7,8,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[3,5,7,8,4,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[2,2,1,1]=>4
[4,6,7,3,2,8,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[4,6,5,3,7,8,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[5,6,2,4,7,8,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,1]=>1
[5,6,3,2,8,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,2,8,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[3,7,4,8,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[5,2,4,8,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,2,6,4,8,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[2,4,7,8,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,4,5,6,8,9,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,4,6,7,8,9,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2,1]=>[4,3,2,2,1]=>9
[3,5,6,7,8,9,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[4,5,6,7,8,9,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,2,6,7,8,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[4,5,6,7,8,9,10,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[4,8,2,7,5,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,2,3,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[3,5,8,1,7,4,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[5,8,6,1,7,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,4,3,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,8,6,7,5,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,2,8,7,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,7,8,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,6,7,8,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,7,6,3,8,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[3,8,1,4,6,2,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,4,5,3,8,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[4,7,5,6,2,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[2,8,4,6,7,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,1,6,7,8,2,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[2,5,8,4,6,1,3,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[4,7,8,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[6,8,4,7,3,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,4,2,8,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,4,8,6,2,1,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,8,6,2,1,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,1,8,2,4,6,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,8,1,3,6,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,5,8,6,1,7,4,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,4,8,6,7,3,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,6,7,8,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[3,2,2]=>2
[3,7,8,6,4,1,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[5,4,2,3,6,7,8,9,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]=>[6,5,4]=>3
[6,5,4,2,3,7,8,9,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]=>[6,5]=>1
[7,6,5,4,2,3,8,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[6]=>0
[4,6,1,5,7,2,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,8,5,3,2,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,8,1,3,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,6,8,7,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,7,8,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[6,8,7,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,8,2,6,7,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,7,6,3,8,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[6,7,4,1,8,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,7,6,8,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,3,4,8,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,7,4,8,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,3,1,6,7,8,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3]=>1
[3,4,7,8,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[2,1,4,7,8,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,4,5,8,1,6,3,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[3,4,6,8,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[3,2,2,1]=>5
[1,8,5,6,4,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,6,2,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,8,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,4,7,2,5,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,7,5,1,8,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,5,6,4,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,7,8,9,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1]=>[3,2,1,1]=>5
[5,7,8,9,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[2,7,1,5,3,8,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,7,2,8,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[2,2,1,1]=>4
[2,4,3,8,5,1,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,8,3,4,1,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,7,6,8,2,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[2,6,7,1,4,5,8,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[2,1,1,1,1]=>4
[6,2,5,3,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[2,7,3,4,1,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,8,1,6,7,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,2,8,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,3,7,2,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,2,4,6,1,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[3,8,4,6,1,5,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,6,4,1,2,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,1,1,1]=>3
[5,2,7,1,4,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,3,1,4,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[6]=>0
[5,2,3,1,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[6,5]=>1
[4,2,7,1,3,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,5,7,2,8,3,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1]=>2
[3,5,1,7,6,2,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[5,4,2,7,1,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[4,1,7,6,5,3,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[2,3,6,7,1,8,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,6,1,2,7,8,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[4,5,1,8,7,6,3,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,1,3,6,7,5,2,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[4,5,1,3,6,8,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[3,8,5,1,2,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,8,4,1,2,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,5,8,1,4,2,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[2,8,5,7,1,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,7,5,1,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,2,7,8,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[1,8,4,7,5,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,5,8,2,1,6,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,1,6,7,5,2,4,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[3,2,2,2]=>3
[4,8,1,5,3,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,1,7,5,2,6,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[5,1,4,6,3,7,8,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[3,6,5,2,4,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,1,1,1]=>3
[1,7,5,4,6,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,8,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,8,5,4,6,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[7,5,1,3,2,6,4,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[7,5,1,3,2,6,4,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7]=>[8,7]=>1
[8,3,6,1,4,2,7,5,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[8]=>0
[7,10,1,3,8,2,6,5,9,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,2,6,1,8,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[5,3,1]=>3
[5,1,8,6,7,3,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,3,2,4,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,5,2,4,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[5,4,8,2,1,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,4,8,3,2,6,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,3,8,4,2,7,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[8,9,10,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,9,5,10,2,4,6,8,1,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[8,9,6,10,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[7,8,9,10,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,9,10,3,4,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,5,9,10,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2]=>0
[7,8,9,10,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,6,9,4,10,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[7,4,8,9,10,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[8,9,5,6,4,10,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[1]=>0
[5,8,4,2,1,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,4,2,8,1,6,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,7,5,4,8,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,8,6,3,5,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,3,2,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,7,6,3,2,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,7,3,2,8,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[4,5,1,6,8,2,7,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[1,6,3,7,2,4,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[4,3,1,6,7,2,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,3]=>2
[6,3,1,5,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,2,1,4,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,2,8,4,1,6,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,7,6,4,1,5,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,7,6,4,5,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,8,1,7,3,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[3,6,8,1,5,7,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,8,3,1,6,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,5,6,8,2,1,7,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[4,5,6,8,1,3,7,2]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[3,2,1]=>3
[4,5,8,3,2,1,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,7,3,2,1,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,8,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[4,7,1,3,5,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,8,3,2,1,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,8,1,4,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,6,3,7,8,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[5,7,1,4,3,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,2,3,7,1,5,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,2,8,1,5,4,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,3,4,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,5,2,7,8,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[2,3,6,5,8,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,2,2,2,1]=>7
[1,5,2,6,8,7,3,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[3,2,6,1,4,7,8,9,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,2,2]=>[6,5,2,2,2]=>7
[4,7,2,5,1,3,8,9,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,3,2,8,9,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3]=>[3,3,3,3]=>0
[6,5,4,3,2,1,8,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,6]=>[6,6]=>0
[6,9,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,4,3,9,2,7,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[6,5,4,3,2,9,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[5,5]=>0
[8,9,4,5,6,1,2,3,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[8,5,6,3,4,1,2,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[5,9,10,2,6,7,1,3,4,8]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,9,4,7,2,5,1,3,10,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1]=>[1,1,1]=>0
[7,5,10,3,8,2,6,1,4,9]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[7,5,4,3,10,2,8,1,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[7,6,5,4,3,2,10,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,6,6]=>[6,6]=>0
[5,3,4,7,2,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[7,6,9,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,5,7,1,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,2,3,7,6,1,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,3]=>0
[4,2,6,3,1,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[6,2,2]=>2
[4,6,3,2,5,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[5,8,4,3,2,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,5,7,4,8,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,1,5,7,3,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,2,7,8,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[3,5,1,7,8,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[3,3,1,1]=>4
[5,2,4,1,7,6,8,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[4,4]=>0
[2,3,4,9,6,7,8,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,5,6,7,8,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,9,4,5,6,7,8,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,3,1,9,6,7,8,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3,1]=>[3,3,3,3,3,1]=>5
[2,1,9,5,6,7,8,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,3,10,5,6,7,8,9,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[1,9,4,5,6,7,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,4,5,6,7,8,9,3,1]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[5,6,4,9,1,8,2,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[5,9,1,8,2,7,3,6,4]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,4,3,8,1,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,7,3,9,1,8,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[6,4,9,1,8,2,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,9,1,8,2,7,3,6]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[5,10,1,9,2,8,3,7,4,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,5,3,9,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[2,10,1,3,4,5,6,9,7,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,9,1,3,4,5,6,7,10,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,11,1,3,4,5,6,7,10,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[3,1,10,2,4,5,6,9,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[4,1,8,2,5,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[5,7,8,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[1,6,4,2,7,3,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,8,2,1,5,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,2,7,1,6,3,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[4,8,2,5,1,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,1,2,4,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,1,7,3,6,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[3,2,7,5,6,1,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,1,6,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[2,2,2,2]=>0
[6,3,1,7,5,4,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[6,2,8,7,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,2,9,8,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,2,8,3,1,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[1,4,7,5,6,2,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,4,8,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,1,4,8,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,2,4,8,3,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,8,6,7,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,8,7,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,4,2,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[6,5,1,8,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,3,8,1,7,6,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[4,7,6,3,2,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[5,7,6,3,8,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,8,4,7,1,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,3,7,6,8,4,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[6,1,5,7,2,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[1,8,7,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,2,6,7,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,5,4,8,7,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,8,7,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,5,7,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,6,1,4,7,8,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,5,7,1,3,6,4,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,4,7,2,5,3,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,5,1,3,8,2,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[6,2,1,7,4,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[4,6,5,2,1,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[6,1,1]=>2
[6,1,5,3,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[3,6,5,4,1,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,1,1,1]=>3
[8,7,6,4,5,3,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[6,8,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,8,7,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,7,8,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,6,1,8,4,3,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[1,8,2,6,7,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,5,1,6,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,5,3,2,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,7,2,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,2,8,1,7,5,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[6,5,1,7,2,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[1,6,8,2,7,3,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,6,8,7,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,1,3,6,7,8,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[4,1,2,6,7,8,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,3,3]=>2
[5,10,4,9,3,8,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,9,3,2,8,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,9,3,2,8,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,9,3,2,1,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,9,8,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,9,8,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,9,2,8,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,9,2,8,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,9,2,1,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,2,9,8,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,2,9,8,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,2,9,1,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,10,4,3,2,1,9,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,4,3,2,10,9,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[5,4,3,2,10,9,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[5,4,3,2,10,9,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[5,4,3,2,10,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[3,4,7,8,9,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,1]=>[3,2,2,2,1]=>7
[3,6,7,8,9,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1,1]=>[3,2,1,1,1]=>7
[3,4,1,5,9,2,6,7,8]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,3,1]=>[4,4,4,3,1]=>7
[1,3,7,8,9,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,2,1,1]=>[3,2,2,2,2,1,1]=>14
[2,6,7,8,9,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[3,6,7,8,9,10,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[3,7,8,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,3,7,1,8,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[3,7,8,1,5,2,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[2,1,10,7,5,9,4,3,6,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,8,5,3,6,4,9,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,9,4,6,7,3,5,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,3,9,6,4,8,5,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,3,4,5,7,8,9,6]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[8,5,3,7,2,1,4,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,6,3,1,4,2,7,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,7,2,4,5,1,3,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,1,7,4,2,6,3,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,1,2,3,5,6,7,4,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[10,5,3,7,2,9,4,1,6,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,5,3,8,2,1,6,4,9,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,6,3,9,4,2,7,1,5,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,6,3,1,9,2,4,8,5,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,7,3,1,4,5,2,8,9,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,7,2,4,5,9,3,1,6,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,8,2,4,5,1,6,3,9,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,7,4,2,6,3,1,5,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,8,4,9,6,2,3,5,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,8,4,2,5,7,3,9,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,2,3,5,6,7,1,4,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,9,3,5,6,2,8,4,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,2,9,5,3,7,8,4,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,2,3,4,6,7,8,9,5,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[1,5,4,7,8,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[5,2,4,7,8,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,1,4,7,8,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,8,1,5,6,2,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,4,1,7,3,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[4,3,7,8,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[3,7,8,5,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[1,7,4,5,6,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,4,5,6,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,4,7,8,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,4,3,6,8,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[3,7,4,5,8,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[1,4,6,5,8,2,7,3]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[4,6,1,7,3,2,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[1,7,3,6,4,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,3,5,1,2,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[1,6,4,2,3,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[4,8,3,5,2,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,8,4,7,5,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,7,1,6,8,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,6,5,8,2,3,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[5,7,8,2,3,4,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[5,2,3,8,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[2,7,6,4,8,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,7,5,8,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[3,1,1,1,1]=>4
[4,2,3,6,8,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,3,3]=>2
[4,7,3,2,6,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,3,7,8,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[4,8,7,2,1,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,3,8,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[6,3,5,8,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,8,7,5,1,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,7,5,1,3,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,3,6,8,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,7,6,4,1,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[5,2,8,4,7,1,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,1,3,5,7,2,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,3]=>2
[5,1,8,2,4,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,8,2,1,4,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,2,7,3,6,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,5,8,6,7,2,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[6,8,2,1,4,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,1,10,7,4,9,6,3,8,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,9,4,3,6,7,8,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,9,4,5,6,3,8,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,3,8,5,4,7,6,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[8,5,2,7,4,1,6,3,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,7,2,1,4,5,6,3,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,7,2,3,4,1,6,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[8,1,6,3,2,5,4,7,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[10,5,2,7,4,9,6,1,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,5,2,9,4,1,6,7,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,7,2,9,4,5,6,1,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,2,1,8,5,4,7,6,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,2,1,4,5,6,7,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,7,2,3,4,9,6,1,8,5,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,2,3,4,1,6,7,8,5,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,6,3,2,5,4,1,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,6,3,8,5,2,7,4,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,8,3,2,5,6,7,4,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,9,2,3,4,5,6,1,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,8,3,4,5,2,7,6,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,2,7,4,3,6,5,8,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,2,3,4,5,6,7,8,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[1,5,4,8,7,3,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[6,1,5,2,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,8,6,4,1,5,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,8,6,4,5,1,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,7,6,4,5,1,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[4,6,2,5,7,8,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,6,3,5,7,1,2,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,1,1]=>2
[4,7,3,5,8,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[4,8,3,5,7,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,5,6,1,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,7,2,5,6,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[4,8,2,5,6,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,4,7,2,6,5,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,5,7,2,6,4,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,2,7,8,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,6,2,8,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,7,8,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,7,6,8,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,1,7,8,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,3,3,1]=>3
[2,4,8,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,1,3,4,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[6,5,1,8,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,7,2,4,6,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,2,7,5,8,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[2,2,2,2]=>0
[2,4,5,3,8,1,7,6]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[4,4,2,1,1]=>8
[1,8,7,3,5,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,4,8,3,6,5,7,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[3,1,8,2,6,5,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,6,7,8,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[2,1,1]=>2
[4,7,2,1,8,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,6,2,8,4,1,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[5,7,2,4,8,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,7,2,4,8,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[6,7,3,2,8,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[1,7,3,4,8,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,3,8,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,6,4,3,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,3,4,8,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,8,3,4,6,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,8,4,2,5,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,4,7,6,2,3,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,4,6,7,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,1,6,4,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,3,6,5,8,2,4,7]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[4,2,2,2,1,1]=>11
[1,4,6,3,2,8,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[6,8,4,1,5,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,6,7,4,1,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,2]=>1
[5,8,2,6,3,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,8,1,6,3,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,1,6,2,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[5,2,6,8,1,4,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[6,7,3,8,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1]=>0
[2,7,3,5,4,1,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,7,4,1,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,1,4,8,5,3,7,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[3,3,3,2,2]=>6
[2,7,3,8,4,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,1,5,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[1,5,8,3,4,7,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,3,8,1,4,6,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,5,8,1,3,6,2,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,1,3,8,5,7,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[4,1,3,7,2,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,3,3]=>0
[4,6,3,1,7,2,8,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[4,8,7,2,5,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,3,2,8,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,8,1,7,5,4,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,3,1,5,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,4,3,6,1,7,8,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[3,2,7,8,5,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,8,3,2,1,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,2,6,4,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[7,1,2,3,4,9,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[5]=>0
[7,1,2,3,4,8,6,9,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,5]=>[5]=>0
[7,1,2,3,9,5,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[6,1,2,3,7,5,8,9,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4]=>[6,4]=>1
[6,1,2,8,4,5,9,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,3,3]=>[3,3]=>0
[5,1,2,7,4,9,6,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[5,1,2,6,4,7,8,9,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3]=>[6,5,3]=>3
[4,1,5,3,6,7,8,9,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2]=>[6,5,4,2]=>6
[8,1,2,3,4,5,10,7,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]=>[6]=>0
[8,1,2,3,4,10,6,7,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,1,2,3,10,5,6,7,9,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4]=>0
[7,1,2,3,10,5,6,8,9,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[1,9,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,9,8,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,9,8,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,9,8,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,9,8,5,6,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,8,4,5,6,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,9,6,7,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,7,8,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>6
[1,10,8,7,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[4,7,6,1,5,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,4,8,1,6,7,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[3,6,7,8,4,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[2,1,1,1]=>3
[2,3,7,8,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,3,7,8,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,1,7,8,4,6,2,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,3,8,1,6,7,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,8,7,3,6,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,4,3,7,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,8,3,7,5,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[2,4,8,3,6,7,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,6,5,8,7,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,6,4,8,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,8,3,7,6,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,4,7,1,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[7,8,9,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,7,8,9,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,9,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[8,9,10,2,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,10,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[5,6,7,8,9,10,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[4,5,6,7,8,1,9,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1]=>[4,3,2,1]=>6
[4,5,6,7,8,9,10,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>10
[6,8,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,7,1,4,5,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[7,9,3,4,5,6,2,1,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,9,2,1,5,6,7,8,4]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,1,4,5,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[3,8,1,4,5,6,7,2,9]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1]=>[1,1,1,1,1]=>0
[8,10,3,4,5,6,7,2,1,9]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,9,3,4,5,2,7,1,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,8,2,4,5,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,9,2,4,1,6,7,8,5]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,2,1,5,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[3,6,8,1,5,4,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[3,8,9,1,5,6,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,10,2,1,5,6,7,8,9,4]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,9,1,4,5,6,7,8,2,10]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,4,6,3,5,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,2,5,6,4,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,6,8,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[2,5,7,8,4,3,1,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,8,5,3,2,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,8,5,3,2,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,6,1,8,7,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[1,3,7,6,8,5,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[4,1,7,8,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,4,3,7,6,1,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,7,6,1,2,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,5,2,6,7,8,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[2,8,7,6,5,4,3,1,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,1,4,9,8,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,2]=>[3,3,3,3,2,2]=>8
[1,7,6,2,3,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,5,1,3,7,6,2,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,4,1]=>2
[1,5,4,3,8,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[4,4,1,1,1,1]=>8
[1,3,7,5,8,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,5,7,1,6,4,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[2,2,1,1]=>4
[3,7,5,6,1,4,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,6,3,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,1,2,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,1,3,7,8,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,8,1,2,7,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,6,7,4,5,3,2,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,2,4,6,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,8,7,2,3,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[4,1,3,6,5,8,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[5,3,3]=>2
[4,3,7,1,5,8,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[1,8,6,5,2,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,6,2,7,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,1,8,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,5,8,7,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,5,4,1,7,8,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,4,1,1]=>4
[2,9,8,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,9,8,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,9,8,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,10,9,8,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,9,8,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,9,8,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,10,9,8,1,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,10,9,1,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,1,3,5,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,8,1,5,6,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,6,7,5,8,4,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[6,8,4,7,3,2,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,8,7,2,6,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,8,7,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,5,7,8,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,4,8,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,2,7,3,1,6,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[4,8,5,2,7,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,3,1,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,8,5,2,6,7,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[7,8,1,9,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]=>[1]=>0
[6,7,8,1,9,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1]=>[2,1]=>1
[5,6,7,8,1,9,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1]=>[3,2,1]=>3
[1,5,7,2,4,3,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,2,7,5,8,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,1,3,8,2,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,7,1,3,2,8,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[1,4,7,8,3,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,8,2,7,6,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,4,3,5,1,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,8,5,7,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,2,7,4,6,1,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[6,3,5,2,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,5,3,1,7,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[2,1,10,3,5,4,7,6,9,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[2,1,10,3,6,5,9,4,8,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[8,1,3,2,5,4,7,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[7,4,10,1,3,2,6,5,9,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,1,4,3,7,2,6,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[8]=>0
[7,2,6,3,10,1,5,4,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[8,3,10,1,5,4,9,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[10,1,3,2,5,4,7,6,9,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,3,2,6,5,9,4,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,4,3,7,2,6,5,9,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,4,3,8,5,9,2,7,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[10,1,5,4,9,2,6,3,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]=>[10]=>0
[4,7,6,2,3,1,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,7,6,1,3,2,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[7,2,6,5,4,3,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[3,2,1,9,5,8,7,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[6,3,5,4,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6]=>[6,6]=>0
[4,3,2,1,9,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4]=>[4,4,4,4]=>0
[2,8,1,3,5,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,3,4,7,8,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[1,6,4,7,8,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[6,7,2,3,8,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[2,7,8,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,2,6,8,7,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[1,8,3,7,5,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,5,2,6,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,1,6,7,5,2,8,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]=>[3,2,2,2]=>3
[4,1,6,2,3,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[4,1,7,6,5,2,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[2,8,4,7,3,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,4,8,3,2,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[1,5,7,6,3,8,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,6,3,1,7,8,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,1,7,8,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[2,2,2,2,2]=>0
[1,5,8,6,7,4,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[4,7,6,5,8,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,1,4,7,6,8,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[5,6,4,7,1,8,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[5,3,7,4,6,1,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,1,5,7,8,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[3,6,7,1,5,4,8,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[2,1,1,1]=>3
[3,6,4,7,5,8,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,1,1,1]=>3
[7,1,2,3,4,9,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[5]=>0
[4,1,9,2,3,5,6,8,7]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[3,8,1,2,4,5,6,9,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1]=>[1,1,1,1,1]=>0
[8,1,2,3,4,5,10,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]=>[6]=>0
[6,1,2,3,9,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[3,9,1,4,2,5,6,8,7]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,9,1,2,4,5,6,7,10,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,7,1,5,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,8,1,3,5,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,5,2,8,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,1,7,2,5,8,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,2,5,8,6,1,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[4,5,1,7,2,8,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[3,3,1]=>2
[2,8,5,3,6,7,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,3,4,9,7,5,8,6,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]=>[3,3,3,3,2,1]=>9
[2,3,9,6,4,7,8,5,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,8,6,3,4,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,9,5,3,6,7,8,4,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,7,1,8,5,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,4,7,2,5,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,8,7,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,3,8,7,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,2,6,7,4,3,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,2]=>1
[1,7,2,8,5,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,7,1,4,8,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[4,1,7,3,2,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,3,7,8,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[6,1,3,7,8,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[7,6,9,1,4,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,6,8,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[2,6,4,7,5,3,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,6,3,7,2,8,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1]=>1
[4,5,1,8,6,2,7,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[5,6,1,8,7,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[4,5,1,6,8,7,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,9,2,4,5,6,7,8,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,6,1,5,2,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,2,8,1,5,6,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,8,7,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,4,7,6,8,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[2,2,2,1]=>3
[2,8,1,3,7,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,2,5,6,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,7,1,5,8,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[4,2,7,1,5,8,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,1,6,2,5,8,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[1,8,2,5,7,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,6,3,8,5,2,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[4,5,6,3,1,7,2,8]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]=>[5,2,1]=>3
[1,4,7,5,2,3,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,6,5,8,2,3,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[4,2,2,1,1,1]=>11
[1,4,8,3,7,6,2,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,5,7,6,8,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,1,6,7,2,8,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,2,2,2]=>3
[1,5,3,6,8,4,7,2]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[4,3,1,1,1,1]=>9
[6,5,1,3,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,7,4,8,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,7,5,6,8,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[3,4,7,8,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[2,2,2,1]=>3
[4,8,1,7,5,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,8,7,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,3,4,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,3,6,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,5,8,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,4,7,2,3,6,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,2,5,6,3,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,2,6,5,8,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[1,5,8,2,6,3,4,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[6,8,3,2,7,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,5,7,2,6,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,2]=>2
[5,7,2,1,3,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[7,1,10,9,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,1,9,10,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>6
[8,7,1,10,2,3,4,5,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[3,5,6,7,2,4,1,8]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]=>[3,2,1,1]=>5
[6,4,7,5,2,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[1,5,6,4,8,3,2,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[4,2,1,1,1,1]=>9
[5,1,4,7,8,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[1,6,7,2,8,5,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,3,2,1,7,8,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[4,3,7,1,5,8,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[1,9,6,5,2,7,3,10,8,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[4,8,7,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,8,2,1,7,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,8,4,1,7,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,7,4,3,2,1,5,8,9]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1]=>[7,1]=>1
[7,5,4,3,1,2,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[6,3,1,8,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,3,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[6]=>0
[4,1,7,8,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[5,4,7,1,3,6,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,8,2,1,3,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[7,6,4,3,5,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[7,6,3,5,4,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[7]=>0
[5,7,6,3,4,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[7,8,9,10,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,7,8,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[1,1,1]=>0
[2,7,5,6,4,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,6,5,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,5,1,2,6,8,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,4,1,1]=>5
[5,4,1,2,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[5,5]=>0
[1,6,7,2,5,8,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,3,8,6,2,4,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,7,4,6,3,8,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,4,7,8,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[2,7,4,8,3,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,8,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,2,8,1,3,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,2,6,7,5,1,8,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[3,2,2]=>2
[4,7,2,5,3,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,5,7,4,2,8,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[2,2,1,1]=>4
[2,4,7,6,3,8,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[4,6,8,5,1,2,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,5,7,1,2,3,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,1,1]=>2
[4,6,5,7,1,3,8,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[3,4,7,6,1,8,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[7,10,2,1,8,4,3,5,6,9]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,9,1,10,7,4,3,5,6,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[8,1,9,2,10,6,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[8,1,9,2,10,5,3,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[4,2,8,5,7,1,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[6,8,7,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,2,6,7,4,8,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,2]=>1
[6,5,8,1,7,3,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,4,8,1,5,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,6,1,5,3,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,1,1,1,1]=>4
[3,8,7,5,4,2,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,7,8,2,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[1,1]=>0
[2,8,7,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,1,2,4,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,1]=>1
[3,8,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,6,7,1,3,2,8,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[6,4,7,5,3,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,7,3,4,2,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[6,4,8,3,1,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,5,3,8,6,4,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[6,7,1,5,4,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[5,8,4,1,3,2,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,4,7,6,1,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[4,5,2,1,6,3,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[6,4,1]=>3
[4,5,2,1,6,7,3,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]=>[5,4,1]=>3
[5,3,8,6,2,4,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,2,8,5,7,1,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,6,8,1,5,7,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,6,5,8,1,7,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,1,1]=>2
[4,8,1,2,7,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,4,3,8,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[4,5,1,6,8,7,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[3,4,7,2,5,8,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,1]=>3
[2,5,1,8,6,4,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[2,5,8,7,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[2,2,1,1,1]=>6
[3,8,7,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[2,5,1,8,3,6,4,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[3,3,1,1,1]=>6
[5,8,4,7,3,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,6,8,4,2,7,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[5,8,1,3,4,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,4,6,2,1,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,4,1,7,8,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[5,3,4,7,8,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3]=>0
[4,3,7,6,5,1,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[2,2,2]=>0
[5,1,4,8,2,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[3,2,8,5,4,1,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[7,8,9,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[6,1,2,9,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,2,8,3,4,6,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,7,1,2,6,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[1,2,7,5,6,3,4,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[5,1,4,7,2,3,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,8,1,2,3,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,4,6,8,1,9,7,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,3,2,2,1,1]=>[3,3,2,2,1,1]=>12
[6,8,5,4,3,2,1,9,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1]=>0
[7,9,6,5,4,3,2,1,10,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>[1,1]=>0
[6,2,3,8,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,7,5,1,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[5,3,1,6,2,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[6,7,2,4,1,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[5,1,6,3,2,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[5,2]=>1
[5,2,1,6,4,7,3,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[5,3]=>1
[5,4,1,6,2,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[6,7,2,5,4,1,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[4,2,8,6,5,1,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,8,5,4,7,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,4,8,3,6,2,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[6,3,2,4,8,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[3,6,2,5,7,4,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[2,7,1,5,8,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,7,2,3,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[6,1,8,5,7,4,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[6,1,8,5,4,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,1,6,8,7,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[4,6,7,5,3,1,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[5,3,2,6,8,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[4,3]=>1
[5,4,6,2,8,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[4,2]=>1
[4,5,8,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,7,6,1,2,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[2,2,1]=>2
[4,6,5,7,2,1,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[3,1,1]=>2
[2,3,4,7,8,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,1]=>7
[6,3,7,1,4,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,6,3,5,1,8,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[3,5,6,7,8,9,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[3,4,6,7,8,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,2,2,1]=>5
[2,5,6,7,3,8,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]=>[3,2,1,1,1]=>7
[2,5,6,7,8,9,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1]=>[4,3,2,1,1,1]=>12
[5,8,4,6,2,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,7,5,8,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[2,2,2,1,1]=>6
[1,6,8,3,4,2,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[4,1,7,6,2,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[4,1,8,2,7,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,7,2,8,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[2,5,6,3,7,4,8,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]=>[4,2,1,1,1]=>7
[2,6,5,3,8,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[2,6,5,3,7,4,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,7,3,2,8,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[2,8,6,1,7,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,6,8,1,7,5,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[1,4,6,5,3,8,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[5,2,2,1,1,1]=>11
[2,4,5,8,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[3,1,6,8,7,5,4,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[3,2,2,2]=>3
[3,1,8,7,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[5,1,8,7,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[2,8,5,7,6,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,8,7,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,4,7,6,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,5,6,7,8,9,1,10,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,5,4,3,2,1]=>[5,4,3,2,1]=>10
[4,5,1,8,7,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[3,8,5,2,6,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,3,8,5,2,6,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[3,6,4,7,5,2,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[3,1,1,1]=>3
[5,7,4,1,2,6,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[2,8,6,7,5,3,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,8,3,2,6,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,3,7,6,1,5,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[2,2,2]=>0
[4,6,8,5,3,1,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[5,6,8,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,1]=>1
[1,4,8,7,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,8,5,4,3,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,6,7,2,3,8,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[2,1]=>1
[1,7,4,2,8,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,5,7,1,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[3]=>0
[4,8,5,3,1,2,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,4,7,2,1,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[6,7,3,1,2,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[3,1,8,7,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[1,3,8,6,7,2,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,2,3,6,1,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[3,2,6,4,7,1,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[4,2,2,2]=>3
[3,6,2,5,7,8,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[4,1,1,1]=>3
[2,7,4,6,8,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,8,1,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[1,5,7,6,8,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[2,7,4,6,8,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,6,8,5,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[2,7,1,8,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,3,4,7,6,2,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[4,1,8,5,7,2,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[4,1,8,2,7,5,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,2,4,8,5,7,3,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[2,7,1,5,6,4,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,5,7,8,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,4,8,5,7,6,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[2,8,1,5,6,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,7,2,8,1,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[1,1,1,1]=>0
[3,6,2,1,8,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[3,5,1,7,6,4,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,1,1]=>4
[5,4,7,6,2,1,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[3,5,2,8,7,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[3,7,6,5,4,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,6,5,3,1,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,5,2,6,7,3,8,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,1]=>3
[4,7,1,8,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[6,4,1,2,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,1,5,4,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[6,4,2,3,1,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[3,4,6,1,8,2,7,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[4,2,2,1]=>5
[5,3,1,4,7,6,2,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,4]=>0
[6,4,5,2,7,1,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,4,3,7,1,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,1,2,7,6,4,5,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]=>[3,3,3,3]=>0
[5,1,2,7,6,3,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,6,1,7,2,4,3,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,1]=>1
[3,5,6,8,1,2,7,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[2,6,5,7,1,3,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,1,1,1,1]=>4
[2,3,7,1,5,6,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[2,2,2,2,1]=>4
[2,6,5,3,4,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[2,6,1,3,5,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,1,1,1,1]=>4
[4,6,1,5,2,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[6,1,5,4,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[4,6,1,5,2,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[2,8,6,5,1,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,1,8,6,2,7,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[3,6,8,2,7,5,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,6,4,1,7,2,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[4,1]=>1
[3,8,6,1,5,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,4,2,3,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,3,6,2,5,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[1,6,4,5,7,3,2,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,6,4,5,7,2,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[1,7,5,6,4,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,5,6,7,3,2,4,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[3,2,1,1,1,1]=>9
[5,7,2,6,4,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,5,6,1,3,8,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,2,1]=>3
[6,3,5,7,4,2,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[1,3,8,6,5,2,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,7,3,8,5,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,2,8,5,7,4,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[1,6,8,5,4,7,2,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[5,7,1,8,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[2,1,3,8,6,4,7,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[5,8,4,3,7,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,1,8,7,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,5,8,6,4,3,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[5,8,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,6,1,8,4,7,5,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[5,3,8,6,1,2,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,8,1,4,6,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,6,2,1,4,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[4,6,2,3,7,1,8,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,1,1]=>2
[6,8,7,5,1,3,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,4,3,2,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[2,7,6,1,5,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,5,8,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,7,8,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3]=>0
[6,4,3,8,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[5,4,7,2,1,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[7,8,2,3,4,5,1,6,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[1]=>0
[1,8,9,3,4,5,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[2,6,4,5,7,1,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,7,4,6,1,5,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[3,4,6,5,2,8,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,2,2,1]=>5
[4,6,7,5,8,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[2,5,7,6,4,1,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[2,2,1,1,1]=>6
[5,1,4,6,2,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[5,3]=>1
[4,8,3,5,1,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,3,7,2,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[3,8,5,4,1,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[3,1,5,8,2,6,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[3,3,2,2]=>4
[2,8,5,3,1,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,5,2,3,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[6,2,4,5,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[2,3,8,7,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,2,7,5,6,8,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[6,8,2,5,4,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,2,3,4,5,6,9,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[6]=>0
[6,2,3,4,5,9,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[5,5]=>0
[5,2,3,4,9,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4]=>0
[4,2,3,9,1,5,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[3,3,3,3]=>0
[3,2,9,1,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[2,7,6,3,8,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,6,8,2,3,1,7,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[2,1,1]=>2
[4,7,2,3,5,1,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[6,4,2,1,3,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[5]=>0
[5,3,2,7,6,1,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3]=>0
[5,6,4,2,8,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,7,4,2,6,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[5,4,7,1,6,2,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,5,8,7,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,4,7,1,2,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2]=>0
[4,5,10,6,9,3,8,2,7,1]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[8,2,6,10,9,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[8,2,10,4,5,6,7,1,9,3]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,5,10,6,8,2,7,1,9,3]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,5,10,8,2,6,7,1,9,3]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[8,2,6,10,4,5,7,1,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,10,8,2,5,6,7,1,9,3]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[8,2,6,10,5,7,1,9,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[4,9,3,10,5,7,1,8,2,6]=>[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[4,9,3,10,7,1,8,2,5,6]=>[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,10,7,1,8,2,4,3,9,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[6,1,7,3,8,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[1,8,7,2,3,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,3,7,6,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,3,8,2,5,6,4,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[1,3,8,4,6,2,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,6,4,2,1,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[5,1]=>1
[2,5,7,6,3,8,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[2,2,1,1,1]=>6
[6,4,7,1,2,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[4,5,6,7,8,9,1,2,10,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[8,5,4,3,2,1]=>[5,4,3,2,1]=>10
[4,5,6,7,8,1,3,9,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1]=>[4,3,2,1]=>6
[1,2,7,5,8,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[2,2,2,2,2,1]=>5
[2,1,9,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,9,8,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,9,8,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[2,2,2,2,2,2]=>0
[2,1,10,9,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[2,2,2,2,2,2,2]=>0
[1,7,8,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,3,2,5,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,2,1,5,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5]=>0
[6,2,5,1,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,8,5,1,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,3,10,9,6,1,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,4,10,9,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,3,10,8,4,9,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,4,10,9,6,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,2,10,6,1,3,8,4,9,5]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[8,3,6,1,4,10,9,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[8,3,7,2,6,1,4,10,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[7]=>0
[8,3,10,7,2,6,1,4,9,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[8,3,9,4,10,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[2]=>0
[4,1,7,8,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[6,4,2,1,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[5,8,4,2,1,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,3,6,7,8,9,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1]=>[5,4,3,1]=>6
[5,3,4,6,7,8,9,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3]=>[5,4,3]=>3
[1,7,5,8,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,1,6,4,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,4,7,5,1,8,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,3,7,1,8,5,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,5,1,2,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[3,6,5,7,8,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[3,1,1,1]=>3
[3,6,5,1,8,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[2,8,4,3,5,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,2,4,7,6,8,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[3,1,5,7,4,8,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[3,3,2,2]=>4
[4,1,7,6,8,2,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[2,2,2]=>0
[1,2,6,5,8,3,7,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[4,2,2,2,2,1]=>9
[5,8,3,1,6,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,5,8,1,7,3,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,7,1,6,8,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[1,1,1]=>0
[5,8,7,1,6,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,3,8,2,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,1,8,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[5,7,1,6,4,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[2,7,1,6,5,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,7,1,4,8,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,7,5,4,1,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,2,7,1,4,3,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[2,6,8,4,7,1,3,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>4
[5,2,8,6,3,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[1,6,4,8,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,8,5,6,4,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,4,7,3,5,8,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,7,8,2,5,1,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[6,3,7,8,1,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[5,1,8,6,7,2,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[5,7,1,6,8,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[1,1]=>0
[6,8,4,2,1,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,3,2,8,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,4,1,3,7,8,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[6,8,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,7,4,8,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[6,1,2,4,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[2,5,6,8,1,4,7,3]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[3,2,1,1,1]=>7
[4,1,6,5,2,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,2,2]=>2
[4,5,1,7,8,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,3,1]=>2
[6,8,7,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,7,5,3,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,8,6,2,4,7,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,8,6,2,5,7,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,4,7,5,3,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,5,3,2,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,6,8,7,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,7,5,3,2,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,5,4,3,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,5,3,2,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,4,6,8,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,5,8,4,2,6,1,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[2,2,1,1]=>4
[1,6,4,2,9,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1,1,1]=>[4,4,1,1,1,1,1]=>10
[7,5,3,1,9,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[7,5,3,1,10,9,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[5,3,1,4,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[3,6,8,5,1,4,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,2,4,1,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[2,5,3,4,6,8,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[5,4,1,1,1]=>7
[4,7,1,2,5,6,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[6,7,3,1,8,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[1]=>0
[5,4,1,3,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[5,4]=>1
[5,7,4,8,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[1,2,8,9,4,5,6,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[5,3,1,8,4,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,5,3,6,8,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[2,1,6,5,8,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,2,2,2,2]=>4
[6,1,5,4,7,3,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[4]=>0
[3,1,8,4,2,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,8,7,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,2,3,1,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[5,3,2,8,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[4,6,3,2,5,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,1,1]=>2
[4,8,3,2,6,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,8,3,6,5,2,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,4,3,8,6,1,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[3,3,3,1,1]=>6
[2,6,3,8,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[3,1,1,1,1]=>4
[6,1,3,2,5,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,8,4,2,5,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[6,8,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,5,4,6,1,2,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[6,3,1,1]=>5
[3,1,9,4,2,6,7,8,5]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[5,7,6,3,4,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[4,6,7,2,3,5,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[2,1,1]=>2
[6,5,4,8,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,2,8,9,10,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,2,8,9,10,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,2,8,9,10,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,2]=>1
[7,8,2,3,9,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,2,3,9,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,2,3,9,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[4,1]=>1
[7,8,2,9,3,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1]=>[3,1]=>1
[7,8,2,9,3,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1]=>[3,1]=>1
[7,8,2,9,3,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1]=>[3,1]=>1
[7,8,2,9,10,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,2,9,10,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,2,9,10,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,2,9,10,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[3,1]=>1
[7,8,9,10,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[4,8,7,6,5,3,2,1,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1]=>[1,1,1,1]=>0
[5,9,8,7,6,4,3,2,1,10]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1]=>[1,1,1,1]=>0
[5,8,7,4,6,3,2,1,9]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1]=>[1,1,1]=>0
[5,7,4,3,6,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[6,9,8,5,7,4,1,3,2]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,9,5,2,3,8,4,6,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,2,9,4,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,6,2,3,4,9,5,7,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,8,5,2,3,4,6,9,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,8,5,6,2,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,9,8,1,2,5,3,6,7]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,8,3,9,4,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,2,5,4,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[3,8,2,6,1,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[5,3,7,8,2,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[4,5,8,3,6,1,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,5,8,7,2,3,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,3,1,8,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,3,6,8,7,4,5,2]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[3,2,2,2,1,1]=>11
[5,7,1,3,6,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,7,5,2,3,6,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,6,4,1,2,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[6,1,1,1]=>3
[4,7,1,3,2,5,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,7,1,3,2,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[5,7,1,3,6,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,8,2,5,7,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,8,5,2,3,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,7,5,4,2,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[4,6,5,1,7,8,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,1,1]=>2
[4,7,1,3,2,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[1,1,1]=>0
[3,6,5,1,8,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[4,1,1,1]=>3
[5,8,7,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,9,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,8,4,3,2,1,7,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2]=>[2,2]=>0
[5,9,8,4,3,2,1,6,7]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[7,10,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,3,1,5,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,7,6,3,5,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[1,7,5,3,4,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,2,3,4,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[5,3,1,6,4,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[5,3]=>1
[3,4,8,5,7,2,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[6,7,10,1,2,3,4,5,8,9]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[3,7,8,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,3,8,7,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,5,3,8,4,7,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[4,7,2,3,6,5,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[3,8,2,6,4,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,5,8,6,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,5,1,7,4,8,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[3]=>0
[6,5,4,1,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[3,5,1,8,6,2,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[3,3,1,1]=>4
[6,7,5,8,4,3,2,1,9]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1]=>[3,1]=>1
[7,6,5,3,2,1,4,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[1,8,7,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,4,8,1,5,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[1,6,4,3,5,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[5,1,1,1,1,1]=>5
[5,1,4,3,7,8,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[4,4]=>0
[5,7,1,8,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[1,1]=>0
[5,7,6,3,4,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,1,3,7,6,5,2,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,3]=>0
[4,3,6,1,2,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[5,2,2]=>2
[1,10,9,8,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[2,9,8,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,7,1,5,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2]=>0
[5,8,3,6,7,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,7,1,5,3,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,8,7,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,8,6,2,4,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,6,4,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,7,3,6,4,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,7,5,6,4,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[2,8,5,7,3,4,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,6,4,5,9,2,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,1,1,1]=>6
[2,8,4,1,6,3,7,5,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,7,8,3,1,5,2,9]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,1]=>[3,2,1,1]=>5
[3,5,9,7,1,8,2,6,4]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[2,2,2,1,1]=>6
[5,7,8,3,9,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,1]=>[2,1,1]=>2
[7,8,2,3,4,5,9,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[6,1]=>[1]=>0
[8,9,2,3,4,5,6,10,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[7,1]=>[1]=>0
[6,7,2,3,5,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[1]=>0
[2,1,3,8,5,4,6,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[5,3,6,8,2,4,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2]=>1
[1,7,8,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,7,4,2,5,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[1,8,3,4,5,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,6,7,5,3,8,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[2,1,1,1,1]=>4
[4,5,2,6,8,7,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[4,5,2,6,8,3,1,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,1]=>3
[7,1,2,3,4,6,5,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[7]=>0
[4,5,7,6,2,1,3,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[2,2,1]=>2
[5,3,7,8,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[2,2]=>0
[6,5,8,2,3,4,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,8,7,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,2,4,8,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,8,2,3,7,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[1,7,6,8,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,3,1,8,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,5,2,1,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[4,1,2,10,3,5,9,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[3,3,3,3,3]=>0
[2,8,6,1,5,7,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[6,4,1,5,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,8,7,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,1,7,3,8,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[4,1,3,5,8,2,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,3]=>2
[1,8,5,7,4,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,4,7,6,8,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[1,7,2,8,6,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,1,6,4,2,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[4,8,2,7,5,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[2,8,4,6,7,1,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[3,8,5,1,4,2,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,7,6,2,5,3,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,2,4,3,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,8,5,1,4,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,9,8,5,6,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,5,6,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,9,8,5,4,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,9,5,6,7,8,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[1,9,5,4,6,7,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[1,10,4,5,6,7,8,9,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>0
[5,1,7,3,2,6,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[4,7,2,3,5,1,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[1,1,1]=>0
[4,8,2,3,7,5,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,1,5,7,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[4,1,7,5,6,8,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,7,6,2,1,4,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[1,1,1,1]=>0
[1,6,8,7,2,5,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,4,8,7,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[2,2,2,1,1,1]=>9
[3,1,8,4,5,2,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,3,7,6,1,8,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[2,2,2,2,1]=>4
[4,8,5,2,1,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,8,4,2,1,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,6,7,5,2,3,1,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[2,1,1]=>2
[6,2,5,3,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,2,5,3,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[6,4,5,3,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,6,4,5,8,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[6,4,5,8,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,8,7,5,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,6,5,3,8,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,1,1]=>2
[6,7,2,4,5,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1]=>0
[6,8,7,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[2,8,4,7,5,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,8,7,4,6,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[6,5,8,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[4,8,6,2,5,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,8,1,2,4,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[7,3,4,5,1,2,8,9,10,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6]=>[7,6]=>1
[8,3,4,5,6,1,2,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[4,6,1,3,5,8,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,1,1]=>2
[4,5,1,3,8,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,4,1]=>2
[6,2,7,1,8,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[6,4,5,8,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,2,8,5,1,4,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,4,7,6,1,8,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[2,2,2,1,1]=>6
[2,1,7,8,9,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,2,2]=>[3,2,2,2,2,2]=>5
[2,6,7,8,9,10,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,1,1,1]=>[4,3,2,1,1,1,1]=>15
[5,3,6,4,7,1,8,2,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2]=>[6,4,2]=>3
[4,6,2,7,5,8,1,9,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,1]=>[5,3,1,1]=>5
[7,6,5,9,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,6,5,4,3,9,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[5]=>0
[7,9,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,7,10,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[7,6,9,8,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[8,7,6,10,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,6,5,9,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[3]=>0
[7,6,5,4,9,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4]=>0
[8,7,6,5,4,10,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[5]=>0
[7,6,5,4,3,9,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[5]=>0
[8,7,6,5,4,3,10,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]=>[6]=>0
[1,6,2,3,8,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[3,4,2,6,8,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[4,3,3,1]=>5
[6,8,1,2,7,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[1,6,2,8,7,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,6,8,5,7,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[3,8,1,2,4,7,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[1,1,1,1]=>0
[1,4,5,7,3,6,8,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[2,3,8,1,4,6,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[2,2,2,2,1]=>4
[3,6,2,4,7,5,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[4,1,1,1]=>3
[3,1,8,4,6,2,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,3,5,8,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2]=>0
[3,1,8,4,5,6,2,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[4,2,7,8,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[2,2,2]=>0
[2,3,7,4,8,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[2,2,2,2,1]=>4
[1,6,3,5,8,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[4,1,1,1,1,1]=>5
[2,4,5,7,1,6,8,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]=>[3,3,2,1,1]=>8
[4,1,5,7,8,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[6,1,4,8,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[2,8,5,7,6,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,5,7,8,6,4,1,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[2,2,1,1,1]=>6
[1,7,5,4,6,2,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,2,7,5,3,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2]=>0
[6,1,7,4,8,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2]=>0
[5,6,2,4,8,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1]=>1
[5,6,7,8,9,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,8,9,10,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,6,7,8,9,10,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[7,8,9,10,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,9,10,1,4,5,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,4,5,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,5,6,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,5,6,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,6,7,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,6,7,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,6,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,2,6,7,8,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[3,2,2,2,2,1]=>9
[1,2,4,8,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[2,6,1,4,7,5,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[3,1,5,7,2,6,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,3,2,2]=>4
[3,1,7,5,2,6,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[3,2,7,5,1,6,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[5,2,7,3,1,6,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[2,2]=>0
[6,7,2,1,3,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[1]=>0
[4,6,3,1,2,7,8,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[5,1,1]=>2
[2,3,5,6,8,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]=>[4,3,2,2,1]=>9
[2,3,5,9,4,6,7,8,1]=>[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[3,3,3,2,2,1]=>11
[2,4,5,8,3,6,7,1]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[3,3,2,1,1]=>8
[2,4,9,3,5,6,7,8,1]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[5,9,8,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[4,5,8,7,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,5,9,8,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[6,10,9,8,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[1,6,3,7,8,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[5,3,8,4,6,7,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2]=>0
[4,3,5,8,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[3,3,2]=>2
[3,2,7,8,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[2,2,2,2]=>0
[4,7,3,8,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[1,1,1]=>0
[4,3,8,7,2,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[2,2,2]=>0
[1,7,3,8,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,8,2,6,7,5,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[2,2,2,1]=>3
[1,6,3,8,7,4,5,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[1,4,5,8,7,6,2,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[5,2,1,3,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4]=>0
[2,1,3,8,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,2]=>4
[6,1,4,3,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[6,5,1,3,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[1,4,3,8,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,1,3,8,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[3,3,3]=>0
[6,4,7,8,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2]=>0
[3,5,6,7,1,8,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[3,2,1,1]=>5
[3,5,2,4,8,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,4,1,1]=>4
[3,7,6,1,4,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[2,7,8,3,6,1,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[1,7,8,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,5,4,3,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,5,8,1,7,3,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[4,6,7,1,3,8,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[2,1,1]=>2
[2,6,3,1,4,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[5,1,1,1,1]=>4
[2,9,3,4,5,6,1,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,3,4,1,8,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[1,1,1,1,1]=>0
[2,8,3,4,5,1,6,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[2,7,3,4,1,5,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[4,5,3,8,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[3,3,1]=>2
[2,3,7,8,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[2,2,2,2,1]=>4
[6,5,2,4,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[5,7,2,4,1,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[6,2,5,4,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,2,6,3,5,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[5,2,2]=>2
[6,4,1,8,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[6,3,4,8,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3]=>0
[1,6,7,5,4,8,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[2,1,1,1,1,1]=>5
[1,8,5,4,2,6,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[3,4,5,6,9,2,1,8,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[5,2,6,7,8,9,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[3,4,5,6,9,1,7,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,4,5,9,2,6,1,8,7]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[5,6,3,7,8,9,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[3,7,2,4,8,9,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,2,3,7,8,9,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3]=>[4,3]=>1
[5,2,6,7,8,9,10,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[5,7,3,6,2,1,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[1,1]=>0
[5,8,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,5,7,3,6,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,3,2]=>2
[1,4,5,7,6,8,2,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]=>[3,3,2,1,1,1]=>11
[5,7,2,1,6,8,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[2,6,3,1,7,8,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[6,2,5,7,4,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[3]=>0
[3,6,1,8,7,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[3,1,1,1]=>3
[4,3,9,5,6,7,8,2,1]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[2,2,2,2]=>0
[2,9,4,5,6,7,8,1,10,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[3,2,8,5,6,7,1,9,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2]=>[2,2,2,2,2]=>0
[7,8,4,5,6,1,3,9,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[1]=>0
[3,4,1,9,6,7,8,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,1]=>4
[4,8,9,5,6,7,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[4,3,10,5,6,7,8,9,2,1]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2]=>0
[8,9,4,5,6,7,1,3,10,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[1]=>0
[6,8,4,5,1,3,7,9,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[1,1]=>0
[4,7,1,3,5,6,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[1,1,1]=>0
[4,3,5,7,8,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,2]=>2
[4,7,9,5,6,2,1,8,3]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[4,9,10,5,6,7,8,2,1,3]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
[5,3,2,7,6,4,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3]=>0
[5,3,7,4,6,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[2,2]=>0
[5,7,3,2,1,8,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,7,6,3,2,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,2,7,5,4,1,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2]=>0
[1,7,3,5,4,2,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,3,7,4,1,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[2,2]=>0
[5,3,1,7,6,8,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3]=>0
[6,8,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[3,6,8,7,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[2,1,1,1]=>3
[5,7,3,6,2,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[3,6,5,2,4,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,1,1,1]=>3
[5,6,7,8,9,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>3
[6,7,8,9,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[6,7,8,9,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[7,8,9,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[5,6,7,8,9,10,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[7,8,9,10,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[7,8,9,10,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[2,1]=>1
[8,9,10,3,4,5,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,3,4,5,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,4,5,6,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,5,6,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[8,9,10,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1]=>0
[1,8,3,6,2,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,8,7,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[6,8,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[1]=>0
[8,6,1,2,3,4,5,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[7]=>0
[8,11,1,2,3,4,5,9,10,6,7]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[2,9,1,10,8,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
[6,3,2,1,5,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[5]=>0
[4,3,5,6,2,8,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[5,3,2]=>3
[6,3,5,2,7,8,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4]=>0
[4,5,3,1,6,8,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[5,4,1]=>3
[3,4,6,7,5,1,8,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[3,2,2,1]=>5
[4,8,2,6,7,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[6,5,8,3,7,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[2,3,10,5,6,7,8,9,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,3,10,1,6,7,8,9,4,5]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1]=>6
[2,5,4,7,1,8,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[3,3,1,1,1]=>6
[1,5,4,7,3,8,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[3,3,1,1,1,1]=>8
[3,4,5,6,8,9,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,4,3,2,1]=>[4,4,3,2,1]=>9
[3,4,5,7,8,9,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,3,2,1]=>[4,3,3,2,1]=>9
[3,5,6,7,8,9,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[4,3,2,1,1]=>9
[4,5,6,7,8,9,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>6
[5,1,6,7,8,9,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[1,5,6,7,8,9,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1,1]=>[4,3,2,1,1,1,1]=>15
[3,4,5,9,1,6,7,8,2]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,1]=>7
[5,6,3,7,8,9,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1]=>[4,3,1]=>3
[3,7,8,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[1,1,1,1]=>0
[3,7,1,4,8,9,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,2,6,7,8,9,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2]=>[4,3,2]=>3
[6,1,3,7,8,9,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3]=>[4,3]=>1
[5,1,6,7,8,9,10,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2]=>[5,4,3,2]=>6
[1,3,8,6,7,4,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[2,6,5,3,7,1,8,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,7,1,3,6,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[1,1]=>0
[1,8,6,3,7,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[5,7,3,4,2,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[1,1]=>0
[5,8,3,4,2,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[3,5,6,8,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[3,2,1,1]=>5
[4,8,7,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[3,7,4,2,6,8,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[1,1,1,1]=>0
[6,4,8,7,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[5,6,2,8,7,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,1]=>1
[6,2,8,3,7,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2]=>0
[3,7,5,6,4,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[1,1,1,1]=>0
[5,2,3,8,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3]=>0
[1,4,3,8,5,6,2,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[3,3,3,1,1,1]=>9
[4,5,8,7,2,3,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[2,2,1]=>2
[6,10,5,1,2,3,4,7,8,9]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,1,3,6,4,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[6,3]=>1
[6,1,2,4,7,5,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[4]=>0
[6,4,5,1,8,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4]=>0
[4,3,6,2,5,7,1,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[5,2,2]=>2
[1,6,5,7,3,4,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[3,1,1,1,1,1]=>5
[2,6,5,4,8,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[4,1,1,1,1]=>4
[5,6,7,1,3,2,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[2,1]=>1
[1,8,5,2,7,6,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,6,8,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[1,7,8,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
[4,6,5,7,1,8,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[3,1,1]=>2
[5,4,3,2,1,9,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]=>[5,5,5]=>0
[1,6,3,4,2,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,1,1,1,1,1]=>5
[1,5,7,6,2,3,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[2,2,1,1,1,1]=>8
[1,3,7,4,6,8,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[2,2,2,2,1,1]=>8
[3,7,4,6,8,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[1,1,1,1]=>0
[4,8,3,1,7,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[1,1,1]=>0
[5,6,1,4,3,8,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,1]=>1
[5,8,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[1,1]=>0
[4,1,3,7,8,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3]=>0
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searching the database for the individual values of this statistic
Description
Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape.
Given a partition λ with r parts, the number of semi-standard Young-tableaux of shape kλ and boxes with values in [r] grows as a polynomial in k. This follows by setting q=1 in (7.105) on page 375 of [1], which yields the polynomial
p(k)=∏i<jk(λj−λi)+j−ij−i.
The statistic of the degree of this polynomial.
For example, the partition (3,2,1,1,1) gives
p(k)=−136(k−3)(2k−3)(k−2)2(k−1)3
which has degree 7 in k. Thus, [3,2,1,1,1]↦7.
This is the same as the number of unordered pairs of different parts, which follows from:
degp(k)=∑i<j{1λj≠λi0λi=λj=∑i<jλj≠λi1
Given a partition λ with r parts, the number of semi-standard Young-tableaux of shape kλ and boxes with values in [r] grows as a polynomial in k. This follows by setting q=1 in (7.105) on page 375 of [1], which yields the polynomial
p(k)=∏i<jk(λj−λi)+j−ij−i.
The statistic of the degree of this polynomial.
For example, the partition (3,2,1,1,1) gives
p(k)=−136(k−3)(2k−3)(k−2)2(k−1)3
which has degree 7 in k. Thus, [3,2,1,1,1]↦7.
This is the same as the number of unordered pairs of different parts, which follows from:
degp(k)=∑i<j{1λj≠λi0λi=λj=∑i<jλj≠λi1
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
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