Identifier
-
Mp00060:
Permutations
—Robinson-Schensted tableau shape⟶
Integer partitions
St000003: Integer partitions ⟶ ℤ
Values
=>
Cc0002;cc-rep
[1]=>[1]=>1
[1,2]=>[2]=>1
[2,1]=>[1,1]=>1
[1,2,3]=>[3]=>1
[1,3,2]=>[2,1]=>2
[2,1,3]=>[2,1]=>2
[2,3,1]=>[2,1]=>2
[3,1,2]=>[2,1]=>2
[3,2,1]=>[1,1,1]=>1
[1,2,3,4]=>[4]=>1
[1,2,4,3]=>[3,1]=>3
[1,3,2,4]=>[3,1]=>3
[1,3,4,2]=>[3,1]=>3
[1,4,2,3]=>[3,1]=>3
[1,4,3,2]=>[2,1,1]=>3
[2,1,3,4]=>[3,1]=>3
[2,1,4,3]=>[2,2]=>2
[2,3,1,4]=>[3,1]=>3
[2,3,4,1]=>[3,1]=>3
[2,4,1,3]=>[2,2]=>2
[2,4,3,1]=>[2,1,1]=>3
[3,1,2,4]=>[3,1]=>3
[3,1,4,2]=>[2,2]=>2
[3,2,1,4]=>[2,1,1]=>3
[3,2,4,1]=>[2,1,1]=>3
[3,4,1,2]=>[2,2]=>2
[3,4,2,1]=>[2,1,1]=>3
[4,1,2,3]=>[3,1]=>3
[4,1,3,2]=>[2,1,1]=>3
[4,2,1,3]=>[2,1,1]=>3
[4,2,3,1]=>[2,1,1]=>3
[4,3,1,2]=>[2,1,1]=>3
[4,3,2,1]=>[1,1,1,1]=>1
[1,2,3,4,5]=>[5]=>1
[1,2,3,5,4]=>[4,1]=>4
[1,2,4,3,5]=>[4,1]=>4
[1,2,4,5,3]=>[4,1]=>4
[1,2,5,3,4]=>[4,1]=>4
[1,2,5,4,3]=>[3,1,1]=>6
[1,3,2,4,5]=>[4,1]=>4
[1,3,2,5,4]=>[3,2]=>5
[1,3,4,2,5]=>[4,1]=>4
[1,3,4,5,2]=>[4,1]=>4
[1,3,5,2,4]=>[3,2]=>5
[1,3,5,4,2]=>[3,1,1]=>6
[1,4,2,3,5]=>[4,1]=>4
[1,4,2,5,3]=>[3,2]=>5
[1,4,3,2,5]=>[3,1,1]=>6
[1,4,3,5,2]=>[3,1,1]=>6
[1,4,5,2,3]=>[3,2]=>5
[1,4,5,3,2]=>[3,1,1]=>6
[1,5,2,3,4]=>[4,1]=>4
[1,5,2,4,3]=>[3,1,1]=>6
[1,5,3,2,4]=>[3,1,1]=>6
[1,5,3,4,2]=>[3,1,1]=>6
[1,5,4,2,3]=>[3,1,1]=>6
[1,5,4,3,2]=>[2,1,1,1]=>4
[2,1,3,4,5]=>[4,1]=>4
[2,1,3,5,4]=>[3,2]=>5
[2,1,4,3,5]=>[3,2]=>5
[2,1,4,5,3]=>[3,2]=>5
[2,1,5,3,4]=>[3,2]=>5
[2,1,5,4,3]=>[2,2,1]=>5
[2,3,1,4,5]=>[4,1]=>4
[2,3,1,5,4]=>[3,2]=>5
[2,3,4,1,5]=>[4,1]=>4
[2,3,4,5,1]=>[4,1]=>4
[2,3,5,1,4]=>[3,2]=>5
[2,3,5,4,1]=>[3,1,1]=>6
[2,4,1,3,5]=>[3,2]=>5
[2,4,1,5,3]=>[3,2]=>5
[2,4,3,1,5]=>[3,1,1]=>6
[2,4,3,5,1]=>[3,1,1]=>6
[2,4,5,1,3]=>[3,2]=>5
[2,4,5,3,1]=>[3,1,1]=>6
[2,5,1,3,4]=>[3,2]=>5
[2,5,1,4,3]=>[2,2,1]=>5
[2,5,3,1,4]=>[3,1,1]=>6
[2,5,3,4,1]=>[3,1,1]=>6
[2,5,4,1,3]=>[2,2,1]=>5
[2,5,4,3,1]=>[2,1,1,1]=>4
[3,1,2,4,5]=>[4,1]=>4
[3,1,2,5,4]=>[3,2]=>5
[3,1,4,2,5]=>[3,2]=>5
[3,1,4,5,2]=>[3,2]=>5
[3,1,5,2,4]=>[3,2]=>5
[3,1,5,4,2]=>[2,2,1]=>5
[3,2,1,4,5]=>[3,1,1]=>6
[3,2,1,5,4]=>[2,2,1]=>5
[3,2,4,1,5]=>[3,1,1]=>6
[3,2,4,5,1]=>[3,1,1]=>6
[3,2,5,1,4]=>[2,2,1]=>5
[3,2,5,4,1]=>[2,2,1]=>5
[3,4,1,2,5]=>[3,2]=>5
[3,4,1,5,2]=>[3,2]=>5
[3,4,2,1,5]=>[3,1,1]=>6
[3,4,2,5,1]=>[3,1,1]=>6
[3,4,5,1,2]=>[3,2]=>5
[3,4,5,2,1]=>[3,1,1]=>6
[3,5,1,2,4]=>[3,2]=>5
[3,5,1,4,2]=>[2,2,1]=>5
[3,5,2,1,4]=>[2,2,1]=>5
[3,5,2,4,1]=>[2,2,1]=>5
[3,5,4,1,2]=>[2,2,1]=>5
[3,5,4,2,1]=>[2,1,1,1]=>4
[4,1,2,3,5]=>[4,1]=>4
[4,1,2,5,3]=>[3,2]=>5
[4,1,3,2,5]=>[3,1,1]=>6
[4,1,3,5,2]=>[3,1,1]=>6
[4,1,5,2,3]=>[3,2]=>5
[4,1,5,3,2]=>[2,2,1]=>5
[4,2,1,3,5]=>[3,1,1]=>6
[4,2,1,5,3]=>[2,2,1]=>5
[4,2,3,1,5]=>[3,1,1]=>6
[4,2,3,5,1]=>[3,1,1]=>6
[4,2,5,1,3]=>[2,2,1]=>5
[4,2,5,3,1]=>[2,2,1]=>5
[4,3,1,2,5]=>[3,1,1]=>6
[4,3,1,5,2]=>[2,2,1]=>5
[4,3,2,1,5]=>[2,1,1,1]=>4
[4,3,2,5,1]=>[2,1,1,1]=>4
[4,3,5,1,2]=>[2,2,1]=>5
[4,3,5,2,1]=>[2,1,1,1]=>4
[4,5,1,2,3]=>[3,2]=>5
[4,5,1,3,2]=>[2,2,1]=>5
[4,5,2,1,3]=>[2,2,1]=>5
[4,5,2,3,1]=>[2,2,1]=>5
[4,5,3,1,2]=>[2,2,1]=>5
[4,5,3,2,1]=>[2,1,1,1]=>4
[5,1,2,3,4]=>[4,1]=>4
[5,1,2,4,3]=>[3,1,1]=>6
[5,1,3,2,4]=>[3,1,1]=>6
[5,1,3,4,2]=>[3,1,1]=>6
[5,1,4,2,3]=>[3,1,1]=>6
[5,1,4,3,2]=>[2,1,1,1]=>4
[5,2,1,3,4]=>[3,1,1]=>6
[5,2,1,4,3]=>[2,2,1]=>5
[5,2,3,1,4]=>[3,1,1]=>6
[5,2,3,4,1]=>[3,1,1]=>6
[5,2,4,1,3]=>[2,2,1]=>5
[5,2,4,3,1]=>[2,1,1,1]=>4
[5,3,1,2,4]=>[3,1,1]=>6
[5,3,1,4,2]=>[2,2,1]=>5
[5,3,2,1,4]=>[2,1,1,1]=>4
[5,3,2,4,1]=>[2,1,1,1]=>4
[5,3,4,1,2]=>[2,2,1]=>5
[5,3,4,2,1]=>[2,1,1,1]=>4
[5,4,1,2,3]=>[3,1,1]=>6
[5,4,1,3,2]=>[2,1,1,1]=>4
[5,4,2,1,3]=>[2,1,1,1]=>4
[5,4,2,3,1]=>[2,1,1,1]=>4
[5,4,3,1,2]=>[2,1,1,1]=>4
[5,4,3,2,1]=>[1,1,1,1,1]=>1
[1,2,3,4,5,6]=>[6]=>1
[1,2,3,4,6,5]=>[5,1]=>5
[1,2,3,5,4,6]=>[5,1]=>5
[1,2,3,5,6,4]=>[5,1]=>5
[1,2,3,6,4,5]=>[5,1]=>5
[1,2,3,6,5,4]=>[4,1,1]=>10
[1,2,4,3,5,6]=>[5,1]=>5
[1,2,4,3,6,5]=>[4,2]=>9
[1,2,4,5,3,6]=>[5,1]=>5
[1,2,4,5,6,3]=>[5,1]=>5
[1,2,4,6,3,5]=>[4,2]=>9
[1,2,4,6,5,3]=>[4,1,1]=>10
[1,2,5,3,4,6]=>[5,1]=>5
[1,2,5,3,6,4]=>[4,2]=>9
[1,2,5,4,3,6]=>[4,1,1]=>10
[1,2,5,4,6,3]=>[4,1,1]=>10
[1,2,5,6,3,4]=>[4,2]=>9
[1,2,5,6,4,3]=>[4,1,1]=>10
[1,2,6,3,4,5]=>[5,1]=>5
[1,2,6,3,5,4]=>[4,1,1]=>10
[1,2,6,4,3,5]=>[4,1,1]=>10
[1,2,6,4,5,3]=>[4,1,1]=>10
[1,2,6,5,3,4]=>[4,1,1]=>10
[1,2,6,5,4,3]=>[3,1,1,1]=>10
[1,3,2,4,5,6]=>[5,1]=>5
[1,3,2,4,6,5]=>[4,2]=>9
[1,3,2,5,4,6]=>[4,2]=>9
[1,3,2,5,6,4]=>[4,2]=>9
[1,3,2,6,4,5]=>[4,2]=>9
[1,3,2,6,5,4]=>[3,2,1]=>16
[1,3,4,2,5,6]=>[5,1]=>5
[1,3,4,2,6,5]=>[4,2]=>9
[1,3,4,5,2,6]=>[5,1]=>5
[1,3,4,5,6,2]=>[5,1]=>5
[1,3,4,6,2,5]=>[4,2]=>9
[1,3,4,6,5,2]=>[4,1,1]=>10
[1,3,5,2,4,6]=>[4,2]=>9
[1,3,5,2,6,4]=>[4,2]=>9
[1,3,5,4,2,6]=>[4,1,1]=>10
[1,3,5,4,6,2]=>[4,1,1]=>10
[1,3,5,6,2,4]=>[4,2]=>9
[1,3,5,6,4,2]=>[4,1,1]=>10
[1,3,6,2,4,5]=>[4,2]=>9
[1,3,6,2,5,4]=>[3,2,1]=>16
[1,3,6,4,2,5]=>[4,1,1]=>10
[1,3,6,4,5,2]=>[4,1,1]=>10
[1,3,6,5,2,4]=>[3,2,1]=>16
[1,3,6,5,4,2]=>[3,1,1,1]=>10
[1,4,2,3,5,6]=>[5,1]=>5
[1,4,2,3,6,5]=>[4,2]=>9
[1,4,2,5,3,6]=>[4,2]=>9
[1,4,2,5,6,3]=>[4,2]=>9
[1,4,2,6,3,5]=>[4,2]=>9
[1,4,2,6,5,3]=>[3,2,1]=>16
[1,4,3,2,5,6]=>[4,1,1]=>10
[1,4,3,2,6,5]=>[3,2,1]=>16
[1,4,3,5,2,6]=>[4,1,1]=>10
[1,4,3,5,6,2]=>[4,1,1]=>10
[1,4,3,6,2,5]=>[3,2,1]=>16
[1,4,3,6,5,2]=>[3,2,1]=>16
[1,4,5,2,3,6]=>[4,2]=>9
[1,4,5,2,6,3]=>[4,2]=>9
[1,4,5,3,2,6]=>[4,1,1]=>10
[1,4,5,3,6,2]=>[4,1,1]=>10
[1,4,5,6,2,3]=>[4,2]=>9
[1,4,5,6,3,2]=>[4,1,1]=>10
[1,4,6,2,3,5]=>[4,2]=>9
[1,4,6,2,5,3]=>[3,2,1]=>16
[1,4,6,3,2,5]=>[3,2,1]=>16
[1,4,6,3,5,2]=>[3,2,1]=>16
[1,4,6,5,2,3]=>[3,2,1]=>16
[1,4,6,5,3,2]=>[3,1,1,1]=>10
[1,5,2,3,4,6]=>[5,1]=>5
[1,5,2,3,6,4]=>[4,2]=>9
[1,5,2,4,3,6]=>[4,1,1]=>10
[1,5,2,4,6,3]=>[4,1,1]=>10
[1,5,2,6,3,4]=>[4,2]=>9
[1,5,2,6,4,3]=>[3,2,1]=>16
[1,5,3,2,4,6]=>[4,1,1]=>10
[1,5,3,2,6,4]=>[3,2,1]=>16
[1,5,3,4,2,6]=>[4,1,1]=>10
[1,5,3,4,6,2]=>[4,1,1]=>10
[1,5,3,6,2,4]=>[3,2,1]=>16
[1,5,3,6,4,2]=>[3,2,1]=>16
[1,5,4,2,3,6]=>[4,1,1]=>10
[1,5,4,2,6,3]=>[3,2,1]=>16
[1,5,4,3,2,6]=>[3,1,1,1]=>10
[1,5,4,3,6,2]=>[3,1,1,1]=>10
[1,5,4,6,2,3]=>[3,2,1]=>16
[1,5,4,6,3,2]=>[3,1,1,1]=>10
[1,5,6,2,3,4]=>[4,2]=>9
[1,5,6,2,4,3]=>[3,2,1]=>16
[1,5,6,3,2,4]=>[3,2,1]=>16
[1,5,6,3,4,2]=>[3,2,1]=>16
[1,5,6,4,2,3]=>[3,2,1]=>16
[1,5,6,4,3,2]=>[3,1,1,1]=>10
[1,6,2,3,4,5]=>[5,1]=>5
[1,6,2,3,5,4]=>[4,1,1]=>10
[1,6,2,4,3,5]=>[4,1,1]=>10
[1,6,2,4,5,3]=>[4,1,1]=>10
[1,6,2,5,3,4]=>[4,1,1]=>10
[1,6,2,5,4,3]=>[3,1,1,1]=>10
[1,6,3,2,4,5]=>[4,1,1]=>10
[1,6,3,2,5,4]=>[3,2,1]=>16
[1,6,3,4,2,5]=>[4,1,1]=>10
[1,6,3,4,5,2]=>[4,1,1]=>10
[1,6,3,5,2,4]=>[3,2,1]=>16
[1,6,3,5,4,2]=>[3,1,1,1]=>10
[1,6,4,2,3,5]=>[4,1,1]=>10
[1,6,4,2,5,3]=>[3,2,1]=>16
[1,6,4,3,2,5]=>[3,1,1,1]=>10
[1,6,4,3,5,2]=>[3,1,1,1]=>10
[1,6,4,5,2,3]=>[3,2,1]=>16
[1,6,4,5,3,2]=>[3,1,1,1]=>10
[1,6,5,2,3,4]=>[4,1,1]=>10
[1,6,5,2,4,3]=>[3,1,1,1]=>10
[1,6,5,3,2,4]=>[3,1,1,1]=>10
[1,6,5,3,4,2]=>[3,1,1,1]=>10
[1,6,5,4,2,3]=>[3,1,1,1]=>10
[1,6,5,4,3,2]=>[2,1,1,1,1]=>5
[2,1,3,4,5,6]=>[5,1]=>5
[2,1,3,4,6,5]=>[4,2]=>9
[2,1,3,5,4,6]=>[4,2]=>9
[2,1,3,5,6,4]=>[4,2]=>9
[2,1,3,6,4,5]=>[4,2]=>9
[2,1,3,6,5,4]=>[3,2,1]=>16
[2,1,4,3,5,6]=>[4,2]=>9
[2,1,4,3,6,5]=>[3,3]=>5
[2,1,4,5,3,6]=>[4,2]=>9
[2,1,4,5,6,3]=>[4,2]=>9
[2,1,4,6,3,5]=>[3,3]=>5
[2,1,4,6,5,3]=>[3,2,1]=>16
[2,1,5,3,4,6]=>[4,2]=>9
[2,1,5,3,6,4]=>[3,3]=>5
[2,1,5,4,3,6]=>[3,2,1]=>16
[2,1,5,4,6,3]=>[3,2,1]=>16
[2,1,5,6,3,4]=>[3,3]=>5
[2,1,5,6,4,3]=>[3,2,1]=>16
[2,1,6,3,4,5]=>[4,2]=>9
[2,1,6,3,5,4]=>[3,2,1]=>16
[2,1,6,4,3,5]=>[3,2,1]=>16
[2,1,6,4,5,3]=>[3,2,1]=>16
[2,1,6,5,3,4]=>[3,2,1]=>16
[2,1,6,5,4,3]=>[2,2,1,1]=>9
[2,3,1,4,5,6]=>[5,1]=>5
[2,3,1,4,6,5]=>[4,2]=>9
[2,3,1,5,4,6]=>[4,2]=>9
[2,3,1,5,6,4]=>[4,2]=>9
[2,3,1,6,4,5]=>[4,2]=>9
[2,3,1,6,5,4]=>[3,2,1]=>16
[2,3,4,1,5,6]=>[5,1]=>5
[2,3,4,1,6,5]=>[4,2]=>9
[2,3,4,5,1,6]=>[5,1]=>5
[2,3,4,5,6,1]=>[5,1]=>5
[2,3,4,6,1,5]=>[4,2]=>9
[2,3,4,6,5,1]=>[4,1,1]=>10
[2,3,5,1,4,6]=>[4,2]=>9
[2,3,5,1,6,4]=>[4,2]=>9
[2,3,5,4,1,6]=>[4,1,1]=>10
[2,3,5,4,6,1]=>[4,1,1]=>10
[2,3,5,6,1,4]=>[4,2]=>9
[2,3,5,6,4,1]=>[4,1,1]=>10
[2,3,6,1,4,5]=>[4,2]=>9
[2,3,6,1,5,4]=>[3,2,1]=>16
[2,3,6,4,1,5]=>[4,1,1]=>10
[2,3,6,4,5,1]=>[4,1,1]=>10
[2,3,6,5,1,4]=>[3,2,1]=>16
[2,3,6,5,4,1]=>[3,1,1,1]=>10
[2,4,1,3,5,6]=>[4,2]=>9
[2,4,1,3,6,5]=>[3,3]=>5
[2,4,1,5,3,6]=>[4,2]=>9
[2,4,1,5,6,3]=>[4,2]=>9
[2,4,1,6,3,5]=>[3,3]=>5
[2,4,1,6,5,3]=>[3,2,1]=>16
[2,4,3,1,5,6]=>[4,1,1]=>10
[2,4,3,1,6,5]=>[3,2,1]=>16
[2,4,3,5,1,6]=>[4,1,1]=>10
[2,4,3,5,6,1]=>[4,1,1]=>10
[2,4,3,6,1,5]=>[3,2,1]=>16
[2,4,3,6,5,1]=>[3,2,1]=>16
[2,4,5,1,3,6]=>[4,2]=>9
[2,4,5,1,6,3]=>[4,2]=>9
[2,4,5,3,1,6]=>[4,1,1]=>10
[2,4,5,3,6,1]=>[4,1,1]=>10
[2,4,5,6,1,3]=>[4,2]=>9
[2,4,5,6,3,1]=>[4,1,1]=>10
[2,4,6,1,3,5]=>[3,3]=>5
[2,4,6,1,5,3]=>[3,2,1]=>16
[2,4,6,3,1,5]=>[3,2,1]=>16
[2,4,6,3,5,1]=>[3,2,1]=>16
[2,4,6,5,1,3]=>[3,2,1]=>16
[2,4,6,5,3,1]=>[3,1,1,1]=>10
[2,5,1,3,4,6]=>[4,2]=>9
[2,5,1,3,6,4]=>[3,3]=>5
[2,5,1,4,3,6]=>[3,2,1]=>16
[2,5,1,4,6,3]=>[3,2,1]=>16
[2,5,1,6,3,4]=>[3,3]=>5
[2,5,1,6,4,3]=>[3,2,1]=>16
[2,5,3,1,4,6]=>[4,1,1]=>10
[2,5,3,1,6,4]=>[3,2,1]=>16
[2,5,3,4,1,6]=>[4,1,1]=>10
[2,5,3,4,6,1]=>[4,1,1]=>10
[2,5,3,6,1,4]=>[3,2,1]=>16
[2,5,3,6,4,1]=>[3,2,1]=>16
[2,5,4,1,3,6]=>[3,2,1]=>16
[2,5,4,1,6,3]=>[3,2,1]=>16
[2,5,4,3,1,6]=>[3,1,1,1]=>10
[2,5,4,3,6,1]=>[3,1,1,1]=>10
[2,5,4,6,1,3]=>[3,2,1]=>16
[2,5,4,6,3,1]=>[3,1,1,1]=>10
[2,5,6,1,3,4]=>[3,3]=>5
[2,5,6,1,4,3]=>[3,2,1]=>16
[2,5,6,3,1,4]=>[3,2,1]=>16
[2,5,6,3,4,1]=>[3,2,1]=>16
[2,5,6,4,1,3]=>[3,2,1]=>16
[2,5,6,4,3,1]=>[3,1,1,1]=>10
[2,6,1,3,4,5]=>[4,2]=>9
[2,6,1,3,5,4]=>[3,2,1]=>16
[2,6,1,4,3,5]=>[3,2,1]=>16
[2,6,1,4,5,3]=>[3,2,1]=>16
[2,6,1,5,3,4]=>[3,2,1]=>16
[2,6,1,5,4,3]=>[2,2,1,1]=>9
[2,6,3,1,4,5]=>[4,1,1]=>10
[2,6,3,1,5,4]=>[3,2,1]=>16
[2,6,3,4,1,5]=>[4,1,1]=>10
[2,6,3,4,5,1]=>[4,1,1]=>10
[2,6,3,5,1,4]=>[3,2,1]=>16
[2,6,3,5,4,1]=>[3,1,1,1]=>10
[2,6,4,1,3,5]=>[3,2,1]=>16
[2,6,4,1,5,3]=>[3,2,1]=>16
[2,6,4,3,1,5]=>[3,1,1,1]=>10
[2,6,4,3,5,1]=>[3,1,1,1]=>10
[2,6,4,5,1,3]=>[3,2,1]=>16
[2,6,4,5,3,1]=>[3,1,1,1]=>10
[2,6,5,1,3,4]=>[3,2,1]=>16
[2,6,5,1,4,3]=>[2,2,1,1]=>9
[2,6,5,3,1,4]=>[3,1,1,1]=>10
[2,6,5,3,4,1]=>[3,1,1,1]=>10
[2,6,5,4,1,3]=>[2,2,1,1]=>9
[2,6,5,4,3,1]=>[2,1,1,1,1]=>5
[3,1,2,4,5,6]=>[5,1]=>5
[3,1,2,4,6,5]=>[4,2]=>9
[3,1,2,5,4,6]=>[4,2]=>9
[3,1,2,5,6,4]=>[4,2]=>9
[3,1,2,6,4,5]=>[4,2]=>9
[3,1,2,6,5,4]=>[3,2,1]=>16
[3,1,4,2,5,6]=>[4,2]=>9
[3,1,4,2,6,5]=>[3,3]=>5
[3,1,4,5,2,6]=>[4,2]=>9
[3,1,4,5,6,2]=>[4,2]=>9
[3,1,4,6,2,5]=>[3,3]=>5
[3,1,4,6,5,2]=>[3,2,1]=>16
[3,1,5,2,4,6]=>[4,2]=>9
[3,1,5,2,6,4]=>[3,3]=>5
[3,1,5,4,2,6]=>[3,2,1]=>16
[3,1,5,4,6,2]=>[3,2,1]=>16
[3,1,5,6,2,4]=>[3,3]=>5
[3,1,5,6,4,2]=>[3,2,1]=>16
[3,1,6,2,4,5]=>[4,2]=>9
[3,1,6,2,5,4]=>[3,2,1]=>16
[3,1,6,4,2,5]=>[3,2,1]=>16
[3,1,6,4,5,2]=>[3,2,1]=>16
[3,1,6,5,2,4]=>[3,2,1]=>16
[3,1,6,5,4,2]=>[2,2,1,1]=>9
[3,2,1,4,5,6]=>[4,1,1]=>10
[3,2,1,4,6,5]=>[3,2,1]=>16
[3,2,1,5,4,6]=>[3,2,1]=>16
[3,2,1,5,6,4]=>[3,2,1]=>16
[3,2,1,6,4,5]=>[3,2,1]=>16
[3,2,1,6,5,4]=>[2,2,2]=>5
[3,2,4,1,5,6]=>[4,1,1]=>10
[3,2,4,1,6,5]=>[3,2,1]=>16
[3,2,4,5,1,6]=>[4,1,1]=>10
[3,2,4,5,6,1]=>[4,1,1]=>10
[3,2,4,6,1,5]=>[3,2,1]=>16
[3,2,4,6,5,1]=>[3,2,1]=>16
[3,2,5,1,4,6]=>[3,2,1]=>16
[3,2,5,1,6,4]=>[3,2,1]=>16
[3,2,5,4,1,6]=>[3,2,1]=>16
[3,2,5,4,6,1]=>[3,2,1]=>16
[3,2,5,6,1,4]=>[3,2,1]=>16
[3,2,5,6,4,1]=>[3,2,1]=>16
[3,2,6,1,4,5]=>[3,2,1]=>16
[3,2,6,1,5,4]=>[2,2,2]=>5
[3,2,6,4,1,5]=>[3,2,1]=>16
[3,2,6,4,5,1]=>[3,2,1]=>16
[3,2,6,5,1,4]=>[2,2,2]=>5
[3,2,6,5,4,1]=>[2,2,1,1]=>9
[3,4,1,2,5,6]=>[4,2]=>9
[3,4,1,2,6,5]=>[3,3]=>5
[3,4,1,5,2,6]=>[4,2]=>9
[3,4,1,5,6,2]=>[4,2]=>9
[3,4,1,6,2,5]=>[3,3]=>5
[3,4,1,6,5,2]=>[3,2,1]=>16
[3,4,2,1,5,6]=>[4,1,1]=>10
[3,4,2,1,6,5]=>[3,2,1]=>16
[3,4,2,5,1,6]=>[4,1,1]=>10
[3,4,2,5,6,1]=>[4,1,1]=>10
[3,4,2,6,1,5]=>[3,2,1]=>16
[3,4,2,6,5,1]=>[3,2,1]=>16
[3,4,5,1,2,6]=>[4,2]=>9
[3,4,5,1,6,2]=>[4,2]=>9
[3,4,5,2,1,6]=>[4,1,1]=>10
[3,4,5,2,6,1]=>[4,1,1]=>10
[3,4,5,6,1,2]=>[4,2]=>9
[3,4,5,6,2,1]=>[4,1,1]=>10
[3,4,6,1,2,5]=>[3,3]=>5
[3,4,6,1,5,2]=>[3,2,1]=>16
[3,4,6,2,1,5]=>[3,2,1]=>16
[3,4,6,2,5,1]=>[3,2,1]=>16
[3,4,6,5,1,2]=>[3,2,1]=>16
[3,4,6,5,2,1]=>[3,1,1,1]=>10
[3,5,1,2,4,6]=>[4,2]=>9
[3,5,1,2,6,4]=>[3,3]=>5
[3,5,1,4,2,6]=>[3,2,1]=>16
[3,5,1,4,6,2]=>[3,2,1]=>16
[3,5,1,6,2,4]=>[3,3]=>5
[3,5,1,6,4,2]=>[3,2,1]=>16
[3,5,2,1,4,6]=>[3,2,1]=>16
[3,5,2,1,6,4]=>[3,2,1]=>16
[3,5,2,4,1,6]=>[3,2,1]=>16
[3,5,2,4,6,1]=>[3,2,1]=>16
[3,5,2,6,1,4]=>[3,2,1]=>16
[3,5,2,6,4,1]=>[3,2,1]=>16
[3,5,4,1,2,6]=>[3,2,1]=>16
[3,5,4,1,6,2]=>[3,2,1]=>16
[3,5,4,2,1,6]=>[3,1,1,1]=>10
[3,5,4,2,6,1]=>[3,1,1,1]=>10
[3,5,4,6,1,2]=>[3,2,1]=>16
[3,5,4,6,2,1]=>[3,1,1,1]=>10
[3,5,6,1,2,4]=>[3,3]=>5
[3,5,6,1,4,2]=>[3,2,1]=>16
[3,5,6,2,1,4]=>[3,2,1]=>16
[3,5,6,2,4,1]=>[3,2,1]=>16
[3,5,6,4,1,2]=>[3,2,1]=>16
[3,5,6,4,2,1]=>[3,1,1,1]=>10
[3,6,1,2,4,5]=>[4,2]=>9
[3,6,1,2,5,4]=>[3,2,1]=>16
[3,6,1,4,2,5]=>[3,2,1]=>16
[3,6,1,4,5,2]=>[3,2,1]=>16
[3,6,1,5,2,4]=>[3,2,1]=>16
[3,6,1,5,4,2]=>[2,2,1,1]=>9
[3,6,2,1,4,5]=>[3,2,1]=>16
[3,6,2,1,5,4]=>[2,2,2]=>5
[3,6,2,4,1,5]=>[3,2,1]=>16
[3,6,2,4,5,1]=>[3,2,1]=>16
[3,6,2,5,1,4]=>[2,2,2]=>5
[3,6,2,5,4,1]=>[2,2,1,1]=>9
[3,6,4,1,2,5]=>[3,2,1]=>16
[3,6,4,1,5,2]=>[3,2,1]=>16
[3,6,4,2,1,5]=>[3,1,1,1]=>10
[3,6,4,2,5,1]=>[3,1,1,1]=>10
[3,6,4,5,1,2]=>[3,2,1]=>16
[3,6,4,5,2,1]=>[3,1,1,1]=>10
[3,6,5,1,2,4]=>[3,2,1]=>16
[3,6,5,1,4,2]=>[2,2,1,1]=>9
[3,6,5,2,1,4]=>[2,2,1,1]=>9
[3,6,5,2,4,1]=>[2,2,1,1]=>9
[3,6,5,4,1,2]=>[2,2,1,1]=>9
[3,6,5,4,2,1]=>[2,1,1,1,1]=>5
[4,1,2,3,5,6]=>[5,1]=>5
[4,1,2,3,6,5]=>[4,2]=>9
[4,1,2,5,3,6]=>[4,2]=>9
[4,1,2,5,6,3]=>[4,2]=>9
[4,1,2,6,3,5]=>[4,2]=>9
[4,1,2,6,5,3]=>[3,2,1]=>16
[4,1,3,2,5,6]=>[4,1,1]=>10
[4,1,3,2,6,5]=>[3,2,1]=>16
[4,1,3,5,2,6]=>[4,1,1]=>10
[4,1,3,5,6,2]=>[4,1,1]=>10
[4,1,3,6,2,5]=>[3,2,1]=>16
[4,1,3,6,5,2]=>[3,2,1]=>16
[4,1,5,2,3,6]=>[4,2]=>9
[4,1,5,2,6,3]=>[3,3]=>5
[4,1,5,3,2,6]=>[3,2,1]=>16
[4,1,5,3,6,2]=>[3,2,1]=>16
[4,1,5,6,2,3]=>[3,3]=>5
[4,1,5,6,3,2]=>[3,2,1]=>16
[4,1,6,2,3,5]=>[4,2]=>9
[4,1,6,2,5,3]=>[3,2,1]=>16
[4,1,6,3,2,5]=>[3,2,1]=>16
[4,1,6,3,5,2]=>[3,2,1]=>16
[4,1,6,5,2,3]=>[3,2,1]=>16
[4,1,6,5,3,2]=>[2,2,1,1]=>9
[4,2,1,3,5,6]=>[4,1,1]=>10
[4,2,1,3,6,5]=>[3,2,1]=>16
[4,2,1,5,3,6]=>[3,2,1]=>16
[4,2,1,5,6,3]=>[3,2,1]=>16
[4,2,1,6,3,5]=>[3,2,1]=>16
[4,2,1,6,5,3]=>[2,2,2]=>5
[4,2,3,1,5,6]=>[4,1,1]=>10
[4,2,3,1,6,5]=>[3,2,1]=>16
[4,2,3,5,1,6]=>[4,1,1]=>10
[4,2,3,5,6,1]=>[4,1,1]=>10
[4,2,3,6,1,5]=>[3,2,1]=>16
[4,2,3,6,5,1]=>[3,2,1]=>16
[4,2,5,1,3,6]=>[3,2,1]=>16
[4,2,5,1,6,3]=>[3,2,1]=>16
[4,2,5,3,1,6]=>[3,2,1]=>16
[4,2,5,3,6,1]=>[3,2,1]=>16
[4,2,5,6,1,3]=>[3,2,1]=>16
[4,2,5,6,3,1]=>[3,2,1]=>16
[4,2,6,1,3,5]=>[3,2,1]=>16
[4,2,6,1,5,3]=>[2,2,2]=>5
[4,2,6,3,1,5]=>[3,2,1]=>16
[4,2,6,3,5,1]=>[3,2,1]=>16
[4,2,6,5,1,3]=>[2,2,2]=>5
[4,2,6,5,3,1]=>[2,2,1,1]=>9
[4,3,1,2,5,6]=>[4,1,1]=>10
[4,3,1,2,6,5]=>[3,2,1]=>16
[4,3,1,5,2,6]=>[3,2,1]=>16
[4,3,1,5,6,2]=>[3,2,1]=>16
[4,3,1,6,2,5]=>[3,2,1]=>16
[4,3,1,6,5,2]=>[2,2,2]=>5
[4,3,2,1,5,6]=>[3,1,1,1]=>10
[4,3,2,1,6,5]=>[2,2,1,1]=>9
[4,3,2,5,1,6]=>[3,1,1,1]=>10
[4,3,2,5,6,1]=>[3,1,1,1]=>10
[4,3,2,6,1,5]=>[2,2,1,1]=>9
[4,3,2,6,5,1]=>[2,2,1,1]=>9
[4,3,5,1,2,6]=>[3,2,1]=>16
[4,3,5,1,6,2]=>[3,2,1]=>16
[4,3,5,2,1,6]=>[3,1,1,1]=>10
[4,3,5,2,6,1]=>[3,1,1,1]=>10
[4,3,5,6,1,2]=>[3,2,1]=>16
[4,3,5,6,2,1]=>[3,1,1,1]=>10
[4,3,6,1,2,5]=>[3,2,1]=>16
[4,3,6,1,5,2]=>[2,2,2]=>5
[4,3,6,2,1,5]=>[2,2,1,1]=>9
[4,3,6,2,5,1]=>[2,2,1,1]=>9
[4,3,6,5,1,2]=>[2,2,2]=>5
[4,3,6,5,2,1]=>[2,2,1,1]=>9
[4,5,1,2,3,6]=>[4,2]=>9
[4,5,1,2,6,3]=>[3,3]=>5
[4,5,1,3,2,6]=>[3,2,1]=>16
[4,5,1,3,6,2]=>[3,2,1]=>16
[4,5,1,6,2,3]=>[3,3]=>5
[4,5,1,6,3,2]=>[3,2,1]=>16
[4,5,2,1,3,6]=>[3,2,1]=>16
[4,5,2,1,6,3]=>[3,2,1]=>16
[4,5,2,3,1,6]=>[3,2,1]=>16
[4,5,2,3,6,1]=>[3,2,1]=>16
[4,5,2,6,1,3]=>[3,2,1]=>16
[4,5,2,6,3,1]=>[3,2,1]=>16
[4,5,3,1,2,6]=>[3,2,1]=>16
[4,5,3,1,6,2]=>[3,2,1]=>16
[4,5,3,2,1,6]=>[3,1,1,1]=>10
[4,5,3,2,6,1]=>[3,1,1,1]=>10
[4,5,3,6,1,2]=>[3,2,1]=>16
[4,5,3,6,2,1]=>[3,1,1,1]=>10
[4,5,6,1,2,3]=>[3,3]=>5
[4,5,6,1,3,2]=>[3,2,1]=>16
[4,5,6,2,1,3]=>[3,2,1]=>16
[4,5,6,2,3,1]=>[3,2,1]=>16
[4,5,6,3,1,2]=>[3,2,1]=>16
[4,5,6,3,2,1]=>[3,1,1,1]=>10
[4,6,1,2,3,5]=>[4,2]=>9
[4,6,1,2,5,3]=>[3,2,1]=>16
[4,6,1,3,2,5]=>[3,2,1]=>16
[4,6,1,3,5,2]=>[3,2,1]=>16
[4,6,1,5,2,3]=>[3,2,1]=>16
[4,6,1,5,3,2]=>[2,2,1,1]=>9
[4,6,2,1,3,5]=>[3,2,1]=>16
[4,6,2,1,5,3]=>[2,2,2]=>5
[4,6,2,3,1,5]=>[3,2,1]=>16
[4,6,2,3,5,1]=>[3,2,1]=>16
[4,6,2,5,1,3]=>[2,2,2]=>5
[4,6,2,5,3,1]=>[2,2,1,1]=>9
[4,6,3,1,2,5]=>[3,2,1]=>16
[4,6,3,1,5,2]=>[2,2,2]=>5
[4,6,3,2,1,5]=>[2,2,1,1]=>9
[4,6,3,2,5,1]=>[2,2,1,1]=>9
[4,6,3,5,1,2]=>[2,2,2]=>5
[4,6,3,5,2,1]=>[2,2,1,1]=>9
[4,6,5,1,2,3]=>[3,2,1]=>16
[4,6,5,1,3,2]=>[2,2,1,1]=>9
[4,6,5,2,1,3]=>[2,2,1,1]=>9
[4,6,5,2,3,1]=>[2,2,1,1]=>9
[4,6,5,3,1,2]=>[2,2,1,1]=>9
[4,6,5,3,2,1]=>[2,1,1,1,1]=>5
[5,1,2,3,4,6]=>[5,1]=>5
[5,1,2,3,6,4]=>[4,2]=>9
[5,1,2,4,3,6]=>[4,1,1]=>10
[5,1,2,4,6,3]=>[4,1,1]=>10
[5,1,2,6,3,4]=>[4,2]=>9
[5,1,2,6,4,3]=>[3,2,1]=>16
[5,1,3,2,4,6]=>[4,1,1]=>10
[5,1,3,2,6,4]=>[3,2,1]=>16
[5,1,3,4,2,6]=>[4,1,1]=>10
[5,1,3,4,6,2]=>[4,1,1]=>10
[5,1,3,6,2,4]=>[3,2,1]=>16
[5,1,3,6,4,2]=>[3,2,1]=>16
[5,1,4,2,3,6]=>[4,1,1]=>10
[5,1,4,2,6,3]=>[3,2,1]=>16
[5,1,4,3,2,6]=>[3,1,1,1]=>10
[5,1,4,3,6,2]=>[3,1,1,1]=>10
[5,1,4,6,2,3]=>[3,2,1]=>16
[5,1,4,6,3,2]=>[3,1,1,1]=>10
[5,1,6,2,3,4]=>[4,2]=>9
[5,1,6,2,4,3]=>[3,2,1]=>16
[5,1,6,3,2,4]=>[3,2,1]=>16
[5,1,6,3,4,2]=>[3,2,1]=>16
[5,1,6,4,2,3]=>[3,2,1]=>16
[5,1,6,4,3,2]=>[2,2,1,1]=>9
[5,2,1,3,4,6]=>[4,1,1]=>10
[5,2,1,3,6,4]=>[3,2,1]=>16
[5,2,1,4,3,6]=>[3,2,1]=>16
[5,2,1,4,6,3]=>[3,2,1]=>16
[5,2,1,6,3,4]=>[3,2,1]=>16
[5,2,1,6,4,3]=>[2,2,2]=>5
[5,2,3,1,4,6]=>[4,1,1]=>10
[5,2,3,1,6,4]=>[3,2,1]=>16
[5,2,3,4,1,6]=>[4,1,1]=>10
[5,2,3,4,6,1]=>[4,1,1]=>10
[5,2,3,6,1,4]=>[3,2,1]=>16
[5,2,3,6,4,1]=>[3,2,1]=>16
[5,2,4,1,3,6]=>[3,2,1]=>16
[5,2,4,1,6,3]=>[3,2,1]=>16
[5,2,4,3,1,6]=>[3,1,1,1]=>10
[5,2,4,3,6,1]=>[3,1,1,1]=>10
[5,2,4,6,1,3]=>[3,2,1]=>16
[5,2,4,6,3,1]=>[3,1,1,1]=>10
[5,2,6,1,3,4]=>[3,2,1]=>16
[5,2,6,1,4,3]=>[2,2,2]=>5
[5,2,6,3,1,4]=>[3,2,1]=>16
[5,2,6,3,4,1]=>[3,2,1]=>16
[5,2,6,4,1,3]=>[2,2,2]=>5
[5,2,6,4,3,1]=>[2,2,1,1]=>9
[5,3,1,2,4,6]=>[4,1,1]=>10
[5,3,1,2,6,4]=>[3,2,1]=>16
[5,3,1,4,2,6]=>[3,2,1]=>16
[5,3,1,4,6,2]=>[3,2,1]=>16
[5,3,1,6,2,4]=>[3,2,1]=>16
[5,3,1,6,4,2]=>[2,2,2]=>5
[5,3,2,1,4,6]=>[3,1,1,1]=>10
[5,3,2,1,6,4]=>[2,2,1,1]=>9
[5,3,2,4,1,6]=>[3,1,1,1]=>10
[5,3,2,4,6,1]=>[3,1,1,1]=>10
[5,3,2,6,1,4]=>[2,2,1,1]=>9
[5,3,2,6,4,1]=>[2,2,1,1]=>9
[5,3,4,1,2,6]=>[3,2,1]=>16
[5,3,4,1,6,2]=>[3,2,1]=>16
[5,3,4,2,1,6]=>[3,1,1,1]=>10
[5,3,4,2,6,1]=>[3,1,1,1]=>10
[5,3,4,6,1,2]=>[3,2,1]=>16
[5,3,4,6,2,1]=>[3,1,1,1]=>10
[5,3,6,1,2,4]=>[3,2,1]=>16
[5,3,6,1,4,2]=>[2,2,2]=>5
[5,3,6,2,1,4]=>[2,2,1,1]=>9
[5,3,6,2,4,1]=>[2,2,1,1]=>9
[5,3,6,4,1,2]=>[2,2,2]=>5
[5,3,6,4,2,1]=>[2,2,1,1]=>9
[5,4,1,2,3,6]=>[4,1,1]=>10
[5,4,1,2,6,3]=>[3,2,1]=>16
[5,4,1,3,2,6]=>[3,1,1,1]=>10
[5,4,1,3,6,2]=>[3,1,1,1]=>10
[5,4,1,6,2,3]=>[3,2,1]=>16
[5,4,1,6,3,2]=>[2,2,1,1]=>9
[5,4,2,1,3,6]=>[3,1,1,1]=>10
[5,4,2,1,6,3]=>[2,2,1,1]=>9
[5,4,2,3,1,6]=>[3,1,1,1]=>10
[5,4,2,3,6,1]=>[3,1,1,1]=>10
[5,4,2,6,1,3]=>[2,2,1,1]=>9
[5,4,2,6,3,1]=>[2,2,1,1]=>9
[5,4,3,1,2,6]=>[3,1,1,1]=>10
[5,4,3,1,6,2]=>[2,2,1,1]=>9
[5,4,3,2,1,6]=>[2,1,1,1,1]=>5
[5,4,3,2,6,1]=>[2,1,1,1,1]=>5
[5,4,3,6,1,2]=>[2,2,1,1]=>9
[5,4,3,6,2,1]=>[2,1,1,1,1]=>5
[5,4,6,1,2,3]=>[3,2,1]=>16
[5,4,6,1,3,2]=>[2,2,1,1]=>9
[5,4,6,2,1,3]=>[2,2,1,1]=>9
[5,4,6,2,3,1]=>[2,2,1,1]=>9
[5,4,6,3,1,2]=>[2,2,1,1]=>9
[5,4,6,3,2,1]=>[2,1,1,1,1]=>5
[5,6,1,2,3,4]=>[4,2]=>9
[5,6,1,2,4,3]=>[3,2,1]=>16
[5,6,1,3,2,4]=>[3,2,1]=>16
[5,6,1,3,4,2]=>[3,2,1]=>16
[5,6,1,4,2,3]=>[3,2,1]=>16
[5,6,1,4,3,2]=>[2,2,1,1]=>9
[5,6,2,1,3,4]=>[3,2,1]=>16
[5,6,2,1,4,3]=>[2,2,2]=>5
[5,6,2,3,1,4]=>[3,2,1]=>16
[5,6,2,3,4,1]=>[3,2,1]=>16
[5,6,2,4,1,3]=>[2,2,2]=>5
[5,6,2,4,3,1]=>[2,2,1,1]=>9
[5,6,3,1,2,4]=>[3,2,1]=>16
[5,6,3,1,4,2]=>[2,2,2]=>5
[5,6,3,2,1,4]=>[2,2,1,1]=>9
[5,6,3,2,4,1]=>[2,2,1,1]=>9
[5,6,3,4,1,2]=>[2,2,2]=>5
[5,6,3,4,2,1]=>[2,2,1,1]=>9
[5,6,4,1,2,3]=>[3,2,1]=>16
[5,6,4,1,3,2]=>[2,2,1,1]=>9
[5,6,4,2,1,3]=>[2,2,1,1]=>9
[5,6,4,2,3,1]=>[2,2,1,1]=>9
[5,6,4,3,1,2]=>[2,2,1,1]=>9
[5,6,4,3,2,1]=>[2,1,1,1,1]=>5
[6,1,2,3,4,5]=>[5,1]=>5
[6,1,2,3,5,4]=>[4,1,1]=>10
[6,1,2,4,3,5]=>[4,1,1]=>10
[6,1,2,4,5,3]=>[4,1,1]=>10
[6,1,2,5,3,4]=>[4,1,1]=>10
[6,1,2,5,4,3]=>[3,1,1,1]=>10
[6,1,3,2,4,5]=>[4,1,1]=>10
[6,1,3,2,5,4]=>[3,2,1]=>16
[6,1,3,4,2,5]=>[4,1,1]=>10
[6,1,3,4,5,2]=>[4,1,1]=>10
[6,1,3,5,2,4]=>[3,2,1]=>16
[6,1,3,5,4,2]=>[3,1,1,1]=>10
[6,1,4,2,3,5]=>[4,1,1]=>10
[6,1,4,2,5,3]=>[3,2,1]=>16
[6,1,4,3,2,5]=>[3,1,1,1]=>10
[6,1,4,3,5,2]=>[3,1,1,1]=>10
[6,1,4,5,2,3]=>[3,2,1]=>16
[6,1,4,5,3,2]=>[3,1,1,1]=>10
[6,1,5,2,3,4]=>[4,1,1]=>10
[6,1,5,2,4,3]=>[3,1,1,1]=>10
[6,1,5,3,2,4]=>[3,1,1,1]=>10
[6,1,5,3,4,2]=>[3,1,1,1]=>10
[6,1,5,4,2,3]=>[3,1,1,1]=>10
[6,1,5,4,3,2]=>[2,1,1,1,1]=>5
[6,2,1,3,4,5]=>[4,1,1]=>10
[6,2,1,3,5,4]=>[3,2,1]=>16
[6,2,1,4,3,5]=>[3,2,1]=>16
[6,2,1,4,5,3]=>[3,2,1]=>16
[6,2,1,5,3,4]=>[3,2,1]=>16
[6,2,1,5,4,3]=>[2,2,1,1]=>9
[6,2,3,1,4,5]=>[4,1,1]=>10
[6,2,3,1,5,4]=>[3,2,1]=>16
[6,2,3,4,1,5]=>[4,1,1]=>10
[6,2,3,4,5,1]=>[4,1,1]=>10
[6,2,3,5,1,4]=>[3,2,1]=>16
[6,2,3,5,4,1]=>[3,1,1,1]=>10
[6,2,4,1,3,5]=>[3,2,1]=>16
[6,2,4,1,5,3]=>[3,2,1]=>16
[6,2,4,3,1,5]=>[3,1,1,1]=>10
[6,2,4,3,5,1]=>[3,1,1,1]=>10
[6,2,4,5,1,3]=>[3,2,1]=>16
[6,2,4,5,3,1]=>[3,1,1,1]=>10
[6,2,5,1,3,4]=>[3,2,1]=>16
[6,2,5,1,4,3]=>[2,2,1,1]=>9
[6,2,5,3,1,4]=>[3,1,1,1]=>10
[6,2,5,3,4,1]=>[3,1,1,1]=>10
[6,2,5,4,1,3]=>[2,2,1,1]=>9
[6,2,5,4,3,1]=>[2,1,1,1,1]=>5
[6,3,1,2,4,5]=>[4,1,1]=>10
[6,3,1,2,5,4]=>[3,2,1]=>16
[6,3,1,4,2,5]=>[3,2,1]=>16
[6,3,1,4,5,2]=>[3,2,1]=>16
[6,3,1,5,2,4]=>[3,2,1]=>16
[6,3,1,5,4,2]=>[2,2,1,1]=>9
[6,3,2,1,4,5]=>[3,1,1,1]=>10
[6,3,2,1,5,4]=>[2,2,1,1]=>9
[6,3,2,4,1,5]=>[3,1,1,1]=>10
[6,3,2,4,5,1]=>[3,1,1,1]=>10
[6,3,2,5,1,4]=>[2,2,1,1]=>9
[6,3,2,5,4,1]=>[2,2,1,1]=>9
[6,3,4,1,2,5]=>[3,2,1]=>16
[6,3,4,1,5,2]=>[3,2,1]=>16
[6,3,4,2,1,5]=>[3,1,1,1]=>10
[6,3,4,2,5,1]=>[3,1,1,1]=>10
[6,3,4,5,1,2]=>[3,2,1]=>16
[6,3,4,5,2,1]=>[3,1,1,1]=>10
[6,3,5,1,2,4]=>[3,2,1]=>16
[6,3,5,1,4,2]=>[2,2,1,1]=>9
[6,3,5,2,1,4]=>[2,2,1,1]=>9
[6,3,5,2,4,1]=>[2,2,1,1]=>9
[6,3,5,4,1,2]=>[2,2,1,1]=>9
[6,3,5,4,2,1]=>[2,1,1,1,1]=>5
[6,4,1,2,3,5]=>[4,1,1]=>10
[6,4,1,2,5,3]=>[3,2,1]=>16
[6,4,1,3,2,5]=>[3,1,1,1]=>10
[6,4,1,3,5,2]=>[3,1,1,1]=>10
[6,4,1,5,2,3]=>[3,2,1]=>16
[6,4,1,5,3,2]=>[2,2,1,1]=>9
[6,4,2,1,3,5]=>[3,1,1,1]=>10
[6,4,2,1,5,3]=>[2,2,1,1]=>9
[6,4,2,3,1,5]=>[3,1,1,1]=>10
[6,4,2,3,5,1]=>[3,1,1,1]=>10
[6,4,2,5,1,3]=>[2,2,1,1]=>9
[6,4,2,5,3,1]=>[2,2,1,1]=>9
[6,4,3,1,2,5]=>[3,1,1,1]=>10
[6,4,3,1,5,2]=>[2,2,1,1]=>9
[6,4,3,2,1,5]=>[2,1,1,1,1]=>5
[6,4,3,2,5,1]=>[2,1,1,1,1]=>5
[6,4,3,5,1,2]=>[2,2,1,1]=>9
[6,4,3,5,2,1]=>[2,1,1,1,1]=>5
[6,4,5,1,2,3]=>[3,2,1]=>16
[6,4,5,1,3,2]=>[2,2,1,1]=>9
[6,4,5,2,1,3]=>[2,2,1,1]=>9
[6,4,5,2,3,1]=>[2,2,1,1]=>9
[6,4,5,3,1,2]=>[2,2,1,1]=>9
[6,4,5,3,2,1]=>[2,1,1,1,1]=>5
[6,5,1,2,3,4]=>[4,1,1]=>10
[6,5,1,2,4,3]=>[3,1,1,1]=>10
[6,5,1,3,2,4]=>[3,1,1,1]=>10
[6,5,1,3,4,2]=>[3,1,1,1]=>10
[6,5,1,4,2,3]=>[3,1,1,1]=>10
[6,5,1,4,3,2]=>[2,1,1,1,1]=>5
[6,5,2,1,3,4]=>[3,1,1,1]=>10
[6,5,2,1,4,3]=>[2,2,1,1]=>9
[6,5,2,3,1,4]=>[3,1,1,1]=>10
[6,5,2,3,4,1]=>[3,1,1,1]=>10
[6,5,2,4,1,3]=>[2,2,1,1]=>9
[6,5,2,4,3,1]=>[2,1,1,1,1]=>5
[6,5,3,1,2,4]=>[3,1,1,1]=>10
[6,5,3,1,4,2]=>[2,2,1,1]=>9
[6,5,3,2,1,4]=>[2,1,1,1,1]=>5
[6,5,3,2,4,1]=>[2,1,1,1,1]=>5
[6,5,3,4,1,2]=>[2,2,1,1]=>9
[6,5,3,4,2,1]=>[2,1,1,1,1]=>5
[6,5,4,1,2,3]=>[3,1,1,1]=>10
[6,5,4,1,3,2]=>[2,1,1,1,1]=>5
[6,5,4,2,1,3]=>[2,1,1,1,1]=>5
[6,5,4,2,3,1]=>[2,1,1,1,1]=>5
[6,5,4,3,1,2]=>[2,1,1,1,1]=>5
[6,5,4,3,2,1]=>[1,1,1,1,1,1]=>1
[1,2,3,4,5,6,7]=>[7]=>1
[1,2,3,4,5,7,6]=>[6,1]=>6
[1,2,3,4,6,5,7]=>[6,1]=>6
[1,2,3,4,6,7,5]=>[6,1]=>6
[1,2,3,4,7,5,6]=>[6,1]=>6
[1,2,3,4,7,6,5]=>[5,1,1]=>15
[1,2,3,5,4,6,7]=>[6,1]=>6
[1,2,3,5,4,7,6]=>[5,2]=>14
[1,2,3,5,6,4,7]=>[6,1]=>6
[1,2,3,5,6,7,4]=>[6,1]=>6
[1,2,3,5,7,4,6]=>[5,2]=>14
[1,2,3,5,7,6,4]=>[5,1,1]=>15
[1,2,3,6,4,5,7]=>[6,1]=>6
[1,2,3,6,4,7,5]=>[5,2]=>14
[1,2,3,6,5,4,7]=>[5,1,1]=>15
[1,2,3,6,5,7,4]=>[5,1,1]=>15
[1,2,3,6,7,4,5]=>[5,2]=>14
[1,2,3,6,7,5,4]=>[5,1,1]=>15
[1,2,3,7,4,5,6]=>[6,1]=>6
[1,2,3,7,4,6,5]=>[5,1,1]=>15
[1,2,3,7,5,4,6]=>[5,1,1]=>15
[1,2,3,7,5,6,4]=>[5,1,1]=>15
[1,2,3,7,6,4,5]=>[5,1,1]=>15
[1,2,3,7,6,5,4]=>[4,1,1,1]=>20
[1,2,4,3,5,6,7]=>[6,1]=>6
[1,2,4,3,5,7,6]=>[5,2]=>14
[1,2,4,3,6,5,7]=>[5,2]=>14
[1,2,4,3,6,7,5]=>[5,2]=>14
[1,2,4,3,7,5,6]=>[5,2]=>14
[1,2,4,3,7,6,5]=>[4,2,1]=>35
[1,2,4,5,3,6,7]=>[6,1]=>6
[1,2,4,5,3,7,6]=>[5,2]=>14
[1,2,4,5,6,3,7]=>[6,1]=>6
[1,2,4,5,6,7,3]=>[6,1]=>6
[1,2,4,5,7,3,6]=>[5,2]=>14
[1,2,4,5,7,6,3]=>[5,1,1]=>15
[1,2,4,6,3,5,7]=>[5,2]=>14
[1,2,4,6,3,7,5]=>[5,2]=>14
[1,2,4,6,5,3,7]=>[5,1,1]=>15
[1,2,4,6,5,7,3]=>[5,1,1]=>15
[1,2,4,6,7,3,5]=>[5,2]=>14
[1,2,4,6,7,5,3]=>[5,1,1]=>15
[1,2,4,7,3,5,6]=>[5,2]=>14
[1,2,4,7,3,6,5]=>[4,2,1]=>35
[1,2,4,7,5,3,6]=>[5,1,1]=>15
[1,2,4,7,5,6,3]=>[5,1,1]=>15
[1,2,4,7,6,3,5]=>[4,2,1]=>35
[1,2,4,7,6,5,3]=>[4,1,1,1]=>20
[1,2,5,3,4,6,7]=>[6,1]=>6
[1,2,5,3,4,7,6]=>[5,2]=>14
[1,2,5,3,6,4,7]=>[5,2]=>14
[1,2,5,3,6,7,4]=>[5,2]=>14
[1,2,5,3,7,4,6]=>[5,2]=>14
[1,2,5,3,7,6,4]=>[4,2,1]=>35
[1,2,5,4,3,6,7]=>[5,1,1]=>15
[1,2,5,4,3,7,6]=>[4,2,1]=>35
[1,2,5,4,6,3,7]=>[5,1,1]=>15
[1,2,5,4,6,7,3]=>[5,1,1]=>15
[1,2,5,4,7,3,6]=>[4,2,1]=>35
[1,2,5,4,7,6,3]=>[4,2,1]=>35
[1,2,5,6,3,4,7]=>[5,2]=>14
[1,2,5,6,3,7,4]=>[5,2]=>14
[1,2,5,6,4,3,7]=>[5,1,1]=>15
[1,2,5,6,4,7,3]=>[5,1,1]=>15
[1,2,5,6,7,3,4]=>[5,2]=>14
[1,2,5,6,7,4,3]=>[5,1,1]=>15
[1,2,5,7,3,4,6]=>[5,2]=>14
[1,2,5,7,3,6,4]=>[4,2,1]=>35
[1,2,5,7,4,3,6]=>[4,2,1]=>35
[1,2,5,7,4,6,3]=>[4,2,1]=>35
[1,2,5,7,6,3,4]=>[4,2,1]=>35
[1,2,5,7,6,4,3]=>[4,1,1,1]=>20
[1,2,6,3,4,5,7]=>[6,1]=>6
[1,2,6,3,4,7,5]=>[5,2]=>14
[1,2,6,3,5,4,7]=>[5,1,1]=>15
[1,2,6,3,5,7,4]=>[5,1,1]=>15
[1,2,6,3,7,4,5]=>[5,2]=>14
[1,2,6,3,7,5,4]=>[4,2,1]=>35
[1,2,6,4,3,5,7]=>[5,1,1]=>15
[1,2,6,4,3,7,5]=>[4,2,1]=>35
[1,2,6,4,5,3,7]=>[5,1,1]=>15
[1,2,6,4,5,7,3]=>[5,1,1]=>15
[1,2,6,4,7,3,5]=>[4,2,1]=>35
[1,2,6,4,7,5,3]=>[4,2,1]=>35
[1,2,6,5,3,4,7]=>[5,1,1]=>15
[1,2,6,5,3,7,4]=>[4,2,1]=>35
[1,2,6,5,4,3,7]=>[4,1,1,1]=>20
[1,2,6,5,4,7,3]=>[4,1,1,1]=>20
[1,2,6,5,7,3,4]=>[4,2,1]=>35
[1,2,6,5,7,4,3]=>[4,1,1,1]=>20
[1,2,6,7,3,4,5]=>[5,2]=>14
[1,2,6,7,3,5,4]=>[4,2,1]=>35
[1,2,6,7,4,3,5]=>[4,2,1]=>35
[1,2,6,7,4,5,3]=>[4,2,1]=>35
[1,2,6,7,5,3,4]=>[4,2,1]=>35
[1,2,6,7,5,4,3]=>[4,1,1,1]=>20
[1,2,7,3,4,5,6]=>[6,1]=>6
[1,2,7,3,4,6,5]=>[5,1,1]=>15
[1,2,7,3,5,4,6]=>[5,1,1]=>15
[1,2,7,3,5,6,4]=>[5,1,1]=>15
[1,2,7,3,6,4,5]=>[5,1,1]=>15
[1,2,7,3,6,5,4]=>[4,1,1,1]=>20
[1,2,7,4,3,5,6]=>[5,1,1]=>15
[1,2,7,4,3,6,5]=>[4,2,1]=>35
[1,2,7,4,5,3,6]=>[5,1,1]=>15
[1,2,7,4,5,6,3]=>[5,1,1]=>15
[1,2,7,4,6,3,5]=>[4,2,1]=>35
[1,2,7,4,6,5,3]=>[4,1,1,1]=>20
[1,2,7,5,3,4,6]=>[5,1,1]=>15
[1,2,7,5,3,6,4]=>[4,2,1]=>35
[1,2,7,5,4,3,6]=>[4,1,1,1]=>20
[1,2,7,5,4,6,3]=>[4,1,1,1]=>20
[1,2,7,5,6,3,4]=>[4,2,1]=>35
[1,2,7,5,6,4,3]=>[4,1,1,1]=>20
[1,2,7,6,3,4,5]=>[5,1,1]=>15
[1,2,7,6,3,5,4]=>[4,1,1,1]=>20
[1,2,7,6,4,3,5]=>[4,1,1,1]=>20
[1,2,7,6,4,5,3]=>[4,1,1,1]=>20
[1,2,7,6,5,3,4]=>[4,1,1,1]=>20
[1,2,7,6,5,4,3]=>[3,1,1,1,1]=>15
[1,3,2,4,5,6,7]=>[6,1]=>6
[1,3,2,4,5,7,6]=>[5,2]=>14
[1,3,2,4,6,5,7]=>[5,2]=>14
[1,3,2,4,6,7,5]=>[5,2]=>14
[1,3,2,4,7,5,6]=>[5,2]=>14
[1,3,2,4,7,6,5]=>[4,2,1]=>35
[1,3,2,5,4,6,7]=>[5,2]=>14
[1,3,2,5,4,7,6]=>[4,3]=>14
[1,3,2,5,6,4,7]=>[5,2]=>14
[1,3,2,5,6,7,4]=>[5,2]=>14
[1,3,2,5,7,4,6]=>[4,3]=>14
[1,3,2,5,7,6,4]=>[4,2,1]=>35
[1,3,2,6,4,5,7]=>[5,2]=>14
[1,3,2,6,4,7,5]=>[4,3]=>14
[1,3,2,6,5,4,7]=>[4,2,1]=>35
[1,3,2,6,5,7,4]=>[4,2,1]=>35
[1,3,2,6,7,4,5]=>[4,3]=>14
[1,3,2,6,7,5,4]=>[4,2,1]=>35
[1,3,2,7,4,5,6]=>[5,2]=>14
[1,3,2,7,4,6,5]=>[4,2,1]=>35
[1,3,2,7,5,4,6]=>[4,2,1]=>35
[1,3,2,7,5,6,4]=>[4,2,1]=>35
[1,3,2,7,6,4,5]=>[4,2,1]=>35
[1,3,2,7,6,5,4]=>[3,2,1,1]=>35
[1,3,4,2,5,6,7]=>[6,1]=>6
[1,3,4,2,5,7,6]=>[5,2]=>14
[1,3,4,2,6,5,7]=>[5,2]=>14
[1,3,4,2,6,7,5]=>[5,2]=>14
[1,3,4,2,7,5,6]=>[5,2]=>14
[1,3,4,2,7,6,5]=>[4,2,1]=>35
[1,3,4,5,2,6,7]=>[6,1]=>6
[1,3,4,5,2,7,6]=>[5,2]=>14
[1,3,4,5,6,2,7]=>[6,1]=>6
[1,3,4,5,6,7,2]=>[6,1]=>6
[1,3,4,5,7,2,6]=>[5,2]=>14
[1,3,4,5,7,6,2]=>[5,1,1]=>15
[1,3,4,6,2,5,7]=>[5,2]=>14
[1,3,4,6,2,7,5]=>[5,2]=>14
[1,3,4,6,5,2,7]=>[5,1,1]=>15
[1,3,4,6,5,7,2]=>[5,1,1]=>15
[1,3,4,6,7,2,5]=>[5,2]=>14
[1,3,4,6,7,5,2]=>[5,1,1]=>15
[1,3,4,7,2,5,6]=>[5,2]=>14
[1,3,4,7,2,6,5]=>[4,2,1]=>35
[1,3,4,7,5,2,6]=>[5,1,1]=>15
[1,3,4,7,5,6,2]=>[5,1,1]=>15
[1,3,4,7,6,2,5]=>[4,2,1]=>35
[1,3,4,7,6,5,2]=>[4,1,1,1]=>20
[1,3,5,2,4,6,7]=>[5,2]=>14
[1,3,5,2,4,7,6]=>[4,3]=>14
[1,3,5,2,6,4,7]=>[5,2]=>14
[1,3,5,2,6,7,4]=>[5,2]=>14
[1,3,5,2,7,4,6]=>[4,3]=>14
[1,3,5,2,7,6,4]=>[4,2,1]=>35
[1,3,5,4,2,6,7]=>[5,1,1]=>15
[1,3,5,4,2,7,6]=>[4,2,1]=>35
[1,3,5,4,6,2,7]=>[5,1,1]=>15
[1,3,5,4,6,7,2]=>[5,1,1]=>15
[1,3,5,4,7,2,6]=>[4,2,1]=>35
[1,3,5,4,7,6,2]=>[4,2,1]=>35
[1,3,5,6,2,4,7]=>[5,2]=>14
[1,3,5,6,2,7,4]=>[5,2]=>14
[1,3,5,6,4,2,7]=>[5,1,1]=>15
[1,3,5,6,4,7,2]=>[5,1,1]=>15
[1,3,5,6,7,2,4]=>[5,2]=>14
[1,3,5,6,7,4,2]=>[5,1,1]=>15
[1,3,5,7,2,4,6]=>[4,3]=>14
[1,3,5,7,2,6,4]=>[4,2,1]=>35
[1,3,5,7,4,2,6]=>[4,2,1]=>35
[1,3,5,7,4,6,2]=>[4,2,1]=>35
[1,3,5,7,6,2,4]=>[4,2,1]=>35
[1,3,5,7,6,4,2]=>[4,1,1,1]=>20
[1,3,6,2,4,5,7]=>[5,2]=>14
[1,3,6,2,4,7,5]=>[4,3]=>14
[1,3,6,2,5,4,7]=>[4,2,1]=>35
[1,3,6,2,5,7,4]=>[4,2,1]=>35
[1,3,6,2,7,4,5]=>[4,3]=>14
[1,3,6,2,7,5,4]=>[4,2,1]=>35
[1,3,6,4,2,5,7]=>[5,1,1]=>15
[1,3,6,4,2,7,5]=>[4,2,1]=>35
[1,3,6,4,5,2,7]=>[5,1,1]=>15
[1,3,6,4,5,7,2]=>[5,1,1]=>15
[1,3,6,4,7,2,5]=>[4,2,1]=>35
[1,3,6,4,7,5,2]=>[4,2,1]=>35
[1,3,6,5,2,4,7]=>[4,2,1]=>35
[1,3,6,5,2,7,4]=>[4,2,1]=>35
[1,3,6,5,4,2,7]=>[4,1,1,1]=>20
[1,3,6,5,4,7,2]=>[4,1,1,1]=>20
[1,3,6,5,7,2,4]=>[4,2,1]=>35
[1,3,6,5,7,4,2]=>[4,1,1,1]=>20
[1,3,6,7,2,4,5]=>[4,3]=>14
[1,3,6,7,2,5,4]=>[4,2,1]=>35
[1,3,6,7,4,2,5]=>[4,2,1]=>35
[1,3,6,7,4,5,2]=>[4,2,1]=>35
[1,3,6,7,5,2,4]=>[4,2,1]=>35
[1,3,6,7,5,4,2]=>[4,1,1,1]=>20
[1,3,7,2,4,5,6]=>[5,2]=>14
[1,3,7,2,4,6,5]=>[4,2,1]=>35
[1,3,7,2,5,4,6]=>[4,2,1]=>35
[1,3,7,2,5,6,4]=>[4,2,1]=>35
[1,3,7,2,6,4,5]=>[4,2,1]=>35
[1,3,7,2,6,5,4]=>[3,2,1,1]=>35
[1,3,7,4,2,5,6]=>[5,1,1]=>15
[1,3,7,4,2,6,5]=>[4,2,1]=>35
[1,3,7,4,5,2,6]=>[5,1,1]=>15
[1,3,7,4,5,6,2]=>[5,1,1]=>15
[1,3,7,4,6,2,5]=>[4,2,1]=>35
[1,3,7,4,6,5,2]=>[4,1,1,1]=>20
[1,3,7,5,2,4,6]=>[4,2,1]=>35
[1,3,7,5,2,6,4]=>[4,2,1]=>35
[1,3,7,5,4,2,6]=>[4,1,1,1]=>20
[1,3,7,5,4,6,2]=>[4,1,1,1]=>20
[1,3,7,5,6,2,4]=>[4,2,1]=>35
[1,3,7,5,6,4,2]=>[4,1,1,1]=>20
[1,3,7,6,2,4,5]=>[4,2,1]=>35
[1,3,7,6,2,5,4]=>[3,2,1,1]=>35
[1,3,7,6,4,2,5]=>[4,1,1,1]=>20
[1,3,7,6,4,5,2]=>[4,1,1,1]=>20
[1,3,7,6,5,2,4]=>[3,2,1,1]=>35
[1,3,7,6,5,4,2]=>[3,1,1,1,1]=>15
[1,4,2,3,5,6,7]=>[6,1]=>6
[1,4,2,3,5,7,6]=>[5,2]=>14
[1,4,2,3,6,5,7]=>[5,2]=>14
[1,4,2,3,6,7,5]=>[5,2]=>14
[1,4,2,3,7,5,6]=>[5,2]=>14
[1,4,2,3,7,6,5]=>[4,2,1]=>35
[1,4,2,5,3,6,7]=>[5,2]=>14
[1,4,2,5,3,7,6]=>[4,3]=>14
[1,4,2,5,6,3,7]=>[5,2]=>14
[1,4,2,5,6,7,3]=>[5,2]=>14
[1,4,2,5,7,3,6]=>[4,3]=>14
[1,4,2,5,7,6,3]=>[4,2,1]=>35
[1,4,2,6,3,5,7]=>[5,2]=>14
[1,4,2,6,3,7,5]=>[4,3]=>14
[1,4,2,6,5,3,7]=>[4,2,1]=>35
[1,4,2,6,5,7,3]=>[4,2,1]=>35
[1,4,2,6,7,3,5]=>[4,3]=>14
[1,4,2,6,7,5,3]=>[4,2,1]=>35
[1,4,2,7,3,5,6]=>[5,2]=>14
[1,4,2,7,3,6,5]=>[4,2,1]=>35
[1,4,2,7,5,3,6]=>[4,2,1]=>35
[1,4,2,7,5,6,3]=>[4,2,1]=>35
[1,4,2,7,6,3,5]=>[4,2,1]=>35
[1,4,2,7,6,5,3]=>[3,2,1,1]=>35
[1,4,3,2,5,6,7]=>[5,1,1]=>15
[1,4,3,2,5,7,6]=>[4,2,1]=>35
[1,4,3,2,6,5,7]=>[4,2,1]=>35
[1,4,3,2,6,7,5]=>[4,2,1]=>35
[1,4,3,2,7,5,6]=>[4,2,1]=>35
[1,4,3,2,7,6,5]=>[3,2,2]=>21
[1,4,3,5,2,6,7]=>[5,1,1]=>15
[1,4,3,5,2,7,6]=>[4,2,1]=>35
[1,4,3,5,6,2,7]=>[5,1,1]=>15
[1,4,3,5,6,7,2]=>[5,1,1]=>15
[1,4,3,5,7,2,6]=>[4,2,1]=>35
[1,4,3,5,7,6,2]=>[4,2,1]=>35
[1,4,3,6,2,5,7]=>[4,2,1]=>35
[1,4,3,6,2,7,5]=>[4,2,1]=>35
[1,4,3,6,5,2,7]=>[4,2,1]=>35
[1,4,3,6,5,7,2]=>[4,2,1]=>35
[1,4,3,6,7,2,5]=>[4,2,1]=>35
[1,4,3,6,7,5,2]=>[4,2,1]=>35
[1,4,3,7,2,5,6]=>[4,2,1]=>35
[1,4,3,7,2,6,5]=>[3,2,2]=>21
[1,4,3,7,5,2,6]=>[4,2,1]=>35
[1,4,3,7,5,6,2]=>[4,2,1]=>35
[1,4,3,7,6,2,5]=>[3,2,2]=>21
[1,4,3,7,6,5,2]=>[3,2,1,1]=>35
[1,4,5,2,3,6,7]=>[5,2]=>14
[1,4,5,2,3,7,6]=>[4,3]=>14
[1,4,5,2,6,3,7]=>[5,2]=>14
[1,4,5,2,6,7,3]=>[5,2]=>14
[1,4,5,2,7,3,6]=>[4,3]=>14
[1,4,5,2,7,6,3]=>[4,2,1]=>35
[1,4,5,3,2,6,7]=>[5,1,1]=>15
[1,4,5,3,2,7,6]=>[4,2,1]=>35
[1,4,5,3,6,2,7]=>[5,1,1]=>15
[1,4,5,3,6,7,2]=>[5,1,1]=>15
[1,4,5,3,7,2,6]=>[4,2,1]=>35
[1,4,5,3,7,6,2]=>[4,2,1]=>35
[1,4,5,6,2,3,7]=>[5,2]=>14
[1,4,5,6,2,7,3]=>[5,2]=>14
[1,4,5,6,3,2,7]=>[5,1,1]=>15
[1,4,5,6,3,7,2]=>[5,1,1]=>15
[1,4,5,6,7,2,3]=>[5,2]=>14
[1,4,5,6,7,3,2]=>[5,1,1]=>15
[1,4,5,7,2,3,6]=>[4,3]=>14
[1,4,5,7,2,6,3]=>[4,2,1]=>35
[1,4,5,7,3,2,6]=>[4,2,1]=>35
[1,4,5,7,3,6,2]=>[4,2,1]=>35
[1,4,5,7,6,2,3]=>[4,2,1]=>35
[1,4,5,7,6,3,2]=>[4,1,1,1]=>20
[1,4,6,2,3,5,7]=>[5,2]=>14
[1,4,6,2,3,7,5]=>[4,3]=>14
[1,4,6,2,5,3,7]=>[4,2,1]=>35
[1,4,6,2,5,7,3]=>[4,2,1]=>35
[1,4,6,2,7,3,5]=>[4,3]=>14
[1,4,6,2,7,5,3]=>[4,2,1]=>35
[1,4,6,3,2,5,7]=>[4,2,1]=>35
[1,4,6,3,2,7,5]=>[4,2,1]=>35
[1,4,6,3,5,2,7]=>[4,2,1]=>35
[1,4,6,3,5,7,2]=>[4,2,1]=>35
[1,4,6,3,7,2,5]=>[4,2,1]=>35
[1,4,6,3,7,5,2]=>[4,2,1]=>35
[1,4,6,5,2,3,7]=>[4,2,1]=>35
[1,4,6,5,2,7,3]=>[4,2,1]=>35
[1,4,6,5,3,2,7]=>[4,1,1,1]=>20
[1,4,6,5,3,7,2]=>[4,1,1,1]=>20
[1,4,6,5,7,2,3]=>[4,2,1]=>35
[1,4,6,5,7,3,2]=>[4,1,1,1]=>20
[1,4,6,7,2,3,5]=>[4,3]=>14
[1,4,6,7,2,5,3]=>[4,2,1]=>35
[1,4,6,7,3,2,5]=>[4,2,1]=>35
[1,4,6,7,3,5,2]=>[4,2,1]=>35
[1,4,6,7,5,2,3]=>[4,2,1]=>35
[1,4,6,7,5,3,2]=>[4,1,1,1]=>20
[1,4,7,2,3,5,6]=>[5,2]=>14
[1,4,7,2,3,6,5]=>[4,2,1]=>35
[1,4,7,2,5,3,6]=>[4,2,1]=>35
[1,4,7,2,5,6,3]=>[4,2,1]=>35
[1,4,7,2,6,3,5]=>[4,2,1]=>35
[1,4,7,2,6,5,3]=>[3,2,1,1]=>35
[1,4,7,3,2,5,6]=>[4,2,1]=>35
[1,4,7,3,2,6,5]=>[3,2,2]=>21
[1,4,7,3,5,2,6]=>[4,2,1]=>35
[1,4,7,3,5,6,2]=>[4,2,1]=>35
[1,4,7,3,6,2,5]=>[3,2,2]=>21
[1,4,7,3,6,5,2]=>[3,2,1,1]=>35
[1,4,7,5,2,3,6]=>[4,2,1]=>35
[1,4,7,5,2,6,3]=>[4,2,1]=>35
[1,4,7,5,3,2,6]=>[4,1,1,1]=>20
[1,4,7,5,3,6,2]=>[4,1,1,1]=>20
[1,4,7,5,6,2,3]=>[4,2,1]=>35
[1,4,7,5,6,3,2]=>[4,1,1,1]=>20
[1,4,7,6,2,3,5]=>[4,2,1]=>35
[1,4,7,6,2,5,3]=>[3,2,1,1]=>35
[1,4,7,6,3,2,5]=>[3,2,1,1]=>35
[1,4,7,6,3,5,2]=>[3,2,1,1]=>35
[1,4,7,6,5,2,3]=>[3,2,1,1]=>35
[1,4,7,6,5,3,2]=>[3,1,1,1,1]=>15
[1,5,2,3,4,6,7]=>[6,1]=>6
[1,5,2,3,4,7,6]=>[5,2]=>14
[1,5,2,3,6,4,7]=>[5,2]=>14
[1,5,2,3,6,7,4]=>[5,2]=>14
[1,5,2,3,7,4,6]=>[5,2]=>14
[1,5,2,3,7,6,4]=>[4,2,1]=>35
[1,5,2,4,3,6,7]=>[5,1,1]=>15
[1,5,2,4,3,7,6]=>[4,2,1]=>35
[1,5,2,4,6,3,7]=>[5,1,1]=>15
[1,5,2,4,6,7,3]=>[5,1,1]=>15
[1,5,2,4,7,3,6]=>[4,2,1]=>35
[1,5,2,4,7,6,3]=>[4,2,1]=>35
[1,5,2,6,3,4,7]=>[5,2]=>14
[1,5,2,6,3,7,4]=>[4,3]=>14
[1,5,2,6,4,3,7]=>[4,2,1]=>35
[1,5,2,6,4,7,3]=>[4,2,1]=>35
[1,5,2,6,7,3,4]=>[4,3]=>14
[1,5,2,6,7,4,3]=>[4,2,1]=>35
[1,5,2,7,3,4,6]=>[5,2]=>14
[1,5,2,7,3,6,4]=>[4,2,1]=>35
[1,5,2,7,4,3,6]=>[4,2,1]=>35
[1,5,2,7,4,6,3]=>[4,2,1]=>35
[1,5,2,7,6,3,4]=>[4,2,1]=>35
[1,5,2,7,6,4,3]=>[3,2,1,1]=>35
[1,5,3,2,4,6,7]=>[5,1,1]=>15
[1,5,3,2,4,7,6]=>[4,2,1]=>35
[1,5,3,2,6,4,7]=>[4,2,1]=>35
[1,5,3,2,6,7,4]=>[4,2,1]=>35
[1,5,3,2,7,4,6]=>[4,2,1]=>35
[1,5,3,2,7,6,4]=>[3,2,2]=>21
[1,5,3,4,2,6,7]=>[5,1,1]=>15
[1,5,3,4,2,7,6]=>[4,2,1]=>35
[1,5,3,4,6,2,7]=>[5,1,1]=>15
[1,5,3,4,6,7,2]=>[5,1,1]=>15
[1,5,3,4,7,2,6]=>[4,2,1]=>35
[1,5,3,4,7,6,2]=>[4,2,1]=>35
[1,5,3,6,2,4,7]=>[4,2,1]=>35
[1,5,3,6,2,7,4]=>[4,2,1]=>35
[1,5,3,6,4,2,7]=>[4,2,1]=>35
[1,5,3,6,4,7,2]=>[4,2,1]=>35
[1,5,3,6,7,2,4]=>[4,2,1]=>35
[1,5,3,6,7,4,2]=>[4,2,1]=>35
[1,5,3,7,2,4,6]=>[4,2,1]=>35
[1,5,3,7,2,6,4]=>[3,2,2]=>21
[1,5,3,7,4,2,6]=>[4,2,1]=>35
[1,5,3,7,4,6,2]=>[4,2,1]=>35
[1,5,3,7,6,2,4]=>[3,2,2]=>21
[1,5,3,7,6,4,2]=>[3,2,1,1]=>35
[1,5,4,2,3,6,7]=>[5,1,1]=>15
[1,5,4,2,3,7,6]=>[4,2,1]=>35
[1,5,4,2,6,3,7]=>[4,2,1]=>35
[1,5,4,2,6,7,3]=>[4,2,1]=>35
[1,5,4,2,7,3,6]=>[4,2,1]=>35
[1,5,4,2,7,6,3]=>[3,2,2]=>21
[1,5,4,3,2,6,7]=>[4,1,1,1]=>20
[1,5,4,3,2,7,6]=>[3,2,1,1]=>35
[1,5,4,3,6,2,7]=>[4,1,1,1]=>20
[1,5,4,3,6,7,2]=>[4,1,1,1]=>20
[1,5,4,3,7,2,6]=>[3,2,1,1]=>35
[1,5,4,3,7,6,2]=>[3,2,1,1]=>35
[1,5,4,6,2,3,7]=>[4,2,1]=>35
[1,5,4,6,2,7,3]=>[4,2,1]=>35
[1,5,4,6,3,2,7]=>[4,1,1,1]=>20
[1,5,4,6,3,7,2]=>[4,1,1,1]=>20
[1,5,4,6,7,2,3]=>[4,2,1]=>35
[1,5,4,6,7,3,2]=>[4,1,1,1]=>20
[1,5,4,7,2,3,6]=>[4,2,1]=>35
[1,5,4,7,2,6,3]=>[3,2,2]=>21
[1,5,4,7,3,2,6]=>[3,2,1,1]=>35
[1,5,4,7,3,6,2]=>[3,2,1,1]=>35
[1,5,4,7,6,2,3]=>[3,2,2]=>21
[1,5,4,7,6,3,2]=>[3,2,1,1]=>35
[1,5,6,2,3,4,7]=>[5,2]=>14
[1,5,6,2,3,7,4]=>[4,3]=>14
[1,5,6,2,4,3,7]=>[4,2,1]=>35
[1,5,6,2,4,7,3]=>[4,2,1]=>35
[1,5,6,2,7,3,4]=>[4,3]=>14
[1,5,6,2,7,4,3]=>[4,2,1]=>35
[1,5,6,3,2,4,7]=>[4,2,1]=>35
[1,5,6,3,2,7,4]=>[4,2,1]=>35
[1,5,6,3,4,2,7]=>[4,2,1]=>35
[1,5,6,3,4,7,2]=>[4,2,1]=>35
[1,5,6,3,7,2,4]=>[4,2,1]=>35
[1,5,6,3,7,4,2]=>[4,2,1]=>35
[1,5,6,4,2,3,7]=>[4,2,1]=>35
[1,5,6,4,2,7,3]=>[4,2,1]=>35
[1,5,6,4,3,2,7]=>[4,1,1,1]=>20
[1,5,6,4,3,7,2]=>[4,1,1,1]=>20
[1,5,6,4,7,2,3]=>[4,2,1]=>35
[1,5,6,4,7,3,2]=>[4,1,1,1]=>20
[1,5,6,7,2,3,4]=>[4,3]=>14
[1,5,6,7,2,4,3]=>[4,2,1]=>35
[1,5,6,7,3,2,4]=>[4,2,1]=>35
[1,5,6,7,3,4,2]=>[4,2,1]=>35
[1,5,6,7,4,2,3]=>[4,2,1]=>35
[1,5,6,7,4,3,2]=>[4,1,1,1]=>20
[1,5,7,2,3,4,6]=>[5,2]=>14
[1,5,7,2,3,6,4]=>[4,2,1]=>35
[1,5,7,2,4,3,6]=>[4,2,1]=>35
[1,5,7,2,4,6,3]=>[4,2,1]=>35
[1,5,7,2,6,3,4]=>[4,2,1]=>35
[1,5,7,2,6,4,3]=>[3,2,1,1]=>35
[1,5,7,3,2,4,6]=>[4,2,1]=>35
[1,5,7,3,2,6,4]=>[3,2,2]=>21
[1,5,7,3,4,2,6]=>[4,2,1]=>35
[1,5,7,3,4,6,2]=>[4,2,1]=>35
[1,5,7,3,6,2,4]=>[3,2,2]=>21
[1,5,7,3,6,4,2]=>[3,2,1,1]=>35
[1,5,7,4,2,3,6]=>[4,2,1]=>35
[1,5,7,4,2,6,3]=>[3,2,2]=>21
[1,5,7,4,3,2,6]=>[3,2,1,1]=>35
[1,5,7,4,3,6,2]=>[3,2,1,1]=>35
[1,5,7,4,6,2,3]=>[3,2,2]=>21
[1,5,7,4,6,3,2]=>[3,2,1,1]=>35
[1,5,7,6,2,3,4]=>[4,2,1]=>35
[1,5,7,6,2,4,3]=>[3,2,1,1]=>35
[1,5,7,6,3,2,4]=>[3,2,1,1]=>35
[1,5,7,6,3,4,2]=>[3,2,1,1]=>35
[1,5,7,6,4,2,3]=>[3,2,1,1]=>35
[1,5,7,6,4,3,2]=>[3,1,1,1,1]=>15
[1,6,2,3,4,5,7]=>[6,1]=>6
[1,6,2,3,4,7,5]=>[5,2]=>14
[1,6,2,3,5,4,7]=>[5,1,1]=>15
[1,6,2,3,5,7,4]=>[5,1,1]=>15
[1,6,2,3,7,4,5]=>[5,2]=>14
[1,6,2,3,7,5,4]=>[4,2,1]=>35
[1,6,2,4,3,5,7]=>[5,1,1]=>15
[1,6,2,4,3,7,5]=>[4,2,1]=>35
[1,6,2,4,5,3,7]=>[5,1,1]=>15
[1,6,2,4,5,7,3]=>[5,1,1]=>15
[1,6,2,4,7,3,5]=>[4,2,1]=>35
[1,6,2,4,7,5,3]=>[4,2,1]=>35
[1,6,2,5,3,4,7]=>[5,1,1]=>15
[1,6,2,5,3,7,4]=>[4,2,1]=>35
[1,6,2,5,4,3,7]=>[4,1,1,1]=>20
[1,6,2,5,4,7,3]=>[4,1,1,1]=>20
[1,6,2,5,7,3,4]=>[4,2,1]=>35
[1,6,2,5,7,4,3]=>[4,1,1,1]=>20
[1,6,2,7,3,4,5]=>[5,2]=>14
[1,6,2,7,3,5,4]=>[4,2,1]=>35
[1,6,2,7,4,3,5]=>[4,2,1]=>35
[1,6,2,7,4,5,3]=>[4,2,1]=>35
[1,6,2,7,5,3,4]=>[4,2,1]=>35
[1,6,2,7,5,4,3]=>[3,2,1,1]=>35
[1,6,3,2,4,5,7]=>[5,1,1]=>15
[1,6,3,2,4,7,5]=>[4,2,1]=>35
[1,6,3,2,5,4,7]=>[4,2,1]=>35
[1,6,3,2,5,7,4]=>[4,2,1]=>35
[1,6,3,2,7,4,5]=>[4,2,1]=>35
[1,6,3,2,7,5,4]=>[3,2,2]=>21
[1,6,3,4,2,5,7]=>[5,1,1]=>15
[1,6,3,4,2,7,5]=>[4,2,1]=>35
[1,6,3,4,5,2,7]=>[5,1,1]=>15
[1,6,3,4,5,7,2]=>[5,1,1]=>15
[1,6,3,4,7,2,5]=>[4,2,1]=>35
[1,6,3,4,7,5,2]=>[4,2,1]=>35
[1,6,3,5,2,4,7]=>[4,2,1]=>35
[1,6,3,5,2,7,4]=>[4,2,1]=>35
[1,6,3,5,4,2,7]=>[4,1,1,1]=>20
[1,6,3,5,4,7,2]=>[4,1,1,1]=>20
[1,6,3,5,7,2,4]=>[4,2,1]=>35
[1,6,3,5,7,4,2]=>[4,1,1,1]=>20
[1,6,3,7,2,4,5]=>[4,2,1]=>35
[1,6,3,7,2,5,4]=>[3,2,2]=>21
[1,6,3,7,4,2,5]=>[4,2,1]=>35
[1,6,3,7,4,5,2]=>[4,2,1]=>35
[1,6,3,7,5,2,4]=>[3,2,2]=>21
[1,6,3,7,5,4,2]=>[3,2,1,1]=>35
[1,6,4,2,3,5,7]=>[5,1,1]=>15
[1,6,4,2,3,7,5]=>[4,2,1]=>35
[1,6,4,2,5,3,7]=>[4,2,1]=>35
[1,6,4,2,5,7,3]=>[4,2,1]=>35
[1,6,4,2,7,3,5]=>[4,2,1]=>35
[1,6,4,2,7,5,3]=>[3,2,2]=>21
[1,6,4,3,2,5,7]=>[4,1,1,1]=>20
[1,6,4,3,2,7,5]=>[3,2,1,1]=>35
[1,6,4,3,5,2,7]=>[4,1,1,1]=>20
[1,6,4,3,5,7,2]=>[4,1,1,1]=>20
[1,6,4,3,7,2,5]=>[3,2,1,1]=>35
[1,6,4,3,7,5,2]=>[3,2,1,1]=>35
[1,6,4,5,2,3,7]=>[4,2,1]=>35
[1,6,4,5,2,7,3]=>[4,2,1]=>35
[1,6,4,5,3,2,7]=>[4,1,1,1]=>20
[1,6,4,5,3,7,2]=>[4,1,1,1]=>20
[1,6,4,5,7,2,3]=>[4,2,1]=>35
[1,6,4,5,7,3,2]=>[4,1,1,1]=>20
[1,6,4,7,2,3,5]=>[4,2,1]=>35
[1,6,4,7,2,5,3]=>[3,2,2]=>21
[1,6,4,7,3,2,5]=>[3,2,1,1]=>35
[1,6,4,7,3,5,2]=>[3,2,1,1]=>35
[1,6,4,7,5,2,3]=>[3,2,2]=>21
[1,6,4,7,5,3,2]=>[3,2,1,1]=>35
[1,6,5,2,3,4,7]=>[5,1,1]=>15
[1,6,5,2,3,7,4]=>[4,2,1]=>35
[1,6,5,2,4,3,7]=>[4,1,1,1]=>20
[1,6,5,2,4,7,3]=>[4,1,1,1]=>20
[1,6,5,2,7,3,4]=>[4,2,1]=>35
[1,6,5,2,7,4,3]=>[3,2,1,1]=>35
[1,6,5,3,2,4,7]=>[4,1,1,1]=>20
[1,6,5,3,2,7,4]=>[3,2,1,1]=>35
[1,6,5,3,4,2,7]=>[4,1,1,1]=>20
[1,6,5,3,4,7,2]=>[4,1,1,1]=>20
[1,6,5,3,7,2,4]=>[3,2,1,1]=>35
[1,6,5,3,7,4,2]=>[3,2,1,1]=>35
[1,6,5,4,2,3,7]=>[4,1,1,1]=>20
[1,6,5,4,2,7,3]=>[3,2,1,1]=>35
[1,6,5,4,3,2,7]=>[3,1,1,1,1]=>15
[1,6,5,4,3,7,2]=>[3,1,1,1,1]=>15
[1,6,5,4,7,2,3]=>[3,2,1,1]=>35
[1,6,5,4,7,3,2]=>[3,1,1,1,1]=>15
[1,6,5,7,2,3,4]=>[4,2,1]=>35
[1,6,5,7,2,4,3]=>[3,2,1,1]=>35
[1,6,5,7,3,2,4]=>[3,2,1,1]=>35
[1,6,5,7,3,4,2]=>[3,2,1,1]=>35
[1,6,5,7,4,2,3]=>[3,2,1,1]=>35
[1,6,5,7,4,3,2]=>[3,1,1,1,1]=>15
[1,6,7,2,3,4,5]=>[5,2]=>14
[1,6,7,2,3,5,4]=>[4,2,1]=>35
[1,6,7,2,4,3,5]=>[4,2,1]=>35
[1,6,7,2,4,5,3]=>[4,2,1]=>35
[1,6,7,2,5,3,4]=>[4,2,1]=>35
[1,6,7,2,5,4,3]=>[3,2,1,1]=>35
[1,6,7,3,2,4,5]=>[4,2,1]=>35
[1,6,7,3,2,5,4]=>[3,2,2]=>21
[1,6,7,3,4,2,5]=>[4,2,1]=>35
[1,6,7,3,4,5,2]=>[4,2,1]=>35
[1,6,7,3,5,2,4]=>[3,2,2]=>21
[1,6,7,3,5,4,2]=>[3,2,1,1]=>35
[1,6,7,4,2,3,5]=>[4,2,1]=>35
[1,6,7,4,2,5,3]=>[3,2,2]=>21
[1,6,7,4,3,2,5]=>[3,2,1,1]=>35
[1,6,7,4,3,5,2]=>[3,2,1,1]=>35
[1,6,7,4,5,2,3]=>[3,2,2]=>21
[1,6,7,4,5,3,2]=>[3,2,1,1]=>35
[1,6,7,5,2,3,4]=>[4,2,1]=>35
[1,6,7,5,2,4,3]=>[3,2,1,1]=>35
[1,6,7,5,3,2,4]=>[3,2,1,1]=>35
[1,6,7,5,3,4,2]=>[3,2,1,1]=>35
[1,6,7,5,4,2,3]=>[3,2,1,1]=>35
[1,6,7,5,4,3,2]=>[3,1,1,1,1]=>15
[1,7,2,3,4,5,6]=>[6,1]=>6
[1,7,2,3,4,6,5]=>[5,1,1]=>15
[1,7,2,3,5,4,6]=>[5,1,1]=>15
[1,7,2,3,5,6,4]=>[5,1,1]=>15
[1,7,2,3,6,4,5]=>[5,1,1]=>15
[1,7,2,3,6,5,4]=>[4,1,1,1]=>20
[1,7,2,4,3,5,6]=>[5,1,1]=>15
[1,7,2,4,3,6,5]=>[4,2,1]=>35
[1,7,2,4,5,3,6]=>[5,1,1]=>15
[1,7,2,4,5,6,3]=>[5,1,1]=>15
[1,7,2,4,6,3,5]=>[4,2,1]=>35
[1,7,2,4,6,5,3]=>[4,1,1,1]=>20
[1,7,2,5,3,4,6]=>[5,1,1]=>15
[1,7,2,5,3,6,4]=>[4,2,1]=>35
[1,7,2,5,4,3,6]=>[4,1,1,1]=>20
[1,7,2,5,4,6,3]=>[4,1,1,1]=>20
[1,7,2,5,6,3,4]=>[4,2,1]=>35
[1,7,2,5,6,4,3]=>[4,1,1,1]=>20
[1,7,2,6,3,4,5]=>[5,1,1]=>15
[1,7,2,6,3,5,4]=>[4,1,1,1]=>20
[1,7,2,6,4,3,5]=>[4,1,1,1]=>20
[1,7,2,6,4,5,3]=>[4,1,1,1]=>20
[1,7,2,6,5,3,4]=>[4,1,1,1]=>20
[1,7,2,6,5,4,3]=>[3,1,1,1,1]=>15
[1,7,3,2,4,5,6]=>[5,1,1]=>15
[1,7,3,2,4,6,5]=>[4,2,1]=>35
[1,7,3,2,5,4,6]=>[4,2,1]=>35
[1,7,3,2,5,6,4]=>[4,2,1]=>35
[1,7,3,2,6,4,5]=>[4,2,1]=>35
[1,7,3,2,6,5,4]=>[3,2,1,1]=>35
[1,7,3,4,2,5,6]=>[5,1,1]=>15
[1,7,3,4,2,6,5]=>[4,2,1]=>35
[1,7,3,4,5,2,6]=>[5,1,1]=>15
[1,7,3,4,5,6,2]=>[5,1,1]=>15
[1,7,3,4,6,2,5]=>[4,2,1]=>35
[1,7,3,4,6,5,2]=>[4,1,1,1]=>20
[1,7,3,5,2,4,6]=>[4,2,1]=>35
[1,7,3,5,2,6,4]=>[4,2,1]=>35
[1,7,3,5,4,2,6]=>[4,1,1,1]=>20
[1,7,3,5,4,6,2]=>[4,1,1,1]=>20
[1,7,3,5,6,2,4]=>[4,2,1]=>35
[1,7,3,5,6,4,2]=>[4,1,1,1]=>20
[1,7,3,6,2,4,5]=>[4,2,1]=>35
[1,7,3,6,2,5,4]=>[3,2,1,1]=>35
[1,7,3,6,4,2,5]=>[4,1,1,1]=>20
[1,7,3,6,4,5,2]=>[4,1,1,1]=>20
[1,7,3,6,5,2,4]=>[3,2,1,1]=>35
[1,7,3,6,5,4,2]=>[3,1,1,1,1]=>15
[1,7,4,2,3,5,6]=>[5,1,1]=>15
[1,7,4,2,3,6,5]=>[4,2,1]=>35
[1,7,4,2,5,3,6]=>[4,2,1]=>35
[1,7,4,2,5,6,3]=>[4,2,1]=>35
[1,7,4,2,6,3,5]=>[4,2,1]=>35
[1,7,4,2,6,5,3]=>[3,2,1,1]=>35
[1,7,4,3,2,5,6]=>[4,1,1,1]=>20
[1,7,4,3,2,6,5]=>[3,2,1,1]=>35
[1,7,4,3,5,2,6]=>[4,1,1,1]=>20
[1,7,4,3,5,6,2]=>[4,1,1,1]=>20
[1,7,4,3,6,2,5]=>[3,2,1,1]=>35
[1,7,4,3,6,5,2]=>[3,2,1,1]=>35
[1,7,4,5,2,3,6]=>[4,2,1]=>35
[1,7,4,5,2,6,3]=>[4,2,1]=>35
[1,7,4,5,3,2,6]=>[4,1,1,1]=>20
[1,7,4,5,3,6,2]=>[4,1,1,1]=>20
[1,7,4,5,6,2,3]=>[4,2,1]=>35
[1,7,4,5,6,3,2]=>[4,1,1,1]=>20
[1,7,4,6,2,3,5]=>[4,2,1]=>35
[1,7,4,6,2,5,3]=>[3,2,1,1]=>35
[1,7,4,6,3,2,5]=>[3,2,1,1]=>35
[1,7,4,6,3,5,2]=>[3,2,1,1]=>35
[1,7,4,6,5,2,3]=>[3,2,1,1]=>35
[1,7,4,6,5,3,2]=>[3,1,1,1,1]=>15
[1,7,5,2,3,4,6]=>[5,1,1]=>15
[1,7,5,2,3,6,4]=>[4,2,1]=>35
[1,7,5,2,4,3,6]=>[4,1,1,1]=>20
[1,7,5,2,4,6,3]=>[4,1,1,1]=>20
[1,7,5,2,6,3,4]=>[4,2,1]=>35
[1,7,5,2,6,4,3]=>[3,2,1,1]=>35
[1,7,5,3,2,4,6]=>[4,1,1,1]=>20
[1,7,5,3,2,6,4]=>[3,2,1,1]=>35
[1,7,5,3,4,2,6]=>[4,1,1,1]=>20
[1,7,5,3,4,6,2]=>[4,1,1,1]=>20
[1,7,5,3,6,2,4]=>[3,2,1,1]=>35
[1,7,5,3,6,4,2]=>[3,2,1,1]=>35
[1,7,5,4,2,3,6]=>[4,1,1,1]=>20
[1,7,5,4,2,6,3]=>[3,2,1,1]=>35
[1,7,5,4,3,2,6]=>[3,1,1,1,1]=>15
[1,7,5,4,3,6,2]=>[3,1,1,1,1]=>15
[1,7,5,4,6,2,3]=>[3,2,1,1]=>35
[1,7,5,4,6,3,2]=>[3,1,1,1,1]=>15
[1,7,5,6,2,3,4]=>[4,2,1]=>35
[1,7,5,6,2,4,3]=>[3,2,1,1]=>35
[1,7,5,6,3,2,4]=>[3,2,1,1]=>35
[1,7,5,6,3,4,2]=>[3,2,1,1]=>35
[1,7,5,6,4,2,3]=>[3,2,1,1]=>35
[1,7,5,6,4,3,2]=>[3,1,1,1,1]=>15
[1,7,6,2,3,4,5]=>[5,1,1]=>15
[1,7,6,2,3,5,4]=>[4,1,1,1]=>20
[1,7,6,2,4,3,5]=>[4,1,1,1]=>20
[1,7,6,2,4,5,3]=>[4,1,1,1]=>20
[1,7,6,2,5,3,4]=>[4,1,1,1]=>20
[1,7,6,2,5,4,3]=>[3,1,1,1,1]=>15
[1,7,6,3,2,4,5]=>[4,1,1,1]=>20
[1,7,6,3,2,5,4]=>[3,2,1,1]=>35
[1,7,6,3,4,2,5]=>[4,1,1,1]=>20
[1,7,6,3,4,5,2]=>[4,1,1,1]=>20
[1,7,6,3,5,2,4]=>[3,2,1,1]=>35
[1,7,6,3,5,4,2]=>[3,1,1,1,1]=>15
[1,7,6,4,2,3,5]=>[4,1,1,1]=>20
[1,7,6,4,2,5,3]=>[3,2,1,1]=>35
[1,7,6,4,3,2,5]=>[3,1,1,1,1]=>15
[1,7,6,4,3,5,2]=>[3,1,1,1,1]=>15
[1,7,6,4,5,2,3]=>[3,2,1,1]=>35
[1,7,6,4,5,3,2]=>[3,1,1,1,1]=>15
[1,7,6,5,2,3,4]=>[4,1,1,1]=>20
[1,7,6,5,2,4,3]=>[3,1,1,1,1]=>15
[1,7,6,5,3,2,4]=>[3,1,1,1,1]=>15
[1,7,6,5,3,4,2]=>[3,1,1,1,1]=>15
[1,7,6,5,4,2,3]=>[3,1,1,1,1]=>15
[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]=>6
[2,1,3,4,5,6,7]=>[6,1]=>6
[2,1,3,4,5,7,6]=>[5,2]=>14
[2,1,3,4,6,5,7]=>[5,2]=>14
[2,1,3,4,6,7,5]=>[5,2]=>14
[2,1,3,4,7,5,6]=>[5,2]=>14
[2,1,3,4,7,6,5]=>[4,2,1]=>35
[2,1,3,5,4,6,7]=>[5,2]=>14
[2,1,3,5,4,7,6]=>[4,3]=>14
[2,1,3,5,6,4,7]=>[5,2]=>14
[2,1,3,5,6,7,4]=>[5,2]=>14
[2,1,3,5,7,4,6]=>[4,3]=>14
[2,1,3,5,7,6,4]=>[4,2,1]=>35
[2,1,3,6,4,5,7]=>[5,2]=>14
[2,1,3,6,4,7,5]=>[4,3]=>14
[2,1,3,6,5,4,7]=>[4,2,1]=>35
[2,1,3,6,5,7,4]=>[4,2,1]=>35
[2,1,3,6,7,4,5]=>[4,3]=>14
[2,1,3,6,7,5,4]=>[4,2,1]=>35
[2,1,3,7,4,5,6]=>[5,2]=>14
[2,1,3,7,4,6,5]=>[4,2,1]=>35
[2,1,3,7,5,4,6]=>[4,2,1]=>35
[2,1,3,7,5,6,4]=>[4,2,1]=>35
[2,1,3,7,6,4,5]=>[4,2,1]=>35
[2,1,3,7,6,5,4]=>[3,2,1,1]=>35
[2,1,4,3,5,6,7]=>[5,2]=>14
[2,1,4,3,5,7,6]=>[4,3]=>14
[2,1,4,3,6,5,7]=>[4,3]=>14
[2,1,4,3,6,7,5]=>[4,3]=>14
[2,1,4,3,7,5,6]=>[4,3]=>14
[2,1,4,3,7,6,5]=>[3,3,1]=>21
[2,1,4,5,3,6,7]=>[5,2]=>14
[2,1,4,5,3,7,6]=>[4,3]=>14
[2,1,4,5,6,3,7]=>[5,2]=>14
[2,1,4,5,6,7,3]=>[5,2]=>14
[2,1,4,5,7,3,6]=>[4,3]=>14
[2,1,4,5,7,6,3]=>[4,2,1]=>35
[2,1,4,6,3,5,7]=>[4,3]=>14
[2,1,4,6,3,7,5]=>[4,3]=>14
[2,1,4,6,5,3,7]=>[4,2,1]=>35
[2,1,4,6,5,7,3]=>[4,2,1]=>35
[2,1,4,6,7,3,5]=>[4,3]=>14
[2,1,4,6,7,5,3]=>[4,2,1]=>35
[2,1,4,7,3,5,6]=>[4,3]=>14
[2,1,4,7,3,6,5]=>[3,3,1]=>21
[2,1,4,7,5,3,6]=>[4,2,1]=>35
[2,1,4,7,5,6,3]=>[4,2,1]=>35
[2,1,4,7,6,3,5]=>[3,3,1]=>21
[2,1,4,7,6,5,3]=>[3,2,1,1]=>35
[2,1,5,3,4,6,7]=>[5,2]=>14
[2,1,5,3,4,7,6]=>[4,3]=>14
[2,1,5,3,6,4,7]=>[4,3]=>14
[2,1,5,3,6,7,4]=>[4,3]=>14
[2,1,5,3,7,4,6]=>[4,3]=>14
[2,1,5,3,7,6,4]=>[3,3,1]=>21
[2,1,5,4,3,6,7]=>[4,2,1]=>35
[2,1,5,4,3,7,6]=>[3,3,1]=>21
[2,1,5,4,6,3,7]=>[4,2,1]=>35
[2,1,5,4,6,7,3]=>[4,2,1]=>35
[2,1,5,4,7,3,6]=>[3,3,1]=>21
[2,1,5,4,7,6,3]=>[3,3,1]=>21
[2,1,5,6,3,4,7]=>[4,3]=>14
[2,1,5,6,3,7,4]=>[4,3]=>14
[2,1,5,6,4,3,7]=>[4,2,1]=>35
[2,1,5,6,4,7,3]=>[4,2,1]=>35
[2,1,5,6,7,3,4]=>[4,3]=>14
[2,1,5,6,7,4,3]=>[4,2,1]=>35
[2,1,5,7,3,4,6]=>[4,3]=>14
[2,1,5,7,3,6,4]=>[3,3,1]=>21
[2,1,5,7,4,3,6]=>[3,3,1]=>21
[2,1,5,7,4,6,3]=>[3,3,1]=>21
[2,1,5,7,6,3,4]=>[3,3,1]=>21
[2,1,5,7,6,4,3]=>[3,2,1,1]=>35
[2,1,6,3,4,5,7]=>[5,2]=>14
[2,1,6,3,4,7,5]=>[4,3]=>14
[2,1,6,3,5,4,7]=>[4,2,1]=>35
[2,1,6,3,5,7,4]=>[4,2,1]=>35
[2,1,6,3,7,4,5]=>[4,3]=>14
[2,1,6,3,7,5,4]=>[3,3,1]=>21
[2,1,6,4,3,5,7]=>[4,2,1]=>35
[2,1,6,4,3,7,5]=>[3,3,1]=>21
[2,1,6,4,5,3,7]=>[4,2,1]=>35
[2,1,6,4,5,7,3]=>[4,2,1]=>35
[2,1,6,4,7,3,5]=>[3,3,1]=>21
[2,1,6,4,7,5,3]=>[3,3,1]=>21
[2,1,6,5,3,4,7]=>[4,2,1]=>35
[2,1,6,5,3,7,4]=>[3,3,1]=>21
[2,1,6,5,4,3,7]=>[3,2,1,1]=>35
[2,1,6,5,4,7,3]=>[3,2,1,1]=>35
[2,1,6,5,7,3,4]=>[3,3,1]=>21
[2,1,6,5,7,4,3]=>[3,2,1,1]=>35
[2,1,6,7,3,4,5]=>[4,3]=>14
[2,1,6,7,3,5,4]=>[3,3,1]=>21
[2,1,6,7,4,3,5]=>[3,3,1]=>21
[2,1,6,7,4,5,3]=>[3,3,1]=>21
[2,1,6,7,5,3,4]=>[3,3,1]=>21
[2,1,6,7,5,4,3]=>[3,2,1,1]=>35
[2,1,7,3,4,5,6]=>[5,2]=>14
[2,1,7,3,4,6,5]=>[4,2,1]=>35
[2,1,7,3,5,4,6]=>[4,2,1]=>35
[2,1,7,3,5,6,4]=>[4,2,1]=>35
[2,1,7,3,6,4,5]=>[4,2,1]=>35
[2,1,7,3,6,5,4]=>[3,2,1,1]=>35
[2,1,7,4,3,5,6]=>[4,2,1]=>35
[2,1,7,4,3,6,5]=>[3,3,1]=>21
[2,1,7,4,5,3,6]=>[4,2,1]=>35
[2,1,7,4,5,6,3]=>[4,2,1]=>35
[2,1,7,4,6,3,5]=>[3,3,1]=>21
[2,1,7,4,6,5,3]=>[3,2,1,1]=>35
[2,1,7,5,3,4,6]=>[4,2,1]=>35
[2,1,7,5,3,6,4]=>[3,3,1]=>21
[2,1,7,5,4,3,6]=>[3,2,1,1]=>35
[2,1,7,5,4,6,3]=>[3,2,1,1]=>35
[2,1,7,5,6,3,4]=>[3,3,1]=>21
[2,1,7,5,6,4,3]=>[3,2,1,1]=>35
[2,1,7,6,3,4,5]=>[4,2,1]=>35
[2,1,7,6,3,5,4]=>[3,2,1,1]=>35
[2,1,7,6,4,3,5]=>[3,2,1,1]=>35
[2,1,7,6,4,5,3]=>[3,2,1,1]=>35
[2,1,7,6,5,3,4]=>[3,2,1,1]=>35
[2,1,7,6,5,4,3]=>[2,2,1,1,1]=>14
[2,3,1,4,5,6,7]=>[6,1]=>6
[2,3,1,4,5,7,6]=>[5,2]=>14
[2,3,1,4,6,5,7]=>[5,2]=>14
[2,3,1,4,6,7,5]=>[5,2]=>14
[2,3,1,4,7,5,6]=>[5,2]=>14
[2,3,1,4,7,6,5]=>[4,2,1]=>35
[2,3,1,5,4,6,7]=>[5,2]=>14
[2,3,1,5,4,7,6]=>[4,3]=>14
[2,3,1,5,6,4,7]=>[5,2]=>14
[2,3,1,5,6,7,4]=>[5,2]=>14
[2,3,1,5,7,4,6]=>[4,3]=>14
[2,3,1,5,7,6,4]=>[4,2,1]=>35
[2,3,1,6,4,5,7]=>[5,2]=>14
[2,3,1,6,4,7,5]=>[4,3]=>14
[2,3,1,6,5,4,7]=>[4,2,1]=>35
[2,3,1,6,5,7,4]=>[4,2,1]=>35
[2,3,1,6,7,4,5]=>[4,3]=>14
[2,3,1,6,7,5,4]=>[4,2,1]=>35
[2,3,1,7,4,5,6]=>[5,2]=>14
[2,3,1,7,4,6,5]=>[4,2,1]=>35
[2,3,1,7,5,4,6]=>[4,2,1]=>35
[2,3,1,7,5,6,4]=>[4,2,1]=>35
[2,3,1,7,6,4,5]=>[4,2,1]=>35
[2,3,1,7,6,5,4]=>[3,2,1,1]=>35
[2,3,4,1,5,6,7]=>[6,1]=>6
[2,3,4,1,5,7,6]=>[5,2]=>14
[2,3,4,1,6,5,7]=>[5,2]=>14
[2,3,4,1,6,7,5]=>[5,2]=>14
[2,3,4,1,7,5,6]=>[5,2]=>14
[2,3,4,1,7,6,5]=>[4,2,1]=>35
[2,3,4,5,1,6,7]=>[6,1]=>6
[2,3,4,5,1,7,6]=>[5,2]=>14
[2,3,4,5,6,1,7]=>[6,1]=>6
[2,3,4,5,6,7,1]=>[6,1]=>6
[2,3,4,5,7,1,6]=>[5,2]=>14
[2,3,4,5,7,6,1]=>[5,1,1]=>15
[2,3,4,6,1,5,7]=>[5,2]=>14
[2,3,4,6,1,7,5]=>[5,2]=>14
[2,3,4,6,5,1,7]=>[5,1,1]=>15
[2,3,4,6,5,7,1]=>[5,1,1]=>15
[2,3,4,6,7,1,5]=>[5,2]=>14
[2,3,4,6,7,5,1]=>[5,1,1]=>15
[2,3,4,7,1,5,6]=>[5,2]=>14
[2,3,4,7,1,6,5]=>[4,2,1]=>35
[2,3,4,7,5,1,6]=>[5,1,1]=>15
[2,3,4,7,5,6,1]=>[5,1,1]=>15
[2,3,4,7,6,1,5]=>[4,2,1]=>35
[2,3,4,7,6,5,1]=>[4,1,1,1]=>20
[2,3,5,1,4,6,7]=>[5,2]=>14
[2,3,5,1,4,7,6]=>[4,3]=>14
[2,3,5,1,6,4,7]=>[5,2]=>14
[2,3,5,1,6,7,4]=>[5,2]=>14
[2,3,5,1,7,4,6]=>[4,3]=>14
[2,3,5,1,7,6,4]=>[4,2,1]=>35
[2,3,5,4,1,6,7]=>[5,1,1]=>15
[2,3,5,4,1,7,6]=>[4,2,1]=>35
[2,3,5,4,6,1,7]=>[5,1,1]=>15
[2,3,5,4,6,7,1]=>[5,1,1]=>15
[2,3,5,4,7,1,6]=>[4,2,1]=>35
[2,3,5,4,7,6,1]=>[4,2,1]=>35
[2,3,5,6,1,4,7]=>[5,2]=>14
[2,3,5,6,1,7,4]=>[5,2]=>14
[2,3,5,6,4,1,7]=>[5,1,1]=>15
[2,3,5,6,4,7,1]=>[5,1,1]=>15
[2,3,5,6,7,1,4]=>[5,2]=>14
[2,3,5,6,7,4,1]=>[5,1,1]=>15
[2,3,5,7,1,4,6]=>[4,3]=>14
[2,3,5,7,1,6,4]=>[4,2,1]=>35
[2,3,5,7,4,1,6]=>[4,2,1]=>35
[2,3,5,7,4,6,1]=>[4,2,1]=>35
[2,3,5,7,6,1,4]=>[4,2,1]=>35
[2,3,5,7,6,4,1]=>[4,1,1,1]=>20
[2,3,6,1,4,5,7]=>[5,2]=>14
[2,3,6,1,4,7,5]=>[4,3]=>14
[2,3,6,1,5,4,7]=>[4,2,1]=>35
[2,3,6,1,5,7,4]=>[4,2,1]=>35
[2,3,6,1,7,4,5]=>[4,3]=>14
[2,3,6,1,7,5,4]=>[4,2,1]=>35
[2,3,6,4,1,5,7]=>[5,1,1]=>15
[2,3,6,4,1,7,5]=>[4,2,1]=>35
[2,3,6,4,5,1,7]=>[5,1,1]=>15
[2,3,6,4,5,7,1]=>[5,1,1]=>15
[2,3,6,4,7,1,5]=>[4,2,1]=>35
[2,3,6,4,7,5,1]=>[4,2,1]=>35
[2,3,6,5,1,4,7]=>[4,2,1]=>35
[2,3,6,5,1,7,4]=>[4,2,1]=>35
[2,3,6,5,4,1,7]=>[4,1,1,1]=>20
[2,3,6,5,4,7,1]=>[4,1,1,1]=>20
[2,3,6,5,7,1,4]=>[4,2,1]=>35
[2,3,6,5,7,4,1]=>[4,1,1,1]=>20
[2,3,6,7,1,4,5]=>[4,3]=>14
[2,3,6,7,1,5,4]=>[4,2,1]=>35
[2,3,6,7,4,1,5]=>[4,2,1]=>35
[2,3,6,7,4,5,1]=>[4,2,1]=>35
[2,3,6,7,5,1,4]=>[4,2,1]=>35
[2,3,6,7,5,4,1]=>[4,1,1,1]=>20
[2,3,7,1,4,5,6]=>[5,2]=>14
[2,3,7,1,4,6,5]=>[4,2,1]=>35
[2,3,7,1,5,4,6]=>[4,2,1]=>35
[2,3,7,1,5,6,4]=>[4,2,1]=>35
[2,3,7,1,6,4,5]=>[4,2,1]=>35
[2,3,7,1,6,5,4]=>[3,2,1,1]=>35
[2,3,7,4,1,5,6]=>[5,1,1]=>15
[2,3,7,4,1,6,5]=>[4,2,1]=>35
[2,3,7,4,5,1,6]=>[5,1,1]=>15
[2,3,7,4,5,6,1]=>[5,1,1]=>15
[2,3,7,4,6,1,5]=>[4,2,1]=>35
[2,3,7,4,6,5,1]=>[4,1,1,1]=>20
[2,3,7,5,1,4,6]=>[4,2,1]=>35
[2,3,7,5,1,6,4]=>[4,2,1]=>35
[2,3,7,5,4,1,6]=>[4,1,1,1]=>20
[2,3,7,5,4,6,1]=>[4,1,1,1]=>20
[2,3,7,5,6,1,4]=>[4,2,1]=>35
[2,3,7,5,6,4,1]=>[4,1,1,1]=>20
[2,3,7,6,1,4,5]=>[4,2,1]=>35
[2,3,7,6,1,5,4]=>[3,2,1,1]=>35
[2,3,7,6,4,1,5]=>[4,1,1,1]=>20
[2,3,7,6,4,5,1]=>[4,1,1,1]=>20
[2,3,7,6,5,1,4]=>[3,2,1,1]=>35
[2,3,7,6,5,4,1]=>[3,1,1,1,1]=>15
[2,4,1,3,5,6,7]=>[5,2]=>14
[2,4,1,3,5,7,6]=>[4,3]=>14
[2,4,1,3,6,5,7]=>[4,3]=>14
[2,4,1,3,6,7,5]=>[4,3]=>14
[2,4,1,3,7,5,6]=>[4,3]=>14
[2,4,1,3,7,6,5]=>[3,3,1]=>21
[2,4,1,5,3,6,7]=>[5,2]=>14
[2,4,1,5,3,7,6]=>[4,3]=>14
[2,4,1,5,6,3,7]=>[5,2]=>14
[2,4,1,5,6,7,3]=>[5,2]=>14
[2,4,1,5,7,3,6]=>[4,3]=>14
[2,4,1,5,7,6,3]=>[4,2,1]=>35
[2,4,1,6,3,5,7]=>[4,3]=>14
[2,4,1,6,3,7,5]=>[4,3]=>14
[2,4,1,6,5,3,7]=>[4,2,1]=>35
[2,4,1,6,5,7,3]=>[4,2,1]=>35
[2,4,1,6,7,3,5]=>[4,3]=>14
[2,4,1,6,7,5,3]=>[4,2,1]=>35
[2,4,1,7,3,5,6]=>[4,3]=>14
[2,4,1,7,3,6,5]=>[3,3,1]=>21
[2,4,1,7,5,3,6]=>[4,2,1]=>35
[2,4,1,7,5,6,3]=>[4,2,1]=>35
[2,4,1,7,6,3,5]=>[3,3,1]=>21
[2,4,1,7,6,5,3]=>[3,2,1,1]=>35
[2,4,3,1,5,6,7]=>[5,1,1]=>15
[2,4,3,1,5,7,6]=>[4,2,1]=>35
[2,4,3,1,6,5,7]=>[4,2,1]=>35
[2,4,3,1,6,7,5]=>[4,2,1]=>35
[2,4,3,1,7,5,6]=>[4,2,1]=>35
[2,4,3,1,7,6,5]=>[3,2,2]=>21
[2,4,3,5,1,6,7]=>[5,1,1]=>15
[2,4,3,5,1,7,6]=>[4,2,1]=>35
[2,4,3,5,6,1,7]=>[5,1,1]=>15
[2,4,3,5,6,7,1]=>[5,1,1]=>15
[2,4,3,5,7,1,6]=>[4,2,1]=>35
[2,4,3,5,7,6,1]=>[4,2,1]=>35
[2,4,3,6,1,5,7]=>[4,2,1]=>35
[2,4,3,6,1,7,5]=>[4,2,1]=>35
[2,4,3,6,5,1,7]=>[4,2,1]=>35
[2,4,3,6,5,7,1]=>[4,2,1]=>35
[2,4,3,6,7,1,5]=>[4,2,1]=>35
[2,4,3,6,7,5,1]=>[4,2,1]=>35
[2,4,3,7,1,5,6]=>[4,2,1]=>35
[2,4,3,7,1,6,5]=>[3,2,2]=>21
[2,4,3,7,5,1,6]=>[4,2,1]=>35
[2,4,3,7,5,6,1]=>[4,2,1]=>35
[2,4,3,7,6,1,5]=>[3,2,2]=>21
[2,4,3,7,6,5,1]=>[3,2,1,1]=>35
[2,4,5,1,3,6,7]=>[5,2]=>14
[2,4,5,1,3,7,6]=>[4,3]=>14
[2,4,5,1,6,3,7]=>[5,2]=>14
[2,4,5,1,6,7,3]=>[5,2]=>14
[2,4,5,1,7,3,6]=>[4,3]=>14
[2,4,5,1,7,6,3]=>[4,2,1]=>35
[2,4,5,3,1,6,7]=>[5,1,1]=>15
[2,4,5,3,1,7,6]=>[4,2,1]=>35
[2,4,5,3,6,1,7]=>[5,1,1]=>15
[2,4,5,3,6,7,1]=>[5,1,1]=>15
[2,4,5,3,7,1,6]=>[4,2,1]=>35
[2,4,5,3,7,6,1]=>[4,2,1]=>35
[2,4,5,6,1,3,7]=>[5,2]=>14
[2,4,5,6,1,7,3]=>[5,2]=>14
[2,4,5,6,3,1,7]=>[5,1,1]=>15
[2,4,5,6,3,7,1]=>[5,1,1]=>15
[2,4,5,6,7,1,3]=>[5,2]=>14
[2,4,5,6,7,3,1]=>[5,1,1]=>15
[2,4,5,7,1,3,6]=>[4,3]=>14
[2,4,5,7,1,6,3]=>[4,2,1]=>35
[2,4,5,7,3,1,6]=>[4,2,1]=>35
[2,4,5,7,3,6,1]=>[4,2,1]=>35
[2,4,5,7,6,1,3]=>[4,2,1]=>35
[2,4,5,7,6,3,1]=>[4,1,1,1]=>20
[2,4,6,1,3,5,7]=>[4,3]=>14
[2,4,6,1,3,7,5]=>[4,3]=>14
[2,4,6,1,5,3,7]=>[4,2,1]=>35
[2,4,6,1,5,7,3]=>[4,2,1]=>35
[2,4,6,1,7,3,5]=>[4,3]=>14
[2,4,6,1,7,5,3]=>[4,2,1]=>35
[2,4,6,3,1,5,7]=>[4,2,1]=>35
[2,4,6,3,1,7,5]=>[4,2,1]=>35
[2,4,6,3,5,1,7]=>[4,2,1]=>35
[2,4,6,3,5,7,1]=>[4,2,1]=>35
[2,4,6,3,7,1,5]=>[4,2,1]=>35
[2,4,6,3,7,5,1]=>[4,2,1]=>35
[2,4,6,5,1,3,7]=>[4,2,1]=>35
[2,4,6,5,1,7,3]=>[4,2,1]=>35
[2,4,6,5,3,1,7]=>[4,1,1,1]=>20
[2,4,6,5,3,7,1]=>[4,1,1,1]=>20
[2,4,6,5,7,1,3]=>[4,2,1]=>35
[2,4,6,5,7,3,1]=>[4,1,1,1]=>20
[2,4,6,7,1,3,5]=>[4,3]=>14
[2,4,6,7,1,5,3]=>[4,2,1]=>35
[2,4,6,7,3,1,5]=>[4,2,1]=>35
[2,4,6,7,3,5,1]=>[4,2,1]=>35
[2,4,6,7,5,1,3]=>[4,2,1]=>35
[2,4,6,7,5,3,1]=>[4,1,1,1]=>20
[2,4,7,1,3,5,6]=>[4,3]=>14
[2,4,7,1,3,6,5]=>[3,3,1]=>21
[2,4,7,1,5,3,6]=>[4,2,1]=>35
[2,4,7,1,5,6,3]=>[4,2,1]=>35
[2,4,7,1,6,3,5]=>[3,3,1]=>21
[2,4,7,1,6,5,3]=>[3,2,1,1]=>35
[2,4,7,3,1,5,6]=>[4,2,1]=>35
[2,4,7,3,1,6,5]=>[3,2,2]=>21
[2,4,7,3,5,1,6]=>[4,2,1]=>35
[2,4,7,3,5,6,1]=>[4,2,1]=>35
[2,4,7,3,6,1,5]=>[3,2,2]=>21
[2,4,7,3,6,5,1]=>[3,2,1,1]=>35
[2,4,7,5,1,3,6]=>[4,2,1]=>35
[2,4,7,5,1,6,3]=>[4,2,1]=>35
[2,4,7,5,3,1,6]=>[4,1,1,1]=>20
[2,4,7,5,3,6,1]=>[4,1,1,1]=>20
[2,4,7,5,6,1,3]=>[4,2,1]=>35
[2,4,7,5,6,3,1]=>[4,1,1,1]=>20
[2,4,7,6,1,3,5]=>[3,3,1]=>21
[2,4,7,6,1,5,3]=>[3,2,1,1]=>35
[2,4,7,6,3,1,5]=>[3,2,1,1]=>35
[2,4,7,6,3,5,1]=>[3,2,1,1]=>35
[2,4,7,6,5,1,3]=>[3,2,1,1]=>35
[2,4,7,6,5,3,1]=>[3,1,1,1,1]=>15
[2,5,1,3,4,6,7]=>[5,2]=>14
[2,5,1,3,4,7,6]=>[4,3]=>14
[2,5,1,3,6,4,7]=>[4,3]=>14
[2,5,1,3,6,7,4]=>[4,3]=>14
[2,5,1,3,7,4,6]=>[4,3]=>14
[2,5,1,3,7,6,4]=>[3,3,1]=>21
[2,5,1,4,3,6,7]=>[4,2,1]=>35
[2,5,1,4,3,7,6]=>[3,3,1]=>21
[2,5,1,4,6,3,7]=>[4,2,1]=>35
[2,5,1,4,6,7,3]=>[4,2,1]=>35
[2,5,1,4,7,3,6]=>[3,3,1]=>21
[2,5,1,4,7,6,3]=>[3,3,1]=>21
[2,5,1,6,3,4,7]=>[4,3]=>14
[2,5,1,6,3,7,4]=>[4,3]=>14
[2,5,1,6,4,3,7]=>[4,2,1]=>35
[2,5,1,6,4,7,3]=>[4,2,1]=>35
[2,5,1,6,7,3,4]=>[4,3]=>14
[2,5,1,6,7,4,3]=>[4,2,1]=>35
[2,5,1,7,3,4,6]=>[4,3]=>14
[2,5,1,7,3,6,4]=>[3,3,1]=>21
[2,5,1,7,4,3,6]=>[3,3,1]=>21
[2,5,1,7,4,6,3]=>[3,3,1]=>21
[2,5,1,7,6,3,4]=>[3,3,1]=>21
[2,5,1,7,6,4,3]=>[3,2,1,1]=>35
[2,5,3,1,4,6,7]=>[5,1,1]=>15
[2,5,3,1,4,7,6]=>[4,2,1]=>35
[2,5,3,1,6,4,7]=>[4,2,1]=>35
[2,5,3,1,6,7,4]=>[4,2,1]=>35
[2,5,3,1,7,4,6]=>[4,2,1]=>35
[2,5,3,1,7,6,4]=>[3,2,2]=>21
[2,5,3,4,1,6,7]=>[5,1,1]=>15
[2,5,3,4,1,7,6]=>[4,2,1]=>35
[2,5,3,4,6,1,7]=>[5,1,1]=>15
[2,5,3,4,6,7,1]=>[5,1,1]=>15
[2,5,3,4,7,1,6]=>[4,2,1]=>35
[2,5,3,4,7,6,1]=>[4,2,1]=>35
[2,5,3,6,1,4,7]=>[4,2,1]=>35
[2,5,3,6,1,7,4]=>[4,2,1]=>35
[2,5,3,6,4,1,7]=>[4,2,1]=>35
[2,5,3,6,4,7,1]=>[4,2,1]=>35
[2,5,3,6,7,1,4]=>[4,2,1]=>35
[2,5,3,6,7,4,1]=>[4,2,1]=>35
[2,5,3,7,1,4,6]=>[4,2,1]=>35
[2,5,3,7,1,6,4]=>[3,2,2]=>21
[2,5,3,7,4,1,6]=>[4,2,1]=>35
[2,5,3,7,4,6,1]=>[4,2,1]=>35
[2,5,3,7,6,1,4]=>[3,2,2]=>21
[2,5,3,7,6,4,1]=>[3,2,1,1]=>35
[2,5,4,1,3,6,7]=>[4,2,1]=>35
[2,5,4,1,3,7,6]=>[3,3,1]=>21
[2,5,4,1,6,3,7]=>[4,2,1]=>35
[2,5,4,1,6,7,3]=>[4,2,1]=>35
[2,5,4,1,7,3,6]=>[3,3,1]=>21
[2,5,4,1,7,6,3]=>[3,2,2]=>21
[2,5,4,3,1,6,7]=>[4,1,1,1]=>20
[2,5,4,3,1,7,6]=>[3,2,1,1]=>35
[2,5,4,3,6,1,7]=>[4,1,1,1]=>20
[2,5,4,3,6,7,1]=>[4,1,1,1]=>20
[2,5,4,3,7,1,6]=>[3,2,1,1]=>35
[2,5,4,3,7,6,1]=>[3,2,1,1]=>35
[2,5,4,6,1,3,7]=>[4,2,1]=>35
[2,5,4,6,1,7,3]=>[4,2,1]=>35
[2,5,4,6,3,1,7]=>[4,1,1,1]=>20
[2,5,4,6,3,7,1]=>[4,1,1,1]=>20
[2,5,4,6,7,1,3]=>[4,2,1]=>35
[2,5,4,6,7,3,1]=>[4,1,1,1]=>20
[2,5,4,7,1,3,6]=>[3,3,1]=>21
[2,5,4,7,1,6,3]=>[3,2,2]=>21
[2,5,4,7,3,1,6]=>[3,2,1,1]=>35
[2,5,4,7,3,6,1]=>[3,2,1,1]=>35
[2,5,4,7,6,1,3]=>[3,2,2]=>21
[2,5,4,7,6,3,1]=>[3,2,1,1]=>35
[2,5,6,1,3,4,7]=>[4,3]=>14
[2,5,6,1,3,7,4]=>[4,3]=>14
[2,5,6,1,4,3,7]=>[4,2,1]=>35
[2,5,6,1,4,7,3]=>[4,2,1]=>35
[2,5,6,1,7,3,4]=>[4,3]=>14
[2,5,6,1,7,4,3]=>[4,2,1]=>35
[2,5,6,3,1,4,7]=>[4,2,1]=>35
[2,5,6,3,1,7,4]=>[4,2,1]=>35
[2,5,6,3,4,1,7]=>[4,2,1]=>35
[2,5,6,3,4,7,1]=>[4,2,1]=>35
[2,5,6,3,7,1,4]=>[4,2,1]=>35
[2,5,6,3,7,4,1]=>[4,2,1]=>35
[2,5,6,4,1,3,7]=>[4,2,1]=>35
[2,5,6,4,1,7,3]=>[4,2,1]=>35
[2,5,6,4,3,1,7]=>[4,1,1,1]=>20
[2,5,6,4,3,7,1]=>[4,1,1,1]=>20
[2,5,6,4,7,1,3]=>[4,2,1]=>35
[2,5,6,4,7,3,1]=>[4,1,1,1]=>20
[2,5,6,7,1,3,4]=>[4,3]=>14
[2,5,6,7,1,4,3]=>[4,2,1]=>35
[2,5,6,7,3,1,4]=>[4,2,1]=>35
[2,5,6,7,3,4,1]=>[4,2,1]=>35
[2,5,6,7,4,1,3]=>[4,2,1]=>35
[2,5,6,7,4,3,1]=>[4,1,1,1]=>20
[2,5,7,1,3,4,6]=>[4,3]=>14
[2,5,7,1,3,6,4]=>[3,3,1]=>21
[2,5,7,1,4,3,6]=>[3,3,1]=>21
[2,5,7,1,4,6,3]=>[3,3,1]=>21
[2,5,7,1,6,3,4]=>[3,3,1]=>21
[2,5,7,1,6,4,3]=>[3,2,1,1]=>35
[2,5,7,3,1,4,6]=>[4,2,1]=>35
[2,5,7,3,1,6,4]=>[3,2,2]=>21
[2,5,7,3,4,1,6]=>[4,2,1]=>35
[2,5,7,3,4,6,1]=>[4,2,1]=>35
[2,5,7,3,6,1,4]=>[3,2,2]=>21
[2,5,7,3,6,4,1]=>[3,2,1,1]=>35
[2,5,7,4,1,3,6]=>[3,3,1]=>21
[2,5,7,4,1,6,3]=>[3,2,2]=>21
[2,5,7,4,3,1,6]=>[3,2,1,1]=>35
[2,5,7,4,3,6,1]=>[3,2,1,1]=>35
[2,5,7,4,6,1,3]=>[3,2,2]=>21
[2,5,7,4,6,3,1]=>[3,2,1,1]=>35
[2,5,7,6,1,3,4]=>[3,3,1]=>21
[2,5,7,6,1,4,3]=>[3,2,1,1]=>35
[2,5,7,6,3,1,4]=>[3,2,1,1]=>35
[2,5,7,6,3,4,1]=>[3,2,1,1]=>35
[2,5,7,6,4,1,3]=>[3,2,1,1]=>35
[2,5,7,6,4,3,1]=>[3,1,1,1,1]=>15
[2,6,1,3,4,5,7]=>[5,2]=>14
[2,6,1,3,4,7,5]=>[4,3]=>14
[2,6,1,3,5,4,7]=>[4,2,1]=>35
[2,6,1,3,5,7,4]=>[4,2,1]=>35
[2,6,1,3,7,4,5]=>[4,3]=>14
[2,6,1,3,7,5,4]=>[3,3,1]=>21
[2,6,1,4,3,5,7]=>[4,2,1]=>35
[2,6,1,4,3,7,5]=>[3,3,1]=>21
[2,6,1,4,5,3,7]=>[4,2,1]=>35
[2,6,1,4,5,7,3]=>[4,2,1]=>35
[2,6,1,4,7,3,5]=>[3,3,1]=>21
[2,6,1,4,7,5,3]=>[3,3,1]=>21
[2,6,1,5,3,4,7]=>[4,2,1]=>35
[2,6,1,5,3,7,4]=>[3,3,1]=>21
[2,6,1,5,4,3,7]=>[3,2,1,1]=>35
[2,6,1,5,4,7,3]=>[3,2,1,1]=>35
[2,6,1,5,7,3,4]=>[3,3,1]=>21
[2,6,1,5,7,4,3]=>[3,2,1,1]=>35
[2,6,1,7,3,4,5]=>[4,3]=>14
[2,6,1,7,3,5,4]=>[3,3,1]=>21
[2,6,1,7,4,3,5]=>[3,3,1]=>21
[2,6,1,7,4,5,3]=>[3,3,1]=>21
[2,6,1,7,5,3,4]=>[3,3,1]=>21
[2,6,1,7,5,4,3]=>[3,2,1,1]=>35
[2,6,3,1,4,5,7]=>[5,1,1]=>15
[2,6,3,1,4,7,5]=>[4,2,1]=>35
[2,6,3,1,5,4,7]=>[4,2,1]=>35
[2,6,3,1,5,7,4]=>[4,2,1]=>35
[2,6,3,1,7,4,5]=>[4,2,1]=>35
[2,6,3,1,7,5,4]=>[3,2,2]=>21
[2,6,3,4,1,5,7]=>[5,1,1]=>15
[2,6,3,4,1,7,5]=>[4,2,1]=>35
[2,6,3,4,5,1,7]=>[5,1,1]=>15
[2,6,3,4,5,7,1]=>[5,1,1]=>15
[2,6,3,4,7,1,5]=>[4,2,1]=>35
[2,6,3,4,7,5,1]=>[4,2,1]=>35
[2,6,3,5,1,4,7]=>[4,2,1]=>35
[2,6,3,5,1,7,4]=>[4,2,1]=>35
[2,6,3,5,4,1,7]=>[4,1,1,1]=>20
[2,6,3,5,4,7,1]=>[4,1,1,1]=>20
[2,6,3,5,7,1,4]=>[4,2,1]=>35
[2,6,3,5,7,4,1]=>[4,1,1,1]=>20
[2,6,3,7,1,4,5]=>[4,2,1]=>35
[2,6,3,7,1,5,4]=>[3,2,2]=>21
[2,6,3,7,4,1,5]=>[4,2,1]=>35
[2,6,3,7,4,5,1]=>[4,2,1]=>35
[2,6,3,7,5,1,4]=>[3,2,2]=>21
[2,6,3,7,5,4,1]=>[3,2,1,1]=>35
[2,6,4,1,3,5,7]=>[4,2,1]=>35
[2,6,4,1,3,7,5]=>[3,3,1]=>21
[2,6,4,1,5,3,7]=>[4,2,1]=>35
[2,6,4,1,5,7,3]=>[4,2,1]=>35
[2,6,4,1,7,3,5]=>[3,3,1]=>21
[2,6,4,1,7,5,3]=>[3,2,2]=>21
[2,6,4,3,1,5,7]=>[4,1,1,1]=>20
[2,6,4,3,1,7,5]=>[3,2,1,1]=>35
[2,6,4,3,5,1,7]=>[4,1,1,1]=>20
[2,6,4,3,5,7,1]=>[4,1,1,1]=>20
[2,6,4,3,7,1,5]=>[3,2,1,1]=>35
[2,6,4,3,7,5,1]=>[3,2,1,1]=>35
[2,6,4,5,1,3,7]=>[4,2,1]=>35
[2,6,4,5,1,7,3]=>[4,2,1]=>35
[2,6,4,5,3,1,7]=>[4,1,1,1]=>20
[2,6,4,5,3,7,1]=>[4,1,1,1]=>20
[2,6,4,5,7,1,3]=>[4,2,1]=>35
[2,6,4,5,7,3,1]=>[4,1,1,1]=>20
[2,6,4,7,1,3,5]=>[3,3,1]=>21
[2,6,4,7,1,5,3]=>[3,2,2]=>21
[2,6,4,7,3,1,5]=>[3,2,1,1]=>35
[2,6,4,7,3,5,1]=>[3,2,1,1]=>35
[2,6,4,7,5,1,3]=>[3,2,2]=>21
[2,6,4,7,5,3,1]=>[3,2,1,1]=>35
[2,6,5,1,3,4,7]=>[4,2,1]=>35
[2,6,5,1,3,7,4]=>[3,3,1]=>21
[2,6,5,1,4,3,7]=>[3,2,1,1]=>35
[2,6,5,1,4,7,3]=>[3,2,1,1]=>35
[2,6,5,1,7,3,4]=>[3,3,1]=>21
[2,6,5,1,7,4,3]=>[3,2,1,1]=>35
[2,6,5,3,1,4,7]=>[4,1,1,1]=>20
[2,6,5,3,1,7,4]=>[3,2,1,1]=>35
[2,6,5,3,4,1,7]=>[4,1,1,1]=>20
[2,6,5,3,4,7,1]=>[4,1,1,1]=>20
[2,6,5,3,7,1,4]=>[3,2,1,1]=>35
[2,6,5,3,7,4,1]=>[3,2,1,1]=>35
[2,6,5,4,1,3,7]=>[3,2,1,1]=>35
[2,6,5,4,1,7,3]=>[3,2,1,1]=>35
[2,6,5,4,3,1,7]=>[3,1,1,1,1]=>15
[2,6,5,4,3,7,1]=>[3,1,1,1,1]=>15
[2,6,5,4,7,1,3]=>[3,2,1,1]=>35
[2,6,5,4,7,3,1]=>[3,1,1,1,1]=>15
[2,6,5,7,1,3,4]=>[3,3,1]=>21
[2,6,5,7,1,4,3]=>[3,2,1,1]=>35
[2,6,5,7,3,1,4]=>[3,2,1,1]=>35
[2,6,5,7,3,4,1]=>[3,2,1,1]=>35
[2,6,5,7,4,1,3]=>[3,2,1,1]=>35
[2,6,5,7,4,3,1]=>[3,1,1,1,1]=>15
[2,6,7,1,3,4,5]=>[4,3]=>14
[2,6,7,1,3,5,4]=>[3,3,1]=>21
[2,6,7,1,4,3,5]=>[3,3,1]=>21
[2,6,7,1,4,5,3]=>[3,3,1]=>21
[2,6,7,1,5,3,4]=>[3,3,1]=>21
[2,6,7,1,5,4,3]=>[3,2,1,1]=>35
[2,6,7,3,1,4,5]=>[4,2,1]=>35
[2,6,7,3,1,5,4]=>[3,2,2]=>21
[2,6,7,3,4,1,5]=>[4,2,1]=>35
[2,6,7,3,4,5,1]=>[4,2,1]=>35
[2,6,7,3,5,1,4]=>[3,2,2]=>21
[2,6,7,3,5,4,1]=>[3,2,1,1]=>35
[2,6,7,4,1,3,5]=>[3,3,1]=>21
[2,6,7,4,1,5,3]=>[3,2,2]=>21
[2,6,7,4,3,1,5]=>[3,2,1,1]=>35
[2,6,7,4,3,5,1]=>[3,2,1,1]=>35
[2,6,7,4,5,1,3]=>[3,2,2]=>21
[2,6,7,4,5,3,1]=>[3,2,1,1]=>35
[2,6,7,5,1,3,4]=>[3,3,1]=>21
[2,6,7,5,1,4,3]=>[3,2,1,1]=>35
[2,6,7,5,3,1,4]=>[3,2,1,1]=>35
[2,6,7,5,3,4,1]=>[3,2,1,1]=>35
[2,6,7,5,4,1,3]=>[3,2,1,1]=>35
[2,6,7,5,4,3,1]=>[3,1,1,1,1]=>15
[2,7,1,3,4,5,6]=>[5,2]=>14
[2,7,1,3,4,6,5]=>[4,2,1]=>35
[2,7,1,3,5,4,6]=>[4,2,1]=>35
[2,7,1,3,5,6,4]=>[4,2,1]=>35
[2,7,1,3,6,4,5]=>[4,2,1]=>35
[2,7,1,3,6,5,4]=>[3,2,1,1]=>35
[2,7,1,4,3,5,6]=>[4,2,1]=>35
[2,7,1,4,3,6,5]=>[3,3,1]=>21
[2,7,1,4,5,3,6]=>[4,2,1]=>35
[2,7,1,4,5,6,3]=>[4,2,1]=>35
[2,7,1,4,6,3,5]=>[3,3,1]=>21
[2,7,1,4,6,5,3]=>[3,2,1,1]=>35
[2,7,1,5,3,4,6]=>[4,2,1]=>35
[2,7,1,5,3,6,4]=>[3,3,1]=>21
[2,7,1,5,4,3,6]=>[3,2,1,1]=>35
[2,7,1,5,4,6,3]=>[3,2,1,1]=>35
[2,7,1,5,6,3,4]=>[3,3,1]=>21
[2,7,1,5,6,4,3]=>[3,2,1,1]=>35
[2,7,1,6,3,4,5]=>[4,2,1]=>35
[2,7,1,6,3,5,4]=>[3,2,1,1]=>35
[2,7,1,6,4,3,5]=>[3,2,1,1]=>35
[2,7,1,6,4,5,3]=>[3,2,1,1]=>35
[2,7,1,6,5,3,4]=>[3,2,1,1]=>35
[2,7,1,6,5,4,3]=>[2,2,1,1,1]=>14
[2,7,3,1,4,5,6]=>[5,1,1]=>15
[2,7,3,1,4,6,5]=>[4,2,1]=>35
[2,7,3,1,5,4,6]=>[4,2,1]=>35
[2,7,3,1,5,6,4]=>[4,2,1]=>35
[2,7,3,1,6,4,5]=>[4,2,1]=>35
[2,7,3,1,6,5,4]=>[3,2,1,1]=>35
[2,7,3,4,1,5,6]=>[5,1,1]=>15
[2,7,3,4,1,6,5]=>[4,2,1]=>35
[2,7,3,4,5,1,6]=>[5,1,1]=>15
[2,7,3,4,5,6,1]=>[5,1,1]=>15
[2,7,3,4,6,1,5]=>[4,2,1]=>35
[2,7,3,4,6,5,1]=>[4,1,1,1]=>20
[2,7,3,5,1,4,6]=>[4,2,1]=>35
[2,7,3,5,1,6,4]=>[4,2,1]=>35
[2,7,3,5,4,1,6]=>[4,1,1,1]=>20
[2,7,3,5,4,6,1]=>[4,1,1,1]=>20
[2,7,3,5,6,1,4]=>[4,2,1]=>35
[2,7,3,5,6,4,1]=>[4,1,1,1]=>20
[2,7,3,6,1,4,5]=>[4,2,1]=>35
[2,7,3,6,1,5,4]=>[3,2,1,1]=>35
[2,7,3,6,4,1,5]=>[4,1,1,1]=>20
[2,7,3,6,4,5,1]=>[4,1,1,1]=>20
[2,7,3,6,5,1,4]=>[3,2,1,1]=>35
[2,7,3,6,5,4,1]=>[3,1,1,1,1]=>15
[2,7,4,1,3,5,6]=>[4,2,1]=>35
[2,7,4,1,3,6,5]=>[3,3,1]=>21
[2,7,4,1,5,3,6]=>[4,2,1]=>35
[2,7,4,1,5,6,3]=>[4,2,1]=>35
[2,7,4,1,6,3,5]=>[3,3,1]=>21
[2,7,4,1,6,5,3]=>[3,2,1,1]=>35
[2,7,4,3,1,5,6]=>[4,1,1,1]=>20
[2,7,4,3,1,6,5]=>[3,2,1,1]=>35
[2,7,4,3,5,1,6]=>[4,1,1,1]=>20
[2,7,4,3,5,6,1]=>[4,1,1,1]=>20
[2,7,4,3,6,1,5]=>[3,2,1,1]=>35
[2,7,4,3,6,5,1]=>[3,2,1,1]=>35
[2,7,4,5,1,3,6]=>[4,2,1]=>35
[2,7,4,5,1,6,3]=>[4,2,1]=>35
[2,7,4,5,3,1,6]=>[4,1,1,1]=>20
[2,7,4,5,3,6,1]=>[4,1,1,1]=>20
[2,7,4,5,6,1,3]=>[4,2,1]=>35
[2,7,4,5,6,3,1]=>[4,1,1,1]=>20
[2,7,4,6,1,3,5]=>[3,3,1]=>21
[2,7,4,6,1,5,3]=>[3,2,1,1]=>35
[2,7,4,6,3,1,5]=>[3,2,1,1]=>35
[2,7,4,6,3,5,1]=>[3,2,1,1]=>35
[2,7,4,6,5,1,3]=>[3,2,1,1]=>35
[2,7,4,6,5,3,1]=>[3,1,1,1,1]=>15
[2,7,5,1,3,4,6]=>[4,2,1]=>35
[2,7,5,1,3,6,4]=>[3,3,1]=>21
[2,7,5,1,4,3,6]=>[3,2,1,1]=>35
[2,7,5,1,4,6,3]=>[3,2,1,1]=>35
[2,7,5,1,6,3,4]=>[3,3,1]=>21
[2,7,5,1,6,4,3]=>[3,2,1,1]=>35
[2,7,5,3,1,4,6]=>[4,1,1,1]=>20
[2,7,5,3,1,6,4]=>[3,2,1,1]=>35
[2,7,5,3,4,1,6]=>[4,1,1,1]=>20
[2,7,5,3,4,6,1]=>[4,1,1,1]=>20
[2,7,5,3,6,1,4]=>[3,2,1,1]=>35
[2,7,5,3,6,4,1]=>[3,2,1,1]=>35
[2,7,5,4,1,3,6]=>[3,2,1,1]=>35
[2,7,5,4,1,6,3]=>[3,2,1,1]=>35
[2,7,5,4,3,1,6]=>[3,1,1,1,1]=>15
[2,7,5,4,3,6,1]=>[3,1,1,1,1]=>15
[2,7,5,4,6,1,3]=>[3,2,1,1]=>35
[2,7,5,4,6,3,1]=>[3,1,1,1,1]=>15
[2,7,5,6,1,3,4]=>[3,3,1]=>21
[2,7,5,6,1,4,3]=>[3,2,1,1]=>35
[2,7,5,6,3,1,4]=>[3,2,1,1]=>35
[2,7,5,6,3,4,1]=>[3,2,1,1]=>35
[2,7,5,6,4,1,3]=>[3,2,1,1]=>35
[2,7,5,6,4,3,1]=>[3,1,1,1,1]=>15
[2,7,6,1,3,4,5]=>[4,2,1]=>35
[2,7,6,1,3,5,4]=>[3,2,1,1]=>35
[2,7,6,1,4,3,5]=>[3,2,1,1]=>35
[2,7,6,1,4,5,3]=>[3,2,1,1]=>35
[2,7,6,1,5,3,4]=>[3,2,1,1]=>35
[2,7,6,1,5,4,3]=>[2,2,1,1,1]=>14
[2,7,6,3,1,4,5]=>[4,1,1,1]=>20
[2,7,6,3,1,5,4]=>[3,2,1,1]=>35
[2,7,6,3,4,1,5]=>[4,1,1,1]=>20
[2,7,6,3,4,5,1]=>[4,1,1,1]=>20
[2,7,6,3,5,1,4]=>[3,2,1,1]=>35
[2,7,6,3,5,4,1]=>[3,1,1,1,1]=>15
[2,7,6,4,1,3,5]=>[3,2,1,1]=>35
[2,7,6,4,1,5,3]=>[3,2,1,1]=>35
[2,7,6,4,3,1,5]=>[3,1,1,1,1]=>15
[2,7,6,4,3,5,1]=>[3,1,1,1,1]=>15
[2,7,6,4,5,1,3]=>[3,2,1,1]=>35
[2,7,6,4,5,3,1]=>[3,1,1,1,1]=>15
[2,7,6,5,1,3,4]=>[3,2,1,1]=>35
[2,7,6,5,1,4,3]=>[2,2,1,1,1]=>14
[2,7,6,5,3,1,4]=>[3,1,1,1,1]=>15
[2,7,6,5,3,4,1]=>[3,1,1,1,1]=>15
[2,7,6,5,4,1,3]=>[2,2,1,1,1]=>14
[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]=>6
[3,1,2,4,5,6,7]=>[6,1]=>6
[3,1,2,4,5,7,6]=>[5,2]=>14
[3,1,2,4,6,5,7]=>[5,2]=>14
[3,1,2,4,6,7,5]=>[5,2]=>14
[3,1,2,4,7,5,6]=>[5,2]=>14
[3,1,2,4,7,6,5]=>[4,2,1]=>35
[3,1,2,5,4,6,7]=>[5,2]=>14
[3,1,2,5,4,7,6]=>[4,3]=>14
[3,1,2,5,6,4,7]=>[5,2]=>14
[3,1,2,5,6,7,4]=>[5,2]=>14
[3,1,2,5,7,4,6]=>[4,3]=>14
[3,1,2,5,7,6,4]=>[4,2,1]=>35
[3,1,2,6,4,5,7]=>[5,2]=>14
[3,1,2,6,4,7,5]=>[4,3]=>14
[3,1,2,6,5,4,7]=>[4,2,1]=>35
[3,1,2,6,5,7,4]=>[4,2,1]=>35
[3,1,2,6,7,4,5]=>[4,3]=>14
[3,1,2,6,7,5,4]=>[4,2,1]=>35
[3,1,2,7,4,5,6]=>[5,2]=>14
[3,1,2,7,4,6,5]=>[4,2,1]=>35
[3,1,2,7,5,4,6]=>[4,2,1]=>35
[3,1,2,7,5,6,4]=>[4,2,1]=>35
[3,1,2,7,6,4,5]=>[4,2,1]=>35
[3,1,2,7,6,5,4]=>[3,2,1,1]=>35
[3,1,4,2,5,6,7]=>[5,2]=>14
[3,1,4,2,5,7,6]=>[4,3]=>14
[3,1,4,2,6,5,7]=>[4,3]=>14
[3,1,4,2,6,7,5]=>[4,3]=>14
[3,1,4,2,7,5,6]=>[4,3]=>14
[3,1,4,2,7,6,5]=>[3,3,1]=>21
[3,1,4,5,2,6,7]=>[5,2]=>14
[3,1,4,5,2,7,6]=>[4,3]=>14
[3,1,4,5,6,2,7]=>[5,2]=>14
[3,1,4,5,6,7,2]=>[5,2]=>14
[3,1,4,5,7,2,6]=>[4,3]=>14
[3,1,4,5,7,6,2]=>[4,2,1]=>35
[3,1,4,6,2,5,7]=>[4,3]=>14
[3,1,4,6,2,7,5]=>[4,3]=>14
[3,1,4,6,5,2,7]=>[4,2,1]=>35
[3,1,4,6,5,7,2]=>[4,2,1]=>35
[3,1,4,6,7,2,5]=>[4,3]=>14
[3,1,4,6,7,5,2]=>[4,2,1]=>35
[3,1,4,7,2,5,6]=>[4,3]=>14
[3,1,4,7,2,6,5]=>[3,3,1]=>21
[3,1,4,7,5,2,6]=>[4,2,1]=>35
[3,1,4,7,5,6,2]=>[4,2,1]=>35
[3,1,4,7,6,2,5]=>[3,3,1]=>21
[3,1,4,7,6,5,2]=>[3,2,1,1]=>35
[3,1,5,2,4,6,7]=>[5,2]=>14
[3,1,5,2,4,7,6]=>[4,3]=>14
[3,1,5,2,6,4,7]=>[4,3]=>14
[3,1,5,2,6,7,4]=>[4,3]=>14
[3,1,5,2,7,4,6]=>[4,3]=>14
[3,1,5,2,7,6,4]=>[3,3,1]=>21
[3,1,5,4,2,6,7]=>[4,2,1]=>35
[3,1,5,4,2,7,6]=>[3,3,1]=>21
[3,1,5,4,6,2,7]=>[4,2,1]=>35
[3,1,5,4,6,7,2]=>[4,2,1]=>35
[3,1,5,4,7,2,6]=>[3,3,1]=>21
[3,1,5,4,7,6,2]=>[3,3,1]=>21
[3,1,5,6,2,4,7]=>[4,3]=>14
[3,1,5,6,2,7,4]=>[4,3]=>14
[3,1,5,6,4,2,7]=>[4,2,1]=>35
[3,1,5,6,4,7,2]=>[4,2,1]=>35
[3,1,5,6,7,2,4]=>[4,3]=>14
[3,1,5,6,7,4,2]=>[4,2,1]=>35
[3,1,5,7,2,4,6]=>[4,3]=>14
[3,1,5,7,2,6,4]=>[3,3,1]=>21
[3,1,5,7,4,2,6]=>[3,3,1]=>21
[3,1,5,7,4,6,2]=>[3,3,1]=>21
[3,1,5,7,6,2,4]=>[3,3,1]=>21
[3,1,5,7,6,4,2]=>[3,2,1,1]=>35
[3,1,6,2,4,5,7]=>[5,2]=>14
[3,1,6,2,4,7,5]=>[4,3]=>14
[3,1,6,2,5,4,7]=>[4,2,1]=>35
[3,1,6,2,5,7,4]=>[4,2,1]=>35
[3,1,6,2,7,4,5]=>[4,3]=>14
[3,1,6,2,7,5,4]=>[3,3,1]=>21
[3,1,6,4,2,5,7]=>[4,2,1]=>35
[3,1,6,4,2,7,5]=>[3,3,1]=>21
[3,1,6,4,5,2,7]=>[4,2,1]=>35
[3,1,6,4,5,7,2]=>[4,2,1]=>35
[3,1,6,4,7,2,5]=>[3,3,1]=>21
[3,1,6,4,7,5,2]=>[3,3,1]=>21
[3,1,6,5,2,4,7]=>[4,2,1]=>35
[3,1,6,5,2,7,4]=>[3,3,1]=>21
[3,1,6,5,4,2,7]=>[3,2,1,1]=>35
[3,1,6,5,4,7,2]=>[3,2,1,1]=>35
[3,1,6,5,7,2,4]=>[3,3,1]=>21
[3,1,6,5,7,4,2]=>[3,2,1,1]=>35
[3,1,6,7,2,4,5]=>[4,3]=>14
[3,1,6,7,2,5,4]=>[3,3,1]=>21
[3,1,6,7,4,2,5]=>[3,3,1]=>21
[3,1,6,7,4,5,2]=>[3,3,1]=>21
[3,1,6,7,5,2,4]=>[3,3,1]=>21
[3,1,6,7,5,4,2]=>[3,2,1,1]=>35
[3,1,7,2,4,5,6]=>[5,2]=>14
[3,1,7,2,4,6,5]=>[4,2,1]=>35
[3,1,7,2,5,4,6]=>[4,2,1]=>35
[3,1,7,2,5,6,4]=>[4,2,1]=>35
[3,1,7,2,6,4,5]=>[4,2,1]=>35
[3,1,7,2,6,5,4]=>[3,2,1,1]=>35
[3,1,7,4,2,5,6]=>[4,2,1]=>35
[3,1,7,4,2,6,5]=>[3,3,1]=>21
[3,1,7,4,5,2,6]=>[4,2,1]=>35
[3,1,7,4,5,6,2]=>[4,2,1]=>35
[3,1,7,4,6,2,5]=>[3,3,1]=>21
[3,1,7,4,6,5,2]=>[3,2,1,1]=>35
[3,1,7,5,2,4,6]=>[4,2,1]=>35
[3,1,7,5,2,6,4]=>[3,3,1]=>21
[3,1,7,5,4,2,6]=>[3,2,1,1]=>35
[3,1,7,5,4,6,2]=>[3,2,1,1]=>35
[3,1,7,5,6,2,4]=>[3,3,1]=>21
[3,1,7,5,6,4,2]=>[3,2,1,1]=>35
[3,1,7,6,2,4,5]=>[4,2,1]=>35
[3,1,7,6,2,5,4]=>[3,2,1,1]=>35
[3,1,7,6,4,2,5]=>[3,2,1,1]=>35
[3,1,7,6,4,5,2]=>[3,2,1,1]=>35
[3,1,7,6,5,2,4]=>[3,2,1,1]=>35
[3,1,7,6,5,4,2]=>[2,2,1,1,1]=>14
[3,2,1,4,5,6,7]=>[5,1,1]=>15
[3,2,1,4,5,7,6]=>[4,2,1]=>35
[3,2,1,4,6,5,7]=>[4,2,1]=>35
[3,2,1,4,6,7,5]=>[4,2,1]=>35
[3,2,1,4,7,5,6]=>[4,2,1]=>35
[3,2,1,4,7,6,5]=>[3,2,2]=>21
[3,2,1,5,4,6,7]=>[4,2,1]=>35
[3,2,1,5,4,7,6]=>[3,3,1]=>21
[3,2,1,5,6,4,7]=>[4,2,1]=>35
[3,2,1,5,6,7,4]=>[4,2,1]=>35
[3,2,1,5,7,4,6]=>[3,3,1]=>21
[3,2,1,5,7,6,4]=>[3,2,2]=>21
[3,2,1,6,4,5,7]=>[4,2,1]=>35
[3,2,1,6,4,7,5]=>[3,3,1]=>21
[3,2,1,6,5,4,7]=>[3,2,2]=>21
[3,2,1,6,5,7,4]=>[3,2,2]=>21
[3,2,1,6,7,4,5]=>[3,3,1]=>21
[3,2,1,6,7,5,4]=>[3,2,2]=>21
[3,2,1,7,4,5,6]=>[4,2,1]=>35
[3,2,1,7,4,6,5]=>[3,2,2]=>21
[3,2,1,7,5,4,6]=>[3,2,2]=>21
[3,2,1,7,5,6,4]=>[3,2,2]=>21
[3,2,1,7,6,4,5]=>[3,2,2]=>21
[3,2,1,7,6,5,4]=>[2,2,2,1]=>14
[3,2,4,1,5,6,7]=>[5,1,1]=>15
[3,2,4,1,5,7,6]=>[4,2,1]=>35
[3,2,4,1,6,5,7]=>[4,2,1]=>35
[3,2,4,1,6,7,5]=>[4,2,1]=>35
[3,2,4,1,7,5,6]=>[4,2,1]=>35
[3,2,4,1,7,6,5]=>[3,2,2]=>21
[3,2,4,5,1,6,7]=>[5,1,1]=>15
[3,2,4,5,1,7,6]=>[4,2,1]=>35
[3,2,4,5,6,1,7]=>[5,1,1]=>15
[3,2,4,5,6,7,1]=>[5,1,1]=>15
[3,2,4,5,7,1,6]=>[4,2,1]=>35
[3,2,4,5,7,6,1]=>[4,2,1]=>35
[3,2,4,6,1,5,7]=>[4,2,1]=>35
[3,2,4,6,1,7,5]=>[4,2,1]=>35
[3,2,4,6,5,1,7]=>[4,2,1]=>35
[3,2,4,6,5,7,1]=>[4,2,1]=>35
[3,2,4,6,7,1,5]=>[4,2,1]=>35
[3,2,4,6,7,5,1]=>[4,2,1]=>35
[3,2,4,7,1,5,6]=>[4,2,1]=>35
[3,2,4,7,1,6,5]=>[3,2,2]=>21
[3,2,4,7,5,1,6]=>[4,2,1]=>35
[3,2,4,7,5,6,1]=>[4,2,1]=>35
[3,2,4,7,6,1,5]=>[3,2,2]=>21
[3,2,4,7,6,5,1]=>[3,2,1,1]=>35
[3,2,5,1,4,6,7]=>[4,2,1]=>35
[3,2,5,1,4,7,6]=>[3,3,1]=>21
[3,2,5,1,6,4,7]=>[4,2,1]=>35
[3,2,5,1,6,7,4]=>[4,2,1]=>35
[3,2,5,1,7,4,6]=>[3,3,1]=>21
[3,2,5,1,7,6,4]=>[3,2,2]=>21
[3,2,5,4,1,6,7]=>[4,2,1]=>35
[3,2,5,4,1,7,6]=>[3,3,1]=>21
[3,2,5,4,6,1,7]=>[4,2,1]=>35
[3,2,5,4,6,7,1]=>[4,2,1]=>35
[3,2,5,4,7,1,6]=>[3,3,1]=>21
[3,2,5,4,7,6,1]=>[3,3,1]=>21
[3,2,5,6,1,4,7]=>[4,2,1]=>35
[3,2,5,6,1,7,4]=>[4,2,1]=>35
[3,2,5,6,4,1,7]=>[4,2,1]=>35
[3,2,5,6,4,7,1]=>[4,2,1]=>35
[3,2,5,6,7,1,4]=>[4,2,1]=>35
[3,2,5,6,7,4,1]=>[4,2,1]=>35
[3,2,5,7,1,4,6]=>[3,3,1]=>21
[3,2,5,7,1,6,4]=>[3,2,2]=>21
[3,2,5,7,4,1,6]=>[3,3,1]=>21
[3,2,5,7,4,6,1]=>[3,3,1]=>21
[3,2,5,7,6,1,4]=>[3,2,2]=>21
[3,2,5,7,6,4,1]=>[3,2,1,1]=>35
[3,2,6,1,4,5,7]=>[4,2,1]=>35
[3,2,6,1,4,7,5]=>[3,3,1]=>21
[3,2,6,1,5,4,7]=>[3,2,2]=>21
[3,2,6,1,5,7,4]=>[3,2,2]=>21
[3,2,6,1,7,4,5]=>[3,3,1]=>21
[3,2,6,1,7,5,4]=>[3,2,2]=>21
[3,2,6,4,1,5,7]=>[4,2,1]=>35
[3,2,6,4,1,7,5]=>[3,3,1]=>21
[3,2,6,4,5,1,7]=>[4,2,1]=>35
[3,2,6,4,5,7,1]=>[4,2,1]=>35
[3,2,6,4,7,1,5]=>[3,3,1]=>21
[3,2,6,4,7,5,1]=>[3,3,1]=>21
[3,2,6,5,1,4,7]=>[3,2,2]=>21
[3,2,6,5,1,7,4]=>[3,2,2]=>21
[3,2,6,5,4,1,7]=>[3,2,1,1]=>35
[3,2,6,5,4,7,1]=>[3,2,1,1]=>35
[3,2,6,5,7,1,4]=>[3,2,2]=>21
[3,2,6,5,7,4,1]=>[3,2,1,1]=>35
[3,2,6,7,1,4,5]=>[3,3,1]=>21
[3,2,6,7,1,5,4]=>[3,2,2]=>21
[3,2,6,7,4,1,5]=>[3,3,1]=>21
[3,2,6,7,4,5,1]=>[3,3,1]=>21
[3,2,6,7,5,1,4]=>[3,2,2]=>21
[3,2,6,7,5,4,1]=>[3,2,1,1]=>35
[3,2,7,1,4,5,6]=>[4,2,1]=>35
[3,2,7,1,4,6,5]=>[3,2,2]=>21
[3,2,7,1,5,4,6]=>[3,2,2]=>21
[3,2,7,1,5,6,4]=>[3,2,2]=>21
[3,2,7,1,6,4,5]=>[3,2,2]=>21
[3,2,7,1,6,5,4]=>[2,2,2,1]=>14
[3,2,7,4,1,5,6]=>[4,2,1]=>35
[3,2,7,4,1,6,5]=>[3,2,2]=>21
[3,2,7,4,5,1,6]=>[4,2,1]=>35
[3,2,7,4,5,6,1]=>[4,2,1]=>35
[3,2,7,4,6,1,5]=>[3,2,2]=>21
[3,2,7,4,6,5,1]=>[3,2,1,1]=>35
[3,2,7,5,1,4,6]=>[3,2,2]=>21
[3,2,7,5,1,6,4]=>[3,2,2]=>21
[3,2,7,5,4,1,6]=>[3,2,1,1]=>35
[3,2,7,5,4,6,1]=>[3,2,1,1]=>35
[3,2,7,5,6,1,4]=>[3,2,2]=>21
[3,2,7,5,6,4,1]=>[3,2,1,1]=>35
[3,2,7,6,1,4,5]=>[3,2,2]=>21
[3,2,7,6,1,5,4]=>[2,2,2,1]=>14
[3,2,7,6,4,1,5]=>[3,2,1,1]=>35
[3,2,7,6,4,5,1]=>[3,2,1,1]=>35
[3,2,7,6,5,1,4]=>[2,2,2,1]=>14
[3,2,7,6,5,4,1]=>[2,2,1,1,1]=>14
[3,4,1,2,5,6,7]=>[5,2]=>14
[3,4,1,2,5,7,6]=>[4,3]=>14
[3,4,1,2,6,5,7]=>[4,3]=>14
[3,4,1,2,6,7,5]=>[4,3]=>14
[3,4,1,2,7,5,6]=>[4,3]=>14
[3,4,1,2,7,6,5]=>[3,3,1]=>21
[3,4,1,5,2,6,7]=>[5,2]=>14
[3,4,1,5,2,7,6]=>[4,3]=>14
[3,4,1,5,6,2,7]=>[5,2]=>14
[3,4,1,5,6,7,2]=>[5,2]=>14
[3,4,1,5,7,2,6]=>[4,3]=>14
[3,4,1,5,7,6,2]=>[4,2,1]=>35
[3,4,1,6,2,5,7]=>[4,3]=>14
[3,4,1,6,2,7,5]=>[4,3]=>14
[3,4,1,6,5,2,7]=>[4,2,1]=>35
[3,4,1,6,5,7,2]=>[4,2,1]=>35
[3,4,1,6,7,2,5]=>[4,3]=>14
[3,4,1,6,7,5,2]=>[4,2,1]=>35
[3,4,1,7,2,5,6]=>[4,3]=>14
[3,4,1,7,2,6,5]=>[3,3,1]=>21
[3,4,1,7,5,2,6]=>[4,2,1]=>35
[3,4,1,7,5,6,2]=>[4,2,1]=>35
[3,4,1,7,6,2,5]=>[3,3,1]=>21
[3,4,1,7,6,5,2]=>[3,2,1,1]=>35
[3,4,2,1,5,6,7]=>[5,1,1]=>15
[3,4,2,1,5,7,6]=>[4,2,1]=>35
[3,4,2,1,6,5,7]=>[4,2,1]=>35
[3,4,2,1,6,7,5]=>[4,2,1]=>35
[3,4,2,1,7,5,6]=>[4,2,1]=>35
[3,4,2,1,7,6,5]=>[3,2,2]=>21
[3,4,2,5,1,6,7]=>[5,1,1]=>15
[3,4,2,5,1,7,6]=>[4,2,1]=>35
[3,4,2,5,6,1,7]=>[5,1,1]=>15
[3,4,2,5,6,7,1]=>[5,1,1]=>15
[3,4,2,5,7,1,6]=>[4,2,1]=>35
[3,4,2,5,7,6,1]=>[4,2,1]=>35
[3,4,2,6,1,5,7]=>[4,2,1]=>35
[3,4,2,6,1,7,5]=>[4,2,1]=>35
[3,4,2,6,5,1,7]=>[4,2,1]=>35
[3,4,2,6,5,7,1]=>[4,2,1]=>35
[3,4,2,6,7,1,5]=>[4,2,1]=>35
[3,4,2,6,7,5,1]=>[4,2,1]=>35
[3,4,2,7,1,5,6]=>[4,2,1]=>35
[3,4,2,7,1,6,5]=>[3,2,2]=>21
[3,4,2,7,5,1,6]=>[4,2,1]=>35
[3,4,2,7,5,6,1]=>[4,2,1]=>35
[3,4,2,7,6,1,5]=>[3,2,2]=>21
[3,4,2,7,6,5,1]=>[3,2,1,1]=>35
[3,4,5,1,2,6,7]=>[5,2]=>14
[3,4,5,1,2,7,6]=>[4,3]=>14
[3,4,5,1,6,2,7]=>[5,2]=>14
[3,4,5,1,6,7,2]=>[5,2]=>14
[3,4,5,1,7,2,6]=>[4,3]=>14
[3,4,5,1,7,6,2]=>[4,2,1]=>35
[3,4,5,2,1,6,7]=>[5,1,1]=>15
[3,4,5,2,1,7,6]=>[4,2,1]=>35
[3,4,5,2,6,1,7]=>[5,1,1]=>15
[3,4,5,2,6,7,1]=>[5,1,1]=>15
[3,4,5,2,7,1,6]=>[4,2,1]=>35
[3,4,5,2,7,6,1]=>[4,2,1]=>35
[3,4,5,6,1,2,7]=>[5,2]=>14
[3,4,5,6,1,7,2]=>[5,2]=>14
[3,4,5,6,2,1,7]=>[5,1,1]=>15
[3,4,5,6,2,7,1]=>[5,1,1]=>15
[3,4,5,6,7,1,2]=>[5,2]=>14
[3,4,5,6,7,2,1]=>[5,1,1]=>15
[3,4,5,7,1,2,6]=>[4,3]=>14
[3,4,5,7,1,6,2]=>[4,2,1]=>35
[3,4,5,7,2,1,6]=>[4,2,1]=>35
[3,4,5,7,2,6,1]=>[4,2,1]=>35
[3,4,5,7,6,1,2]=>[4,2,1]=>35
[3,4,5,7,6,2,1]=>[4,1,1,1]=>20
[3,4,6,1,2,5,7]=>[4,3]=>14
[3,4,6,1,2,7,5]=>[4,3]=>14
[3,4,6,1,5,2,7]=>[4,2,1]=>35
[3,4,6,1,5,7,2]=>[4,2,1]=>35
[3,4,6,1,7,2,5]=>[4,3]=>14
[3,4,6,1,7,5,2]=>[4,2,1]=>35
[3,4,6,2,1,5,7]=>[4,2,1]=>35
[3,4,6,2,1,7,5]=>[4,2,1]=>35
[3,4,6,2,5,1,7]=>[4,2,1]=>35
[3,4,6,2,5,7,1]=>[4,2,1]=>35
[3,4,6,2,7,1,5]=>[4,2,1]=>35
[3,4,6,2,7,5,1]=>[4,2,1]=>35
[3,4,6,5,1,2,7]=>[4,2,1]=>35
[3,4,6,5,1,7,2]=>[4,2,1]=>35
[3,4,6,5,2,1,7]=>[4,1,1,1]=>20
[3,4,6,5,2,7,1]=>[4,1,1,1]=>20
[3,4,6,5,7,1,2]=>[4,2,1]=>35
[3,4,6,5,7,2,1]=>[4,1,1,1]=>20
[3,4,6,7,1,2,5]=>[4,3]=>14
[3,4,6,7,1,5,2]=>[4,2,1]=>35
[3,4,6,7,2,1,5]=>[4,2,1]=>35
[3,4,6,7,2,5,1]=>[4,2,1]=>35
[3,4,6,7,5,1,2]=>[4,2,1]=>35
[3,4,6,7,5,2,1]=>[4,1,1,1]=>20
[3,4,7,1,2,5,6]=>[4,3]=>14
[3,4,7,1,2,6,5]=>[3,3,1]=>21
[3,4,7,1,5,2,6]=>[4,2,1]=>35
[3,4,7,1,5,6,2]=>[4,2,1]=>35
[3,4,7,1,6,2,5]=>[3,3,1]=>21
[3,4,7,1,6,5,2]=>[3,2,1,1]=>35
[3,4,7,2,1,5,6]=>[4,2,1]=>35
[3,4,7,2,1,6,5]=>[3,2,2]=>21
[3,4,7,2,5,1,6]=>[4,2,1]=>35
[3,4,7,2,5,6,1]=>[4,2,1]=>35
[3,4,7,2,6,1,5]=>[3,2,2]=>21
[3,4,7,2,6,5,1]=>[3,2,1,1]=>35
[3,4,7,5,1,2,6]=>[4,2,1]=>35
[3,4,7,5,1,6,2]=>[4,2,1]=>35
[3,4,7,5,2,1,6]=>[4,1,1,1]=>20
[3,4,7,5,2,6,1]=>[4,1,1,1]=>20
[3,4,7,5,6,1,2]=>[4,2,1]=>35
[3,4,7,5,6,2,1]=>[4,1,1,1]=>20
[3,4,7,6,1,2,5]=>[3,3,1]=>21
[3,4,7,6,1,5,2]=>[3,2,1,1]=>35
[3,4,7,6,2,1,5]=>[3,2,1,1]=>35
[3,4,7,6,2,5,1]=>[3,2,1,1]=>35
[3,4,7,6,5,1,2]=>[3,2,1,1]=>35
[3,4,7,6,5,2,1]=>[3,1,1,1,1]=>15
[3,5,1,2,4,6,7]=>[5,2]=>14
[3,5,1,2,4,7,6]=>[4,3]=>14
[3,5,1,2,6,4,7]=>[4,3]=>14
[3,5,1,2,6,7,4]=>[4,3]=>14
[3,5,1,2,7,4,6]=>[4,3]=>14
[3,5,1,2,7,6,4]=>[3,3,1]=>21
[3,5,1,4,2,6,7]=>[4,2,1]=>35
[3,5,1,4,2,7,6]=>[3,3,1]=>21
[3,5,1,4,6,2,7]=>[4,2,1]=>35
[3,5,1,4,6,7,2]=>[4,2,1]=>35
[3,5,1,4,7,2,6]=>[3,3,1]=>21
[3,5,1,4,7,6,2]=>[3,3,1]=>21
[3,5,1,6,2,4,7]=>[4,3]=>14
[3,5,1,6,2,7,4]=>[4,3]=>14
[3,5,1,6,4,2,7]=>[4,2,1]=>35
[3,5,1,6,4,7,2]=>[4,2,1]=>35
[3,5,1,6,7,2,4]=>[4,3]=>14
[3,5,1,6,7,4,2]=>[4,2,1]=>35
[3,5,1,7,2,4,6]=>[4,3]=>14
[3,5,1,7,2,6,4]=>[3,3,1]=>21
[3,5,1,7,4,2,6]=>[3,3,1]=>21
[3,5,1,7,4,6,2]=>[3,3,1]=>21
[3,5,1,7,6,2,4]=>[3,3,1]=>21
[3,5,1,7,6,4,2]=>[3,2,1,1]=>35
[3,5,2,1,4,6,7]=>[4,2,1]=>35
[3,5,2,1,4,7,6]=>[3,3,1]=>21
[3,5,2,1,6,4,7]=>[4,2,1]=>35
[3,5,2,1,6,7,4]=>[4,2,1]=>35
[3,5,2,1,7,4,6]=>[3,3,1]=>21
[3,5,2,1,7,6,4]=>[3,2,2]=>21
[3,5,2,4,1,6,7]=>[4,2,1]=>35
[3,5,2,4,1,7,6]=>[3,3,1]=>21
[3,5,2,4,6,1,7]=>[4,2,1]=>35
[3,5,2,4,6,7,1]=>[4,2,1]=>35
[3,5,2,4,7,1,6]=>[3,3,1]=>21
[3,5,2,4,7,6,1]=>[3,3,1]=>21
[3,5,2,6,1,4,7]=>[4,2,1]=>35
[3,5,2,6,1,7,4]=>[4,2,1]=>35
[3,5,2,6,4,1,7]=>[4,2,1]=>35
[3,5,2,6,4,7,1]=>[4,2,1]=>35
[3,5,2,6,7,1,4]=>[4,2,1]=>35
[3,5,2,6,7,4,1]=>[4,2,1]=>35
[3,5,2,7,1,4,6]=>[3,3,1]=>21
[3,5,2,7,1,6,4]=>[3,2,2]=>21
[3,5,2,7,4,1,6]=>[3,3,1]=>21
[3,5,2,7,4,6,1]=>[3,3,1]=>21
[3,5,2,7,6,1,4]=>[3,2,2]=>21
[3,5,2,7,6,4,1]=>[3,2,1,1]=>35
[3,5,4,1,2,6,7]=>[4,2,1]=>35
[3,5,4,1,2,7,6]=>[3,3,1]=>21
[3,5,4,1,6,2,7]=>[4,2,1]=>35
[3,5,4,1,6,7,2]=>[4,2,1]=>35
[3,5,4,1,7,2,6]=>[3,3,1]=>21
[3,5,4,1,7,6,2]=>[3,2,2]=>21
[3,5,4,2,1,6,7]=>[4,1,1,1]=>20
[3,5,4,2,1,7,6]=>[3,2,1,1]=>35
[3,5,4,2,6,1,7]=>[4,1,1,1]=>20
[3,5,4,2,6,7,1]=>[4,1,1,1]=>20
[3,5,4,2,7,1,6]=>[3,2,1,1]=>35
[3,5,4,2,7,6,1]=>[3,2,1,1]=>35
[3,5,4,6,1,2,7]=>[4,2,1]=>35
[3,5,4,6,1,7,2]=>[4,2,1]=>35
[3,5,4,6,2,1,7]=>[4,1,1,1]=>20
[3,5,4,6,2,7,1]=>[4,1,1,1]=>20
[3,5,4,6,7,1,2]=>[4,2,1]=>35
[3,5,4,6,7,2,1]=>[4,1,1,1]=>20
[3,5,4,7,1,2,6]=>[3,3,1]=>21
[3,5,4,7,1,6,2]=>[3,2,2]=>21
[3,5,4,7,2,1,6]=>[3,2,1,1]=>35
[3,5,4,7,2,6,1]=>[3,2,1,1]=>35
[3,5,4,7,6,1,2]=>[3,2,2]=>21
[3,5,4,7,6,2,1]=>[3,2,1,1]=>35
[3,5,6,1,2,4,7]=>[4,3]=>14
[3,5,6,1,2,7,4]=>[4,3]=>14
[3,5,6,1,4,2,7]=>[4,2,1]=>35
[3,5,6,1,4,7,2]=>[4,2,1]=>35
[3,5,6,1,7,2,4]=>[4,3]=>14
[3,5,6,1,7,4,2]=>[4,2,1]=>35
[3,5,6,2,1,4,7]=>[4,2,1]=>35
[3,5,6,2,1,7,4]=>[4,2,1]=>35
[3,5,6,2,4,1,7]=>[4,2,1]=>35
[3,5,6,2,4,7,1]=>[4,2,1]=>35
[3,5,6,2,7,1,4]=>[4,2,1]=>35
[3,5,6,2,7,4,1]=>[4,2,1]=>35
[3,5,6,4,1,2,7]=>[4,2,1]=>35
[3,5,6,4,1,7,2]=>[4,2,1]=>35
[3,5,6,4,2,1,7]=>[4,1,1,1]=>20
[3,5,6,4,2,7,1]=>[4,1,1,1]=>20
[3,5,6,4,7,1,2]=>[4,2,1]=>35
[3,5,6,4,7,2,1]=>[4,1,1,1]=>20
[3,5,6,7,1,2,4]=>[4,3]=>14
[3,5,6,7,1,4,2]=>[4,2,1]=>35
[3,5,6,7,2,1,4]=>[4,2,1]=>35
[3,5,6,7,2,4,1]=>[4,2,1]=>35
[3,5,6,7,4,1,2]=>[4,2,1]=>35
[3,5,6,7,4,2,1]=>[4,1,1,1]=>20
[3,5,7,1,2,4,6]=>[4,3]=>14
[3,5,7,1,2,6,4]=>[3,3,1]=>21
[3,5,7,1,4,2,6]=>[3,3,1]=>21
[3,5,7,1,4,6,2]=>[3,3,1]=>21
[3,5,7,1,6,2,4]=>[3,3,1]=>21
[3,5,7,1,6,4,2]=>[3,2,1,1]=>35
[3,5,7,2,1,4,6]=>[3,3,1]=>21
[3,5,7,2,1,6,4]=>[3,2,2]=>21
[3,5,7,2,4,1,6]=>[3,3,1]=>21
[3,5,7,2,4,6,1]=>[3,3,1]=>21
[3,5,7,2,6,1,4]=>[3,2,2]=>21
[3,5,7,2,6,4,1]=>[3,2,1,1]=>35
[3,5,7,4,1,2,6]=>[3,3,1]=>21
[3,5,7,4,1,6,2]=>[3,2,2]=>21
[3,5,7,4,2,1,6]=>[3,2,1,1]=>35
[3,5,7,4,2,6,1]=>[3,2,1,1]=>35
[3,5,7,4,6,1,2]=>[3,2,2]=>21
[3,5,7,4,6,2,1]=>[3,2,1,1]=>35
[3,5,7,6,1,2,4]=>[3,3,1]=>21
[3,5,7,6,1,4,2]=>[3,2,1,1]=>35
[3,5,7,6,2,1,4]=>[3,2,1,1]=>35
[3,5,7,6,2,4,1]=>[3,2,1,1]=>35
[3,5,7,6,4,1,2]=>[3,2,1,1]=>35
[3,5,7,6,4,2,1]=>[3,1,1,1,1]=>15
[3,6,1,2,4,5,7]=>[5,2]=>14
[3,6,1,2,4,7,5]=>[4,3]=>14
[3,6,1,2,5,4,7]=>[4,2,1]=>35
[3,6,1,2,5,7,4]=>[4,2,1]=>35
[3,6,1,2,7,4,5]=>[4,3]=>14
[3,6,1,2,7,5,4]=>[3,3,1]=>21
[3,6,1,4,2,5,7]=>[4,2,1]=>35
[3,6,1,4,2,7,5]=>[3,3,1]=>21
[3,6,1,4,5,2,7]=>[4,2,1]=>35
[3,6,1,4,5,7,2]=>[4,2,1]=>35
[3,6,1,4,7,2,5]=>[3,3,1]=>21
[3,6,1,4,7,5,2]=>[3,3,1]=>21
[3,6,1,5,2,4,7]=>[4,2,1]=>35
[3,6,1,5,2,7,4]=>[3,3,1]=>21
[3,6,1,5,4,2,7]=>[3,2,1,1]=>35
[3,6,1,5,4,7,2]=>[3,2,1,1]=>35
[3,6,1,5,7,2,4]=>[3,3,1]=>21
[3,6,1,5,7,4,2]=>[3,2,1,1]=>35
[3,6,1,7,2,4,5]=>[4,3]=>14
[3,6,1,7,2,5,4]=>[3,3,1]=>21
[3,6,1,7,4,2,5]=>[3,3,1]=>21
[3,6,1,7,4,5,2]=>[3,3,1]=>21
[3,6,1,7,5,2,4]=>[3,3,1]=>21
[3,6,1,7,5,4,2]=>[3,2,1,1]=>35
[3,6,2,1,4,5,7]=>[4,2,1]=>35
[3,6,2,1,4,7,5]=>[3,3,1]=>21
[3,6,2,1,5,4,7]=>[3,2,2]=>21
[3,6,2,1,5,7,4]=>[3,2,2]=>21
[3,6,2,1,7,4,5]=>[3,3,1]=>21
[3,6,2,1,7,5,4]=>[3,2,2]=>21
[3,6,2,4,1,5,7]=>[4,2,1]=>35
[3,6,2,4,1,7,5]=>[3,3,1]=>21
[3,6,2,4,5,1,7]=>[4,2,1]=>35
[3,6,2,4,5,7,1]=>[4,2,1]=>35
[3,6,2,4,7,1,5]=>[3,3,1]=>21
[3,6,2,4,7,5,1]=>[3,3,1]=>21
[3,6,2,5,1,4,7]=>[3,2,2]=>21
[3,6,2,5,1,7,4]=>[3,2,2]=>21
[3,6,2,5,4,1,7]=>[3,2,1,1]=>35
[3,6,2,5,4,7,1]=>[3,2,1,1]=>35
[3,6,2,5,7,1,4]=>[3,2,2]=>21
[3,6,2,5,7,4,1]=>[3,2,1,1]=>35
[3,6,2,7,1,4,5]=>[3,3,1]=>21
[3,6,2,7,1,5,4]=>[3,2,2]=>21
[3,6,2,7,4,1,5]=>[3,3,1]=>21
[3,6,2,7,4,5,1]=>[3,3,1]=>21
[3,6,2,7,5,1,4]=>[3,2,2]=>21
[3,6,2,7,5,4,1]=>[3,2,1,1]=>35
[3,6,4,1,2,5,7]=>[4,2,1]=>35
[3,6,4,1,2,7,5]=>[3,3,1]=>21
[3,6,4,1,5,2,7]=>[4,2,1]=>35
[3,6,4,1,5,7,2]=>[4,2,1]=>35
[3,6,4,1,7,2,5]=>[3,3,1]=>21
[3,6,4,1,7,5,2]=>[3,2,2]=>21
[3,6,4,2,1,5,7]=>[4,1,1,1]=>20
[3,6,4,2,1,7,5]=>[3,2,1,1]=>35
[3,6,4,2,5,1,7]=>[4,1,1,1]=>20
[3,6,4,2,5,7,1]=>[4,1,1,1]=>20
[3,6,4,2,7,1,5]=>[3,2,1,1]=>35
[3,6,4,2,7,5,1]=>[3,2,1,1]=>35
[3,6,4,5,1,2,7]=>[4,2,1]=>35
[3,6,4,5,1,7,2]=>[4,2,1]=>35
[3,6,4,5,2,1,7]=>[4,1,1,1]=>20
[3,6,4,5,2,7,1]=>[4,1,1,1]=>20
[3,6,4,5,7,1,2]=>[4,2,1]=>35
[3,6,4,5,7,2,1]=>[4,1,1,1]=>20
[3,6,4,7,1,2,5]=>[3,3,1]=>21
[3,6,4,7,1,5,2]=>[3,2,2]=>21
[3,6,4,7,2,1,5]=>[3,2,1,1]=>35
[3,6,4,7,2,5,1]=>[3,2,1,1]=>35
[3,6,4,7,5,1,2]=>[3,2,2]=>21
[3,6,4,7,5,2,1]=>[3,2,1,1]=>35
[3,6,5,1,2,4,7]=>[4,2,1]=>35
[3,6,5,1,2,7,4]=>[3,3,1]=>21
[3,6,5,1,4,2,7]=>[3,2,1,1]=>35
[3,6,5,1,4,7,2]=>[3,2,1,1]=>35
[3,6,5,1,7,2,4]=>[3,3,1]=>21
[3,6,5,1,7,4,2]=>[3,2,1,1]=>35
[3,6,5,2,1,4,7]=>[3,2,1,1]=>35
[3,6,5,2,1,7,4]=>[3,2,1,1]=>35
[3,6,5,2,4,1,7]=>[3,2,1,1]=>35
[3,6,5,2,4,7,1]=>[3,2,1,1]=>35
[3,6,5,2,7,1,4]=>[3,2,1,1]=>35
[3,6,5,2,7,4,1]=>[3,2,1,1]=>35
[3,6,5,4,1,2,7]=>[3,2,1,1]=>35
[3,6,5,4,1,7,2]=>[3,2,1,1]=>35
[3,6,5,4,2,1,7]=>[3,1,1,1,1]=>15
[3,6,5,4,2,7,1]=>[3,1,1,1,1]=>15
[3,6,5,4,7,1,2]=>[3,2,1,1]=>35
[3,6,5,4,7,2,1]=>[3,1,1,1,1]=>15
[3,6,5,7,1,2,4]=>[3,3,1]=>21
[3,6,5,7,1,4,2]=>[3,2,1,1]=>35
[3,6,5,7,2,1,4]=>[3,2,1,1]=>35
[3,6,5,7,2,4,1]=>[3,2,1,1]=>35
[3,6,5,7,4,1,2]=>[3,2,1,1]=>35
[3,6,5,7,4,2,1]=>[3,1,1,1,1]=>15
[3,6,7,1,2,4,5]=>[4,3]=>14
[3,6,7,1,2,5,4]=>[3,3,1]=>21
[3,6,7,1,4,2,5]=>[3,3,1]=>21
[3,6,7,1,4,5,2]=>[3,3,1]=>21
[3,6,7,1,5,2,4]=>[3,3,1]=>21
[3,6,7,1,5,4,2]=>[3,2,1,1]=>35
[3,6,7,2,1,4,5]=>[3,3,1]=>21
[3,6,7,2,1,5,4]=>[3,2,2]=>21
[3,6,7,2,4,1,5]=>[3,3,1]=>21
[3,6,7,2,4,5,1]=>[3,3,1]=>21
[3,6,7,2,5,1,4]=>[3,2,2]=>21
[3,6,7,2,5,4,1]=>[3,2,1,1]=>35
[3,6,7,4,1,2,5]=>[3,3,1]=>21
[3,6,7,4,1,5,2]=>[3,2,2]=>21
[3,6,7,4,2,1,5]=>[3,2,1,1]=>35
[3,6,7,4,2,5,1]=>[3,2,1,1]=>35
[3,6,7,4,5,1,2]=>[3,2,2]=>21
[3,6,7,4,5,2,1]=>[3,2,1,1]=>35
[3,6,7,5,1,2,4]=>[3,3,1]=>21
[3,6,7,5,1,4,2]=>[3,2,1,1]=>35
[3,6,7,5,2,1,4]=>[3,2,1,1]=>35
[3,6,7,5,2,4,1]=>[3,2,1,1]=>35
[3,6,7,5,4,1,2]=>[3,2,1,1]=>35
[3,6,7,5,4,2,1]=>[3,1,1,1,1]=>15
[3,7,1,2,4,5,6]=>[5,2]=>14
[3,7,1,2,4,6,5]=>[4,2,1]=>35
[3,7,1,2,5,4,6]=>[4,2,1]=>35
[3,7,1,2,5,6,4]=>[4,2,1]=>35
[3,7,1,2,6,4,5]=>[4,2,1]=>35
[3,7,1,2,6,5,4]=>[3,2,1,1]=>35
[3,7,1,4,2,5,6]=>[4,2,1]=>35
[3,7,1,4,2,6,5]=>[3,3,1]=>21
[3,7,1,4,5,2,6]=>[4,2,1]=>35
[3,7,1,4,5,6,2]=>[4,2,1]=>35
[3,7,1,4,6,2,5]=>[3,3,1]=>21
[3,7,1,4,6,5,2]=>[3,2,1,1]=>35
[3,7,1,5,2,4,6]=>[4,2,1]=>35
[3,7,1,5,2,6,4]=>[3,3,1]=>21
[3,7,1,5,4,2,6]=>[3,2,1,1]=>35
[3,7,1,5,4,6,2]=>[3,2,1,1]=>35
[3,7,1,5,6,2,4]=>[3,3,1]=>21
[3,7,1,5,6,4,2]=>[3,2,1,1]=>35
[3,7,1,6,2,4,5]=>[4,2,1]=>35
[3,7,1,6,2,5,4]=>[3,2,1,1]=>35
[3,7,1,6,4,2,5]=>[3,2,1,1]=>35
[3,7,1,6,4,5,2]=>[3,2,1,1]=>35
[3,7,1,6,5,2,4]=>[3,2,1,1]=>35
[3,7,1,6,5,4,2]=>[2,2,1,1,1]=>14
[3,7,2,1,4,5,6]=>[4,2,1]=>35
[3,7,2,1,4,6,5]=>[3,2,2]=>21
[3,7,2,1,5,4,6]=>[3,2,2]=>21
[3,7,2,1,5,6,4]=>[3,2,2]=>21
[3,7,2,1,6,4,5]=>[3,2,2]=>21
[3,7,2,1,6,5,4]=>[2,2,2,1]=>14
[3,7,2,4,1,5,6]=>[4,2,1]=>35
[3,7,2,4,1,6,5]=>[3,2,2]=>21
[3,7,2,4,5,1,6]=>[4,2,1]=>35
[3,7,2,4,5,6,1]=>[4,2,1]=>35
[3,7,2,4,6,1,5]=>[3,2,2]=>21
[3,7,2,4,6,5,1]=>[3,2,1,1]=>35
[3,7,2,5,1,4,6]=>[3,2,2]=>21
[3,7,2,5,1,6,4]=>[3,2,2]=>21
[3,7,2,5,4,1,6]=>[3,2,1,1]=>35
[3,7,2,5,4,6,1]=>[3,2,1,1]=>35
[3,7,2,5,6,1,4]=>[3,2,2]=>21
[3,7,2,5,6,4,1]=>[3,2,1,1]=>35
[3,7,2,6,1,4,5]=>[3,2,2]=>21
[3,7,2,6,1,5,4]=>[2,2,2,1]=>14
[3,7,2,6,4,1,5]=>[3,2,1,1]=>35
[3,7,2,6,4,5,1]=>[3,2,1,1]=>35
[3,7,2,6,5,1,4]=>[2,2,2,1]=>14
[3,7,2,6,5,4,1]=>[2,2,1,1,1]=>14
[3,7,4,1,2,5,6]=>[4,2,1]=>35
[3,7,4,1,2,6,5]=>[3,3,1]=>21
[3,7,4,1,5,2,6]=>[4,2,1]=>35
[3,7,4,1,5,6,2]=>[4,2,1]=>35
[3,7,4,1,6,2,5]=>[3,3,1]=>21
[3,7,4,1,6,5,2]=>[3,2,1,1]=>35
[3,7,4,2,1,5,6]=>[4,1,1,1]=>20
[3,7,4,2,1,6,5]=>[3,2,1,1]=>35
[3,7,4,2,5,1,6]=>[4,1,1,1]=>20
[3,7,4,2,5,6,1]=>[4,1,1,1]=>20
[3,7,4,2,6,1,5]=>[3,2,1,1]=>35
[3,7,4,2,6,5,1]=>[3,2,1,1]=>35
[3,7,4,5,1,2,6]=>[4,2,1]=>35
[3,7,4,5,1,6,2]=>[4,2,1]=>35
[3,7,4,5,2,1,6]=>[4,1,1,1]=>20
[3,7,4,5,2,6,1]=>[4,1,1,1]=>20
[3,7,4,5,6,1,2]=>[4,2,1]=>35
[3,7,4,5,6,2,1]=>[4,1,1,1]=>20
[3,7,4,6,1,2,5]=>[3,3,1]=>21
[3,7,4,6,1,5,2]=>[3,2,1,1]=>35
[3,7,4,6,2,1,5]=>[3,2,1,1]=>35
[3,7,4,6,2,5,1]=>[3,2,1,1]=>35
[3,7,4,6,5,1,2]=>[3,2,1,1]=>35
[3,7,4,6,5,2,1]=>[3,1,1,1,1]=>15
[3,7,5,1,2,4,6]=>[4,2,1]=>35
[3,7,5,1,2,6,4]=>[3,3,1]=>21
[3,7,5,1,4,2,6]=>[3,2,1,1]=>35
[3,7,5,1,4,6,2]=>[3,2,1,1]=>35
[3,7,5,1,6,2,4]=>[3,3,1]=>21
[3,7,5,1,6,4,2]=>[3,2,1,1]=>35
[3,7,5,2,1,4,6]=>[3,2,1,1]=>35
[3,7,5,2,1,6,4]=>[3,2,1,1]=>35
[3,7,5,2,4,1,6]=>[3,2,1,1]=>35
[3,7,5,2,4,6,1]=>[3,2,1,1]=>35
[3,7,5,2,6,1,4]=>[3,2,1,1]=>35
[3,7,5,2,6,4,1]=>[3,2,1,1]=>35
[3,7,5,4,1,2,6]=>[3,2,1,1]=>35
[3,7,5,4,1,6,2]=>[3,2,1,1]=>35
[3,7,5,4,2,1,6]=>[3,1,1,1,1]=>15
[3,7,5,4,2,6,1]=>[3,1,1,1,1]=>15
[3,7,5,4,6,1,2]=>[3,2,1,1]=>35
[3,7,5,4,6,2,1]=>[3,1,1,1,1]=>15
[3,7,5,6,1,2,4]=>[3,3,1]=>21
[3,7,5,6,1,4,2]=>[3,2,1,1]=>35
[3,7,5,6,2,1,4]=>[3,2,1,1]=>35
[3,7,5,6,2,4,1]=>[3,2,1,1]=>35
[3,7,5,6,4,1,2]=>[3,2,1,1]=>35
[3,7,5,6,4,2,1]=>[3,1,1,1,1]=>15
[3,7,6,1,2,4,5]=>[4,2,1]=>35
[3,7,6,1,2,5,4]=>[3,2,1,1]=>35
[3,7,6,1,4,2,5]=>[3,2,1,1]=>35
[3,7,6,1,4,5,2]=>[3,2,1,1]=>35
[3,7,6,1,5,2,4]=>[3,2,1,1]=>35
[3,7,6,1,5,4,2]=>[2,2,1,1,1]=>14
[3,7,6,2,1,4,5]=>[3,2,1,1]=>35
[3,7,6,2,1,5,4]=>[2,2,2,1]=>14
[3,7,6,2,4,1,5]=>[3,2,1,1]=>35
[3,7,6,2,4,5,1]=>[3,2,1,1]=>35
[3,7,6,2,5,1,4]=>[2,2,2,1]=>14
[3,7,6,2,5,4,1]=>[2,2,1,1,1]=>14
[3,7,6,4,1,2,5]=>[3,2,1,1]=>35
[3,7,6,4,1,5,2]=>[3,2,1,1]=>35
[3,7,6,4,2,1,5]=>[3,1,1,1,1]=>15
[3,7,6,4,2,5,1]=>[3,1,1,1,1]=>15
[3,7,6,4,5,1,2]=>[3,2,1,1]=>35
[3,7,6,4,5,2,1]=>[3,1,1,1,1]=>15
[3,7,6,5,1,2,4]=>[3,2,1,1]=>35
[3,7,6,5,1,4,2]=>[2,2,1,1,1]=>14
[3,7,6,5,2,1,4]=>[2,2,1,1,1]=>14
[3,7,6,5,2,4,1]=>[2,2,1,1,1]=>14
[3,7,6,5,4,1,2]=>[2,2,1,1,1]=>14
[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]=>6
[4,1,2,3,5,6,7]=>[6,1]=>6
[4,1,2,3,5,7,6]=>[5,2]=>14
[4,1,2,3,6,5,7]=>[5,2]=>14
[4,1,2,3,6,7,5]=>[5,2]=>14
[4,1,2,3,7,5,6]=>[5,2]=>14
[4,1,2,3,7,6,5]=>[4,2,1]=>35
[4,1,2,5,3,6,7]=>[5,2]=>14
[4,1,2,5,3,7,6]=>[4,3]=>14
[4,1,2,5,6,3,7]=>[5,2]=>14
[4,1,2,5,6,7,3]=>[5,2]=>14
[4,1,2,5,7,3,6]=>[4,3]=>14
[4,1,2,5,7,6,3]=>[4,2,1]=>35
[4,1,2,6,3,5,7]=>[5,2]=>14
[4,1,2,6,3,7,5]=>[4,3]=>14
[4,1,2,6,5,3,7]=>[4,2,1]=>35
[4,1,2,6,5,7,3]=>[4,2,1]=>35
[4,1,2,6,7,3,5]=>[4,3]=>14
[4,1,2,6,7,5,3]=>[4,2,1]=>35
[4,1,2,7,3,5,6]=>[5,2]=>14
[4,1,2,7,3,6,5]=>[4,2,1]=>35
[4,1,2,7,5,3,6]=>[4,2,1]=>35
[4,1,2,7,5,6,3]=>[4,2,1]=>35
[4,1,2,7,6,3,5]=>[4,2,1]=>35
[4,1,2,7,6,5,3]=>[3,2,1,1]=>35
[4,1,3,2,5,6,7]=>[5,1,1]=>15
[4,1,3,2,5,7,6]=>[4,2,1]=>35
[4,1,3,2,6,5,7]=>[4,2,1]=>35
[4,1,3,2,6,7,5]=>[4,2,1]=>35
[4,1,3,2,7,5,6]=>[4,2,1]=>35
[4,1,3,2,7,6,5]=>[3,2,2]=>21
[4,1,3,5,2,6,7]=>[5,1,1]=>15
[4,1,3,5,2,7,6]=>[4,2,1]=>35
[4,1,3,5,6,2,7]=>[5,1,1]=>15
[4,1,3,5,6,7,2]=>[5,1,1]=>15
[4,1,3,5,7,2,6]=>[4,2,1]=>35
[4,1,3,5,7,6,2]=>[4,2,1]=>35
[4,1,3,6,2,5,7]=>[4,2,1]=>35
[4,1,3,6,2,7,5]=>[4,2,1]=>35
[4,1,3,6,5,2,7]=>[4,2,1]=>35
[4,1,3,6,5,7,2]=>[4,2,1]=>35
[4,1,3,6,7,2,5]=>[4,2,1]=>35
[4,1,3,6,7,5,2]=>[4,2,1]=>35
[4,1,3,7,2,5,6]=>[4,2,1]=>35
[4,1,3,7,2,6,5]=>[3,2,2]=>21
[4,1,3,7,5,2,6]=>[4,2,1]=>35
[4,1,3,7,5,6,2]=>[4,2,1]=>35
[4,1,3,7,6,2,5]=>[3,2,2]=>21
[4,1,3,7,6,5,2]=>[3,2,1,1]=>35
[4,1,5,2,3,6,7]=>[5,2]=>14
[4,1,5,2,3,7,6]=>[4,3]=>14
[4,1,5,2,6,3,7]=>[4,3]=>14
[4,1,5,2,6,7,3]=>[4,3]=>14
[4,1,5,2,7,3,6]=>[4,3]=>14
[4,1,5,2,7,6,3]=>[3,3,1]=>21
[4,1,5,3,2,6,7]=>[4,2,1]=>35
[4,1,5,3,2,7,6]=>[3,3,1]=>21
[4,1,5,3,6,2,7]=>[4,2,1]=>35
[4,1,5,3,6,7,2]=>[4,2,1]=>35
[4,1,5,3,7,2,6]=>[3,3,1]=>21
[4,1,5,3,7,6,2]=>[3,3,1]=>21
[4,1,5,6,2,3,7]=>[4,3]=>14
[4,1,5,6,2,7,3]=>[4,3]=>14
[4,1,5,6,3,2,7]=>[4,2,1]=>35
[4,1,5,6,3,7,2]=>[4,2,1]=>35
[4,1,5,6,7,2,3]=>[4,3]=>14
[4,1,5,6,7,3,2]=>[4,2,1]=>35
[4,1,5,7,2,3,6]=>[4,3]=>14
[4,1,5,7,2,6,3]=>[3,3,1]=>21
[4,1,5,7,3,2,6]=>[3,3,1]=>21
[4,1,5,7,3,6,2]=>[3,3,1]=>21
[4,1,5,7,6,2,3]=>[3,3,1]=>21
[4,1,5,7,6,3,2]=>[3,2,1,1]=>35
[4,1,6,2,3,5,7]=>[5,2]=>14
[4,1,6,2,3,7,5]=>[4,3]=>14
[4,1,6,2,5,3,7]=>[4,2,1]=>35
[4,1,6,2,5,7,3]=>[4,2,1]=>35
[4,1,6,2,7,3,5]=>[4,3]=>14
[4,1,6,2,7,5,3]=>[3,3,1]=>21
[4,1,6,3,2,5,7]=>[4,2,1]=>35
[4,1,6,3,2,7,5]=>[3,3,1]=>21
[4,1,6,3,5,2,7]=>[4,2,1]=>35
[4,1,6,3,5,7,2]=>[4,2,1]=>35
[4,1,6,3,7,2,5]=>[3,3,1]=>21
[4,1,6,3,7,5,2]=>[3,3,1]=>21
[4,1,6,5,2,3,7]=>[4,2,1]=>35
[4,1,6,5,2,7,3]=>[3,3,1]=>21
[4,1,6,5,3,2,7]=>[3,2,1,1]=>35
[4,1,6,5,3,7,2]=>[3,2,1,1]=>35
[4,1,6,5,7,2,3]=>[3,3,1]=>21
[4,1,6,5,7,3,2]=>[3,2,1,1]=>35
[4,1,6,7,2,3,5]=>[4,3]=>14
[4,1,6,7,2,5,3]=>[3,3,1]=>21
[4,1,6,7,3,2,5]=>[3,3,1]=>21
[4,1,6,7,3,5,2]=>[3,3,1]=>21
[4,1,6,7,5,2,3]=>[3,3,1]=>21
[4,1,6,7,5,3,2]=>[3,2,1,1]=>35
[4,1,7,2,3,5,6]=>[5,2]=>14
[4,1,7,2,3,6,5]=>[4,2,1]=>35
[4,1,7,2,5,3,6]=>[4,2,1]=>35
[4,1,7,2,5,6,3]=>[4,2,1]=>35
[4,1,7,2,6,3,5]=>[4,2,1]=>35
[4,1,7,2,6,5,3]=>[3,2,1,1]=>35
[4,1,7,3,2,5,6]=>[4,2,1]=>35
[4,1,7,3,2,6,5]=>[3,2,2]=>21
[4,1,7,3,5,2,6]=>[4,2,1]=>35
[4,1,7,3,5,6,2]=>[4,2,1]=>35
[4,1,7,3,6,2,5]=>[3,2,2]=>21
[4,1,7,3,6,5,2]=>[3,2,1,1]=>35
[4,1,7,5,2,3,6]=>[4,2,1]=>35
[4,1,7,5,2,6,3]=>[3,3,1]=>21
[4,1,7,5,3,2,6]=>[3,2,1,1]=>35
[4,1,7,5,3,6,2]=>[3,2,1,1]=>35
[4,1,7,5,6,2,3]=>[3,3,1]=>21
[4,1,7,5,6,3,2]=>[3,2,1,1]=>35
[4,1,7,6,2,3,5]=>[4,2,1]=>35
[4,1,7,6,2,5,3]=>[3,2,1,1]=>35
[4,1,7,6,3,2,5]=>[3,2,1,1]=>35
[4,1,7,6,3,5,2]=>[3,2,1,1]=>35
[4,1,7,6,5,2,3]=>[3,2,1,1]=>35
[4,1,7,6,5,3,2]=>[2,2,1,1,1]=>14
[4,2,1,3,5,6,7]=>[5,1,1]=>15
[4,2,1,3,5,7,6]=>[4,2,1]=>35
[4,2,1,3,6,5,7]=>[4,2,1]=>35
[4,2,1,3,6,7,5]=>[4,2,1]=>35
[4,2,1,3,7,5,6]=>[4,2,1]=>35
[4,2,1,3,7,6,5]=>[3,2,2]=>21
[4,2,1,5,3,6,7]=>[4,2,1]=>35
[4,2,1,5,3,7,6]=>[3,3,1]=>21
[4,2,1,5,6,3,7]=>[4,2,1]=>35
[4,2,1,5,6,7,3]=>[4,2,1]=>35
[4,2,1,5,7,3,6]=>[3,3,1]=>21
[4,2,1,5,7,6,3]=>[3,2,2]=>21
[4,2,1,6,3,5,7]=>[4,2,1]=>35
[4,2,1,6,3,7,5]=>[3,3,1]=>21
[4,2,1,6,5,3,7]=>[3,2,2]=>21
[4,2,1,6,5,7,3]=>[3,2,2]=>21
[4,2,1,6,7,3,5]=>[3,3,1]=>21
[4,2,1,6,7,5,3]=>[3,2,2]=>21
[4,2,1,7,3,5,6]=>[4,2,1]=>35
[4,2,1,7,3,6,5]=>[3,2,2]=>21
[4,2,1,7,5,3,6]=>[3,2,2]=>21
[4,2,1,7,5,6,3]=>[3,2,2]=>21
[4,2,1,7,6,3,5]=>[3,2,2]=>21
[4,2,1,7,6,5,3]=>[2,2,2,1]=>14
[4,2,3,1,5,6,7]=>[5,1,1]=>15
[4,2,3,1,5,7,6]=>[4,2,1]=>35
[4,2,3,1,6,5,7]=>[4,2,1]=>35
[4,2,3,1,6,7,5]=>[4,2,1]=>35
[4,2,3,1,7,5,6]=>[4,2,1]=>35
[4,2,3,1,7,6,5]=>[3,2,2]=>21
[4,2,3,5,1,6,7]=>[5,1,1]=>15
[4,2,3,5,1,7,6]=>[4,2,1]=>35
[4,2,3,5,6,1,7]=>[5,1,1]=>15
[4,2,3,5,6,7,1]=>[5,1,1]=>15
[4,2,3,5,7,1,6]=>[4,2,1]=>35
[4,2,3,5,7,6,1]=>[4,2,1]=>35
[4,2,3,6,1,5,7]=>[4,2,1]=>35
[4,2,3,6,1,7,5]=>[4,2,1]=>35
[4,2,3,6,5,1,7]=>[4,2,1]=>35
[4,2,3,6,5,7,1]=>[4,2,1]=>35
[4,2,3,6,7,1,5]=>[4,2,1]=>35
[4,2,3,6,7,5,1]=>[4,2,1]=>35
[4,2,3,7,1,5,6]=>[4,2,1]=>35
[4,2,3,7,1,6,5]=>[3,2,2]=>21
[4,2,3,7,5,1,6]=>[4,2,1]=>35
[4,2,3,7,5,6,1]=>[4,2,1]=>35
[4,2,3,7,6,1,5]=>[3,2,2]=>21
[4,2,3,7,6,5,1]=>[3,2,1,1]=>35
[4,2,5,1,3,6,7]=>[4,2,1]=>35
[4,2,5,1,3,7,6]=>[3,3,1]=>21
[4,2,5,1,6,3,7]=>[4,2,1]=>35
[4,2,5,1,6,7,3]=>[4,2,1]=>35
[4,2,5,1,7,3,6]=>[3,3,1]=>21
[4,2,5,1,7,6,3]=>[3,2,2]=>21
[4,2,5,3,1,6,7]=>[4,2,1]=>35
[4,2,5,3,1,7,6]=>[3,3,1]=>21
[4,2,5,3,6,1,7]=>[4,2,1]=>35
[4,2,5,3,6,7,1]=>[4,2,1]=>35
[4,2,5,3,7,1,6]=>[3,3,1]=>21
[4,2,5,3,7,6,1]=>[3,3,1]=>21
[4,2,5,6,1,3,7]=>[4,2,1]=>35
[4,2,5,6,1,7,3]=>[4,2,1]=>35
[4,2,5,6,3,1,7]=>[4,2,1]=>35
[4,2,5,6,3,7,1]=>[4,2,1]=>35
[4,2,5,6,7,1,3]=>[4,2,1]=>35
[4,2,5,6,7,3,1]=>[4,2,1]=>35
[4,2,5,7,1,3,6]=>[3,3,1]=>21
[4,2,5,7,1,6,3]=>[3,2,2]=>21
[4,2,5,7,3,1,6]=>[3,3,1]=>21
[4,2,5,7,3,6,1]=>[3,3,1]=>21
[4,2,5,7,6,1,3]=>[3,2,2]=>21
[4,2,5,7,6,3,1]=>[3,2,1,1]=>35
[4,2,6,1,3,5,7]=>[4,2,1]=>35
[4,2,6,1,3,7,5]=>[3,3,1]=>21
[4,2,6,1,5,3,7]=>[3,2,2]=>21
[4,2,6,1,5,7,3]=>[3,2,2]=>21
[4,2,6,1,7,3,5]=>[3,3,1]=>21
[4,2,6,1,7,5,3]=>[3,2,2]=>21
[4,2,6,3,1,5,7]=>[4,2,1]=>35
[4,2,6,3,1,7,5]=>[3,3,1]=>21
[4,2,6,3,5,1,7]=>[4,2,1]=>35
[4,2,6,3,5,7,1]=>[4,2,1]=>35
[4,2,6,3,7,1,5]=>[3,3,1]=>21
[4,2,6,3,7,5,1]=>[3,3,1]=>21
[4,2,6,5,1,3,7]=>[3,2,2]=>21
[4,2,6,5,1,7,3]=>[3,2,2]=>21
[4,2,6,5,3,1,7]=>[3,2,1,1]=>35
[4,2,6,5,3,7,1]=>[3,2,1,1]=>35
[4,2,6,5,7,1,3]=>[3,2,2]=>21
[4,2,6,5,7,3,1]=>[3,2,1,1]=>35
[4,2,6,7,1,3,5]=>[3,3,1]=>21
[4,2,6,7,1,5,3]=>[3,2,2]=>21
[4,2,6,7,3,1,5]=>[3,3,1]=>21
[4,2,6,7,3,5,1]=>[3,3,1]=>21
[4,2,6,7,5,1,3]=>[3,2,2]=>21
[4,2,6,7,5,3,1]=>[3,2,1,1]=>35
[4,2,7,1,3,5,6]=>[4,2,1]=>35
[4,2,7,1,3,6,5]=>[3,2,2]=>21
[4,2,7,1,5,3,6]=>[3,2,2]=>21
[4,2,7,1,5,6,3]=>[3,2,2]=>21
[4,2,7,1,6,3,5]=>[3,2,2]=>21
[4,2,7,1,6,5,3]=>[2,2,2,1]=>14
[4,2,7,3,1,5,6]=>[4,2,1]=>35
[4,2,7,3,1,6,5]=>[3,2,2]=>21
[4,2,7,3,5,1,6]=>[4,2,1]=>35
[4,2,7,3,5,6,1]=>[4,2,1]=>35
[4,2,7,3,6,1,5]=>[3,2,2]=>21
[4,2,7,3,6,5,1]=>[3,2,1,1]=>35
[4,2,7,5,1,3,6]=>[3,2,2]=>21
[4,2,7,5,1,6,3]=>[3,2,2]=>21
[4,2,7,5,3,1,6]=>[3,2,1,1]=>35
[4,2,7,5,3,6,1]=>[3,2,1,1]=>35
[4,2,7,5,6,1,3]=>[3,2,2]=>21
[4,2,7,5,6,3,1]=>[3,2,1,1]=>35
[4,2,7,6,1,3,5]=>[3,2,2]=>21
[4,2,7,6,1,5,3]=>[2,2,2,1]=>14
[4,2,7,6,3,1,5]=>[3,2,1,1]=>35
[4,2,7,6,3,5,1]=>[3,2,1,1]=>35
[4,2,7,6,5,1,3]=>[2,2,2,1]=>14
[4,2,7,6,5,3,1]=>[2,2,1,1,1]=>14
[4,3,1,2,5,6,7]=>[5,1,1]=>15
[4,3,1,2,5,7,6]=>[4,2,1]=>35
[4,3,1,2,6,5,7]=>[4,2,1]=>35
[4,3,1,2,6,7,5]=>[4,2,1]=>35
[4,3,1,2,7,5,6]=>[4,2,1]=>35
[4,3,1,2,7,6,5]=>[3,2,2]=>21
[4,3,1,5,2,6,7]=>[4,2,1]=>35
[4,3,1,5,2,7,6]=>[3,3,1]=>21
[4,3,1,5,6,2,7]=>[4,2,1]=>35
[4,3,1,5,6,7,2]=>[4,2,1]=>35
[4,3,1,5,7,2,6]=>[3,3,1]=>21
[4,3,1,5,7,6,2]=>[3,2,2]=>21
[4,3,1,6,2,5,7]=>[4,2,1]=>35
[4,3,1,6,2,7,5]=>[3,3,1]=>21
[4,3,1,6,5,2,7]=>[3,2,2]=>21
[4,3,1,6,5,7,2]=>[3,2,2]=>21
[4,3,1,6,7,2,5]=>[3,3,1]=>21
[4,3,1,6,7,5,2]=>[3,2,2]=>21
[4,3,1,7,2,5,6]=>[4,2,1]=>35
[4,3,1,7,2,6,5]=>[3,2,2]=>21
[4,3,1,7,5,2,6]=>[3,2,2]=>21
[4,3,1,7,5,6,2]=>[3,2,2]=>21
[4,3,1,7,6,2,5]=>[3,2,2]=>21
[4,3,1,7,6,5,2]=>[2,2,2,1]=>14
[4,3,2,1,5,6,7]=>[4,1,1,1]=>20
[4,3,2,1,5,7,6]=>[3,2,1,1]=>35
[4,3,2,1,6,5,7]=>[3,2,1,1]=>35
[4,3,2,1,6,7,5]=>[3,2,1,1]=>35
[4,3,2,1,7,5,6]=>[3,2,1,1]=>35
[4,3,2,1,7,6,5]=>[2,2,2,1]=>14
[4,3,2,5,1,6,7]=>[4,1,1,1]=>20
[4,3,2,5,1,7,6]=>[3,2,1,1]=>35
[4,3,2,5,6,1,7]=>[4,1,1,1]=>20
[4,3,2,5,6,7,1]=>[4,1,1,1]=>20
[4,3,2,5,7,1,6]=>[3,2,1,1]=>35
[4,3,2,5,7,6,1]=>[3,2,1,1]=>35
[4,3,2,6,1,5,7]=>[3,2,1,1]=>35
[4,3,2,6,1,7,5]=>[3,2,1,1]=>35
[4,3,2,6,5,1,7]=>[3,2,1,1]=>35
[4,3,2,6,5,7,1]=>[3,2,1,1]=>35
[4,3,2,6,7,1,5]=>[3,2,1,1]=>35
[4,3,2,6,7,5,1]=>[3,2,1,1]=>35
[4,3,2,7,1,5,6]=>[3,2,1,1]=>35
[4,3,2,7,1,6,5]=>[2,2,2,1]=>14
[4,3,2,7,5,1,6]=>[3,2,1,1]=>35
[4,3,2,7,5,6,1]=>[3,2,1,1]=>35
[4,3,2,7,6,1,5]=>[2,2,2,1]=>14
[4,3,2,7,6,5,1]=>[2,2,2,1]=>14
[4,3,5,1,2,6,7]=>[4,2,1]=>35
[4,3,5,1,2,7,6]=>[3,3,1]=>21
[4,3,5,1,6,2,7]=>[4,2,1]=>35
[4,3,5,1,6,7,2]=>[4,2,1]=>35
[4,3,5,1,7,2,6]=>[3,3,1]=>21
[4,3,5,1,7,6,2]=>[3,2,2]=>21
[4,3,5,2,1,6,7]=>[4,1,1,1]=>20
[4,3,5,2,1,7,6]=>[3,2,1,1]=>35
[4,3,5,2,6,1,7]=>[4,1,1,1]=>20
[4,3,5,2,6,7,1]=>[4,1,1,1]=>20
[4,3,5,2,7,1,6]=>[3,2,1,1]=>35
[4,3,5,2,7,6,1]=>[3,2,1,1]=>35
[4,3,5,6,1,2,7]=>[4,2,1]=>35
[4,3,5,6,1,7,2]=>[4,2,1]=>35
[4,3,5,6,2,1,7]=>[4,1,1,1]=>20
[4,3,5,6,2,7,1]=>[4,1,1,1]=>20
[4,3,5,6,7,1,2]=>[4,2,1]=>35
[4,3,5,6,7,2,1]=>[4,1,1,1]=>20
[4,3,5,7,1,2,6]=>[3,3,1]=>21
[4,3,5,7,1,6,2]=>[3,2,2]=>21
[4,3,5,7,2,1,6]=>[3,2,1,1]=>35
[4,3,5,7,2,6,1]=>[3,2,1,1]=>35
[4,3,5,7,6,1,2]=>[3,2,2]=>21
[4,3,5,7,6,2,1]=>[3,2,1,1]=>35
[4,3,6,1,2,5,7]=>[4,2,1]=>35
[4,3,6,1,2,7,5]=>[3,3,1]=>21
[4,3,6,1,5,2,7]=>[3,2,2]=>21
[4,3,6,1,5,7,2]=>[3,2,2]=>21
[4,3,6,1,7,2,5]=>[3,3,1]=>21
[4,3,6,1,7,5,2]=>[3,2,2]=>21
[4,3,6,2,1,5,7]=>[3,2,1,1]=>35
[4,3,6,2,1,7,5]=>[3,2,1,1]=>35
[4,3,6,2,5,1,7]=>[3,2,1,1]=>35
[4,3,6,2,5,7,1]=>[3,2,1,1]=>35
[4,3,6,2,7,1,5]=>[3,2,1,1]=>35
[4,3,6,2,7,5,1]=>[3,2,1,1]=>35
[4,3,6,5,1,2,7]=>[3,2,2]=>21
[4,3,6,5,1,7,2]=>[3,2,2]=>21
[4,3,6,5,2,1,7]=>[3,2,1,1]=>35
[4,3,6,5,2,7,1]=>[3,2,1,1]=>35
[4,3,6,5,7,1,2]=>[3,2,2]=>21
[4,3,6,5,7,2,1]=>[3,2,1,1]=>35
[4,3,6,7,1,2,5]=>[3,3,1]=>21
[4,3,6,7,1,5,2]=>[3,2,2]=>21
[4,3,6,7,2,1,5]=>[3,2,1,1]=>35
[4,3,6,7,2,5,1]=>[3,2,1,1]=>35
[4,3,6,7,5,1,2]=>[3,2,2]=>21
[4,3,6,7,5,2,1]=>[3,2,1,1]=>35
[4,3,7,1,2,5,6]=>[4,2,1]=>35
[4,3,7,1,2,6,5]=>[3,2,2]=>21
[4,3,7,1,5,2,6]=>[3,2,2]=>21
[4,3,7,1,5,6,2]=>[3,2,2]=>21
[4,3,7,1,6,2,5]=>[3,2,2]=>21
[4,3,7,1,6,5,2]=>[2,2,2,1]=>14
[4,3,7,2,1,5,6]=>[3,2,1,1]=>35
[4,3,7,2,1,6,5]=>[2,2,2,1]=>14
[4,3,7,2,5,1,6]=>[3,2,1,1]=>35
[4,3,7,2,5,6,1]=>[3,2,1,1]=>35
[4,3,7,2,6,1,5]=>[2,2,2,1]=>14
[4,3,7,2,6,5,1]=>[2,2,2,1]=>14
[4,3,7,5,1,2,6]=>[3,2,2]=>21
[4,3,7,5,1,6,2]=>[3,2,2]=>21
[4,3,7,5,2,1,6]=>[3,2,1,1]=>35
[4,3,7,5,2,6,1]=>[3,2,1,1]=>35
[4,3,7,5,6,1,2]=>[3,2,2]=>21
[4,3,7,5,6,2,1]=>[3,2,1,1]=>35
[4,3,7,6,1,2,5]=>[3,2,2]=>21
[4,3,7,6,1,5,2]=>[2,2,2,1]=>14
[4,3,7,6,2,1,5]=>[2,2,2,1]=>14
[4,3,7,6,2,5,1]=>[2,2,2,1]=>14
[4,3,7,6,5,1,2]=>[2,2,2,1]=>14
[4,3,7,6,5,2,1]=>[2,2,1,1,1]=>14
[4,5,1,2,3,6,7]=>[5,2]=>14
[4,5,1,2,3,7,6]=>[4,3]=>14
[4,5,1,2,6,3,7]=>[4,3]=>14
[4,5,1,2,6,7,3]=>[4,3]=>14
[4,5,1,2,7,3,6]=>[4,3]=>14
[4,5,1,2,7,6,3]=>[3,3,1]=>21
[4,5,1,3,2,6,7]=>[4,2,1]=>35
[4,5,1,3,2,7,6]=>[3,3,1]=>21
[4,5,1,3,6,2,7]=>[4,2,1]=>35
[4,5,1,3,6,7,2]=>[4,2,1]=>35
[4,5,1,3,7,2,6]=>[3,3,1]=>21
[4,5,1,3,7,6,2]=>[3,3,1]=>21
[4,5,1,6,2,3,7]=>[4,3]=>14
[4,5,1,6,2,7,3]=>[4,3]=>14
[4,5,1,6,3,2,7]=>[4,2,1]=>35
[4,5,1,6,3,7,2]=>[4,2,1]=>35
[4,5,1,6,7,2,3]=>[4,3]=>14
[4,5,1,6,7,3,2]=>[4,2,1]=>35
[4,5,1,7,2,3,6]=>[4,3]=>14
[4,5,1,7,2,6,3]=>[3,3,1]=>21
[4,5,1,7,3,2,6]=>[3,3,1]=>21
[4,5,1,7,3,6,2]=>[3,3,1]=>21
[4,5,1,7,6,2,3]=>[3,3,1]=>21
[4,5,1,7,6,3,2]=>[3,2,1,1]=>35
[4,5,2,1,3,6,7]=>[4,2,1]=>35
[4,5,2,1,3,7,6]=>[3,3,1]=>21
[4,5,2,1,6,3,7]=>[4,2,1]=>35
[4,5,2,1,6,7,3]=>[4,2,1]=>35
[4,5,2,1,7,3,6]=>[3,3,1]=>21
[4,5,2,1,7,6,3]=>[3,2,2]=>21
[4,5,2,3,1,6,7]=>[4,2,1]=>35
[4,5,2,3,1,7,6]=>[3,3,1]=>21
[4,5,2,3,6,1,7]=>[4,2,1]=>35
[4,5,2,3,6,7,1]=>[4,2,1]=>35
[4,5,2,3,7,1,6]=>[3,3,1]=>21
[4,5,2,3,7,6,1]=>[3,3,1]=>21
[4,5,2,6,1,3,7]=>[4,2,1]=>35
[4,5,2,6,1,7,3]=>[4,2,1]=>35
[4,5,2,6,3,1,7]=>[4,2,1]=>35
[4,5,2,6,3,7,1]=>[4,2,1]=>35
[4,5,2,6,7,1,3]=>[4,2,1]=>35
[4,5,2,6,7,3,1]=>[4,2,1]=>35
[4,5,2,7,1,3,6]=>[3,3,1]=>21
[4,5,2,7,1,6,3]=>[3,2,2]=>21
[4,5,2,7,3,1,6]=>[3,3,1]=>21
[4,5,2,7,3,6,1]=>[3,3,1]=>21
[4,5,2,7,6,1,3]=>[3,2,2]=>21
[4,5,2,7,6,3,1]=>[3,2,1,1]=>35
[4,5,3,1,2,6,7]=>[4,2,1]=>35
[4,5,3,1,2,7,6]=>[3,3,1]=>21
[4,5,3,1,6,2,7]=>[4,2,1]=>35
[4,5,3,1,6,7,2]=>[4,2,1]=>35
[4,5,3,1,7,2,6]=>[3,3,1]=>21
[4,5,3,1,7,6,2]=>[3,2,2]=>21
[4,5,3,2,1,6,7]=>[4,1,1,1]=>20
[4,5,3,2,1,7,6]=>[3,2,1,1]=>35
[4,5,3,2,6,1,7]=>[4,1,1,1]=>20
[4,5,3,2,6,7,1]=>[4,1,1,1]=>20
[4,5,3,2,7,1,6]=>[3,2,1,1]=>35
[4,5,3,2,7,6,1]=>[3,2,1,1]=>35
[4,5,3,6,1,2,7]=>[4,2,1]=>35
[4,5,3,6,1,7,2]=>[4,2,1]=>35
[4,5,3,6,2,1,7]=>[4,1,1,1]=>20
[4,5,3,6,2,7,1]=>[4,1,1,1]=>20
[4,5,3,6,7,1,2]=>[4,2,1]=>35
[4,5,3,6,7,2,1]=>[4,1,1,1]=>20
[4,5,3,7,1,2,6]=>[3,3,1]=>21
[4,5,3,7,1,6,2]=>[3,2,2]=>21
[4,5,3,7,2,1,6]=>[3,2,1,1]=>35
[4,5,3,7,2,6,1]=>[3,2,1,1]=>35
[4,5,3,7,6,1,2]=>[3,2,2]=>21
[4,5,3,7,6,2,1]=>[3,2,1,1]=>35
[4,5,6,1,2,3,7]=>[4,3]=>14
[4,5,6,1,2,7,3]=>[4,3]=>14
[4,5,6,1,3,2,7]=>[4,2,1]=>35
[4,5,6,1,3,7,2]=>[4,2,1]=>35
[4,5,6,1,7,2,3]=>[4,3]=>14
[4,5,6,1,7,3,2]=>[4,2,1]=>35
[4,5,6,2,1,3,7]=>[4,2,1]=>35
[4,5,6,2,1,7,3]=>[4,2,1]=>35
[4,5,6,2,3,1,7]=>[4,2,1]=>35
[4,5,6,2,3,7,1]=>[4,2,1]=>35
[4,5,6,2,7,1,3]=>[4,2,1]=>35
[4,5,6,2,7,3,1]=>[4,2,1]=>35
[4,5,6,3,1,2,7]=>[4,2,1]=>35
[4,5,6,3,1,7,2]=>[4,2,1]=>35
[4,5,6,3,2,1,7]=>[4,1,1,1]=>20
[4,5,6,3,2,7,1]=>[4,1,1,1]=>20
[4,5,6,3,7,1,2]=>[4,2,1]=>35
[4,5,6,3,7,2,1]=>[4,1,1,1]=>20
[4,5,6,7,1,2,3]=>[4,3]=>14
[4,5,6,7,1,3,2]=>[4,2,1]=>35
[4,5,6,7,2,1,3]=>[4,2,1]=>35
[4,5,6,7,2,3,1]=>[4,2,1]=>35
[4,5,6,7,3,1,2]=>[4,2,1]=>35
[4,5,6,7,3,2,1]=>[4,1,1,1]=>20
[4,5,7,1,2,3,6]=>[4,3]=>14
[4,5,7,1,2,6,3]=>[3,3,1]=>21
[4,5,7,1,3,2,6]=>[3,3,1]=>21
[4,5,7,1,3,6,2]=>[3,3,1]=>21
[4,5,7,1,6,2,3]=>[3,3,1]=>21
[4,5,7,1,6,3,2]=>[3,2,1,1]=>35
[4,5,7,2,1,3,6]=>[3,3,1]=>21
[4,5,7,2,1,6,3]=>[3,2,2]=>21
[4,5,7,2,3,1,6]=>[3,3,1]=>21
[4,5,7,2,3,6,1]=>[3,3,1]=>21
[4,5,7,2,6,1,3]=>[3,2,2]=>21
[4,5,7,2,6,3,1]=>[3,2,1,1]=>35
[4,5,7,3,1,2,6]=>[3,3,1]=>21
[4,5,7,3,1,6,2]=>[3,2,2]=>21
[4,5,7,3,2,1,6]=>[3,2,1,1]=>35
[4,5,7,3,2,6,1]=>[3,2,1,1]=>35
[4,5,7,3,6,1,2]=>[3,2,2]=>21
[4,5,7,3,6,2,1]=>[3,2,1,1]=>35
[4,5,7,6,1,2,3]=>[3,3,1]=>21
[4,5,7,6,1,3,2]=>[3,2,1,1]=>35
[4,5,7,6,2,1,3]=>[3,2,1,1]=>35
[4,5,7,6,2,3,1]=>[3,2,1,1]=>35
[4,5,7,6,3,1,2]=>[3,2,1,1]=>35
[4,5,7,6,3,2,1]=>[3,1,1,1,1]=>15
[4,6,1,2,3,5,7]=>[5,2]=>14
[4,6,1,2,3,7,5]=>[4,3]=>14
[4,6,1,2,5,3,7]=>[4,2,1]=>35
[4,6,1,2,5,7,3]=>[4,2,1]=>35
[4,6,1,2,7,3,5]=>[4,3]=>14
[4,6,1,2,7,5,3]=>[3,3,1]=>21
[4,6,1,3,2,5,7]=>[4,2,1]=>35
[4,6,1,3,2,7,5]=>[3,3,1]=>21
[4,6,1,3,5,2,7]=>[4,2,1]=>35
[4,6,1,3,5,7,2]=>[4,2,1]=>35
[4,6,1,3,7,2,5]=>[3,3,1]=>21
[4,6,1,3,7,5,2]=>[3,3,1]=>21
[4,6,1,5,2,3,7]=>[4,2,1]=>35
[4,6,1,5,2,7,3]=>[3,3,1]=>21
[4,6,1,5,3,2,7]=>[3,2,1,1]=>35
[4,6,1,5,3,7,2]=>[3,2,1,1]=>35
[4,6,1,5,7,2,3]=>[3,3,1]=>21
[4,6,1,5,7,3,2]=>[3,2,1,1]=>35
[4,6,1,7,2,3,5]=>[4,3]=>14
[4,6,1,7,2,5,3]=>[3,3,1]=>21
[4,6,1,7,3,2,5]=>[3,3,1]=>21
[4,6,1,7,3,5,2]=>[3,3,1]=>21
[4,6,1,7,5,2,3]=>[3,3,1]=>21
[4,6,1,7,5,3,2]=>[3,2,1,1]=>35
[4,6,2,1,3,5,7]=>[4,2,1]=>35
[4,6,2,1,3,7,5]=>[3,3,1]=>21
[4,6,2,1,5,3,7]=>[3,2,2]=>21
[4,6,2,1,5,7,3]=>[3,2,2]=>21
[4,6,2,1,7,3,5]=>[3,3,1]=>21
[4,6,2,1,7,5,3]=>[3,2,2]=>21
[4,6,2,3,1,5,7]=>[4,2,1]=>35
[4,6,2,3,1,7,5]=>[3,3,1]=>21
[4,6,2,3,5,1,7]=>[4,2,1]=>35
[4,6,2,3,5,7,1]=>[4,2,1]=>35
[4,6,2,3,7,1,5]=>[3,3,1]=>21
[4,6,2,3,7,5,1]=>[3,3,1]=>21
[4,6,2,5,1,3,7]=>[3,2,2]=>21
[4,6,2,5,1,7,3]=>[3,2,2]=>21
[4,6,2,5,3,1,7]=>[3,2,1,1]=>35
[4,6,2,5,3,7,1]=>[3,2,1,1]=>35
[4,6,2,5,7,1,3]=>[3,2,2]=>21
[4,6,2,5,7,3,1]=>[3,2,1,1]=>35
[4,6,2,7,1,3,5]=>[3,3,1]=>21
[4,6,2,7,1,5,3]=>[3,2,2]=>21
[4,6,2,7,3,1,5]=>[3,3,1]=>21
[4,6,2,7,3,5,1]=>[3,3,1]=>21
[4,6,2,7,5,1,3]=>[3,2,2]=>21
[4,6,2,7,5,3,1]=>[3,2,1,1]=>35
[4,6,3,1,2,5,7]=>[4,2,1]=>35
[4,6,3,1,2,7,5]=>[3,3,1]=>21
[4,6,3,1,5,2,7]=>[3,2,2]=>21
[4,6,3,1,5,7,2]=>[3,2,2]=>21
[4,6,3,1,7,2,5]=>[3,3,1]=>21
[4,6,3,1,7,5,2]=>[3,2,2]=>21
[4,6,3,2,1,5,7]=>[3,2,1,1]=>35
[4,6,3,2,1,7,5]=>[3,2,1,1]=>35
[4,6,3,2,5,1,7]=>[3,2,1,1]=>35
[4,6,3,2,5,7,1]=>[3,2,1,1]=>35
[4,6,3,2,7,1,5]=>[3,2,1,1]=>35
[4,6,3,2,7,5,1]=>[3,2,1,1]=>35
[4,6,3,5,1,2,7]=>[3,2,2]=>21
[4,6,3,5,1,7,2]=>[3,2,2]=>21
[4,6,3,5,2,1,7]=>[3,2,1,1]=>35
[4,6,3,5,2,7,1]=>[3,2,1,1]=>35
[4,6,3,5,7,1,2]=>[3,2,2]=>21
[4,6,3,5,7,2,1]=>[3,2,1,1]=>35
[4,6,3,7,1,2,5]=>[3,3,1]=>21
[4,6,3,7,1,5,2]=>[3,2,2]=>21
[4,6,3,7,2,1,5]=>[3,2,1,1]=>35
[4,6,3,7,2,5,1]=>[3,2,1,1]=>35
[4,6,3,7,5,1,2]=>[3,2,2]=>21
[4,6,3,7,5,2,1]=>[3,2,1,1]=>35
[4,6,5,1,2,3,7]=>[4,2,1]=>35
[4,6,5,1,2,7,3]=>[3,3,1]=>21
[4,6,5,1,3,2,7]=>[3,2,1,1]=>35
[4,6,5,1,3,7,2]=>[3,2,1,1]=>35
[4,6,5,1,7,2,3]=>[3,3,1]=>21
[4,6,5,1,7,3,2]=>[3,2,1,1]=>35
[4,6,5,2,1,3,7]=>[3,2,1,1]=>35
[4,6,5,2,1,7,3]=>[3,2,1,1]=>35
[4,6,5,2,3,1,7]=>[3,2,1,1]=>35
[4,6,5,2,3,7,1]=>[3,2,1,1]=>35
[4,6,5,2,7,1,3]=>[3,2,1,1]=>35
[4,6,5,2,7,3,1]=>[3,2,1,1]=>35
[4,6,5,3,1,2,7]=>[3,2,1,1]=>35
[4,6,5,3,1,7,2]=>[3,2,1,1]=>35
[4,6,5,3,2,1,7]=>[3,1,1,1,1]=>15
[4,6,5,3,2,7,1]=>[3,1,1,1,1]=>15
[4,6,5,3,7,1,2]=>[3,2,1,1]=>35
[4,6,5,3,7,2,1]=>[3,1,1,1,1]=>15
[4,6,5,7,1,2,3]=>[3,3,1]=>21
[4,6,5,7,1,3,2]=>[3,2,1,1]=>35
[4,6,5,7,2,1,3]=>[3,2,1,1]=>35
[4,6,5,7,2,3,1]=>[3,2,1,1]=>35
[4,6,5,7,3,1,2]=>[3,2,1,1]=>35
[4,6,5,7,3,2,1]=>[3,1,1,1,1]=>15
[4,6,7,1,2,3,5]=>[4,3]=>14
[4,6,7,1,2,5,3]=>[3,3,1]=>21
[4,6,7,1,3,2,5]=>[3,3,1]=>21
[4,6,7,1,3,5,2]=>[3,3,1]=>21
[4,6,7,1,5,2,3]=>[3,3,1]=>21
[4,6,7,1,5,3,2]=>[3,2,1,1]=>35
[4,6,7,2,1,3,5]=>[3,3,1]=>21
[4,6,7,2,1,5,3]=>[3,2,2]=>21
[4,6,7,2,3,1,5]=>[3,3,1]=>21
[4,6,7,2,3,5,1]=>[3,3,1]=>21
[4,6,7,2,5,1,3]=>[3,2,2]=>21
[4,6,7,2,5,3,1]=>[3,2,1,1]=>35
[4,6,7,3,1,2,5]=>[3,3,1]=>21
[4,6,7,3,1,5,2]=>[3,2,2]=>21
[4,6,7,3,2,1,5]=>[3,2,1,1]=>35
[4,6,7,3,2,5,1]=>[3,2,1,1]=>35
[4,6,7,3,5,1,2]=>[3,2,2]=>21
[4,6,7,3,5,2,1]=>[3,2,1,1]=>35
[4,6,7,5,1,2,3]=>[3,3,1]=>21
[4,6,7,5,1,3,2]=>[3,2,1,1]=>35
[4,6,7,5,2,1,3]=>[3,2,1,1]=>35
[4,6,7,5,2,3,1]=>[3,2,1,1]=>35
[4,6,7,5,3,1,2]=>[3,2,1,1]=>35
[4,6,7,5,3,2,1]=>[3,1,1,1,1]=>15
[4,7,1,2,3,5,6]=>[5,2]=>14
[4,7,1,2,3,6,5]=>[4,2,1]=>35
[4,7,1,2,5,3,6]=>[4,2,1]=>35
[4,7,1,2,5,6,3]=>[4,2,1]=>35
[4,7,1,2,6,3,5]=>[4,2,1]=>35
[4,7,1,2,6,5,3]=>[3,2,1,1]=>35
[4,7,1,3,2,5,6]=>[4,2,1]=>35
[4,7,1,3,2,6,5]=>[3,2,2]=>21
[4,7,1,3,5,2,6]=>[4,2,1]=>35
[4,7,1,3,5,6,2]=>[4,2,1]=>35
[4,7,1,3,6,2,5]=>[3,2,2]=>21
[4,7,1,3,6,5,2]=>[3,2,1,1]=>35
[4,7,1,5,2,3,6]=>[4,2,1]=>35
[4,7,1,5,2,6,3]=>[3,3,1]=>21
[4,7,1,5,3,2,6]=>[3,2,1,1]=>35
[4,7,1,5,3,6,2]=>[3,2,1,1]=>35
[4,7,1,5,6,2,3]=>[3,3,1]=>21
[4,7,1,5,6,3,2]=>[3,2,1,1]=>35
[4,7,1,6,2,3,5]=>[4,2,1]=>35
[4,7,1,6,2,5,3]=>[3,2,1,1]=>35
[4,7,1,6,3,2,5]=>[3,2,1,1]=>35
[4,7,1,6,3,5,2]=>[3,2,1,1]=>35
[4,7,1,6,5,2,3]=>[3,2,1,1]=>35
[4,7,1,6,5,3,2]=>[2,2,1,1,1]=>14
[4,7,2,1,3,5,6]=>[4,2,1]=>35
[4,7,2,1,3,6,5]=>[3,2,2]=>21
[4,7,2,1,5,3,6]=>[3,2,2]=>21
[4,7,2,1,5,6,3]=>[3,2,2]=>21
[4,7,2,1,6,3,5]=>[3,2,2]=>21
[4,7,2,1,6,5,3]=>[2,2,2,1]=>14
[4,7,2,3,1,5,6]=>[4,2,1]=>35
[4,7,2,3,1,6,5]=>[3,2,2]=>21
[4,7,2,3,5,1,6]=>[4,2,1]=>35
[4,7,2,3,5,6,1]=>[4,2,1]=>35
[4,7,2,3,6,1,5]=>[3,2,2]=>21
[4,7,2,3,6,5,1]=>[3,2,1,1]=>35
[4,7,2,5,1,3,6]=>[3,2,2]=>21
[4,7,2,5,1,6,3]=>[3,2,2]=>21
[4,7,2,5,3,1,6]=>[3,2,1,1]=>35
[4,7,2,5,3,6,1]=>[3,2,1,1]=>35
[4,7,2,5,6,1,3]=>[3,2,2]=>21
[4,7,2,5,6,3,1]=>[3,2,1,1]=>35
[4,7,2,6,1,3,5]=>[3,2,2]=>21
[4,7,2,6,1,5,3]=>[2,2,2,1]=>14
[4,7,2,6,3,1,5]=>[3,2,1,1]=>35
[4,7,2,6,3,5,1]=>[3,2,1,1]=>35
[4,7,2,6,5,1,3]=>[2,2,2,1]=>14
[4,7,2,6,5,3,1]=>[2,2,1,1,1]=>14
[4,7,3,1,2,5,6]=>[4,2,1]=>35
[4,7,3,1,2,6,5]=>[3,2,2]=>21
[4,7,3,1,5,2,6]=>[3,2,2]=>21
[4,7,3,1,5,6,2]=>[3,2,2]=>21
[4,7,3,1,6,2,5]=>[3,2,2]=>21
[4,7,3,1,6,5,2]=>[2,2,2,1]=>14
[4,7,3,2,1,5,6]=>[3,2,1,1]=>35
[4,7,3,2,1,6,5]=>[2,2,2,1]=>14
[4,7,3,2,5,1,6]=>[3,2,1,1]=>35
[4,7,3,2,5,6,1]=>[3,2,1,1]=>35
[4,7,3,2,6,1,5]=>[2,2,2,1]=>14
[4,7,3,2,6,5,1]=>[2,2,2,1]=>14
[4,7,3,5,1,2,6]=>[3,2,2]=>21
[4,7,3,5,1,6,2]=>[3,2,2]=>21
[4,7,3,5,2,1,6]=>[3,2,1,1]=>35
[4,7,3,5,2,6,1]=>[3,2,1,1]=>35
[4,7,3,5,6,1,2]=>[3,2,2]=>21
[4,7,3,5,6,2,1]=>[3,2,1,1]=>35
[4,7,3,6,1,2,5]=>[3,2,2]=>21
[4,7,3,6,1,5,2]=>[2,2,2,1]=>14
[4,7,3,6,2,1,5]=>[2,2,2,1]=>14
[4,7,3,6,2,5,1]=>[2,2,2,1]=>14
[4,7,3,6,5,1,2]=>[2,2,2,1]=>14
[4,7,3,6,5,2,1]=>[2,2,1,1,1]=>14
[4,7,5,1,2,3,6]=>[4,2,1]=>35
[4,7,5,1,2,6,3]=>[3,3,1]=>21
[4,7,5,1,3,2,6]=>[3,2,1,1]=>35
[4,7,5,1,3,6,2]=>[3,2,1,1]=>35
[4,7,5,1,6,2,3]=>[3,3,1]=>21
[4,7,5,1,6,3,2]=>[3,2,1,1]=>35
[4,7,5,2,1,3,6]=>[3,2,1,1]=>35
[4,7,5,2,1,6,3]=>[3,2,1,1]=>35
[4,7,5,2,3,1,6]=>[3,2,1,1]=>35
[4,7,5,2,3,6,1]=>[3,2,1,1]=>35
[4,7,5,2,6,1,3]=>[3,2,1,1]=>35
[4,7,5,2,6,3,1]=>[3,2,1,1]=>35
[4,7,5,3,1,2,6]=>[3,2,1,1]=>35
[4,7,5,3,1,6,2]=>[3,2,1,1]=>35
[4,7,5,3,2,1,6]=>[3,1,1,1,1]=>15
[4,7,5,3,2,6,1]=>[3,1,1,1,1]=>15
[4,7,5,3,6,1,2]=>[3,2,1,1]=>35
[4,7,5,3,6,2,1]=>[3,1,1,1,1]=>15
[4,7,5,6,1,2,3]=>[3,3,1]=>21
[4,7,5,6,1,3,2]=>[3,2,1,1]=>35
[4,7,5,6,2,1,3]=>[3,2,1,1]=>35
[4,7,5,6,2,3,1]=>[3,2,1,1]=>35
[4,7,5,6,3,1,2]=>[3,2,1,1]=>35
[4,7,5,6,3,2,1]=>[3,1,1,1,1]=>15
[4,7,6,1,2,3,5]=>[4,2,1]=>35
[4,7,6,1,2,5,3]=>[3,2,1,1]=>35
[4,7,6,1,3,2,5]=>[3,2,1,1]=>35
[4,7,6,1,3,5,2]=>[3,2,1,1]=>35
[4,7,6,1,5,2,3]=>[3,2,1,1]=>35
[4,7,6,1,5,3,2]=>[2,2,1,1,1]=>14
[4,7,6,2,1,3,5]=>[3,2,1,1]=>35
[4,7,6,2,1,5,3]=>[2,2,2,1]=>14
[4,7,6,2,3,1,5]=>[3,2,1,1]=>35
[4,7,6,2,3,5,1]=>[3,2,1,1]=>35
[4,7,6,2,5,1,3]=>[2,2,2,1]=>14
[4,7,6,2,5,3,1]=>[2,2,1,1,1]=>14
[4,7,6,3,1,2,5]=>[3,2,1,1]=>35
[4,7,6,3,1,5,2]=>[2,2,2,1]=>14
[4,7,6,3,2,1,5]=>[2,2,1,1,1]=>14
[4,7,6,3,2,5,1]=>[2,2,1,1,1]=>14
[4,7,6,3,5,1,2]=>[2,2,2,1]=>14
[4,7,6,3,5,2,1]=>[2,2,1,1,1]=>14
[4,7,6,5,1,2,3]=>[3,2,1,1]=>35
[4,7,6,5,1,3,2]=>[2,2,1,1,1]=>14
[4,7,6,5,2,1,3]=>[2,2,1,1,1]=>14
[4,7,6,5,2,3,1]=>[2,2,1,1,1]=>14
[4,7,6,5,3,1,2]=>[2,2,1,1,1]=>14
[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]=>6
[5,1,2,3,4,6,7]=>[6,1]=>6
[5,1,2,3,4,7,6]=>[5,2]=>14
[5,1,2,3,6,4,7]=>[5,2]=>14
[5,1,2,3,6,7,4]=>[5,2]=>14
[5,1,2,3,7,4,6]=>[5,2]=>14
[5,1,2,3,7,6,4]=>[4,2,1]=>35
[5,1,2,4,3,6,7]=>[5,1,1]=>15
[5,1,2,4,3,7,6]=>[4,2,1]=>35
[5,1,2,4,6,3,7]=>[5,1,1]=>15
[5,1,2,4,6,7,3]=>[5,1,1]=>15
[5,1,2,4,7,3,6]=>[4,2,1]=>35
[5,1,2,4,7,6,3]=>[4,2,1]=>35
[5,1,2,6,3,4,7]=>[5,2]=>14
[5,1,2,6,3,7,4]=>[4,3]=>14
[5,1,2,6,4,3,7]=>[4,2,1]=>35
[5,1,2,6,4,7,3]=>[4,2,1]=>35
[5,1,2,6,7,3,4]=>[4,3]=>14
[5,1,2,6,7,4,3]=>[4,2,1]=>35
[5,1,2,7,3,4,6]=>[5,2]=>14
[5,1,2,7,3,6,4]=>[4,2,1]=>35
[5,1,2,7,4,3,6]=>[4,2,1]=>35
[5,1,2,7,4,6,3]=>[4,2,1]=>35
[5,1,2,7,6,3,4]=>[4,2,1]=>35
[5,1,2,7,6,4,3]=>[3,2,1,1]=>35
[5,1,3,2,4,6,7]=>[5,1,1]=>15
[5,1,3,2,4,7,6]=>[4,2,1]=>35
[5,1,3,2,6,4,7]=>[4,2,1]=>35
[5,1,3,2,6,7,4]=>[4,2,1]=>35
[5,1,3,2,7,4,6]=>[4,2,1]=>35
[5,1,3,2,7,6,4]=>[3,2,2]=>21
[5,1,3,4,2,6,7]=>[5,1,1]=>15
[5,1,3,4,2,7,6]=>[4,2,1]=>35
[5,1,3,4,6,2,7]=>[5,1,1]=>15
[5,1,3,4,6,7,2]=>[5,1,1]=>15
[5,1,3,4,7,2,6]=>[4,2,1]=>35
[5,1,3,4,7,6,2]=>[4,2,1]=>35
[5,1,3,6,2,4,7]=>[4,2,1]=>35
[5,1,3,6,2,7,4]=>[4,2,1]=>35
[5,1,3,6,4,2,7]=>[4,2,1]=>35
[5,1,3,6,4,7,2]=>[4,2,1]=>35
[5,1,3,6,7,2,4]=>[4,2,1]=>35
[5,1,3,6,7,4,2]=>[4,2,1]=>35
[5,1,3,7,2,4,6]=>[4,2,1]=>35
[5,1,3,7,2,6,4]=>[3,2,2]=>21
[5,1,3,7,4,2,6]=>[4,2,1]=>35
[5,1,3,7,4,6,2]=>[4,2,1]=>35
[5,1,3,7,6,2,4]=>[3,2,2]=>21
[5,1,3,7,6,4,2]=>[3,2,1,1]=>35
[5,1,4,2,3,6,7]=>[5,1,1]=>15
[5,1,4,2,3,7,6]=>[4,2,1]=>35
[5,1,4,2,6,3,7]=>[4,2,1]=>35
[5,1,4,2,6,7,3]=>[4,2,1]=>35
[5,1,4,2,7,3,6]=>[4,2,1]=>35
[5,1,4,2,7,6,3]=>[3,2,2]=>21
[5,1,4,3,2,6,7]=>[4,1,1,1]=>20
[5,1,4,3,2,7,6]=>[3,2,1,1]=>35
[5,1,4,3,6,2,7]=>[4,1,1,1]=>20
[5,1,4,3,6,7,2]=>[4,1,1,1]=>20
[5,1,4,3,7,2,6]=>[3,2,1,1]=>35
[5,1,4,3,7,6,2]=>[3,2,1,1]=>35
[5,1,4,6,2,3,7]=>[4,2,1]=>35
[5,1,4,6,2,7,3]=>[4,2,1]=>35
[5,1,4,6,3,2,7]=>[4,1,1,1]=>20
[5,1,4,6,3,7,2]=>[4,1,1,1]=>20
[5,1,4,6,7,2,3]=>[4,2,1]=>35
[5,1,4,6,7,3,2]=>[4,1,1,1]=>20
[5,1,4,7,2,3,6]=>[4,2,1]=>35
[5,1,4,7,2,6,3]=>[3,2,2]=>21
[5,1,4,7,3,2,6]=>[3,2,1,1]=>35
[5,1,4,7,3,6,2]=>[3,2,1,1]=>35
[5,1,4,7,6,2,3]=>[3,2,2]=>21
[5,1,4,7,6,3,2]=>[3,2,1,1]=>35
[5,1,6,2,3,4,7]=>[5,2]=>14
[5,1,6,2,3,7,4]=>[4,3]=>14
[5,1,6,2,4,3,7]=>[4,2,1]=>35
[5,1,6,2,4,7,3]=>[4,2,1]=>35
[5,1,6,2,7,3,4]=>[4,3]=>14
[5,1,6,2,7,4,3]=>[3,3,1]=>21
[5,1,6,3,2,4,7]=>[4,2,1]=>35
[5,1,6,3,2,7,4]=>[3,3,1]=>21
[5,1,6,3,4,2,7]=>[4,2,1]=>35
[5,1,6,3,4,7,2]=>[4,2,1]=>35
[5,1,6,3,7,2,4]=>[3,3,1]=>21
[5,1,6,3,7,4,2]=>[3,3,1]=>21
[5,1,6,4,2,3,7]=>[4,2,1]=>35
[5,1,6,4,2,7,3]=>[3,3,1]=>21
[5,1,6,4,3,2,7]=>[3,2,1,1]=>35
[5,1,6,4,3,7,2]=>[3,2,1,1]=>35
[5,1,6,4,7,2,3]=>[3,3,1]=>21
[5,1,6,4,7,3,2]=>[3,2,1,1]=>35
[5,1,6,7,2,3,4]=>[4,3]=>14
[5,1,6,7,2,4,3]=>[3,3,1]=>21
[5,1,6,7,3,2,4]=>[3,3,1]=>21
[5,1,6,7,3,4,2]=>[3,3,1]=>21
[5,1,6,7,4,2,3]=>[3,3,1]=>21
[5,1,6,7,4,3,2]=>[3,2,1,1]=>35
[5,1,7,2,3,4,6]=>[5,2]=>14
[5,1,7,2,3,6,4]=>[4,2,1]=>35
[5,1,7,2,4,3,6]=>[4,2,1]=>35
[5,1,7,2,4,6,3]=>[4,2,1]=>35
[5,1,7,2,6,3,4]=>[4,2,1]=>35
[5,1,7,2,6,4,3]=>[3,2,1,1]=>35
[5,1,7,3,2,4,6]=>[4,2,1]=>35
[5,1,7,3,2,6,4]=>[3,2,2]=>21
[5,1,7,3,4,2,6]=>[4,2,1]=>35
[5,1,7,3,4,6,2]=>[4,2,1]=>35
[5,1,7,3,6,2,4]=>[3,2,2]=>21
[5,1,7,3,6,4,2]=>[3,2,1,1]=>35
[5,1,7,4,2,3,6]=>[4,2,1]=>35
[5,1,7,4,2,6,3]=>[3,2,2]=>21
[5,1,7,4,3,2,6]=>[3,2,1,1]=>35
[5,1,7,4,3,6,2]=>[3,2,1,1]=>35
[5,1,7,4,6,2,3]=>[3,2,2]=>21
[5,1,7,4,6,3,2]=>[3,2,1,1]=>35
[5,1,7,6,2,3,4]=>[4,2,1]=>35
[5,1,7,6,2,4,3]=>[3,2,1,1]=>35
[5,1,7,6,3,2,4]=>[3,2,1,1]=>35
[5,1,7,6,3,4,2]=>[3,2,1,1]=>35
[5,1,7,6,4,2,3]=>[3,2,1,1]=>35
[5,1,7,6,4,3,2]=>[2,2,1,1,1]=>14
[5,2,1,3,4,6,7]=>[5,1,1]=>15
[5,2,1,3,4,7,6]=>[4,2,1]=>35
[5,2,1,3,6,4,7]=>[4,2,1]=>35
[5,2,1,3,6,7,4]=>[4,2,1]=>35
[5,2,1,3,7,4,6]=>[4,2,1]=>35
[5,2,1,3,7,6,4]=>[3,2,2]=>21
[5,2,1,4,3,6,7]=>[4,2,1]=>35
[5,2,1,4,3,7,6]=>[3,3,1]=>21
[5,2,1,4,6,3,7]=>[4,2,1]=>35
[5,2,1,4,6,7,3]=>[4,2,1]=>35
[5,2,1,4,7,3,6]=>[3,3,1]=>21
[5,2,1,4,7,6,3]=>[3,2,2]=>21
[5,2,1,6,3,4,7]=>[4,2,1]=>35
[5,2,1,6,3,7,4]=>[3,3,1]=>21
[5,2,1,6,4,3,7]=>[3,2,2]=>21
[5,2,1,6,4,7,3]=>[3,2,2]=>21
[5,2,1,6,7,3,4]=>[3,3,1]=>21
[5,2,1,6,7,4,3]=>[3,2,2]=>21
[5,2,1,7,3,4,6]=>[4,2,1]=>35
[5,2,1,7,3,6,4]=>[3,2,2]=>21
[5,2,1,7,4,3,6]=>[3,2,2]=>21
[5,2,1,7,4,6,3]=>[3,2,2]=>21
[5,2,1,7,6,3,4]=>[3,2,2]=>21
[5,2,1,7,6,4,3]=>[2,2,2,1]=>14
[5,2,3,1,4,6,7]=>[5,1,1]=>15
[5,2,3,1,4,7,6]=>[4,2,1]=>35
[5,2,3,1,6,4,7]=>[4,2,1]=>35
[5,2,3,1,6,7,4]=>[4,2,1]=>35
[5,2,3,1,7,4,6]=>[4,2,1]=>35
[5,2,3,1,7,6,4]=>[3,2,2]=>21
[5,2,3,4,1,6,7]=>[5,1,1]=>15
[5,2,3,4,1,7,6]=>[4,2,1]=>35
[5,2,3,4,6,1,7]=>[5,1,1]=>15
[5,2,3,4,6,7,1]=>[5,1,1]=>15
[5,2,3,4,7,1,6]=>[4,2,1]=>35
[5,2,3,4,7,6,1]=>[4,2,1]=>35
[5,2,3,6,1,4,7]=>[4,2,1]=>35
[5,2,3,6,1,7,4]=>[4,2,1]=>35
[5,2,3,6,4,1,7]=>[4,2,1]=>35
[5,2,3,6,4,7,1]=>[4,2,1]=>35
[5,2,3,6,7,1,4]=>[4,2,1]=>35
[5,2,3,6,7,4,1]=>[4,2,1]=>35
[5,2,3,7,1,4,6]=>[4,2,1]=>35
[5,2,3,7,1,6,4]=>[3,2,2]=>21
[5,2,3,7,4,1,6]=>[4,2,1]=>35
[5,2,3,7,4,6,1]=>[4,2,1]=>35
[5,2,3,7,6,1,4]=>[3,2,2]=>21
[5,2,3,7,6,4,1]=>[3,2,1,1]=>35
[5,2,4,1,3,6,7]=>[4,2,1]=>35
[5,2,4,1,3,7,6]=>[3,3,1]=>21
[5,2,4,1,6,3,7]=>[4,2,1]=>35
[5,2,4,1,6,7,3]=>[4,2,1]=>35
[5,2,4,1,7,3,6]=>[3,3,1]=>21
[5,2,4,1,7,6,3]=>[3,2,2]=>21
[5,2,4,3,1,6,7]=>[4,1,1,1]=>20
[5,2,4,3,1,7,6]=>[3,2,1,1]=>35
[5,2,4,3,6,1,7]=>[4,1,1,1]=>20
[5,2,4,3,6,7,1]=>[4,1,1,1]=>20
[5,2,4,3,7,1,6]=>[3,2,1,1]=>35
[5,2,4,3,7,6,1]=>[3,2,1,1]=>35
[5,2,4,6,1,3,7]=>[4,2,1]=>35
[5,2,4,6,1,7,3]=>[4,2,1]=>35
[5,2,4,6,3,1,7]=>[4,1,1,1]=>20
[5,2,4,6,3,7,1]=>[4,1,1,1]=>20
[5,2,4,6,7,1,3]=>[4,2,1]=>35
[5,2,4,6,7,3,1]=>[4,1,1,1]=>20
[5,2,4,7,1,3,6]=>[3,3,1]=>21
[5,2,4,7,1,6,3]=>[3,2,2]=>21
[5,2,4,7,3,1,6]=>[3,2,1,1]=>35
[5,2,4,7,3,6,1]=>[3,2,1,1]=>35
[5,2,4,7,6,1,3]=>[3,2,2]=>21
[5,2,4,7,6,3,1]=>[3,2,1,1]=>35
[5,2,6,1,3,4,7]=>[4,2,1]=>35
[5,2,6,1,3,7,4]=>[3,3,1]=>21
[5,2,6,1,4,3,7]=>[3,2,2]=>21
[5,2,6,1,4,7,3]=>[3,2,2]=>21
[5,2,6,1,7,3,4]=>[3,3,1]=>21
[5,2,6,1,7,4,3]=>[3,2,2]=>21
[5,2,6,3,1,4,7]=>[4,2,1]=>35
[5,2,6,3,1,7,4]=>[3,3,1]=>21
[5,2,6,3,4,1,7]=>[4,2,1]=>35
[5,2,6,3,4,7,1]=>[4,2,1]=>35
[5,2,6,3,7,1,4]=>[3,3,1]=>21
[5,2,6,3,7,4,1]=>[3,3,1]=>21
[5,2,6,4,1,3,7]=>[3,2,2]=>21
[5,2,6,4,1,7,3]=>[3,2,2]=>21
[5,2,6,4,3,1,7]=>[3,2,1,1]=>35
[5,2,6,4,3,7,1]=>[3,2,1,1]=>35
[5,2,6,4,7,1,3]=>[3,2,2]=>21
[5,2,6,4,7,3,1]=>[3,2,1,1]=>35
[5,2,6,7,1,3,4]=>[3,3,1]=>21
[5,2,6,7,1,4,3]=>[3,2,2]=>21
[5,2,6,7,3,1,4]=>[3,3,1]=>21
[5,2,6,7,3,4,1]=>[3,3,1]=>21
[5,2,6,7,4,1,3]=>[3,2,2]=>21
[5,2,6,7,4,3,1]=>[3,2,1,1]=>35
[5,2,7,1,3,4,6]=>[4,2,1]=>35
[5,2,7,1,3,6,4]=>[3,2,2]=>21
[5,2,7,1,4,3,6]=>[3,2,2]=>21
[5,2,7,1,4,6,3]=>[3,2,2]=>21
[5,2,7,1,6,3,4]=>[3,2,2]=>21
[5,2,7,1,6,4,3]=>[2,2,2,1]=>14
[5,2,7,3,1,4,6]=>[4,2,1]=>35
[5,2,7,3,1,6,4]=>[3,2,2]=>21
[5,2,7,3,4,1,6]=>[4,2,1]=>35
[5,2,7,3,4,6,1]=>[4,2,1]=>35
[5,2,7,3,6,1,4]=>[3,2,2]=>21
[5,2,7,3,6,4,1]=>[3,2,1,1]=>35
[5,2,7,4,1,3,6]=>[3,2,2]=>21
[5,2,7,4,1,6,3]=>[3,2,2]=>21
[5,2,7,4,3,1,6]=>[3,2,1,1]=>35
[5,2,7,4,3,6,1]=>[3,2,1,1]=>35
[5,2,7,4,6,1,3]=>[3,2,2]=>21
[5,2,7,4,6,3,1]=>[3,2,1,1]=>35
[5,2,7,6,1,3,4]=>[3,2,2]=>21
[5,2,7,6,1,4,3]=>[2,2,2,1]=>14
[5,2,7,6,3,1,4]=>[3,2,1,1]=>35
[5,2,7,6,3,4,1]=>[3,2,1,1]=>35
[5,2,7,6,4,1,3]=>[2,2,2,1]=>14
[5,2,7,6,4,3,1]=>[2,2,1,1,1]=>14
[5,3,1,2,4,6,7]=>[5,1,1]=>15
[5,3,1,2,4,7,6]=>[4,2,1]=>35
[5,3,1,2,6,4,7]=>[4,2,1]=>35
[5,3,1,2,6,7,4]=>[4,2,1]=>35
[5,3,1,2,7,4,6]=>[4,2,1]=>35
[5,3,1,2,7,6,4]=>[3,2,2]=>21
[5,3,1,4,2,6,7]=>[4,2,1]=>35
[5,3,1,4,2,7,6]=>[3,3,1]=>21
[5,3,1,4,6,2,7]=>[4,2,1]=>35
[5,3,1,4,6,7,2]=>[4,2,1]=>35
[5,3,1,4,7,2,6]=>[3,3,1]=>21
[5,3,1,4,7,6,2]=>[3,2,2]=>21
[5,3,1,6,2,4,7]=>[4,2,1]=>35
[5,3,1,6,2,7,4]=>[3,3,1]=>21
[5,3,1,6,4,2,7]=>[3,2,2]=>21
[5,3,1,6,4,7,2]=>[3,2,2]=>21
[5,3,1,6,7,2,4]=>[3,3,1]=>21
[5,3,1,6,7,4,2]=>[3,2,2]=>21
[5,3,1,7,2,4,6]=>[4,2,1]=>35
[5,3,1,7,2,6,4]=>[3,2,2]=>21
[5,3,1,7,4,2,6]=>[3,2,2]=>21
[5,3,1,7,4,6,2]=>[3,2,2]=>21
[5,3,1,7,6,2,4]=>[3,2,2]=>21
[5,3,1,7,6,4,2]=>[2,2,2,1]=>14
[5,3,2,1,4,6,7]=>[4,1,1,1]=>20
[5,3,2,1,4,7,6]=>[3,2,1,1]=>35
[5,3,2,1,6,4,7]=>[3,2,1,1]=>35
[5,3,2,1,6,7,4]=>[3,2,1,1]=>35
[5,3,2,1,7,4,6]=>[3,2,1,1]=>35
[5,3,2,1,7,6,4]=>[2,2,2,1]=>14
[5,3,2,4,1,6,7]=>[4,1,1,1]=>20
[5,3,2,4,1,7,6]=>[3,2,1,1]=>35
[5,3,2,4,6,1,7]=>[4,1,1,1]=>20
[5,3,2,4,6,7,1]=>[4,1,1,1]=>20
[5,3,2,4,7,1,6]=>[3,2,1,1]=>35
[5,3,2,4,7,6,1]=>[3,2,1,1]=>35
[5,3,2,6,1,4,7]=>[3,2,1,1]=>35
[5,3,2,6,1,7,4]=>[3,2,1,1]=>35
[5,3,2,6,4,1,7]=>[3,2,1,1]=>35
[5,3,2,6,4,7,1]=>[3,2,1,1]=>35
[5,3,2,6,7,1,4]=>[3,2,1,1]=>35
[5,3,2,6,7,4,1]=>[3,2,1,1]=>35
[5,3,2,7,1,4,6]=>[3,2,1,1]=>35
[5,3,2,7,1,6,4]=>[2,2,2,1]=>14
[5,3,2,7,4,1,6]=>[3,2,1,1]=>35
[5,3,2,7,4,6,1]=>[3,2,1,1]=>35
[5,3,2,7,6,1,4]=>[2,2,2,1]=>14
[5,3,2,7,6,4,1]=>[2,2,2,1]=>14
[5,3,4,1,2,6,7]=>[4,2,1]=>35
[5,3,4,1,2,7,6]=>[3,3,1]=>21
[5,3,4,1,6,2,7]=>[4,2,1]=>35
[5,3,4,1,6,7,2]=>[4,2,1]=>35
[5,3,4,1,7,2,6]=>[3,3,1]=>21
[5,3,4,1,7,6,2]=>[3,2,2]=>21
[5,3,4,2,1,6,7]=>[4,1,1,1]=>20
[5,3,4,2,1,7,6]=>[3,2,1,1]=>35
[5,3,4,2,6,1,7]=>[4,1,1,1]=>20
[5,3,4,2,6,7,1]=>[4,1,1,1]=>20
[5,3,4,2,7,1,6]=>[3,2,1,1]=>35
[5,3,4,2,7,6,1]=>[3,2,1,1]=>35
[5,3,4,6,1,2,7]=>[4,2,1]=>35
[5,3,4,6,1,7,2]=>[4,2,1]=>35
[5,3,4,6,2,1,7]=>[4,1,1,1]=>20
[5,3,4,6,2,7,1]=>[4,1,1,1]=>20
[5,3,4,6,7,1,2]=>[4,2,1]=>35
[5,3,4,6,7,2,1]=>[4,1,1,1]=>20
[5,3,4,7,1,2,6]=>[3,3,1]=>21
[5,3,4,7,1,6,2]=>[3,2,2]=>21
[5,3,4,7,2,1,6]=>[3,2,1,1]=>35
[5,3,4,7,2,6,1]=>[3,2,1,1]=>35
[5,3,4,7,6,1,2]=>[3,2,2]=>21
[5,3,4,7,6,2,1]=>[3,2,1,1]=>35
[5,3,6,1,2,4,7]=>[4,2,1]=>35
[5,3,6,1,2,7,4]=>[3,3,1]=>21
[5,3,6,1,4,2,7]=>[3,2,2]=>21
[5,3,6,1,4,7,2]=>[3,2,2]=>21
[5,3,6,1,7,2,4]=>[3,3,1]=>21
[5,3,6,1,7,4,2]=>[3,2,2]=>21
[5,3,6,2,1,4,7]=>[3,2,1,1]=>35
[5,3,6,2,1,7,4]=>[3,2,1,1]=>35
[5,3,6,2,4,1,7]=>[3,2,1,1]=>35
[5,3,6,2,4,7,1]=>[3,2,1,1]=>35
[5,3,6,2,7,1,4]=>[3,2,1,1]=>35
[5,3,6,2,7,4,1]=>[3,2,1,1]=>35
[5,3,6,4,1,2,7]=>[3,2,2]=>21
[5,3,6,4,1,7,2]=>[3,2,2]=>21
[5,3,6,4,2,1,7]=>[3,2,1,1]=>35
[5,3,6,4,2,7,1]=>[3,2,1,1]=>35
[5,3,6,4,7,1,2]=>[3,2,2]=>21
[5,3,6,4,7,2,1]=>[3,2,1,1]=>35
[5,3,6,7,1,2,4]=>[3,3,1]=>21
[5,3,6,7,1,4,2]=>[3,2,2]=>21
[5,3,6,7,2,1,4]=>[3,2,1,1]=>35
[5,3,6,7,2,4,1]=>[3,2,1,1]=>35
[5,3,6,7,4,1,2]=>[3,2,2]=>21
[5,3,6,7,4,2,1]=>[3,2,1,1]=>35
[5,3,7,1,2,4,6]=>[4,2,1]=>35
[5,3,7,1,2,6,4]=>[3,2,2]=>21
[5,3,7,1,4,2,6]=>[3,2,2]=>21
[5,3,7,1,4,6,2]=>[3,2,2]=>21
[5,3,7,1,6,2,4]=>[3,2,2]=>21
[5,3,7,1,6,4,2]=>[2,2,2,1]=>14
[5,3,7,2,1,4,6]=>[3,2,1,1]=>35
[5,3,7,2,1,6,4]=>[2,2,2,1]=>14
[5,3,7,2,4,1,6]=>[3,2,1,1]=>35
[5,3,7,2,4,6,1]=>[3,2,1,1]=>35
[5,3,7,2,6,1,4]=>[2,2,2,1]=>14
[5,3,7,2,6,4,1]=>[2,2,2,1]=>14
[5,3,7,4,1,2,6]=>[3,2,2]=>21
[5,3,7,4,1,6,2]=>[3,2,2]=>21
[5,3,7,4,2,1,6]=>[3,2,1,1]=>35
[5,3,7,4,2,6,1]=>[3,2,1,1]=>35
[5,3,7,4,6,1,2]=>[3,2,2]=>21
[5,3,7,4,6,2,1]=>[3,2,1,1]=>35
[5,3,7,6,1,2,4]=>[3,2,2]=>21
[5,3,7,6,1,4,2]=>[2,2,2,1]=>14
[5,3,7,6,2,1,4]=>[2,2,2,1]=>14
[5,3,7,6,2,4,1]=>[2,2,2,1]=>14
[5,3,7,6,4,1,2]=>[2,2,2,1]=>14
[5,3,7,6,4,2,1]=>[2,2,1,1,1]=>14
[5,4,1,2,3,6,7]=>[5,1,1]=>15
[5,4,1,2,3,7,6]=>[4,2,1]=>35
[5,4,1,2,6,3,7]=>[4,2,1]=>35
[5,4,1,2,6,7,3]=>[4,2,1]=>35
[5,4,1,2,7,3,6]=>[4,2,1]=>35
[5,4,1,2,7,6,3]=>[3,2,2]=>21
[5,4,1,3,2,6,7]=>[4,1,1,1]=>20
[5,4,1,3,2,7,6]=>[3,2,1,1]=>35
[5,4,1,3,6,2,7]=>[4,1,1,1]=>20
[5,4,1,3,6,7,2]=>[4,1,1,1]=>20
[5,4,1,3,7,2,6]=>[3,2,1,1]=>35
[5,4,1,3,7,6,2]=>[3,2,1,1]=>35
[5,4,1,6,2,3,7]=>[4,2,1]=>35
[5,4,1,6,2,7,3]=>[3,3,1]=>21
[5,4,1,6,3,2,7]=>[3,2,1,1]=>35
[5,4,1,6,3,7,2]=>[3,2,1,1]=>35
[5,4,1,6,7,2,3]=>[3,3,1]=>21
[5,4,1,6,7,3,2]=>[3,2,1,1]=>35
[5,4,1,7,2,3,6]=>[4,2,1]=>35
[5,4,1,7,2,6,3]=>[3,2,2]=>21
[5,4,1,7,3,2,6]=>[3,2,1,1]=>35
[5,4,1,7,3,6,2]=>[3,2,1,1]=>35
[5,4,1,7,6,2,3]=>[3,2,2]=>21
[5,4,1,7,6,3,2]=>[2,2,2,1]=>14
[5,4,2,1,3,6,7]=>[4,1,1,1]=>20
[5,4,2,1,3,7,6]=>[3,2,1,1]=>35
[5,4,2,1,6,3,7]=>[3,2,1,1]=>35
[5,4,2,1,6,7,3]=>[3,2,1,1]=>35
[5,4,2,1,7,3,6]=>[3,2,1,1]=>35
[5,4,2,1,7,6,3]=>[2,2,2,1]=>14
[5,4,2,3,1,6,7]=>[4,1,1,1]=>20
[5,4,2,3,1,7,6]=>[3,2,1,1]=>35
[5,4,2,3,6,1,7]=>[4,1,1,1]=>20
[5,4,2,3,6,7,1]=>[4,1,1,1]=>20
[5,4,2,3,7,1,6]=>[3,2,1,1]=>35
[5,4,2,3,7,6,1]=>[3,2,1,1]=>35
[5,4,2,6,1,3,7]=>[3,2,1,1]=>35
[5,4,2,6,1,7,3]=>[3,2,1,1]=>35
[5,4,2,6,3,1,7]=>[3,2,1,1]=>35
[5,4,2,6,3,7,1]=>[3,2,1,1]=>35
[5,4,2,6,7,1,3]=>[3,2,1,1]=>35
[5,4,2,6,7,3,1]=>[3,2,1,1]=>35
[5,4,2,7,1,3,6]=>[3,2,1,1]=>35
[5,4,2,7,1,6,3]=>[2,2,2,1]=>14
[5,4,2,7,3,1,6]=>[3,2,1,1]=>35
[5,4,2,7,3,6,1]=>[3,2,1,1]=>35
[5,4,2,7,6,1,3]=>[2,2,2,1]=>14
[5,4,2,7,6,3,1]=>[2,2,2,1]=>14
[5,4,3,1,2,6,7]=>[4,1,1,1]=>20
[5,4,3,1,2,7,6]=>[3,2,1,1]=>35
[5,4,3,1,6,2,7]=>[3,2,1,1]=>35
[5,4,3,1,6,7,2]=>[3,2,1,1]=>35
[5,4,3,1,7,2,6]=>[3,2,1,1]=>35
[5,4,3,1,7,6,2]=>[2,2,2,1]=>14
[5,4,3,2,1,6,7]=>[3,1,1,1,1]=>15
[5,4,3,2,1,7,6]=>[2,2,1,1,1]=>14
[5,4,3,2,6,1,7]=>[3,1,1,1,1]=>15
[5,4,3,2,6,7,1]=>[3,1,1,1,1]=>15
[5,4,3,2,7,1,6]=>[2,2,1,1,1]=>14
[5,4,3,2,7,6,1]=>[2,2,1,1,1]=>14
[5,4,3,6,1,2,7]=>[3,2,1,1]=>35
[5,4,3,6,1,7,2]=>[3,2,1,1]=>35
[5,4,3,6,2,1,7]=>[3,1,1,1,1]=>15
[5,4,3,6,2,7,1]=>[3,1,1,1,1]=>15
[5,4,3,6,7,1,2]=>[3,2,1,1]=>35
[5,4,3,6,7,2,1]=>[3,1,1,1,1]=>15
[5,4,3,7,1,2,6]=>[3,2,1,1]=>35
[5,4,3,7,1,6,2]=>[2,2,2,1]=>14
[5,4,3,7,2,1,6]=>[2,2,1,1,1]=>14
[5,4,3,7,2,6,1]=>[2,2,1,1,1]=>14
[5,4,3,7,6,1,2]=>[2,2,2,1]=>14
[5,4,3,7,6,2,1]=>[2,2,1,1,1]=>14
[5,4,6,1,2,3,7]=>[4,2,1]=>35
[5,4,6,1,2,7,3]=>[3,3,1]=>21
[5,4,6,1,3,2,7]=>[3,2,1,1]=>35
[5,4,6,1,3,7,2]=>[3,2,1,1]=>35
[5,4,6,1,7,2,3]=>[3,3,1]=>21
[5,4,6,1,7,3,2]=>[3,2,1,1]=>35
[5,4,6,2,1,3,7]=>[3,2,1,1]=>35
[5,4,6,2,1,7,3]=>[3,2,1,1]=>35
[5,4,6,2,3,1,7]=>[3,2,1,1]=>35
[5,4,6,2,3,7,1]=>[3,2,1,1]=>35
[5,4,6,2,7,1,3]=>[3,2,1,1]=>35
[5,4,6,2,7,3,1]=>[3,2,1,1]=>35
[5,4,6,3,1,2,7]=>[3,2,1,1]=>35
[5,4,6,3,1,7,2]=>[3,2,1,1]=>35
[5,4,6,3,2,1,7]=>[3,1,1,1,1]=>15
[5,4,6,3,2,7,1]=>[3,1,1,1,1]=>15
[5,4,6,3,7,1,2]=>[3,2,1,1]=>35
[5,4,6,3,7,2,1]=>[3,1,1,1,1]=>15
[5,4,6,7,1,2,3]=>[3,3,1]=>21
[5,4,6,7,1,3,2]=>[3,2,1,1]=>35
[5,4,6,7,2,1,3]=>[3,2,1,1]=>35
[5,4,6,7,2,3,1]=>[3,2,1,1]=>35
[5,4,6,7,3,1,2]=>[3,2,1,1]=>35
[5,4,6,7,3,2,1]=>[3,1,1,1,1]=>15
[5,4,7,1,2,3,6]=>[4,2,1]=>35
[5,4,7,1,2,6,3]=>[3,2,2]=>21
[5,4,7,1,3,2,6]=>[3,2,1,1]=>35
[5,4,7,1,3,6,2]=>[3,2,1,1]=>35
[5,4,7,1,6,2,3]=>[3,2,2]=>21
[5,4,7,1,6,3,2]=>[2,2,2,1]=>14
[5,4,7,2,1,3,6]=>[3,2,1,1]=>35
[5,4,7,2,1,6,3]=>[2,2,2,1]=>14
[5,4,7,2,3,1,6]=>[3,2,1,1]=>35
[5,4,7,2,3,6,1]=>[3,2,1,1]=>35
[5,4,7,2,6,1,3]=>[2,2,2,1]=>14
[5,4,7,2,6,3,1]=>[2,2,2,1]=>14
[5,4,7,3,1,2,6]=>[3,2,1,1]=>35
[5,4,7,3,1,6,2]=>[2,2,2,1]=>14
[5,4,7,3,2,1,6]=>[2,2,1,1,1]=>14
[5,4,7,3,2,6,1]=>[2,2,1,1,1]=>14
[5,4,7,3,6,1,2]=>[2,2,2,1]=>14
[5,4,7,3,6,2,1]=>[2,2,1,1,1]=>14
[5,4,7,6,1,2,3]=>[3,2,2]=>21
[5,4,7,6,1,3,2]=>[2,2,2,1]=>14
[5,4,7,6,2,1,3]=>[2,2,2,1]=>14
[5,4,7,6,2,3,1]=>[2,2,2,1]=>14
[5,4,7,6,3,1,2]=>[2,2,2,1]=>14
[5,4,7,6,3,2,1]=>[2,2,1,1,1]=>14
[5,6,1,2,3,4,7]=>[5,2]=>14
[5,6,1,2,3,7,4]=>[4,3]=>14
[5,6,1,2,4,3,7]=>[4,2,1]=>35
[5,6,1,2,4,7,3]=>[4,2,1]=>35
[5,6,1,2,7,3,4]=>[4,3]=>14
[5,6,1,2,7,4,3]=>[3,3,1]=>21
[5,6,1,3,2,4,7]=>[4,2,1]=>35
[5,6,1,3,2,7,4]=>[3,3,1]=>21
[5,6,1,3,4,2,7]=>[4,2,1]=>35
[5,6,1,3,4,7,2]=>[4,2,1]=>35
[5,6,1,3,7,2,4]=>[3,3,1]=>21
[5,6,1,3,7,4,2]=>[3,3,1]=>21
[5,6,1,4,2,3,7]=>[4,2,1]=>35
[5,6,1,4,2,7,3]=>[3,3,1]=>21
[5,6,1,4,3,2,7]=>[3,2,1,1]=>35
[5,6,1,4,3,7,2]=>[3,2,1,1]=>35
[5,6,1,4,7,2,3]=>[3,3,1]=>21
[5,6,1,4,7,3,2]=>[3,2,1,1]=>35
[5,6,1,7,2,3,4]=>[4,3]=>14
[5,6,1,7,2,4,3]=>[3,3,1]=>21
[5,6,1,7,3,2,4]=>[3,3,1]=>21
[5,6,1,7,3,4,2]=>[3,3,1]=>21
[5,6,1,7,4,2,3]=>[3,3,1]=>21
[5,6,1,7,4,3,2]=>[3,2,1,1]=>35
[5,6,2,1,3,4,7]=>[4,2,1]=>35
[5,6,2,1,3,7,4]=>[3,3,1]=>21
[5,6,2,1,4,3,7]=>[3,2,2]=>21
[5,6,2,1,4,7,3]=>[3,2,2]=>21
[5,6,2,1,7,3,4]=>[3,3,1]=>21
[5,6,2,1,7,4,3]=>[3,2,2]=>21
[5,6,2,3,1,4,7]=>[4,2,1]=>35
[5,6,2,3,1,7,4]=>[3,3,1]=>21
[5,6,2,3,4,1,7]=>[4,2,1]=>35
[5,6,2,3,4,7,1]=>[4,2,1]=>35
[5,6,2,3,7,1,4]=>[3,3,1]=>21
[5,6,2,3,7,4,1]=>[3,3,1]=>21
[5,6,2,4,1,3,7]=>[3,2,2]=>21
[5,6,2,4,1,7,3]=>[3,2,2]=>21
[5,6,2,4,3,1,7]=>[3,2,1,1]=>35
[5,6,2,4,3,7,1]=>[3,2,1,1]=>35
[5,6,2,4,7,1,3]=>[3,2,2]=>21
[5,6,2,4,7,3,1]=>[3,2,1,1]=>35
[5,6,2,7,1,3,4]=>[3,3,1]=>21
[5,6,2,7,1,4,3]=>[3,2,2]=>21
[5,6,2,7,3,1,4]=>[3,3,1]=>21
[5,6,2,7,3,4,1]=>[3,3,1]=>21
[5,6,2,7,4,1,3]=>[3,2,2]=>21
[5,6,2,7,4,3,1]=>[3,2,1,1]=>35
[5,6,3,1,2,4,7]=>[4,2,1]=>35
[5,6,3,1,2,7,4]=>[3,3,1]=>21
[5,6,3,1,4,2,7]=>[3,2,2]=>21
[5,6,3,1,4,7,2]=>[3,2,2]=>21
[5,6,3,1,7,2,4]=>[3,3,1]=>21
[5,6,3,1,7,4,2]=>[3,2,2]=>21
[5,6,3,2,1,4,7]=>[3,2,1,1]=>35
[5,6,3,2,1,7,4]=>[3,2,1,1]=>35
[5,6,3,2,4,1,7]=>[3,2,1,1]=>35
[5,6,3,2,4,7,1]=>[3,2,1,1]=>35
[5,6,3,2,7,1,4]=>[3,2,1,1]=>35
[5,6,3,2,7,4,1]=>[3,2,1,1]=>35
[5,6,3,4,1,2,7]=>[3,2,2]=>21
[5,6,3,4,1,7,2]=>[3,2,2]=>21
[5,6,3,4,2,1,7]=>[3,2,1,1]=>35
[5,6,3,4,2,7,1]=>[3,2,1,1]=>35
[5,6,3,4,7,1,2]=>[3,2,2]=>21
[5,6,3,4,7,2,1]=>[3,2,1,1]=>35
[5,6,3,7,1,2,4]=>[3,3,1]=>21
[5,6,3,7,1,4,2]=>[3,2,2]=>21
[5,6,3,7,2,1,4]=>[3,2,1,1]=>35
[5,6,3,7,2,4,1]=>[3,2,1,1]=>35
[5,6,3,7,4,1,2]=>[3,2,2]=>21
[5,6,3,7,4,2,1]=>[3,2,1,1]=>35
[5,6,4,1,2,3,7]=>[4,2,1]=>35
[5,6,4,1,2,7,3]=>[3,3,1]=>21
[5,6,4,1,3,2,7]=>[3,2,1,1]=>35
[5,6,4,1,3,7,2]=>[3,2,1,1]=>35
[5,6,4,1,7,2,3]=>[3,3,1]=>21
[5,6,4,1,7,3,2]=>[3,2,1,1]=>35
[5,6,4,2,1,3,7]=>[3,2,1,1]=>35
[5,6,4,2,1,7,3]=>[3,2,1,1]=>35
[5,6,4,2,3,1,7]=>[3,2,1,1]=>35
[5,6,4,2,3,7,1]=>[3,2,1,1]=>35
[5,6,4,2,7,1,3]=>[3,2,1,1]=>35
[5,6,4,2,7,3,1]=>[3,2,1,1]=>35
[5,6,4,3,1,2,7]=>[3,2,1,1]=>35
[5,6,4,3,1,7,2]=>[3,2,1,1]=>35
[5,6,4,3,2,1,7]=>[3,1,1,1,1]=>15
[5,6,4,3,2,7,1]=>[3,1,1,1,1]=>15
[5,6,4,3,7,1,2]=>[3,2,1,1]=>35
[5,6,4,3,7,2,1]=>[3,1,1,1,1]=>15
[5,6,4,7,1,2,3]=>[3,3,1]=>21
[5,6,4,7,1,3,2]=>[3,2,1,1]=>35
[5,6,4,7,2,1,3]=>[3,2,1,1]=>35
[5,6,4,7,2,3,1]=>[3,2,1,1]=>35
[5,6,4,7,3,1,2]=>[3,2,1,1]=>35
[5,6,4,7,3,2,1]=>[3,1,1,1,1]=>15
[5,6,7,1,2,3,4]=>[4,3]=>14
[5,6,7,1,2,4,3]=>[3,3,1]=>21
[5,6,7,1,3,2,4]=>[3,3,1]=>21
[5,6,7,1,3,4,2]=>[3,3,1]=>21
[5,6,7,1,4,2,3]=>[3,3,1]=>21
[5,6,7,1,4,3,2]=>[3,2,1,1]=>35
[5,6,7,2,1,3,4]=>[3,3,1]=>21
[5,6,7,2,1,4,3]=>[3,2,2]=>21
[5,6,7,2,3,1,4]=>[3,3,1]=>21
[5,6,7,2,3,4,1]=>[3,3,1]=>21
[5,6,7,2,4,1,3]=>[3,2,2]=>21
[5,6,7,2,4,3,1]=>[3,2,1,1]=>35
[5,6,7,3,1,2,4]=>[3,3,1]=>21
[5,6,7,3,1,4,2]=>[3,2,2]=>21
[5,6,7,3,2,1,4]=>[3,2,1,1]=>35
[5,6,7,3,2,4,1]=>[3,2,1,1]=>35
[5,6,7,3,4,1,2]=>[3,2,2]=>21
[5,6,7,3,4,2,1]=>[3,2,1,1]=>35
[5,6,7,4,1,2,3]=>[3,3,1]=>21
[5,6,7,4,1,3,2]=>[3,2,1,1]=>35
[5,6,7,4,2,1,3]=>[3,2,1,1]=>35
[5,6,7,4,2,3,1]=>[3,2,1,1]=>35
[5,6,7,4,3,1,2]=>[3,2,1,1]=>35
[5,6,7,4,3,2,1]=>[3,1,1,1,1]=>15
[5,7,1,2,3,4,6]=>[5,2]=>14
[5,7,1,2,3,6,4]=>[4,2,1]=>35
[5,7,1,2,4,3,6]=>[4,2,1]=>35
[5,7,1,2,4,6,3]=>[4,2,1]=>35
[5,7,1,2,6,3,4]=>[4,2,1]=>35
[5,7,1,2,6,4,3]=>[3,2,1,1]=>35
[5,7,1,3,2,4,6]=>[4,2,1]=>35
[5,7,1,3,2,6,4]=>[3,2,2]=>21
[5,7,1,3,4,2,6]=>[4,2,1]=>35
[5,7,1,3,4,6,2]=>[4,2,1]=>35
[5,7,1,3,6,2,4]=>[3,2,2]=>21
[5,7,1,3,6,4,2]=>[3,2,1,1]=>35
[5,7,1,4,2,3,6]=>[4,2,1]=>35
[5,7,1,4,2,6,3]=>[3,2,2]=>21
[5,7,1,4,3,2,6]=>[3,2,1,1]=>35
[5,7,1,4,3,6,2]=>[3,2,1,1]=>35
[5,7,1,4,6,2,3]=>[3,2,2]=>21
[5,7,1,4,6,3,2]=>[3,2,1,1]=>35
[5,7,1,6,2,3,4]=>[4,2,1]=>35
[5,7,1,6,2,4,3]=>[3,2,1,1]=>35
[5,7,1,6,3,2,4]=>[3,2,1,1]=>35
[5,7,1,6,3,4,2]=>[3,2,1,1]=>35
[5,7,1,6,4,2,3]=>[3,2,1,1]=>35
[5,7,1,6,4,3,2]=>[2,2,1,1,1]=>14
[5,7,2,1,3,4,6]=>[4,2,1]=>35
[5,7,2,1,3,6,4]=>[3,2,2]=>21
[5,7,2,1,4,3,6]=>[3,2,2]=>21
[5,7,2,1,4,6,3]=>[3,2,2]=>21
[5,7,2,1,6,3,4]=>[3,2,2]=>21
[5,7,2,1,6,4,3]=>[2,2,2,1]=>14
[5,7,2,3,1,4,6]=>[4,2,1]=>35
[5,7,2,3,1,6,4]=>[3,2,2]=>21
[5,7,2,3,4,1,6]=>[4,2,1]=>35
[5,7,2,3,4,6,1]=>[4,2,1]=>35
[5,7,2,3,6,1,4]=>[3,2,2]=>21
[5,7,2,3,6,4,1]=>[3,2,1,1]=>35
[5,7,2,4,1,3,6]=>[3,2,2]=>21
[5,7,2,4,1,6,3]=>[3,2,2]=>21
[5,7,2,4,3,1,6]=>[3,2,1,1]=>35
[5,7,2,4,3,6,1]=>[3,2,1,1]=>35
[5,7,2,4,6,1,3]=>[3,2,2]=>21
[5,7,2,4,6,3,1]=>[3,2,1,1]=>35
[5,7,2,6,1,3,4]=>[3,2,2]=>21
[5,7,2,6,1,4,3]=>[2,2,2,1]=>14
[5,7,2,6,3,1,4]=>[3,2,1,1]=>35
[5,7,2,6,3,4,1]=>[3,2,1,1]=>35
[5,7,2,6,4,1,3]=>[2,2,2,1]=>14
[5,7,2,6,4,3,1]=>[2,2,1,1,1]=>14
[5,7,3,1,2,4,6]=>[4,2,1]=>35
[5,7,3,1,2,6,4]=>[3,2,2]=>21
[5,7,3,1,4,2,6]=>[3,2,2]=>21
[5,7,3,1,4,6,2]=>[3,2,2]=>21
[5,7,3,1,6,2,4]=>[3,2,2]=>21
[5,7,3,1,6,4,2]=>[2,2,2,1]=>14
[5,7,3,2,1,4,6]=>[3,2,1,1]=>35
[5,7,3,2,1,6,4]=>[2,2,2,1]=>14
[5,7,3,2,4,1,6]=>[3,2,1,1]=>35
[5,7,3,2,4,6,1]=>[3,2,1,1]=>35
[5,7,3,2,6,1,4]=>[2,2,2,1]=>14
[5,7,3,2,6,4,1]=>[2,2,2,1]=>14
[5,7,3,4,1,2,6]=>[3,2,2]=>21
[5,7,3,4,1,6,2]=>[3,2,2]=>21
[5,7,3,4,2,1,6]=>[3,2,1,1]=>35
[5,7,3,4,2,6,1]=>[3,2,1,1]=>35
[5,7,3,4,6,1,2]=>[3,2,2]=>21
[5,7,3,4,6,2,1]=>[3,2,1,1]=>35
[5,7,3,6,1,2,4]=>[3,2,2]=>21
[5,7,3,6,1,4,2]=>[2,2,2,1]=>14
[5,7,3,6,2,1,4]=>[2,2,2,1]=>14
[5,7,3,6,2,4,1]=>[2,2,2,1]=>14
[5,7,3,6,4,1,2]=>[2,2,2,1]=>14
[5,7,3,6,4,2,1]=>[2,2,1,1,1]=>14
[5,7,4,1,2,3,6]=>[4,2,1]=>35
[5,7,4,1,2,6,3]=>[3,2,2]=>21
[5,7,4,1,3,2,6]=>[3,2,1,1]=>35
[5,7,4,1,3,6,2]=>[3,2,1,1]=>35
[5,7,4,1,6,2,3]=>[3,2,2]=>21
[5,7,4,1,6,3,2]=>[2,2,2,1]=>14
[5,7,4,2,1,3,6]=>[3,2,1,1]=>35
[5,7,4,2,1,6,3]=>[2,2,2,1]=>14
[5,7,4,2,3,1,6]=>[3,2,1,1]=>35
[5,7,4,2,3,6,1]=>[3,2,1,1]=>35
[5,7,4,2,6,1,3]=>[2,2,2,1]=>14
[5,7,4,2,6,3,1]=>[2,2,2,1]=>14
[5,7,4,3,1,2,6]=>[3,2,1,1]=>35
[5,7,4,3,1,6,2]=>[2,2,2,1]=>14
[5,7,4,3,2,1,6]=>[2,2,1,1,1]=>14
[5,7,4,3,2,6,1]=>[2,2,1,1,1]=>14
[5,7,4,3,6,1,2]=>[2,2,2,1]=>14
[5,7,4,3,6,2,1]=>[2,2,1,1,1]=>14
[5,7,4,6,1,2,3]=>[3,2,2]=>21
[5,7,4,6,1,3,2]=>[2,2,2,1]=>14
[5,7,4,6,2,1,3]=>[2,2,2,1]=>14
[5,7,4,6,2,3,1]=>[2,2,2,1]=>14
[5,7,4,6,3,1,2]=>[2,2,2,1]=>14
[5,7,4,6,3,2,1]=>[2,2,1,1,1]=>14
[5,7,6,1,2,3,4]=>[4,2,1]=>35
[5,7,6,1,2,4,3]=>[3,2,1,1]=>35
[5,7,6,1,3,2,4]=>[3,2,1,1]=>35
[5,7,6,1,3,4,2]=>[3,2,1,1]=>35
[5,7,6,1,4,2,3]=>[3,2,1,1]=>35
[5,7,6,1,4,3,2]=>[2,2,1,1,1]=>14
[5,7,6,2,1,3,4]=>[3,2,1,1]=>35
[5,7,6,2,1,4,3]=>[2,2,2,1]=>14
[5,7,6,2,3,1,4]=>[3,2,1,1]=>35
[5,7,6,2,3,4,1]=>[3,2,1,1]=>35
[5,7,6,2,4,1,3]=>[2,2,2,1]=>14
[5,7,6,2,4,3,1]=>[2,2,1,1,1]=>14
[5,7,6,3,1,2,4]=>[3,2,1,1]=>35
[5,7,6,3,1,4,2]=>[2,2,2,1]=>14
[5,7,6,3,2,1,4]=>[2,2,1,1,1]=>14
[5,7,6,3,2,4,1]=>[2,2,1,1,1]=>14
[5,7,6,3,4,1,2]=>[2,2,2,1]=>14
[5,7,6,3,4,2,1]=>[2,2,1,1,1]=>14
[5,7,6,4,1,2,3]=>[3,2,1,1]=>35
[5,7,6,4,1,3,2]=>[2,2,1,1,1]=>14
[5,7,6,4,2,1,3]=>[2,2,1,1,1]=>14
[5,7,6,4,2,3,1]=>[2,2,1,1,1]=>14
[5,7,6,4,3,1,2]=>[2,2,1,1,1]=>14
[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]=>6
[6,1,2,3,4,5,7]=>[6,1]=>6
[6,1,2,3,4,7,5]=>[5,2]=>14
[6,1,2,3,5,4,7]=>[5,1,1]=>15
[6,1,2,3,5,7,4]=>[5,1,1]=>15
[6,1,2,3,7,4,5]=>[5,2]=>14
[6,1,2,3,7,5,4]=>[4,2,1]=>35
[6,1,2,4,3,5,7]=>[5,1,1]=>15
[6,1,2,4,3,7,5]=>[4,2,1]=>35
[6,1,2,4,5,3,7]=>[5,1,1]=>15
[6,1,2,4,5,7,3]=>[5,1,1]=>15
[6,1,2,4,7,3,5]=>[4,2,1]=>35
[6,1,2,4,7,5,3]=>[4,2,1]=>35
[6,1,2,5,3,4,7]=>[5,1,1]=>15
[6,1,2,5,3,7,4]=>[4,2,1]=>35
[6,1,2,5,4,3,7]=>[4,1,1,1]=>20
[6,1,2,5,4,7,3]=>[4,1,1,1]=>20
[6,1,2,5,7,3,4]=>[4,2,1]=>35
[6,1,2,5,7,4,3]=>[4,1,1,1]=>20
[6,1,2,7,3,4,5]=>[5,2]=>14
[6,1,2,7,3,5,4]=>[4,2,1]=>35
[6,1,2,7,4,3,5]=>[4,2,1]=>35
[6,1,2,7,4,5,3]=>[4,2,1]=>35
[6,1,2,7,5,3,4]=>[4,2,1]=>35
[6,1,2,7,5,4,3]=>[3,2,1,1]=>35
[6,1,3,2,4,5,7]=>[5,1,1]=>15
[6,1,3,2,4,7,5]=>[4,2,1]=>35
[6,1,3,2,5,4,7]=>[4,2,1]=>35
[6,1,3,2,5,7,4]=>[4,2,1]=>35
[6,1,3,2,7,4,5]=>[4,2,1]=>35
[6,1,3,2,7,5,4]=>[3,2,2]=>21
[6,1,3,4,2,5,7]=>[5,1,1]=>15
[6,1,3,4,2,7,5]=>[4,2,1]=>35
[6,1,3,4,5,2,7]=>[5,1,1]=>15
[6,1,3,4,5,7,2]=>[5,1,1]=>15
[6,1,3,4,7,2,5]=>[4,2,1]=>35
[6,1,3,4,7,5,2]=>[4,2,1]=>35
[6,1,3,5,2,4,7]=>[4,2,1]=>35
[6,1,3,5,2,7,4]=>[4,2,1]=>35
[6,1,3,5,4,2,7]=>[4,1,1,1]=>20
[6,1,3,5,4,7,2]=>[4,1,1,1]=>20
[6,1,3,5,7,2,4]=>[4,2,1]=>35
[6,1,3,5,7,4,2]=>[4,1,1,1]=>20
[6,1,3,7,2,4,5]=>[4,2,1]=>35
[6,1,3,7,2,5,4]=>[3,2,2]=>21
[6,1,3,7,4,2,5]=>[4,2,1]=>35
[6,1,3,7,4,5,2]=>[4,2,1]=>35
[6,1,3,7,5,2,4]=>[3,2,2]=>21
[6,1,3,7,5,4,2]=>[3,2,1,1]=>35
[6,1,4,2,3,5,7]=>[5,1,1]=>15
[6,1,4,2,3,7,5]=>[4,2,1]=>35
[6,1,4,2,5,3,7]=>[4,2,1]=>35
[6,1,4,2,5,7,3]=>[4,2,1]=>35
[6,1,4,2,7,3,5]=>[4,2,1]=>35
[6,1,4,2,7,5,3]=>[3,2,2]=>21
[6,1,4,3,2,5,7]=>[4,1,1,1]=>20
[6,1,4,3,2,7,5]=>[3,2,1,1]=>35
[6,1,4,3,5,2,7]=>[4,1,1,1]=>20
[6,1,4,3,5,7,2]=>[4,1,1,1]=>20
[6,1,4,3,7,2,5]=>[3,2,1,1]=>35
[6,1,4,3,7,5,2]=>[3,2,1,1]=>35
[6,1,4,5,2,3,7]=>[4,2,1]=>35
[6,1,4,5,2,7,3]=>[4,2,1]=>35
[6,1,4,5,3,2,7]=>[4,1,1,1]=>20
[6,1,4,5,3,7,2]=>[4,1,1,1]=>20
[6,1,4,5,7,2,3]=>[4,2,1]=>35
[6,1,4,5,7,3,2]=>[4,1,1,1]=>20
[6,1,4,7,2,3,5]=>[4,2,1]=>35
[6,1,4,7,2,5,3]=>[3,2,2]=>21
[6,1,4,7,3,2,5]=>[3,2,1,1]=>35
[6,1,4,7,3,5,2]=>[3,2,1,1]=>35
[6,1,4,7,5,2,3]=>[3,2,2]=>21
[6,1,4,7,5,3,2]=>[3,2,1,1]=>35
[6,1,5,2,3,4,7]=>[5,1,1]=>15
[6,1,5,2,3,7,4]=>[4,2,1]=>35
[6,1,5,2,4,3,7]=>[4,1,1,1]=>20
[6,1,5,2,4,7,3]=>[4,1,1,1]=>20
[6,1,5,2,7,3,4]=>[4,2,1]=>35
[6,1,5,2,7,4,3]=>[3,2,1,1]=>35
[6,1,5,3,2,4,7]=>[4,1,1,1]=>20
[6,1,5,3,2,7,4]=>[3,2,1,1]=>35
[6,1,5,3,4,2,7]=>[4,1,1,1]=>20
[6,1,5,3,4,7,2]=>[4,1,1,1]=>20
[6,1,5,3,7,2,4]=>[3,2,1,1]=>35
[6,1,5,3,7,4,2]=>[3,2,1,1]=>35
[6,1,5,4,2,3,7]=>[4,1,1,1]=>20
[6,1,5,4,2,7,3]=>[3,2,1,1]=>35
[6,1,5,4,3,2,7]=>[3,1,1,1,1]=>15
[6,1,5,4,3,7,2]=>[3,1,1,1,1]=>15
[6,1,5,4,7,2,3]=>[3,2,1,1]=>35
[6,1,5,4,7,3,2]=>[3,1,1,1,1]=>15
[6,1,5,7,2,3,4]=>[4,2,1]=>35
[6,1,5,7,2,4,3]=>[3,2,1,1]=>35
[6,1,5,7,3,2,4]=>[3,2,1,1]=>35
[6,1,5,7,3,4,2]=>[3,2,1,1]=>35
[6,1,5,7,4,2,3]=>[3,2,1,1]=>35
[6,1,5,7,4,3,2]=>[3,1,1,1,1]=>15
[6,1,7,2,3,4,5]=>[5,2]=>14
[6,1,7,2,3,5,4]=>[4,2,1]=>35
[6,1,7,2,4,3,5]=>[4,2,1]=>35
[6,1,7,2,4,5,3]=>[4,2,1]=>35
[6,1,7,2,5,3,4]=>[4,2,1]=>35
[6,1,7,2,5,4,3]=>[3,2,1,1]=>35
[6,1,7,3,2,4,5]=>[4,2,1]=>35
[6,1,7,3,2,5,4]=>[3,2,2]=>21
[6,1,7,3,4,2,5]=>[4,2,1]=>35
[6,1,7,3,4,5,2]=>[4,2,1]=>35
[6,1,7,3,5,2,4]=>[3,2,2]=>21
[6,1,7,3,5,4,2]=>[3,2,1,1]=>35
[6,1,7,4,2,3,5]=>[4,2,1]=>35
[6,1,7,4,2,5,3]=>[3,2,2]=>21
[6,1,7,4,3,2,5]=>[3,2,1,1]=>35
[6,1,7,4,3,5,2]=>[3,2,1,1]=>35
[6,1,7,4,5,2,3]=>[3,2,2]=>21
[6,1,7,4,5,3,2]=>[3,2,1,1]=>35
[6,1,7,5,2,3,4]=>[4,2,1]=>35
[6,1,7,5,2,4,3]=>[3,2,1,1]=>35
[6,1,7,5,3,2,4]=>[3,2,1,1]=>35
[6,1,7,5,3,4,2]=>[3,2,1,1]=>35
[6,1,7,5,4,2,3]=>[3,2,1,1]=>35
[6,1,7,5,4,3,2]=>[2,2,1,1,1]=>14
[6,2,1,3,4,5,7]=>[5,1,1]=>15
[6,2,1,3,4,7,5]=>[4,2,1]=>35
[6,2,1,3,5,4,7]=>[4,2,1]=>35
[6,2,1,3,5,7,4]=>[4,2,1]=>35
[6,2,1,3,7,4,5]=>[4,2,1]=>35
[6,2,1,3,7,5,4]=>[3,2,2]=>21
[6,2,1,4,3,5,7]=>[4,2,1]=>35
[6,2,1,4,3,7,5]=>[3,3,1]=>21
[6,2,1,4,5,3,7]=>[4,2,1]=>35
[6,2,1,4,5,7,3]=>[4,2,1]=>35
[6,2,1,4,7,3,5]=>[3,3,1]=>21
[6,2,1,4,7,5,3]=>[3,2,2]=>21
[6,2,1,5,3,4,7]=>[4,2,1]=>35
[6,2,1,5,3,7,4]=>[3,3,1]=>21
[6,2,1,5,4,3,7]=>[3,2,1,1]=>35
[6,2,1,5,4,7,3]=>[3,2,1,1]=>35
[6,2,1,5,7,3,4]=>[3,3,1]=>21
[6,2,1,5,7,4,3]=>[3,2,1,1]=>35
[6,2,1,7,3,4,5]=>[4,2,1]=>35
[6,2,1,7,3,5,4]=>[3,2,2]=>21
[6,2,1,7,4,3,5]=>[3,2,2]=>21
[6,2,1,7,4,5,3]=>[3,2,2]=>21
[6,2,1,7,5,3,4]=>[3,2,2]=>21
[6,2,1,7,5,4,3]=>[2,2,2,1]=>14
[6,2,3,1,4,5,7]=>[5,1,1]=>15
[6,2,3,1,4,7,5]=>[4,2,1]=>35
[6,2,3,1,5,4,7]=>[4,2,1]=>35
[6,2,3,1,5,7,4]=>[4,2,1]=>35
[6,2,3,1,7,4,5]=>[4,2,1]=>35
[6,2,3,1,7,5,4]=>[3,2,2]=>21
[6,2,3,4,1,5,7]=>[5,1,1]=>15
[6,2,3,4,1,7,5]=>[4,2,1]=>35
[6,2,3,4,5,1,7]=>[5,1,1]=>15
[6,2,3,4,5,7,1]=>[5,1,1]=>15
[6,2,3,4,7,1,5]=>[4,2,1]=>35
[6,2,3,4,7,5,1]=>[4,2,1]=>35
[6,2,3,5,1,4,7]=>[4,2,1]=>35
[6,2,3,5,1,7,4]=>[4,2,1]=>35
[6,2,3,5,4,1,7]=>[4,1,1,1]=>20
[6,2,3,5,4,7,1]=>[4,1,1,1]=>20
[6,2,3,5,7,1,4]=>[4,2,1]=>35
[6,2,3,5,7,4,1]=>[4,1,1,1]=>20
[6,2,3,7,1,4,5]=>[4,2,1]=>35
[6,2,3,7,1,5,4]=>[3,2,2]=>21
[6,2,3,7,4,1,5]=>[4,2,1]=>35
[6,2,3,7,4,5,1]=>[4,2,1]=>35
[6,2,3,7,5,1,4]=>[3,2,2]=>21
[6,2,3,7,5,4,1]=>[3,2,1,1]=>35
[6,2,4,1,3,5,7]=>[4,2,1]=>35
[6,2,4,1,3,7,5]=>[3,3,1]=>21
[6,2,4,1,5,3,7]=>[4,2,1]=>35
[6,2,4,1,5,7,3]=>[4,2,1]=>35
[6,2,4,1,7,3,5]=>[3,3,1]=>21
[6,2,4,1,7,5,3]=>[3,2,2]=>21
[6,2,4,3,1,5,7]=>[4,1,1,1]=>20
[6,2,4,3,1,7,5]=>[3,2,1,1]=>35
[6,2,4,3,5,1,7]=>[4,1,1,1]=>20
[6,2,4,3,5,7,1]=>[4,1,1,1]=>20
[6,2,4,3,7,1,5]=>[3,2,1,1]=>35
[6,2,4,3,7,5,1]=>[3,2,1,1]=>35
[6,2,4,5,1,3,7]=>[4,2,1]=>35
[6,2,4,5,1,7,3]=>[4,2,1]=>35
[6,2,4,5,3,1,7]=>[4,1,1,1]=>20
[6,2,4,5,3,7,1]=>[4,1,1,1]=>20
[6,2,4,5,7,1,3]=>[4,2,1]=>35
[6,2,4,5,7,3,1]=>[4,1,1,1]=>20
[6,2,4,7,1,3,5]=>[3,3,1]=>21
[6,2,4,7,1,5,3]=>[3,2,2]=>21
[6,2,4,7,3,1,5]=>[3,2,1,1]=>35
[6,2,4,7,3,5,1]=>[3,2,1,1]=>35
[6,2,4,7,5,1,3]=>[3,2,2]=>21
[6,2,4,7,5,3,1]=>[3,2,1,1]=>35
[6,2,5,1,3,4,7]=>[4,2,1]=>35
[6,2,5,1,3,7,4]=>[3,3,1]=>21
[6,2,5,1,4,3,7]=>[3,2,1,1]=>35
[6,2,5,1,4,7,3]=>[3,2,1,1]=>35
[6,2,5,1,7,3,4]=>[3,3,1]=>21
[6,2,5,1,7,4,3]=>[3,2,1,1]=>35
[6,2,5,3,1,4,7]=>[4,1,1,1]=>20
[6,2,5,3,1,7,4]=>[3,2,1,1]=>35
[6,2,5,3,4,1,7]=>[4,1,1,1]=>20
[6,2,5,3,4,7,1]=>[4,1,1,1]=>20
[6,2,5,3,7,1,4]=>[3,2,1,1]=>35
[6,2,5,3,7,4,1]=>[3,2,1,1]=>35
[6,2,5,4,1,3,7]=>[3,2,1,1]=>35
[6,2,5,4,1,7,3]=>[3,2,1,1]=>35
[6,2,5,4,3,1,7]=>[3,1,1,1,1]=>15
[6,2,5,4,3,7,1]=>[3,1,1,1,1]=>15
[6,2,5,4,7,1,3]=>[3,2,1,1]=>35
[6,2,5,4,7,3,1]=>[3,1,1,1,1]=>15
[6,2,5,7,1,3,4]=>[3,3,1]=>21
[6,2,5,7,1,4,3]=>[3,2,1,1]=>35
[6,2,5,7,3,1,4]=>[3,2,1,1]=>35
[6,2,5,7,3,4,1]=>[3,2,1,1]=>35
[6,2,5,7,4,1,3]=>[3,2,1,1]=>35
[6,2,5,7,4,3,1]=>[3,1,1,1,1]=>15
[6,2,7,1,3,4,5]=>[4,2,1]=>35
[6,2,7,1,3,5,4]=>[3,2,2]=>21
[6,2,7,1,4,3,5]=>[3,2,2]=>21
[6,2,7,1,4,5,3]=>[3,2,2]=>21
[6,2,7,1,5,3,4]=>[3,2,2]=>21
[6,2,7,1,5,4,3]=>[2,2,2,1]=>14
[6,2,7,3,1,4,5]=>[4,2,1]=>35
[6,2,7,3,1,5,4]=>[3,2,2]=>21
[6,2,7,3,4,1,5]=>[4,2,1]=>35
[6,2,7,3,4,5,1]=>[4,2,1]=>35
[6,2,7,3,5,1,4]=>[3,2,2]=>21
[6,2,7,3,5,4,1]=>[3,2,1,1]=>35
[6,2,7,4,1,3,5]=>[3,2,2]=>21
[6,2,7,4,1,5,3]=>[3,2,2]=>21
[6,2,7,4,3,1,5]=>[3,2,1,1]=>35
[6,2,7,4,3,5,1]=>[3,2,1,1]=>35
[6,2,7,4,5,1,3]=>[3,2,2]=>21
[6,2,7,4,5,3,1]=>[3,2,1,1]=>35
[6,2,7,5,1,3,4]=>[3,2,2]=>21
[6,2,7,5,1,4,3]=>[2,2,2,1]=>14
[6,2,7,5,3,1,4]=>[3,2,1,1]=>35
[6,2,7,5,3,4,1]=>[3,2,1,1]=>35
[6,2,7,5,4,1,3]=>[2,2,2,1]=>14
[6,2,7,5,4,3,1]=>[2,2,1,1,1]=>14
[6,3,1,2,4,5,7]=>[5,1,1]=>15
[6,3,1,2,4,7,5]=>[4,2,1]=>35
[6,3,1,2,5,4,7]=>[4,2,1]=>35
[6,3,1,2,5,7,4]=>[4,2,1]=>35
[6,3,1,2,7,4,5]=>[4,2,1]=>35
[6,3,1,2,7,5,4]=>[3,2,2]=>21
[6,3,1,4,2,5,7]=>[4,2,1]=>35
[6,3,1,4,2,7,5]=>[3,3,1]=>21
[6,3,1,4,5,2,7]=>[4,2,1]=>35
[6,3,1,4,5,7,2]=>[4,2,1]=>35
[6,3,1,4,7,2,5]=>[3,3,1]=>21
[6,3,1,4,7,5,2]=>[3,2,2]=>21
[6,3,1,5,2,4,7]=>[4,2,1]=>35
[6,3,1,5,2,7,4]=>[3,3,1]=>21
[6,3,1,5,4,2,7]=>[3,2,1,1]=>35
[6,3,1,5,4,7,2]=>[3,2,1,1]=>35
[6,3,1,5,7,2,4]=>[3,3,1]=>21
[6,3,1,5,7,4,2]=>[3,2,1,1]=>35
[6,3,1,7,2,4,5]=>[4,2,1]=>35
[6,3,1,7,2,5,4]=>[3,2,2]=>21
[6,3,1,7,4,2,5]=>[3,2,2]=>21
[6,3,1,7,4,5,2]=>[3,2,2]=>21
[6,3,1,7,5,2,4]=>[3,2,2]=>21
[6,3,1,7,5,4,2]=>[2,2,2,1]=>14
[6,3,2,1,4,5,7]=>[4,1,1,1]=>20
[6,3,2,1,4,7,5]=>[3,2,1,1]=>35
[6,3,2,1,5,4,7]=>[3,2,1,1]=>35
[6,3,2,1,5,7,4]=>[3,2,1,1]=>35
[6,3,2,1,7,4,5]=>[3,2,1,1]=>35
[6,3,2,1,7,5,4]=>[2,2,2,1]=>14
[6,3,2,4,1,5,7]=>[4,1,1,1]=>20
[6,3,2,4,1,7,5]=>[3,2,1,1]=>35
[6,3,2,4,5,1,7]=>[4,1,1,1]=>20
[6,3,2,4,5,7,1]=>[4,1,1,1]=>20
[6,3,2,4,7,1,5]=>[3,2,1,1]=>35
[6,3,2,4,7,5,1]=>[3,2,1,1]=>35
[6,3,2,5,1,4,7]=>[3,2,1,1]=>35
[6,3,2,5,1,7,4]=>[3,2,1,1]=>35
[6,3,2,5,4,1,7]=>[3,2,1,1]=>35
[6,3,2,5,4,7,1]=>[3,2,1,1]=>35
[6,3,2,5,7,1,4]=>[3,2,1,1]=>35
[6,3,2,5,7,4,1]=>[3,2,1,1]=>35
[6,3,2,7,1,4,5]=>[3,2,1,1]=>35
[6,3,2,7,1,5,4]=>[2,2,2,1]=>14
[6,3,2,7,4,1,5]=>[3,2,1,1]=>35
[6,3,2,7,4,5,1]=>[3,2,1,1]=>35
[6,3,2,7,5,1,4]=>[2,2,2,1]=>14
[6,3,2,7,5,4,1]=>[2,2,2,1]=>14
[6,3,4,1,2,5,7]=>[4,2,1]=>35
[6,3,4,1,2,7,5]=>[3,3,1]=>21
[6,3,4,1,5,2,7]=>[4,2,1]=>35
[6,3,4,1,5,7,2]=>[4,2,1]=>35
[6,3,4,1,7,2,5]=>[3,3,1]=>21
[6,3,4,1,7,5,2]=>[3,2,2]=>21
[6,3,4,2,1,5,7]=>[4,1,1,1]=>20
[6,3,4,2,1,7,5]=>[3,2,1,1]=>35
[6,3,4,2,5,1,7]=>[4,1,1,1]=>20
[6,3,4,2,5,7,1]=>[4,1,1,1]=>20
[6,3,4,2,7,1,5]=>[3,2,1,1]=>35
[6,3,4,2,7,5,1]=>[3,2,1,1]=>35
[6,3,4,5,1,2,7]=>[4,2,1]=>35
[6,3,4,5,1,7,2]=>[4,2,1]=>35
[6,3,4,5,2,1,7]=>[4,1,1,1]=>20
[6,3,4,5,2,7,1]=>[4,1,1,1]=>20
[6,3,4,5,7,1,2]=>[4,2,1]=>35
[6,3,4,5,7,2,1]=>[4,1,1,1]=>20
[6,3,4,7,1,2,5]=>[3,3,1]=>21
[6,3,4,7,1,5,2]=>[3,2,2]=>21
[6,3,4,7,2,1,5]=>[3,2,1,1]=>35
[6,3,4,7,2,5,1]=>[3,2,1,1]=>35
[6,3,4,7,5,1,2]=>[3,2,2]=>21
[6,3,4,7,5,2,1]=>[3,2,1,1]=>35
[6,3,5,1,2,4,7]=>[4,2,1]=>35
[6,3,5,1,2,7,4]=>[3,3,1]=>21
[6,3,5,1,4,2,7]=>[3,2,1,1]=>35
[6,3,5,1,4,7,2]=>[3,2,1,1]=>35
[6,3,5,1,7,2,4]=>[3,3,1]=>21
[6,3,5,1,7,4,2]=>[3,2,1,1]=>35
[6,3,5,2,1,4,7]=>[3,2,1,1]=>35
[6,3,5,2,1,7,4]=>[3,2,1,1]=>35
[6,3,5,2,4,1,7]=>[3,2,1,1]=>35
[6,3,5,2,4,7,1]=>[3,2,1,1]=>35
[6,3,5,2,7,1,4]=>[3,2,1,1]=>35
[6,3,5,2,7,4,1]=>[3,2,1,1]=>35
[6,3,5,4,1,2,7]=>[3,2,1,1]=>35
[6,3,5,4,1,7,2]=>[3,2,1,1]=>35
[6,3,5,4,2,1,7]=>[3,1,1,1,1]=>15
[6,3,5,4,2,7,1]=>[3,1,1,1,1]=>15
[6,3,5,4,7,1,2]=>[3,2,1,1]=>35
[6,3,5,4,7,2,1]=>[3,1,1,1,1]=>15
[6,3,5,7,1,2,4]=>[3,3,1]=>21
[6,3,5,7,1,4,2]=>[3,2,1,1]=>35
[6,3,5,7,2,1,4]=>[3,2,1,1]=>35
[6,3,5,7,2,4,1]=>[3,2,1,1]=>35
[6,3,5,7,4,1,2]=>[3,2,1,1]=>35
[6,3,5,7,4,2,1]=>[3,1,1,1,1]=>15
[6,3,7,1,2,4,5]=>[4,2,1]=>35
[6,3,7,1,2,5,4]=>[3,2,2]=>21
[6,3,7,1,4,2,5]=>[3,2,2]=>21
[6,3,7,1,4,5,2]=>[3,2,2]=>21
[6,3,7,1,5,2,4]=>[3,2,2]=>21
[6,3,7,1,5,4,2]=>[2,2,2,1]=>14
[6,3,7,2,1,4,5]=>[3,2,1,1]=>35
[6,3,7,2,1,5,4]=>[2,2,2,1]=>14
[6,3,7,2,4,1,5]=>[3,2,1,1]=>35
[6,3,7,2,4,5,1]=>[3,2,1,1]=>35
[6,3,7,2,5,1,4]=>[2,2,2,1]=>14
[6,3,7,2,5,4,1]=>[2,2,2,1]=>14
[6,3,7,4,1,2,5]=>[3,2,2]=>21
[6,3,7,4,1,5,2]=>[3,2,2]=>21
[6,3,7,4,2,1,5]=>[3,2,1,1]=>35
[6,3,7,4,2,5,1]=>[3,2,1,1]=>35
[6,3,7,4,5,1,2]=>[3,2,2]=>21
[6,3,7,4,5,2,1]=>[3,2,1,1]=>35
[6,3,7,5,1,2,4]=>[3,2,2]=>21
[6,3,7,5,1,4,2]=>[2,2,2,1]=>14
[6,3,7,5,2,1,4]=>[2,2,2,1]=>14
[6,3,7,5,2,4,1]=>[2,2,2,1]=>14
[6,3,7,5,4,1,2]=>[2,2,2,1]=>14
[6,3,7,5,4,2,1]=>[2,2,1,1,1]=>14
[6,4,1,2,3,5,7]=>[5,1,1]=>15
[6,4,1,2,3,7,5]=>[4,2,1]=>35
[6,4,1,2,5,3,7]=>[4,2,1]=>35
[6,4,1,2,5,7,3]=>[4,2,1]=>35
[6,4,1,2,7,3,5]=>[4,2,1]=>35
[6,4,1,2,7,5,3]=>[3,2,2]=>21
[6,4,1,3,2,5,7]=>[4,1,1,1]=>20
[6,4,1,3,2,7,5]=>[3,2,1,1]=>35
[6,4,1,3,5,2,7]=>[4,1,1,1]=>20
[6,4,1,3,5,7,2]=>[4,1,1,1]=>20
[6,4,1,3,7,2,5]=>[3,2,1,1]=>35
[6,4,1,3,7,5,2]=>[3,2,1,1]=>35
[6,4,1,5,2,3,7]=>[4,2,1]=>35
[6,4,1,5,2,7,3]=>[3,3,1]=>21
[6,4,1,5,3,2,7]=>[3,2,1,1]=>35
[6,4,1,5,3,7,2]=>[3,2,1,1]=>35
[6,4,1,5,7,2,3]=>[3,3,1]=>21
[6,4,1,5,7,3,2]=>[3,2,1,1]=>35
[6,4,1,7,2,3,5]=>[4,2,1]=>35
[6,4,1,7,2,5,3]=>[3,2,2]=>21
[6,4,1,7,3,2,5]=>[3,2,1,1]=>35
[6,4,1,7,3,5,2]=>[3,2,1,1]=>35
[6,4,1,7,5,2,3]=>[3,2,2]=>21
[6,4,1,7,5,3,2]=>[2,2,2,1]=>14
[6,4,2,1,3,5,7]=>[4,1,1,1]=>20
[6,4,2,1,3,7,5]=>[3,2,1,1]=>35
[6,4,2,1,5,3,7]=>[3,2,1,1]=>35
[6,4,2,1,5,7,3]=>[3,2,1,1]=>35
[6,4,2,1,7,3,5]=>[3,2,1,1]=>35
[6,4,2,1,7,5,3]=>[2,2,2,1]=>14
[6,4,2,3,1,5,7]=>[4,1,1,1]=>20
[6,4,2,3,1,7,5]=>[3,2,1,1]=>35
[6,4,2,3,5,1,7]=>[4,1,1,1]=>20
[6,4,2,3,5,7,1]=>[4,1,1,1]=>20
[6,4,2,3,7,1,5]=>[3,2,1,1]=>35
[6,4,2,3,7,5,1]=>[3,2,1,1]=>35
[6,4,2,5,1,3,7]=>[3,2,1,1]=>35
[6,4,2,5,1,7,3]=>[3,2,1,1]=>35
[6,4,2,5,3,1,7]=>[3,2,1,1]=>35
[6,4,2,5,3,7,1]=>[3,2,1,1]=>35
[6,4,2,5,7,1,3]=>[3,2,1,1]=>35
[6,4,2,5,7,3,1]=>[3,2,1,1]=>35
[6,4,2,7,1,3,5]=>[3,2,1,1]=>35
[6,4,2,7,1,5,3]=>[2,2,2,1]=>14
[6,4,2,7,3,1,5]=>[3,2,1,1]=>35
[6,4,2,7,3,5,1]=>[3,2,1,1]=>35
[6,4,2,7,5,1,3]=>[2,2,2,1]=>14
[6,4,2,7,5,3,1]=>[2,2,2,1]=>14
[6,4,3,1,2,5,7]=>[4,1,1,1]=>20
[6,4,3,1,2,7,5]=>[3,2,1,1]=>35
[6,4,3,1,5,2,7]=>[3,2,1,1]=>35
[6,4,3,1,5,7,2]=>[3,2,1,1]=>35
[6,4,3,1,7,2,5]=>[3,2,1,1]=>35
[6,4,3,1,7,5,2]=>[2,2,2,1]=>14
[6,4,3,2,1,5,7]=>[3,1,1,1,1]=>15
[6,4,3,2,1,7,5]=>[2,2,1,1,1]=>14
[6,4,3,2,5,1,7]=>[3,1,1,1,1]=>15
[6,4,3,2,5,7,1]=>[3,1,1,1,1]=>15
[6,4,3,2,7,1,5]=>[2,2,1,1,1]=>14
[6,4,3,2,7,5,1]=>[2,2,1,1,1]=>14
[6,4,3,5,1,2,7]=>[3,2,1,1]=>35
[6,4,3,5,1,7,2]=>[3,2,1,1]=>35
[6,4,3,5,2,1,7]=>[3,1,1,1,1]=>15
[6,4,3,5,2,7,1]=>[3,1,1,1,1]=>15
[6,4,3,5,7,1,2]=>[3,2,1,1]=>35
[6,4,3,5,7,2,1]=>[3,1,1,1,1]=>15
[6,4,3,7,1,2,5]=>[3,2,1,1]=>35
[6,4,3,7,1,5,2]=>[2,2,2,1]=>14
[6,4,3,7,2,1,5]=>[2,2,1,1,1]=>14
[6,4,3,7,2,5,1]=>[2,2,1,1,1]=>14
[6,4,3,7,5,1,2]=>[2,2,2,1]=>14
[6,4,3,7,5,2,1]=>[2,2,1,1,1]=>14
[6,4,5,1,2,3,7]=>[4,2,1]=>35
[6,4,5,1,2,7,3]=>[3,3,1]=>21
[6,4,5,1,3,2,7]=>[3,2,1,1]=>35
[6,4,5,1,3,7,2]=>[3,2,1,1]=>35
[6,4,5,1,7,2,3]=>[3,3,1]=>21
[6,4,5,1,7,3,2]=>[3,2,1,1]=>35
[6,4,5,2,1,3,7]=>[3,2,1,1]=>35
[6,4,5,2,1,7,3]=>[3,2,1,1]=>35
[6,4,5,2,3,1,7]=>[3,2,1,1]=>35
[6,4,5,2,3,7,1]=>[3,2,1,1]=>35
[6,4,5,2,7,1,3]=>[3,2,1,1]=>35
[6,4,5,2,7,3,1]=>[3,2,1,1]=>35
[6,4,5,3,1,2,7]=>[3,2,1,1]=>35
[6,4,5,3,1,7,2]=>[3,2,1,1]=>35
[6,4,5,3,2,1,7]=>[3,1,1,1,1]=>15
[6,4,5,3,2,7,1]=>[3,1,1,1,1]=>15
[6,4,5,3,7,1,2]=>[3,2,1,1]=>35
[6,4,5,3,7,2,1]=>[3,1,1,1,1]=>15
[6,4,5,7,1,2,3]=>[3,3,1]=>21
[6,4,5,7,1,3,2]=>[3,2,1,1]=>35
[6,4,5,7,2,1,3]=>[3,2,1,1]=>35
[6,4,5,7,2,3,1]=>[3,2,1,1]=>35
[6,4,5,7,3,1,2]=>[3,2,1,1]=>35
[6,4,5,7,3,2,1]=>[3,1,1,1,1]=>15
[6,4,7,1,2,3,5]=>[4,2,1]=>35
[6,4,7,1,2,5,3]=>[3,2,2]=>21
[6,4,7,1,3,2,5]=>[3,2,1,1]=>35
[6,4,7,1,3,5,2]=>[3,2,1,1]=>35
[6,4,7,1,5,2,3]=>[3,2,2]=>21
[6,4,7,1,5,3,2]=>[2,2,2,1]=>14
[6,4,7,2,1,3,5]=>[3,2,1,1]=>35
[6,4,7,2,1,5,3]=>[2,2,2,1]=>14
[6,4,7,2,3,1,5]=>[3,2,1,1]=>35
[6,4,7,2,3,5,1]=>[3,2,1,1]=>35
[6,4,7,2,5,1,3]=>[2,2,2,1]=>14
[6,4,7,2,5,3,1]=>[2,2,2,1]=>14
[6,4,7,3,1,2,5]=>[3,2,1,1]=>35
[6,4,7,3,1,5,2]=>[2,2,2,1]=>14
[6,4,7,3,2,1,5]=>[2,2,1,1,1]=>14
[6,4,7,3,2,5,1]=>[2,2,1,1,1]=>14
[6,4,7,3,5,1,2]=>[2,2,2,1]=>14
[6,4,7,3,5,2,1]=>[2,2,1,1,1]=>14
[6,4,7,5,1,2,3]=>[3,2,2]=>21
[6,4,7,5,1,3,2]=>[2,2,2,1]=>14
[6,4,7,5,2,1,3]=>[2,2,2,1]=>14
[6,4,7,5,2,3,1]=>[2,2,2,1]=>14
[6,4,7,5,3,1,2]=>[2,2,2,1]=>14
[6,4,7,5,3,2,1]=>[2,2,1,1,1]=>14
[6,5,1,2,3,4,7]=>[5,1,1]=>15
[6,5,1,2,3,7,4]=>[4,2,1]=>35
[6,5,1,2,4,3,7]=>[4,1,1,1]=>20
[6,5,1,2,4,7,3]=>[4,1,1,1]=>20
[6,5,1,2,7,3,4]=>[4,2,1]=>35
[6,5,1,2,7,4,3]=>[3,2,1,1]=>35
[6,5,1,3,2,4,7]=>[4,1,1,1]=>20
[6,5,1,3,2,7,4]=>[3,2,1,1]=>35
[6,5,1,3,4,2,7]=>[4,1,1,1]=>20
[6,5,1,3,4,7,2]=>[4,1,1,1]=>20
[6,5,1,3,7,2,4]=>[3,2,1,1]=>35
[6,5,1,3,7,4,2]=>[3,2,1,1]=>35
[6,5,1,4,2,3,7]=>[4,1,1,1]=>20
[6,5,1,4,2,7,3]=>[3,2,1,1]=>35
[6,5,1,4,3,2,7]=>[3,1,1,1,1]=>15
[6,5,1,4,3,7,2]=>[3,1,1,1,1]=>15
[6,5,1,4,7,2,3]=>[3,2,1,1]=>35
[6,5,1,4,7,3,2]=>[3,1,1,1,1]=>15
[6,5,1,7,2,3,4]=>[4,2,1]=>35
[6,5,1,7,2,4,3]=>[3,2,1,1]=>35
[6,5,1,7,3,2,4]=>[3,2,1,1]=>35
[6,5,1,7,3,4,2]=>[3,2,1,1]=>35
[6,5,1,7,4,2,3]=>[3,2,1,1]=>35
[6,5,1,7,4,3,2]=>[2,2,1,1,1]=>14
[6,5,2,1,3,4,7]=>[4,1,1,1]=>20
[6,5,2,1,3,7,4]=>[3,2,1,1]=>35
[6,5,2,1,4,3,7]=>[3,2,1,1]=>35
[6,5,2,1,4,7,3]=>[3,2,1,1]=>35
[6,5,2,1,7,3,4]=>[3,2,1,1]=>35
[6,5,2,1,7,4,3]=>[2,2,2,1]=>14
[6,5,2,3,1,4,7]=>[4,1,1,1]=>20
[6,5,2,3,1,7,4]=>[3,2,1,1]=>35
[6,5,2,3,4,1,7]=>[4,1,1,1]=>20
[6,5,2,3,4,7,1]=>[4,1,1,1]=>20
[6,5,2,3,7,1,4]=>[3,2,1,1]=>35
[6,5,2,3,7,4,1]=>[3,2,1,1]=>35
[6,5,2,4,1,3,7]=>[3,2,1,1]=>35
[6,5,2,4,1,7,3]=>[3,2,1,1]=>35
[6,5,2,4,3,1,7]=>[3,1,1,1,1]=>15
[6,5,2,4,3,7,1]=>[3,1,1,1,1]=>15
[6,5,2,4,7,1,3]=>[3,2,1,1]=>35
[6,5,2,4,7,3,1]=>[3,1,1,1,1]=>15
[6,5,2,7,1,3,4]=>[3,2,1,1]=>35
[6,5,2,7,1,4,3]=>[2,2,2,1]=>14
[6,5,2,7,3,1,4]=>[3,2,1,1]=>35
[6,5,2,7,3,4,1]=>[3,2,1,1]=>35
[6,5,2,7,4,1,3]=>[2,2,2,1]=>14
[6,5,2,7,4,3,1]=>[2,2,1,1,1]=>14
[6,5,3,1,2,4,7]=>[4,1,1,1]=>20
[6,5,3,1,2,7,4]=>[3,2,1,1]=>35
[6,5,3,1,4,2,7]=>[3,2,1,1]=>35
[6,5,3,1,4,7,2]=>[3,2,1,1]=>35
[6,5,3,1,7,2,4]=>[3,2,1,1]=>35
[6,5,3,1,7,4,2]=>[2,2,2,1]=>14
[6,5,3,2,1,4,7]=>[3,1,1,1,1]=>15
[6,5,3,2,1,7,4]=>[2,2,1,1,1]=>14
[6,5,3,2,4,1,7]=>[3,1,1,1,1]=>15
[6,5,3,2,4,7,1]=>[3,1,1,1,1]=>15
[6,5,3,2,7,1,4]=>[2,2,1,1,1]=>14
[6,5,3,2,7,4,1]=>[2,2,1,1,1]=>14
[6,5,3,4,1,2,7]=>[3,2,1,1]=>35
[6,5,3,4,1,7,2]=>[3,2,1,1]=>35
[6,5,3,4,2,1,7]=>[3,1,1,1,1]=>15
[6,5,3,4,2,7,1]=>[3,1,1,1,1]=>15
[6,5,3,4,7,1,2]=>[3,2,1,1]=>35
[6,5,3,4,7,2,1]=>[3,1,1,1,1]=>15
[6,5,3,7,1,2,4]=>[3,2,1,1]=>35
[6,5,3,7,1,4,2]=>[2,2,2,1]=>14
[6,5,3,7,2,1,4]=>[2,2,1,1,1]=>14
[6,5,3,7,2,4,1]=>[2,2,1,1,1]=>14
[6,5,3,7,4,1,2]=>[2,2,2,1]=>14
[6,5,3,7,4,2,1]=>[2,2,1,1,1]=>14
[6,5,4,1,2,3,7]=>[4,1,1,1]=>20
[6,5,4,1,2,7,3]=>[3,2,1,1]=>35
[6,5,4,1,3,2,7]=>[3,1,1,1,1]=>15
[6,5,4,1,3,7,2]=>[3,1,1,1,1]=>15
[6,5,4,1,7,2,3]=>[3,2,1,1]=>35
[6,5,4,1,7,3,2]=>[2,2,1,1,1]=>14
[6,5,4,2,1,3,7]=>[3,1,1,1,1]=>15
[6,5,4,2,1,7,3]=>[2,2,1,1,1]=>14
[6,5,4,2,3,1,7]=>[3,1,1,1,1]=>15
[6,5,4,2,3,7,1]=>[3,1,1,1,1]=>15
[6,5,4,2,7,1,3]=>[2,2,1,1,1]=>14
[6,5,4,2,7,3,1]=>[2,2,1,1,1]=>14
[6,5,4,3,1,2,7]=>[3,1,1,1,1]=>15
[6,5,4,3,1,7,2]=>[2,2,1,1,1]=>14
[6,5,4,3,2,1,7]=>[2,1,1,1,1,1]=>6
[6,5,4,3,2,7,1]=>[2,1,1,1,1,1]=>6
[6,5,4,3,7,1,2]=>[2,2,1,1,1]=>14
[6,5,4,3,7,2,1]=>[2,1,1,1,1,1]=>6
[6,5,4,7,1,2,3]=>[3,2,1,1]=>35
[6,5,4,7,1,3,2]=>[2,2,1,1,1]=>14
[6,5,4,7,2,1,3]=>[2,2,1,1,1]=>14
[6,5,4,7,2,3,1]=>[2,2,1,1,1]=>14
[6,5,4,7,3,1,2]=>[2,2,1,1,1]=>14
[6,5,4,7,3,2,1]=>[2,1,1,1,1,1]=>6
[6,5,7,1,2,3,4]=>[4,2,1]=>35
[6,5,7,1,2,4,3]=>[3,2,1,1]=>35
[6,5,7,1,3,2,4]=>[3,2,1,1]=>35
[6,5,7,1,3,4,2]=>[3,2,1,1]=>35
[6,5,7,1,4,2,3]=>[3,2,1,1]=>35
[6,5,7,1,4,3,2]=>[2,2,1,1,1]=>14
[6,5,7,2,1,3,4]=>[3,2,1,1]=>35
[6,5,7,2,1,4,3]=>[2,2,2,1]=>14
[6,5,7,2,3,1,4]=>[3,2,1,1]=>35
[6,5,7,2,3,4,1]=>[3,2,1,1]=>35
[6,5,7,2,4,1,3]=>[2,2,2,1]=>14
[6,5,7,2,4,3,1]=>[2,2,1,1,1]=>14
[6,5,7,3,1,2,4]=>[3,2,1,1]=>35
[6,5,7,3,1,4,2]=>[2,2,2,1]=>14
[6,5,7,3,2,1,4]=>[2,2,1,1,1]=>14
[6,5,7,3,2,4,1]=>[2,2,1,1,1]=>14
[6,5,7,3,4,1,2]=>[2,2,2,1]=>14
[6,5,7,3,4,2,1]=>[2,2,1,1,1]=>14
[6,5,7,4,1,2,3]=>[3,2,1,1]=>35
[6,5,7,4,1,3,2]=>[2,2,1,1,1]=>14
[6,5,7,4,2,1,3]=>[2,2,1,1,1]=>14
[6,5,7,4,2,3,1]=>[2,2,1,1,1]=>14
[6,5,7,4,3,1,2]=>[2,2,1,1,1]=>14
[6,5,7,4,3,2,1]=>[2,1,1,1,1,1]=>6
[6,7,1,2,3,4,5]=>[5,2]=>14
[6,7,1,2,3,5,4]=>[4,2,1]=>35
[6,7,1,2,4,3,5]=>[4,2,1]=>35
[6,7,1,2,4,5,3]=>[4,2,1]=>35
[6,7,1,2,5,3,4]=>[4,2,1]=>35
[6,7,1,2,5,4,3]=>[3,2,1,1]=>35
[6,7,1,3,2,4,5]=>[4,2,1]=>35
[6,7,1,3,2,5,4]=>[3,2,2]=>21
[6,7,1,3,4,2,5]=>[4,2,1]=>35
[6,7,1,3,4,5,2]=>[4,2,1]=>35
[6,7,1,3,5,2,4]=>[3,2,2]=>21
[6,7,1,3,5,4,2]=>[3,2,1,1]=>35
[6,7,1,4,2,3,5]=>[4,2,1]=>35
[6,7,1,4,2,5,3]=>[3,2,2]=>21
[6,7,1,4,3,2,5]=>[3,2,1,1]=>35
[6,7,1,4,3,5,2]=>[3,2,1,1]=>35
[6,7,1,4,5,2,3]=>[3,2,2]=>21
[6,7,1,4,5,3,2]=>[3,2,1,1]=>35
[6,7,1,5,2,3,4]=>[4,2,1]=>35
[6,7,1,5,2,4,3]=>[3,2,1,1]=>35
[6,7,1,5,3,2,4]=>[3,2,1,1]=>35
[6,7,1,5,3,4,2]=>[3,2,1,1]=>35
[6,7,1,5,4,2,3]=>[3,2,1,1]=>35
[6,7,1,5,4,3,2]=>[2,2,1,1,1]=>14
[6,7,2,1,3,4,5]=>[4,2,1]=>35
[6,7,2,1,3,5,4]=>[3,2,2]=>21
[6,7,2,1,4,3,5]=>[3,2,2]=>21
[6,7,2,1,4,5,3]=>[3,2,2]=>21
[6,7,2,1,5,3,4]=>[3,2,2]=>21
[6,7,2,1,5,4,3]=>[2,2,2,1]=>14
[6,7,2,3,1,4,5]=>[4,2,1]=>35
[6,7,2,3,1,5,4]=>[3,2,2]=>21
[6,7,2,3,4,1,5]=>[4,2,1]=>35
[6,7,2,3,4,5,1]=>[4,2,1]=>35
[6,7,2,3,5,1,4]=>[3,2,2]=>21
[6,7,2,3,5,4,1]=>[3,2,1,1]=>35
[6,7,2,4,1,3,5]=>[3,2,2]=>21
[6,7,2,4,1,5,3]=>[3,2,2]=>21
[6,7,2,4,3,1,5]=>[3,2,1,1]=>35
[6,7,2,4,3,5,1]=>[3,2,1,1]=>35
[6,7,2,4,5,1,3]=>[3,2,2]=>21
[6,7,2,4,5,3,1]=>[3,2,1,1]=>35
[6,7,2,5,1,3,4]=>[3,2,2]=>21
[6,7,2,5,1,4,3]=>[2,2,2,1]=>14
[6,7,2,5,3,1,4]=>[3,2,1,1]=>35
[6,7,2,5,3,4,1]=>[3,2,1,1]=>35
[6,7,2,5,4,1,3]=>[2,2,2,1]=>14
[6,7,2,5,4,3,1]=>[2,2,1,1,1]=>14
[6,7,3,1,2,4,5]=>[4,2,1]=>35
[6,7,3,1,2,5,4]=>[3,2,2]=>21
[6,7,3,1,4,2,5]=>[3,2,2]=>21
[6,7,3,1,4,5,2]=>[3,2,2]=>21
[6,7,3,1,5,2,4]=>[3,2,2]=>21
[6,7,3,1,5,4,2]=>[2,2,2,1]=>14
[6,7,3,2,1,4,5]=>[3,2,1,1]=>35
[6,7,3,2,1,5,4]=>[2,2,2,1]=>14
[6,7,3,2,4,1,5]=>[3,2,1,1]=>35
[6,7,3,2,4,5,1]=>[3,2,1,1]=>35
[6,7,3,2,5,1,4]=>[2,2,2,1]=>14
[6,7,3,2,5,4,1]=>[2,2,2,1]=>14
[6,7,3,4,1,2,5]=>[3,2,2]=>21
[6,7,3,4,1,5,2]=>[3,2,2]=>21
[6,7,3,4,2,1,5]=>[3,2,1,1]=>35
[6,7,3,4,2,5,1]=>[3,2,1,1]=>35
[6,7,3,4,5,1,2]=>[3,2,2]=>21
[6,7,3,4,5,2,1]=>[3,2,1,1]=>35
[6,7,3,5,1,2,4]=>[3,2,2]=>21
[6,7,3,5,1,4,2]=>[2,2,2,1]=>14
[6,7,3,5,2,1,4]=>[2,2,2,1]=>14
[6,7,3,5,2,4,1]=>[2,2,2,1]=>14
[6,7,3,5,4,1,2]=>[2,2,2,1]=>14
[6,7,3,5,4,2,1]=>[2,2,1,1,1]=>14
[6,7,4,1,2,3,5]=>[4,2,1]=>35
[6,7,4,1,2,5,3]=>[3,2,2]=>21
[6,7,4,1,3,2,5]=>[3,2,1,1]=>35
[6,7,4,1,3,5,2]=>[3,2,1,1]=>35
[6,7,4,1,5,2,3]=>[3,2,2]=>21
[6,7,4,1,5,3,2]=>[2,2,2,1]=>14
[6,7,4,2,1,3,5]=>[3,2,1,1]=>35
[6,7,4,2,1,5,3]=>[2,2,2,1]=>14
[6,7,4,2,3,1,5]=>[3,2,1,1]=>35
[6,7,4,2,3,5,1]=>[3,2,1,1]=>35
[6,7,4,2,5,1,3]=>[2,2,2,1]=>14
[6,7,4,2,5,3,1]=>[2,2,2,1]=>14
[6,7,4,3,1,2,5]=>[3,2,1,1]=>35
[6,7,4,3,1,5,2]=>[2,2,2,1]=>14
[6,7,4,3,2,1,5]=>[2,2,1,1,1]=>14
[6,7,4,3,2,5,1]=>[2,2,1,1,1]=>14
[6,7,4,3,5,1,2]=>[2,2,2,1]=>14
[6,7,4,3,5,2,1]=>[2,2,1,1,1]=>14
[6,7,4,5,1,2,3]=>[3,2,2]=>21
[6,7,4,5,1,3,2]=>[2,2,2,1]=>14
[6,7,4,5,2,1,3]=>[2,2,2,1]=>14
[6,7,4,5,2,3,1]=>[2,2,2,1]=>14
[6,7,4,5,3,1,2]=>[2,2,2,1]=>14
[6,7,4,5,3,2,1]=>[2,2,1,1,1]=>14
[6,7,5,1,2,3,4]=>[4,2,1]=>35
[6,7,5,1,2,4,3]=>[3,2,1,1]=>35
[6,7,5,1,3,2,4]=>[3,2,1,1]=>35
[6,7,5,1,3,4,2]=>[3,2,1,1]=>35
[6,7,5,1,4,2,3]=>[3,2,1,1]=>35
[6,7,5,1,4,3,2]=>[2,2,1,1,1]=>14
[6,7,5,2,1,3,4]=>[3,2,1,1]=>35
[6,7,5,2,1,4,3]=>[2,2,2,1]=>14
[6,7,5,2,3,1,4]=>[3,2,1,1]=>35
[6,7,5,2,3,4,1]=>[3,2,1,1]=>35
[6,7,5,2,4,1,3]=>[2,2,2,1]=>14
[6,7,5,2,4,3,1]=>[2,2,1,1,1]=>14
[6,7,5,3,1,2,4]=>[3,2,1,1]=>35
[6,7,5,3,1,4,2]=>[2,2,2,1]=>14
[6,7,5,3,2,1,4]=>[2,2,1,1,1]=>14
[6,7,5,3,2,4,1]=>[2,2,1,1,1]=>14
[6,7,5,3,4,1,2]=>[2,2,2,1]=>14
[6,7,5,3,4,2,1]=>[2,2,1,1,1]=>14
[6,7,5,4,1,2,3]=>[3,2,1,1]=>35
[6,7,5,4,1,3,2]=>[2,2,1,1,1]=>14
[6,7,5,4,2,1,3]=>[2,2,1,1,1]=>14
[6,7,5,4,2,3,1]=>[2,2,1,1,1]=>14
[6,7,5,4,3,1,2]=>[2,2,1,1,1]=>14
[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>6
[7,1,2,3,4,5,6]=>[6,1]=>6
[7,1,2,3,4,6,5]=>[5,1,1]=>15
[7,1,2,3,5,4,6]=>[5,1,1]=>15
[7,1,2,3,5,6,4]=>[5,1,1]=>15
[7,1,2,3,6,4,5]=>[5,1,1]=>15
[7,1,2,3,6,5,4]=>[4,1,1,1]=>20
[7,1,2,4,3,5,6]=>[5,1,1]=>15
[7,1,2,4,3,6,5]=>[4,2,1]=>35
[7,1,2,4,5,3,6]=>[5,1,1]=>15
[7,1,2,4,5,6,3]=>[5,1,1]=>15
[7,1,2,4,6,3,5]=>[4,2,1]=>35
[7,1,2,4,6,5,3]=>[4,1,1,1]=>20
[7,1,2,5,3,4,6]=>[5,1,1]=>15
[7,1,2,5,3,6,4]=>[4,2,1]=>35
[7,1,2,5,4,3,6]=>[4,1,1,1]=>20
[7,1,2,5,4,6,3]=>[4,1,1,1]=>20
[7,1,2,5,6,3,4]=>[4,2,1]=>35
[7,1,2,5,6,4,3]=>[4,1,1,1]=>20
[7,1,2,6,3,4,5]=>[5,1,1]=>15
[7,1,2,6,3,5,4]=>[4,1,1,1]=>20
[7,1,2,6,4,3,5]=>[4,1,1,1]=>20
[7,1,2,6,4,5,3]=>[4,1,1,1]=>20
[7,1,2,6,5,3,4]=>[4,1,1,1]=>20
[7,1,2,6,5,4,3]=>[3,1,1,1,1]=>15
[7,1,3,2,4,5,6]=>[5,1,1]=>15
[7,1,3,2,4,6,5]=>[4,2,1]=>35
[7,1,3,2,5,4,6]=>[4,2,1]=>35
[7,1,3,2,5,6,4]=>[4,2,1]=>35
[7,1,3,2,6,4,5]=>[4,2,1]=>35
[7,1,3,2,6,5,4]=>[3,2,1,1]=>35
[7,1,3,4,2,5,6]=>[5,1,1]=>15
[7,1,3,4,2,6,5]=>[4,2,1]=>35
[7,1,3,4,5,2,6]=>[5,1,1]=>15
[7,1,3,4,5,6,2]=>[5,1,1]=>15
[7,1,3,4,6,2,5]=>[4,2,1]=>35
[7,1,3,4,6,5,2]=>[4,1,1,1]=>20
[7,1,3,5,2,4,6]=>[4,2,1]=>35
[7,1,3,5,2,6,4]=>[4,2,1]=>35
[7,1,3,5,4,2,6]=>[4,1,1,1]=>20
[7,1,3,5,4,6,2]=>[4,1,1,1]=>20
[7,1,3,5,6,2,4]=>[4,2,1]=>35
[7,1,3,5,6,4,2]=>[4,1,1,1]=>20
[7,1,3,6,2,4,5]=>[4,2,1]=>35
[7,1,3,6,2,5,4]=>[3,2,1,1]=>35
[7,1,3,6,4,2,5]=>[4,1,1,1]=>20
[7,1,3,6,4,5,2]=>[4,1,1,1]=>20
[7,1,3,6,5,2,4]=>[3,2,1,1]=>35
[7,1,3,6,5,4,2]=>[3,1,1,1,1]=>15
[7,1,4,2,3,5,6]=>[5,1,1]=>15
[7,1,4,2,3,6,5]=>[4,2,1]=>35
[7,1,4,2,5,3,6]=>[4,2,1]=>35
[7,1,4,2,5,6,3]=>[4,2,1]=>35
[7,1,4,2,6,3,5]=>[4,2,1]=>35
[7,1,4,2,6,5,3]=>[3,2,1,1]=>35
[7,1,4,3,2,5,6]=>[4,1,1,1]=>20
[7,1,4,3,2,6,5]=>[3,2,1,1]=>35
[7,1,4,3,5,2,6]=>[4,1,1,1]=>20
[7,1,4,3,5,6,2]=>[4,1,1,1]=>20
[7,1,4,3,6,2,5]=>[3,2,1,1]=>35
[7,1,4,3,6,5,2]=>[3,2,1,1]=>35
[7,1,4,5,2,3,6]=>[4,2,1]=>35
[7,1,4,5,2,6,3]=>[4,2,1]=>35
[7,1,4,5,3,2,6]=>[4,1,1,1]=>20
[7,1,4,5,3,6,2]=>[4,1,1,1]=>20
[7,1,4,5,6,2,3]=>[4,2,1]=>35
[7,1,4,5,6,3,2]=>[4,1,1,1]=>20
[7,1,4,6,2,3,5]=>[4,2,1]=>35
[7,1,4,6,2,5,3]=>[3,2,1,1]=>35
[7,1,4,6,3,2,5]=>[3,2,1,1]=>35
[7,1,4,6,3,5,2]=>[3,2,1,1]=>35
[7,1,4,6,5,2,3]=>[3,2,1,1]=>35
[7,1,4,6,5,3,2]=>[3,1,1,1,1]=>15
[7,1,5,2,3,4,6]=>[5,1,1]=>15
[7,1,5,2,3,6,4]=>[4,2,1]=>35
[7,1,5,2,4,3,6]=>[4,1,1,1]=>20
[7,1,5,2,4,6,3]=>[4,1,1,1]=>20
[7,1,5,2,6,3,4]=>[4,2,1]=>35
[7,1,5,2,6,4,3]=>[3,2,1,1]=>35
[7,1,5,3,2,4,6]=>[4,1,1,1]=>20
[7,1,5,3,2,6,4]=>[3,2,1,1]=>35
[7,1,5,3,4,2,6]=>[4,1,1,1]=>20
[7,1,5,3,4,6,2]=>[4,1,1,1]=>20
[7,1,5,3,6,2,4]=>[3,2,1,1]=>35
[7,1,5,3,6,4,2]=>[3,2,1,1]=>35
[7,1,5,4,2,3,6]=>[4,1,1,1]=>20
[7,1,5,4,2,6,3]=>[3,2,1,1]=>35
[7,1,5,4,3,2,6]=>[3,1,1,1,1]=>15
[7,1,5,4,3,6,2]=>[3,1,1,1,1]=>15
[7,1,5,4,6,2,3]=>[3,2,1,1]=>35
[7,1,5,4,6,3,2]=>[3,1,1,1,1]=>15
[7,1,5,6,2,3,4]=>[4,2,1]=>35
[7,1,5,6,2,4,3]=>[3,2,1,1]=>35
[7,1,5,6,3,2,4]=>[3,2,1,1]=>35
[7,1,5,6,3,4,2]=>[3,2,1,1]=>35
[7,1,5,6,4,2,3]=>[3,2,1,1]=>35
[7,1,5,6,4,3,2]=>[3,1,1,1,1]=>15
[7,1,6,2,3,4,5]=>[5,1,1]=>15
[7,1,6,2,3,5,4]=>[4,1,1,1]=>20
[7,1,6,2,4,3,5]=>[4,1,1,1]=>20
[7,1,6,2,4,5,3]=>[4,1,1,1]=>20
[7,1,6,2,5,3,4]=>[4,1,1,1]=>20
[7,1,6,2,5,4,3]=>[3,1,1,1,1]=>15
[7,1,6,3,2,4,5]=>[4,1,1,1]=>20
[7,1,6,3,2,5,4]=>[3,2,1,1]=>35
[7,1,6,3,4,2,5]=>[4,1,1,1]=>20
[7,1,6,3,4,5,2]=>[4,1,1,1]=>20
[7,1,6,3,5,2,4]=>[3,2,1,1]=>35
[7,1,6,3,5,4,2]=>[3,1,1,1,1]=>15
[7,1,6,4,2,3,5]=>[4,1,1,1]=>20
[7,1,6,4,2,5,3]=>[3,2,1,1]=>35
[7,1,6,4,3,2,5]=>[3,1,1,1,1]=>15
[7,1,6,4,3,5,2]=>[3,1,1,1,1]=>15
[7,1,6,4,5,2,3]=>[3,2,1,1]=>35
[7,1,6,4,5,3,2]=>[3,1,1,1,1]=>15
[7,1,6,5,2,3,4]=>[4,1,1,1]=>20
[7,1,6,5,2,4,3]=>[3,1,1,1,1]=>15
[7,1,6,5,3,2,4]=>[3,1,1,1,1]=>15
[7,1,6,5,3,4,2]=>[3,1,1,1,1]=>15
[7,1,6,5,4,2,3]=>[3,1,1,1,1]=>15
[7,1,6,5,4,3,2]=>[2,1,1,1,1,1]=>6
[7,2,1,3,4,5,6]=>[5,1,1]=>15
[7,2,1,3,4,6,5]=>[4,2,1]=>35
[7,2,1,3,5,4,6]=>[4,2,1]=>35
[7,2,1,3,5,6,4]=>[4,2,1]=>35
[7,2,1,3,6,4,5]=>[4,2,1]=>35
[7,2,1,3,6,5,4]=>[3,2,1,1]=>35
[7,2,1,4,3,5,6]=>[4,2,1]=>35
[7,2,1,4,3,6,5]=>[3,3,1]=>21
[7,2,1,4,5,3,6]=>[4,2,1]=>35
[7,2,1,4,5,6,3]=>[4,2,1]=>35
[7,2,1,4,6,3,5]=>[3,3,1]=>21
[7,2,1,4,6,5,3]=>[3,2,1,1]=>35
[7,2,1,5,3,4,6]=>[4,2,1]=>35
[7,2,1,5,3,6,4]=>[3,3,1]=>21
[7,2,1,5,4,3,6]=>[3,2,1,1]=>35
[7,2,1,5,4,6,3]=>[3,2,1,1]=>35
[7,2,1,5,6,3,4]=>[3,3,1]=>21
[7,2,1,5,6,4,3]=>[3,2,1,1]=>35
[7,2,1,6,3,4,5]=>[4,2,1]=>35
[7,2,1,6,3,5,4]=>[3,2,1,1]=>35
[7,2,1,6,4,3,5]=>[3,2,1,1]=>35
[7,2,1,6,4,5,3]=>[3,2,1,1]=>35
[7,2,1,6,5,3,4]=>[3,2,1,1]=>35
[7,2,1,6,5,4,3]=>[2,2,1,1,1]=>14
[7,2,3,1,4,5,6]=>[5,1,1]=>15
[7,2,3,1,4,6,5]=>[4,2,1]=>35
[7,2,3,1,5,4,6]=>[4,2,1]=>35
[7,2,3,1,5,6,4]=>[4,2,1]=>35
[7,2,3,1,6,4,5]=>[4,2,1]=>35
[7,2,3,1,6,5,4]=>[3,2,1,1]=>35
[7,2,3,4,1,5,6]=>[5,1,1]=>15
[7,2,3,4,1,6,5]=>[4,2,1]=>35
[7,2,3,4,5,1,6]=>[5,1,1]=>15
[7,2,3,4,5,6,1]=>[5,1,1]=>15
[7,2,3,4,6,1,5]=>[4,2,1]=>35
[7,2,3,4,6,5,1]=>[4,1,1,1]=>20
[7,2,3,5,1,4,6]=>[4,2,1]=>35
[7,2,3,5,1,6,4]=>[4,2,1]=>35
[7,2,3,5,4,1,6]=>[4,1,1,1]=>20
[7,2,3,5,4,6,1]=>[4,1,1,1]=>20
[7,2,3,5,6,1,4]=>[4,2,1]=>35
[7,2,3,5,6,4,1]=>[4,1,1,1]=>20
[7,2,3,6,1,4,5]=>[4,2,1]=>35
[7,2,3,6,1,5,4]=>[3,2,1,1]=>35
[7,2,3,6,4,1,5]=>[4,1,1,1]=>20
[7,2,3,6,4,5,1]=>[4,1,1,1]=>20
[7,2,3,6,5,1,4]=>[3,2,1,1]=>35
[7,2,3,6,5,4,1]=>[3,1,1,1,1]=>15
[7,2,4,1,3,5,6]=>[4,2,1]=>35
[7,2,4,1,3,6,5]=>[3,3,1]=>21
[7,2,4,1,5,3,6]=>[4,2,1]=>35
[7,2,4,1,5,6,3]=>[4,2,1]=>35
[7,2,4,1,6,3,5]=>[3,3,1]=>21
[7,2,4,1,6,5,3]=>[3,2,1,1]=>35
[7,2,4,3,1,5,6]=>[4,1,1,1]=>20
[7,2,4,3,1,6,5]=>[3,2,1,1]=>35
[7,2,4,3,5,1,6]=>[4,1,1,1]=>20
[7,2,4,3,5,6,1]=>[4,1,1,1]=>20
[7,2,4,3,6,1,5]=>[3,2,1,1]=>35
[7,2,4,3,6,5,1]=>[3,2,1,1]=>35
[7,2,4,5,1,3,6]=>[4,2,1]=>35
[7,2,4,5,1,6,3]=>[4,2,1]=>35
[7,2,4,5,3,1,6]=>[4,1,1,1]=>20
[7,2,4,5,3,6,1]=>[4,1,1,1]=>20
[7,2,4,5,6,1,3]=>[4,2,1]=>35
[7,2,4,5,6,3,1]=>[4,1,1,1]=>20
[7,2,4,6,1,3,5]=>[3,3,1]=>21
[7,2,4,6,1,5,3]=>[3,2,1,1]=>35
[7,2,4,6,3,1,5]=>[3,2,1,1]=>35
[7,2,4,6,3,5,1]=>[3,2,1,1]=>35
[7,2,4,6,5,1,3]=>[3,2,1,1]=>35
[7,2,4,6,5,3,1]=>[3,1,1,1,1]=>15
[7,2,5,1,3,4,6]=>[4,2,1]=>35
[7,2,5,1,3,6,4]=>[3,3,1]=>21
[7,2,5,1,4,3,6]=>[3,2,1,1]=>35
[7,2,5,1,4,6,3]=>[3,2,1,1]=>35
[7,2,5,1,6,3,4]=>[3,3,1]=>21
[7,2,5,1,6,4,3]=>[3,2,1,1]=>35
[7,2,5,3,1,4,6]=>[4,1,1,1]=>20
[7,2,5,3,1,6,4]=>[3,2,1,1]=>35
[7,2,5,3,4,1,6]=>[4,1,1,1]=>20
[7,2,5,3,4,6,1]=>[4,1,1,1]=>20
[7,2,5,3,6,1,4]=>[3,2,1,1]=>35
[7,2,5,3,6,4,1]=>[3,2,1,1]=>35
[7,2,5,4,1,3,6]=>[3,2,1,1]=>35
[7,2,5,4,1,6,3]=>[3,2,1,1]=>35
[7,2,5,4,3,1,6]=>[3,1,1,1,1]=>15
[7,2,5,4,3,6,1]=>[3,1,1,1,1]=>15
[7,2,5,4,6,1,3]=>[3,2,1,1]=>35
[7,2,5,4,6,3,1]=>[3,1,1,1,1]=>15
[7,2,5,6,1,3,4]=>[3,3,1]=>21
[7,2,5,6,1,4,3]=>[3,2,1,1]=>35
[7,2,5,6,3,1,4]=>[3,2,1,1]=>35
[7,2,5,6,3,4,1]=>[3,2,1,1]=>35
[7,2,5,6,4,1,3]=>[3,2,1,1]=>35
[7,2,5,6,4,3,1]=>[3,1,1,1,1]=>15
[7,2,6,1,3,4,5]=>[4,2,1]=>35
[7,2,6,1,3,5,4]=>[3,2,1,1]=>35
[7,2,6,1,4,3,5]=>[3,2,1,1]=>35
[7,2,6,1,4,5,3]=>[3,2,1,1]=>35
[7,2,6,1,5,3,4]=>[3,2,1,1]=>35
[7,2,6,1,5,4,3]=>[2,2,1,1,1]=>14
[7,2,6,3,1,4,5]=>[4,1,1,1]=>20
[7,2,6,3,1,5,4]=>[3,2,1,1]=>35
[7,2,6,3,4,1,5]=>[4,1,1,1]=>20
[7,2,6,3,4,5,1]=>[4,1,1,1]=>20
[7,2,6,3,5,1,4]=>[3,2,1,1]=>35
[7,2,6,3,5,4,1]=>[3,1,1,1,1]=>15
[7,2,6,4,1,3,5]=>[3,2,1,1]=>35
[7,2,6,4,1,5,3]=>[3,2,1,1]=>35
[7,2,6,4,3,1,5]=>[3,1,1,1,1]=>15
[7,2,6,4,3,5,1]=>[3,1,1,1,1]=>15
[7,2,6,4,5,1,3]=>[3,2,1,1]=>35
[7,2,6,4,5,3,1]=>[3,1,1,1,1]=>15
[7,2,6,5,1,3,4]=>[3,2,1,1]=>35
[7,2,6,5,1,4,3]=>[2,2,1,1,1]=>14
[7,2,6,5,3,1,4]=>[3,1,1,1,1]=>15
[7,2,6,5,3,4,1]=>[3,1,1,1,1]=>15
[7,2,6,5,4,1,3]=>[2,2,1,1,1]=>14
[7,2,6,5,4,3,1]=>[2,1,1,1,1,1]=>6
[7,3,1,2,4,5,6]=>[5,1,1]=>15
[7,3,1,2,4,6,5]=>[4,2,1]=>35
[7,3,1,2,5,4,6]=>[4,2,1]=>35
[7,3,1,2,5,6,4]=>[4,2,1]=>35
[7,3,1,2,6,4,5]=>[4,2,1]=>35
[7,3,1,2,6,5,4]=>[3,2,1,1]=>35
[7,3,1,4,2,5,6]=>[4,2,1]=>35
[7,3,1,4,2,6,5]=>[3,3,1]=>21
[7,3,1,4,5,2,6]=>[4,2,1]=>35
[7,3,1,4,5,6,2]=>[4,2,1]=>35
[7,3,1,4,6,2,5]=>[3,3,1]=>21
[7,3,1,4,6,5,2]=>[3,2,1,1]=>35
[7,3,1,5,2,4,6]=>[4,2,1]=>35
[7,3,1,5,2,6,4]=>[3,3,1]=>21
[7,3,1,5,4,2,6]=>[3,2,1,1]=>35
[7,3,1,5,4,6,2]=>[3,2,1,1]=>35
[7,3,1,5,6,2,4]=>[3,3,1]=>21
[7,3,1,5,6,4,2]=>[3,2,1,1]=>35
[7,3,1,6,2,4,5]=>[4,2,1]=>35
[7,3,1,6,2,5,4]=>[3,2,1,1]=>35
[7,3,1,6,4,2,5]=>[3,2,1,1]=>35
[7,3,1,6,4,5,2]=>[3,2,1,1]=>35
[7,3,1,6,5,2,4]=>[3,2,1,1]=>35
[7,3,1,6,5,4,2]=>[2,2,1,1,1]=>14
[7,3,2,1,4,5,6]=>[4,1,1,1]=>20
[7,3,2,1,4,6,5]=>[3,2,1,1]=>35
[7,3,2,1,5,4,6]=>[3,2,1,1]=>35
[7,3,2,1,5,6,4]=>[3,2,1,1]=>35
[7,3,2,1,6,4,5]=>[3,2,1,1]=>35
[7,3,2,1,6,5,4]=>[2,2,2,1]=>14
[7,3,2,4,1,5,6]=>[4,1,1,1]=>20
[7,3,2,4,1,6,5]=>[3,2,1,1]=>35
[7,3,2,4,5,1,6]=>[4,1,1,1]=>20
[7,3,2,4,5,6,1]=>[4,1,1,1]=>20
[7,3,2,4,6,1,5]=>[3,2,1,1]=>35
[7,3,2,4,6,5,1]=>[3,2,1,1]=>35
[7,3,2,5,1,4,6]=>[3,2,1,1]=>35
[7,3,2,5,1,6,4]=>[3,2,1,1]=>35
[7,3,2,5,4,1,6]=>[3,2,1,1]=>35
[7,3,2,5,4,6,1]=>[3,2,1,1]=>35
[7,3,2,5,6,1,4]=>[3,2,1,1]=>35
[7,3,2,5,6,4,1]=>[3,2,1,1]=>35
[7,3,2,6,1,4,5]=>[3,2,1,1]=>35
[7,3,2,6,1,5,4]=>[2,2,2,1]=>14
[7,3,2,6,4,1,5]=>[3,2,1,1]=>35
[7,3,2,6,4,5,1]=>[3,2,1,1]=>35
[7,3,2,6,5,1,4]=>[2,2,2,1]=>14
[7,3,2,6,5,4,1]=>[2,2,1,1,1]=>14
[7,3,4,1,2,5,6]=>[4,2,1]=>35
[7,3,4,1,2,6,5]=>[3,3,1]=>21
[7,3,4,1,5,2,6]=>[4,2,1]=>35
[7,3,4,1,5,6,2]=>[4,2,1]=>35
[7,3,4,1,6,2,5]=>[3,3,1]=>21
[7,3,4,1,6,5,2]=>[3,2,1,1]=>35
[7,3,4,2,1,5,6]=>[4,1,1,1]=>20
[7,3,4,2,1,6,5]=>[3,2,1,1]=>35
[7,3,4,2,5,1,6]=>[4,1,1,1]=>20
[7,3,4,2,5,6,1]=>[4,1,1,1]=>20
[7,3,4,2,6,1,5]=>[3,2,1,1]=>35
[7,3,4,2,6,5,1]=>[3,2,1,1]=>35
[7,3,4,5,1,2,6]=>[4,2,1]=>35
[7,3,4,5,1,6,2]=>[4,2,1]=>35
[7,3,4,5,2,1,6]=>[4,1,1,1]=>20
[7,3,4,5,2,6,1]=>[4,1,1,1]=>20
[7,3,4,5,6,1,2]=>[4,2,1]=>35
[7,3,4,5,6,2,1]=>[4,1,1,1]=>20
[7,3,4,6,1,2,5]=>[3,3,1]=>21
[7,3,4,6,1,5,2]=>[3,2,1,1]=>35
[7,3,4,6,2,1,5]=>[3,2,1,1]=>35
[7,3,4,6,2,5,1]=>[3,2,1,1]=>35
[7,3,4,6,5,1,2]=>[3,2,1,1]=>35
[7,3,4,6,5,2,1]=>[3,1,1,1,1]=>15
[7,3,5,1,2,4,6]=>[4,2,1]=>35
[7,3,5,1,2,6,4]=>[3,3,1]=>21
[7,3,5,1,4,2,6]=>[3,2,1,1]=>35
[7,3,5,1,4,6,2]=>[3,2,1,1]=>35
[7,3,5,1,6,2,4]=>[3,3,1]=>21
[7,3,5,1,6,4,2]=>[3,2,1,1]=>35
[7,3,5,2,1,4,6]=>[3,2,1,1]=>35
[7,3,5,2,1,6,4]=>[3,2,1,1]=>35
[7,3,5,2,4,1,6]=>[3,2,1,1]=>35
[7,3,5,2,4,6,1]=>[3,2,1,1]=>35
[7,3,5,2,6,1,4]=>[3,2,1,1]=>35
[7,3,5,2,6,4,1]=>[3,2,1,1]=>35
[7,3,5,4,1,2,6]=>[3,2,1,1]=>35
[7,3,5,4,1,6,2]=>[3,2,1,1]=>35
[7,3,5,4,2,1,6]=>[3,1,1,1,1]=>15
[7,3,5,4,2,6,1]=>[3,1,1,1,1]=>15
[7,3,5,4,6,1,2]=>[3,2,1,1]=>35
[7,3,5,4,6,2,1]=>[3,1,1,1,1]=>15
[7,3,5,6,1,2,4]=>[3,3,1]=>21
[7,3,5,6,1,4,2]=>[3,2,1,1]=>35
[7,3,5,6,2,1,4]=>[3,2,1,1]=>35
[7,3,5,6,2,4,1]=>[3,2,1,1]=>35
[7,3,5,6,4,1,2]=>[3,2,1,1]=>35
[7,3,5,6,4,2,1]=>[3,1,1,1,1]=>15
[7,3,6,1,2,4,5]=>[4,2,1]=>35
[7,3,6,1,2,5,4]=>[3,2,1,1]=>35
[7,3,6,1,4,2,5]=>[3,2,1,1]=>35
[7,3,6,1,4,5,2]=>[3,2,1,1]=>35
[7,3,6,1,5,2,4]=>[3,2,1,1]=>35
[7,3,6,1,5,4,2]=>[2,2,1,1,1]=>14
[7,3,6,2,1,4,5]=>[3,2,1,1]=>35
[7,3,6,2,1,5,4]=>[2,2,2,1]=>14
[7,3,6,2,4,1,5]=>[3,2,1,1]=>35
[7,3,6,2,4,5,1]=>[3,2,1,1]=>35
[7,3,6,2,5,1,4]=>[2,2,2,1]=>14
[7,3,6,2,5,4,1]=>[2,2,1,1,1]=>14
[7,3,6,4,1,2,5]=>[3,2,1,1]=>35
[7,3,6,4,1,5,2]=>[3,2,1,1]=>35
[7,3,6,4,2,1,5]=>[3,1,1,1,1]=>15
[7,3,6,4,2,5,1]=>[3,1,1,1,1]=>15
[7,3,6,4,5,1,2]=>[3,2,1,1]=>35
[7,3,6,4,5,2,1]=>[3,1,1,1,1]=>15
[7,3,6,5,1,2,4]=>[3,2,1,1]=>35
[7,3,6,5,1,4,2]=>[2,2,1,1,1]=>14
[7,3,6,5,2,1,4]=>[2,2,1,1,1]=>14
[7,3,6,5,2,4,1]=>[2,2,1,1,1]=>14
[7,3,6,5,4,1,2]=>[2,2,1,1,1]=>14
[7,3,6,5,4,2,1]=>[2,1,1,1,1,1]=>6
[7,4,1,2,3,5,6]=>[5,1,1]=>15
[7,4,1,2,3,6,5]=>[4,2,1]=>35
[7,4,1,2,5,3,6]=>[4,2,1]=>35
[7,4,1,2,5,6,3]=>[4,2,1]=>35
[7,4,1,2,6,3,5]=>[4,2,1]=>35
[7,4,1,2,6,5,3]=>[3,2,1,1]=>35
[7,4,1,3,2,5,6]=>[4,1,1,1]=>20
[7,4,1,3,2,6,5]=>[3,2,1,1]=>35
[7,4,1,3,5,2,6]=>[4,1,1,1]=>20
[7,4,1,3,5,6,2]=>[4,1,1,1]=>20
[7,4,1,3,6,2,5]=>[3,2,1,1]=>35
[7,4,1,3,6,5,2]=>[3,2,1,1]=>35
[7,4,1,5,2,3,6]=>[4,2,1]=>35
[7,4,1,5,2,6,3]=>[3,3,1]=>21
[7,4,1,5,3,2,6]=>[3,2,1,1]=>35
[7,4,1,5,3,6,2]=>[3,2,1,1]=>35
[7,4,1,5,6,2,3]=>[3,3,1]=>21
[7,4,1,5,6,3,2]=>[3,2,1,1]=>35
[7,4,1,6,2,3,5]=>[4,2,1]=>35
[7,4,1,6,2,5,3]=>[3,2,1,1]=>35
[7,4,1,6,3,2,5]=>[3,2,1,1]=>35
[7,4,1,6,3,5,2]=>[3,2,1,1]=>35
[7,4,1,6,5,2,3]=>[3,2,1,1]=>35
[7,4,1,6,5,3,2]=>[2,2,1,1,1]=>14
[7,4,2,1,3,5,6]=>[4,1,1,1]=>20
[7,4,2,1,3,6,5]=>[3,2,1,1]=>35
[7,4,2,1,5,3,6]=>[3,2,1,1]=>35
[7,4,2,1,5,6,3]=>[3,2,1,1]=>35
[7,4,2,1,6,3,5]=>[3,2,1,1]=>35
[7,4,2,1,6,5,3]=>[2,2,2,1]=>14
[7,4,2,3,1,5,6]=>[4,1,1,1]=>20
[7,4,2,3,1,6,5]=>[3,2,1,1]=>35
[7,4,2,3,5,1,6]=>[4,1,1,1]=>20
[7,4,2,3,5,6,1]=>[4,1,1,1]=>20
[7,4,2,3,6,1,5]=>[3,2,1,1]=>35
[7,4,2,3,6,5,1]=>[3,2,1,1]=>35
[7,4,2,5,1,3,6]=>[3,2,1,1]=>35
[7,4,2,5,1,6,3]=>[3,2,1,1]=>35
[7,4,2,5,3,1,6]=>[3,2,1,1]=>35
[7,4,2,5,3,6,1]=>[3,2,1,1]=>35
[7,4,2,5,6,1,3]=>[3,2,1,1]=>35
[7,4,2,5,6,3,1]=>[3,2,1,1]=>35
[7,4,2,6,1,3,5]=>[3,2,1,1]=>35
[7,4,2,6,1,5,3]=>[2,2,2,1]=>14
[7,4,2,6,3,1,5]=>[3,2,1,1]=>35
[7,4,2,6,3,5,1]=>[3,2,1,1]=>35
[7,4,2,6,5,1,3]=>[2,2,2,1]=>14
[7,4,2,6,5,3,1]=>[2,2,1,1,1]=>14
[7,4,3,1,2,5,6]=>[4,1,1,1]=>20
[7,4,3,1,2,6,5]=>[3,2,1,1]=>35
[7,4,3,1,5,2,6]=>[3,2,1,1]=>35
[7,4,3,1,5,6,2]=>[3,2,1,1]=>35
[7,4,3,1,6,2,5]=>[3,2,1,1]=>35
[7,4,3,1,6,5,2]=>[2,2,2,1]=>14
[7,4,3,2,1,5,6]=>[3,1,1,1,1]=>15
[7,4,3,2,1,6,5]=>[2,2,1,1,1]=>14
[7,4,3,2,5,1,6]=>[3,1,1,1,1]=>15
[7,4,3,2,5,6,1]=>[3,1,1,1,1]=>15
[7,4,3,2,6,1,5]=>[2,2,1,1,1]=>14
[7,4,3,2,6,5,1]=>[2,2,1,1,1]=>14
[7,4,3,5,1,2,6]=>[3,2,1,1]=>35
[7,4,3,5,1,6,2]=>[3,2,1,1]=>35
[7,4,3,5,2,1,6]=>[3,1,1,1,1]=>15
[7,4,3,5,2,6,1]=>[3,1,1,1,1]=>15
[7,4,3,5,6,1,2]=>[3,2,1,1]=>35
[7,4,3,5,6,2,1]=>[3,1,1,1,1]=>15
[7,4,3,6,1,2,5]=>[3,2,1,1]=>35
[7,4,3,6,1,5,2]=>[2,2,2,1]=>14
[7,4,3,6,2,1,5]=>[2,2,1,1,1]=>14
[7,4,3,6,2,5,1]=>[2,2,1,1,1]=>14
[7,4,3,6,5,1,2]=>[2,2,2,1]=>14
[7,4,3,6,5,2,1]=>[2,2,1,1,1]=>14
[7,4,5,1,2,3,6]=>[4,2,1]=>35
[7,4,5,1,2,6,3]=>[3,3,1]=>21
[7,4,5,1,3,2,6]=>[3,2,1,1]=>35
[7,4,5,1,3,6,2]=>[3,2,1,1]=>35
[7,4,5,1,6,2,3]=>[3,3,1]=>21
[7,4,5,1,6,3,2]=>[3,2,1,1]=>35
[7,4,5,2,1,3,6]=>[3,2,1,1]=>35
[7,4,5,2,1,6,3]=>[3,2,1,1]=>35
[7,4,5,2,3,1,6]=>[3,2,1,1]=>35
[7,4,5,2,3,6,1]=>[3,2,1,1]=>35
[7,4,5,2,6,1,3]=>[3,2,1,1]=>35
[7,4,5,2,6,3,1]=>[3,2,1,1]=>35
[7,4,5,3,1,2,6]=>[3,2,1,1]=>35
[7,4,5,3,1,6,2]=>[3,2,1,1]=>35
[7,4,5,3,2,1,6]=>[3,1,1,1,1]=>15
[7,4,5,3,2,6,1]=>[3,1,1,1,1]=>15
[7,4,5,3,6,1,2]=>[3,2,1,1]=>35
[7,4,5,3,6,2,1]=>[3,1,1,1,1]=>15
[7,4,5,6,1,2,3]=>[3,3,1]=>21
[7,4,5,6,1,3,2]=>[3,2,1,1]=>35
[7,4,5,6,2,1,3]=>[3,2,1,1]=>35
[7,4,5,6,2,3,1]=>[3,2,1,1]=>35
[7,4,5,6,3,1,2]=>[3,2,1,1]=>35
[7,4,5,6,3,2,1]=>[3,1,1,1,1]=>15
[7,4,6,1,2,3,5]=>[4,2,1]=>35
[7,4,6,1,2,5,3]=>[3,2,1,1]=>35
[7,4,6,1,3,2,5]=>[3,2,1,1]=>35
[7,4,6,1,3,5,2]=>[3,2,1,1]=>35
[7,4,6,1,5,2,3]=>[3,2,1,1]=>35
[7,4,6,1,5,3,2]=>[2,2,1,1,1]=>14
[7,4,6,2,1,3,5]=>[3,2,1,1]=>35
[7,4,6,2,1,5,3]=>[2,2,2,1]=>14
[7,4,6,2,3,1,5]=>[3,2,1,1]=>35
[7,4,6,2,3,5,1]=>[3,2,1,1]=>35
[7,4,6,2,5,1,3]=>[2,2,2,1]=>14
[7,4,6,2,5,3,1]=>[2,2,1,1,1]=>14
[7,4,6,3,1,2,5]=>[3,2,1,1]=>35
[7,4,6,3,1,5,2]=>[2,2,2,1]=>14
[7,4,6,3,2,1,5]=>[2,2,1,1,1]=>14
[7,4,6,3,2,5,1]=>[2,2,1,1,1]=>14
[7,4,6,3,5,1,2]=>[2,2,2,1]=>14
[7,4,6,3,5,2,1]=>[2,2,1,1,1]=>14
[7,4,6,5,1,2,3]=>[3,2,1,1]=>35
[7,4,6,5,1,3,2]=>[2,2,1,1,1]=>14
[7,4,6,5,2,1,3]=>[2,2,1,1,1]=>14
[7,4,6,5,2,3,1]=>[2,2,1,1,1]=>14
[7,4,6,5,3,1,2]=>[2,2,1,1,1]=>14
[7,4,6,5,3,2,1]=>[2,1,1,1,1,1]=>6
[7,5,1,2,3,4,6]=>[5,1,1]=>15
[7,5,1,2,3,6,4]=>[4,2,1]=>35
[7,5,1,2,4,3,6]=>[4,1,1,1]=>20
[7,5,1,2,4,6,3]=>[4,1,1,1]=>20
[7,5,1,2,6,3,4]=>[4,2,1]=>35
[7,5,1,2,6,4,3]=>[3,2,1,1]=>35
[7,5,1,3,2,4,6]=>[4,1,1,1]=>20
[7,5,1,3,2,6,4]=>[3,2,1,1]=>35
[7,5,1,3,4,2,6]=>[4,1,1,1]=>20
[7,5,1,3,4,6,2]=>[4,1,1,1]=>20
[7,5,1,3,6,2,4]=>[3,2,1,1]=>35
[7,5,1,3,6,4,2]=>[3,2,1,1]=>35
[7,5,1,4,2,3,6]=>[4,1,1,1]=>20
[7,5,1,4,2,6,3]=>[3,2,1,1]=>35
[7,5,1,4,3,2,6]=>[3,1,1,1,1]=>15
[7,5,1,4,3,6,2]=>[3,1,1,1,1]=>15
[7,5,1,4,6,2,3]=>[3,2,1,1]=>35
[7,5,1,4,6,3,2]=>[3,1,1,1,1]=>15
[7,5,1,6,2,3,4]=>[4,2,1]=>35
[7,5,1,6,2,4,3]=>[3,2,1,1]=>35
[7,5,1,6,3,2,4]=>[3,2,1,1]=>35
[7,5,1,6,3,4,2]=>[3,2,1,1]=>35
[7,5,1,6,4,2,3]=>[3,2,1,1]=>35
[7,5,1,6,4,3,2]=>[2,2,1,1,1]=>14
[7,5,2,1,3,4,6]=>[4,1,1,1]=>20
[7,5,2,1,3,6,4]=>[3,2,1,1]=>35
[7,5,2,1,4,3,6]=>[3,2,1,1]=>35
[7,5,2,1,4,6,3]=>[3,2,1,1]=>35
[7,5,2,1,6,3,4]=>[3,2,1,1]=>35
[7,5,2,1,6,4,3]=>[2,2,2,1]=>14
[7,5,2,3,1,4,6]=>[4,1,1,1]=>20
[7,5,2,3,1,6,4]=>[3,2,1,1]=>35
[7,5,2,3,4,1,6]=>[4,1,1,1]=>20
[7,5,2,3,4,6,1]=>[4,1,1,1]=>20
[7,5,2,3,6,1,4]=>[3,2,1,1]=>35
[7,5,2,3,6,4,1]=>[3,2,1,1]=>35
[7,5,2,4,1,3,6]=>[3,2,1,1]=>35
[7,5,2,4,1,6,3]=>[3,2,1,1]=>35
[7,5,2,4,3,1,6]=>[3,1,1,1,1]=>15
[7,5,2,4,3,6,1]=>[3,1,1,1,1]=>15
[7,5,2,4,6,1,3]=>[3,2,1,1]=>35
[7,5,2,4,6,3,1]=>[3,1,1,1,1]=>15
[7,5,2,6,1,3,4]=>[3,2,1,1]=>35
[7,5,2,6,1,4,3]=>[2,2,2,1]=>14
[7,5,2,6,3,1,4]=>[3,2,1,1]=>35
[7,5,2,6,3,4,1]=>[3,2,1,1]=>35
[7,5,2,6,4,1,3]=>[2,2,2,1]=>14
[7,5,2,6,4,3,1]=>[2,2,1,1,1]=>14
[7,5,3,1,2,4,6]=>[4,1,1,1]=>20
[7,5,3,1,2,6,4]=>[3,2,1,1]=>35
[7,5,3,1,4,2,6]=>[3,2,1,1]=>35
[7,5,3,1,4,6,2]=>[3,2,1,1]=>35
[7,5,3,1,6,2,4]=>[3,2,1,1]=>35
[7,5,3,1,6,4,2]=>[2,2,2,1]=>14
[7,5,3,2,1,4,6]=>[3,1,1,1,1]=>15
[7,5,3,2,1,6,4]=>[2,2,1,1,1]=>14
[7,5,3,2,4,1,6]=>[3,1,1,1,1]=>15
[7,5,3,2,4,6,1]=>[3,1,1,1,1]=>15
[7,5,3,2,6,1,4]=>[2,2,1,1,1]=>14
[7,5,3,2,6,4,1]=>[2,2,1,1,1]=>14
[7,5,3,4,1,2,6]=>[3,2,1,1]=>35
[7,5,3,4,1,6,2]=>[3,2,1,1]=>35
[7,5,3,4,2,1,6]=>[3,1,1,1,1]=>15
[7,5,3,4,2,6,1]=>[3,1,1,1,1]=>15
[7,5,3,4,6,1,2]=>[3,2,1,1]=>35
[7,5,3,4,6,2,1]=>[3,1,1,1,1]=>15
[7,5,3,6,1,2,4]=>[3,2,1,1]=>35
[7,5,3,6,1,4,2]=>[2,2,2,1]=>14
[7,5,3,6,2,1,4]=>[2,2,1,1,1]=>14
[7,5,3,6,2,4,1]=>[2,2,1,1,1]=>14
[7,5,3,6,4,1,2]=>[2,2,2,1]=>14
[7,5,3,6,4,2,1]=>[2,2,1,1,1]=>14
[7,5,4,1,2,3,6]=>[4,1,1,1]=>20
[7,5,4,1,2,6,3]=>[3,2,1,1]=>35
[7,5,4,1,3,2,6]=>[3,1,1,1,1]=>15
[7,5,4,1,3,6,2]=>[3,1,1,1,1]=>15
[7,5,4,1,6,2,3]=>[3,2,1,1]=>35
[7,5,4,1,6,3,2]=>[2,2,1,1,1]=>14
[7,5,4,2,1,3,6]=>[3,1,1,1,1]=>15
[7,5,4,2,1,6,3]=>[2,2,1,1,1]=>14
[7,5,4,2,3,1,6]=>[3,1,1,1,1]=>15
[7,5,4,2,3,6,1]=>[3,1,1,1,1]=>15
[7,5,4,2,6,1,3]=>[2,2,1,1,1]=>14
[7,5,4,2,6,3,1]=>[2,2,1,1,1]=>14
[7,5,4,3,1,2,6]=>[3,1,1,1,1]=>15
[7,5,4,3,1,6,2]=>[2,2,1,1,1]=>14
[7,5,4,3,2,1,6]=>[2,1,1,1,1,1]=>6
[7,5,4,3,2,6,1]=>[2,1,1,1,1,1]=>6
[7,5,4,3,6,1,2]=>[2,2,1,1,1]=>14
[7,5,4,3,6,2,1]=>[2,1,1,1,1,1]=>6
[7,5,4,6,1,2,3]=>[3,2,1,1]=>35
[7,5,4,6,1,3,2]=>[2,2,1,1,1]=>14
[7,5,4,6,2,1,3]=>[2,2,1,1,1]=>14
[7,5,4,6,2,3,1]=>[2,2,1,1,1]=>14
[7,5,4,6,3,1,2]=>[2,2,1,1,1]=>14
[7,5,4,6,3,2,1]=>[2,1,1,1,1,1]=>6
[7,5,6,1,2,3,4]=>[4,2,1]=>35
[7,5,6,1,2,4,3]=>[3,2,1,1]=>35
[7,5,6,1,3,2,4]=>[3,2,1,1]=>35
[7,5,6,1,3,4,2]=>[3,2,1,1]=>35
[7,5,6,1,4,2,3]=>[3,2,1,1]=>35
[7,5,6,1,4,3,2]=>[2,2,1,1,1]=>14
[7,5,6,2,1,3,4]=>[3,2,1,1]=>35
[7,5,6,2,1,4,3]=>[2,2,2,1]=>14
[7,5,6,2,3,1,4]=>[3,2,1,1]=>35
[7,5,6,2,3,4,1]=>[3,2,1,1]=>35
[7,5,6,2,4,1,3]=>[2,2,2,1]=>14
[7,5,6,2,4,3,1]=>[2,2,1,1,1]=>14
[7,5,6,3,1,2,4]=>[3,2,1,1]=>35
[7,5,6,3,1,4,2]=>[2,2,2,1]=>14
[7,5,6,3,2,1,4]=>[2,2,1,1,1]=>14
[7,5,6,3,2,4,1]=>[2,2,1,1,1]=>14
[7,5,6,3,4,1,2]=>[2,2,2,1]=>14
[7,5,6,3,4,2,1]=>[2,2,1,1,1]=>14
[7,5,6,4,1,2,3]=>[3,2,1,1]=>35
[7,5,6,4,1,3,2]=>[2,2,1,1,1]=>14
[7,5,6,4,2,1,3]=>[2,2,1,1,1]=>14
[7,5,6,4,2,3,1]=>[2,2,1,1,1]=>14
[7,5,6,4,3,1,2]=>[2,2,1,1,1]=>14
[7,5,6,4,3,2,1]=>[2,1,1,1,1,1]=>6
[7,6,1,2,3,4,5]=>[5,1,1]=>15
[7,6,1,2,3,5,4]=>[4,1,1,1]=>20
[7,6,1,2,4,3,5]=>[4,1,1,1]=>20
[7,6,1,2,4,5,3]=>[4,1,1,1]=>20
[7,6,1,2,5,3,4]=>[4,1,1,1]=>20
[7,6,1,2,5,4,3]=>[3,1,1,1,1]=>15
[7,6,1,3,2,4,5]=>[4,1,1,1]=>20
[7,6,1,3,2,5,4]=>[3,2,1,1]=>35
[7,6,1,3,4,2,5]=>[4,1,1,1]=>20
[7,6,1,3,4,5,2]=>[4,1,1,1]=>20
[7,6,1,3,5,2,4]=>[3,2,1,1]=>35
[7,6,1,3,5,4,2]=>[3,1,1,1,1]=>15
[7,6,1,4,2,3,5]=>[4,1,1,1]=>20
[7,6,1,4,2,5,3]=>[3,2,1,1]=>35
[7,6,1,4,3,2,5]=>[3,1,1,1,1]=>15
[7,6,1,4,3,5,2]=>[3,1,1,1,1]=>15
[7,6,1,4,5,2,3]=>[3,2,1,1]=>35
[7,6,1,4,5,3,2]=>[3,1,1,1,1]=>15
[7,6,1,5,2,3,4]=>[4,1,1,1]=>20
[7,6,1,5,2,4,3]=>[3,1,1,1,1]=>15
[7,6,1,5,3,2,4]=>[3,1,1,1,1]=>15
[7,6,1,5,3,4,2]=>[3,1,1,1,1]=>15
[7,6,1,5,4,2,3]=>[3,1,1,1,1]=>15
[7,6,1,5,4,3,2]=>[2,1,1,1,1,1]=>6
[7,6,2,1,3,4,5]=>[4,1,1,1]=>20
[7,6,2,1,3,5,4]=>[3,2,1,1]=>35
[7,6,2,1,4,3,5]=>[3,2,1,1]=>35
[7,6,2,1,4,5,3]=>[3,2,1,1]=>35
[7,6,2,1,5,3,4]=>[3,2,1,1]=>35
[7,6,2,1,5,4,3]=>[2,2,1,1,1]=>14
[7,6,2,3,1,4,5]=>[4,1,1,1]=>20
[7,6,2,3,1,5,4]=>[3,2,1,1]=>35
[7,6,2,3,4,1,5]=>[4,1,1,1]=>20
[7,6,2,3,4,5,1]=>[4,1,1,1]=>20
[7,6,2,3,5,1,4]=>[3,2,1,1]=>35
[7,6,2,3,5,4,1]=>[3,1,1,1,1]=>15
[7,6,2,4,1,3,5]=>[3,2,1,1]=>35
[7,6,2,4,1,5,3]=>[3,2,1,1]=>35
[7,6,2,4,3,1,5]=>[3,1,1,1,1]=>15
[7,6,2,4,3,5,1]=>[3,1,1,1,1]=>15
[7,6,2,4,5,1,3]=>[3,2,1,1]=>35
[7,6,2,4,5,3,1]=>[3,1,1,1,1]=>15
[7,6,2,5,1,3,4]=>[3,2,1,1]=>35
[7,6,2,5,1,4,3]=>[2,2,1,1,1]=>14
[7,6,2,5,3,1,4]=>[3,1,1,1,1]=>15
[7,6,2,5,3,4,1]=>[3,1,1,1,1]=>15
[7,6,2,5,4,1,3]=>[2,2,1,1,1]=>14
[7,6,2,5,4,3,1]=>[2,1,1,1,1,1]=>6
[7,6,3,1,2,4,5]=>[4,1,1,1]=>20
[7,6,3,1,2,5,4]=>[3,2,1,1]=>35
[7,6,3,1,4,2,5]=>[3,2,1,1]=>35
[7,6,3,1,4,5,2]=>[3,2,1,1]=>35
[7,6,3,1,5,2,4]=>[3,2,1,1]=>35
[7,6,3,1,5,4,2]=>[2,2,1,1,1]=>14
[7,6,3,2,1,4,5]=>[3,1,1,1,1]=>15
[7,6,3,2,1,5,4]=>[2,2,1,1,1]=>14
[7,6,3,2,4,1,5]=>[3,1,1,1,1]=>15
[7,6,3,2,4,5,1]=>[3,1,1,1,1]=>15
[7,6,3,2,5,1,4]=>[2,2,1,1,1]=>14
[7,6,3,2,5,4,1]=>[2,2,1,1,1]=>14
[7,6,3,4,1,2,5]=>[3,2,1,1]=>35
[7,6,3,4,1,5,2]=>[3,2,1,1]=>35
[7,6,3,4,2,1,5]=>[3,1,1,1,1]=>15
[7,6,3,4,2,5,1]=>[3,1,1,1,1]=>15
[7,6,3,4,5,1,2]=>[3,2,1,1]=>35
[7,6,3,4,5,2,1]=>[3,1,1,1,1]=>15
[7,6,3,5,1,2,4]=>[3,2,1,1]=>35
[7,6,3,5,1,4,2]=>[2,2,1,1,1]=>14
[7,6,3,5,2,1,4]=>[2,2,1,1,1]=>14
[7,6,3,5,2,4,1]=>[2,2,1,1,1]=>14
[7,6,3,5,4,1,2]=>[2,2,1,1,1]=>14
[7,6,3,5,4,2,1]=>[2,1,1,1,1,1]=>6
[7,6,4,1,2,3,5]=>[4,1,1,1]=>20
[7,6,4,1,2,5,3]=>[3,2,1,1]=>35
[7,6,4,1,3,2,5]=>[3,1,1,1,1]=>15
[7,6,4,1,3,5,2]=>[3,1,1,1,1]=>15
[7,6,4,1,5,2,3]=>[3,2,1,1]=>35
[7,6,4,1,5,3,2]=>[2,2,1,1,1]=>14
[7,6,4,2,1,3,5]=>[3,1,1,1,1]=>15
[7,6,4,2,1,5,3]=>[2,2,1,1,1]=>14
[7,6,4,2,3,1,5]=>[3,1,1,1,1]=>15
[7,6,4,2,3,5,1]=>[3,1,1,1,1]=>15
[7,6,4,2,5,1,3]=>[2,2,1,1,1]=>14
[7,6,4,2,5,3,1]=>[2,2,1,1,1]=>14
[7,6,4,3,1,2,5]=>[3,1,1,1,1]=>15
[7,6,4,3,1,5,2]=>[2,2,1,1,1]=>14
[7,6,4,3,2,1,5]=>[2,1,1,1,1,1]=>6
[7,6,4,3,2,5,1]=>[2,1,1,1,1,1]=>6
[7,6,4,3,5,1,2]=>[2,2,1,1,1]=>14
[7,6,4,3,5,2,1]=>[2,1,1,1,1,1]=>6
[7,6,4,5,1,2,3]=>[3,2,1,1]=>35
[7,6,4,5,1,3,2]=>[2,2,1,1,1]=>14
[7,6,4,5,2,1,3]=>[2,2,1,1,1]=>14
[7,6,4,5,2,3,1]=>[2,2,1,1,1]=>14
[7,6,4,5,3,1,2]=>[2,2,1,1,1]=>14
[7,6,4,5,3,2,1]=>[2,1,1,1,1,1]=>6
[7,6,5,1,2,3,4]=>[4,1,1,1]=>20
[7,6,5,1,2,4,3]=>[3,1,1,1,1]=>15
[7,6,5,1,3,2,4]=>[3,1,1,1,1]=>15
[7,6,5,1,3,4,2]=>[3,1,1,1,1]=>15
[7,6,5,1,4,2,3]=>[3,1,1,1,1]=>15
[7,6,5,1,4,3,2]=>[2,1,1,1,1,1]=>6
[7,6,5,2,1,3,4]=>[3,1,1,1,1]=>15
[7,6,5,2,1,4,3]=>[2,2,1,1,1]=>14
[7,6,5,2,3,1,4]=>[3,1,1,1,1]=>15
[7,6,5,2,3,4,1]=>[3,1,1,1,1]=>15
[7,6,5,2,4,1,3]=>[2,2,1,1,1]=>14
[7,6,5,2,4,3,1]=>[2,1,1,1,1,1]=>6
[7,6,5,3,1,2,4]=>[3,1,1,1,1]=>15
[7,6,5,3,1,4,2]=>[2,2,1,1,1]=>14
[7,6,5,3,2,1,4]=>[2,1,1,1,1,1]=>6
[7,6,5,3,2,4,1]=>[2,1,1,1,1,1]=>6
[7,6,5,3,4,1,2]=>[2,2,1,1,1]=>14
[7,6,5,3,4,2,1]=>[2,1,1,1,1,1]=>6
[7,6,5,4,1,2,3]=>[3,1,1,1,1]=>15
[7,6,5,4,1,3,2]=>[2,1,1,1,1,1]=>6
[7,6,5,4,2,1,3]=>[2,1,1,1,1,1]=>6
[7,6,5,4,2,3,1]=>[2,1,1,1,1,1]=>6
[7,6,5,4,3,1,2]=>[2,1,1,1,1,1]=>6
[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]=>1
[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]=>1
[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[8,6,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[7,6,8,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]=>21
[8,7,5,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]=>20
[8,6,5,7,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[8,5,6,7,4,3,2,1]=>[3,1,1,1,1,1]=>21
[7,6,5,8,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[6,7,5,8,4,3,2,1]=>[3,1,1,1,1,1]=>21
[7,5,6,8,4,3,2,1]=>[3,1,1,1,1,1]=>21
[6,5,7,8,4,3,2,1]=>[3,1,1,1,1,1]=>21
[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]=>35
[8,7,6,4,5,3,2,1]=>[2,1,1,1,1,1,1]=>7
[8,6,7,4,5,3,2,1]=>[2,2,1,1,1,1]=>20
[8,7,5,4,6,3,2,1]=>[2,1,1,1,1,1,1]=>7
[8,7,4,5,6,3,2,1]=>[3,1,1,1,1,1]=>21
[8,5,6,4,7,3,2,1]=>[3,1,1,1,1,1]=>21
[8,6,4,5,7,3,2,1]=>[3,1,1,1,1,1]=>21
[8,4,5,6,7,3,2,1]=>[4,1,1,1,1]=>35
[7,6,5,4,8,3,2,1]=>[2,1,1,1,1,1,1]=>7
[6,7,5,4,8,3,2,1]=>[3,1,1,1,1,1]=>21
[7,5,6,4,8,3,2,1]=>[3,1,1,1,1,1]=>21
[6,5,7,4,8,3,2,1]=>[3,1,1,1,1,1]=>21
[5,6,7,4,8,3,2,1]=>[4,1,1,1,1]=>35
[7,6,4,5,8,3,2,1]=>[3,1,1,1,1,1]=>21
[6,7,4,5,8,3,2,1]=>[3,2,1,1,1]=>64
[7,5,4,6,8,3,2,1]=>[3,1,1,1,1,1]=>21
[7,4,5,6,8,3,2,1]=>[4,1,1,1,1]=>35
[6,5,4,7,8,3,2,1]=>[3,1,1,1,1,1]=>21
[5,6,4,7,8,3,2,1]=>[4,1,1,1,1]=>35
[6,4,5,7,8,3,2,1]=>[4,1,1,1,1]=>35
[5,4,6,7,8,3,2,1]=>[4,1,1,1,1]=>35
[4,5,6,7,8,3,2,1]=>[5,1,1,1]=>35
[8,7,6,5,3,4,2,1]=>[2,1,1,1,1,1,1]=>7
[7,8,6,5,3,4,2,1]=>[2,2,1,1,1,1]=>20
[7,6,8,5,3,4,2,1]=>[2,2,1,1,1,1]=>20
[8,7,5,6,3,4,2,1]=>[2,2,1,1,1,1]=>20
[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]=>28
[8,5,6,7,3,4,2,1]=>[3,2,1,1,1]=>64
[7,6,5,8,3,4,2,1]=>[2,2,1,1,1,1]=>20
[6,5,7,8,3,4,2,1]=>[3,2,1,1,1]=>64
[5,6,7,8,3,4,2,1]=>[4,2,1,1]=>90
[8,7,6,4,3,5,2,1]=>[2,1,1,1,1,1,1]=>7
[7,8,6,4,3,5,2,1]=>[2,2,1,1,1,1]=>20
[7,6,8,4,3,5,2,1]=>[2,2,1,1,1,1]=>20
[6,7,8,4,3,5,2,1]=>[3,2,1,1,1]=>64
[8,7,6,3,4,5,2,1]=>[3,1,1,1,1,1]=>21
[7,8,6,3,4,5,2,1]=>[3,2,1,1,1]=>64
[8,6,7,3,4,5,2,1]=>[3,2,1,1,1]=>64
[7,6,8,3,4,5,2,1]=>[3,2,1,1,1]=>64
[6,7,8,3,4,5,2,1]=>[3,3,1,1]=>56
[8,7,5,4,3,6,2,1]=>[2,1,1,1,1,1,1]=>7
[7,8,5,4,3,6,2,1]=>[2,2,1,1,1,1]=>20
[7,8,5,3,4,6,2,1]=>[3,2,1,1,1]=>64
[8,7,4,3,5,6,2,1]=>[3,1,1,1,1,1]=>21
[8,7,3,4,5,6,2,1]=>[4,1,1,1,1]=>35
[7,8,3,4,5,6,2,1]=>[4,2,1,1]=>90
[8,6,5,4,3,7,2,1]=>[2,1,1,1,1,1,1]=>7
[8,6,4,3,5,7,2,1]=>[3,1,1,1,1,1]=>21
[8,5,3,4,6,7,2,1]=>[4,1,1,1,1]=>35
[8,4,3,5,6,7,2,1]=>[4,1,1,1,1]=>35
[8,3,4,5,6,7,2,1]=>[5,1,1,1]=>35
[7,6,5,4,3,8,2,1]=>[2,1,1,1,1,1,1]=>7
[6,7,5,4,3,8,2,1]=>[3,1,1,1,1,1]=>21
[7,5,6,4,3,8,2,1]=>[3,1,1,1,1,1]=>21
[5,6,7,4,3,8,2,1]=>[4,1,1,1,1]=>35
[6,7,4,5,3,8,2,1]=>[3,2,1,1,1]=>64
[7,5,4,6,3,8,2,1]=>[3,1,1,1,1,1]=>21
[7,4,5,6,3,8,2,1]=>[4,1,1,1,1]=>35
[6,4,5,7,3,8,2,1]=>[4,1,1,1,1]=>35
[5,4,6,7,3,8,2,1]=>[4,1,1,1,1]=>35
[4,5,6,7,3,8,2,1]=>[5,1,1,1]=>35
[7,6,4,3,5,8,2,1]=>[3,1,1,1,1,1]=>21
[7,5,4,3,6,8,2,1]=>[3,1,1,1,1,1]=>21
[7,5,3,4,6,8,2,1]=>[4,1,1,1,1]=>35
[7,3,4,5,6,8,2,1]=>[5,1,1,1]=>35
[6,5,4,3,7,8,2,1]=>[3,1,1,1,1,1]=>21
[6,5,3,4,7,8,2,1]=>[4,1,1,1,1]=>35
[6,3,4,5,7,8,2,1]=>[5,1,1,1]=>35
[5,4,3,6,7,8,2,1]=>[4,1,1,1,1]=>35
[4,3,5,6,7,8,2,1]=>[5,1,1,1]=>35
[3,4,5,6,7,8,2,1]=>[6,1,1]=>21
[8,7,6,5,4,2,3,1]=>[2,1,1,1,1,1,1]=>7
[7,8,6,5,4,2,3,1]=>[2,2,1,1,1,1]=>20
[8,6,7,5,4,2,3,1]=>[2,2,1,1,1,1]=>20
[8,6,5,7,4,2,3,1]=>[2,2,1,1,1,1]=>20
[8,5,6,7,4,2,3,1]=>[3,2,1,1,1]=>64
[7,5,6,8,4,2,3,1]=>[3,2,1,1,1]=>64
[5,6,7,8,4,2,3,1]=>[4,2,1,1]=>90
[8,6,7,4,5,2,3,1]=>[2,2,2,1,1]=>28
[7,6,8,4,5,2,3,1]=>[2,2,2,1,1]=>28
[8,7,4,5,6,2,3,1]=>[3,2,1,1,1]=>64
[7,8,4,5,6,2,3,1]=>[3,2,2,1]=>70
[8,5,6,4,7,2,3,1]=>[3,2,1,1,1]=>64
[8,6,4,5,7,2,3,1]=>[3,2,1,1,1]=>64
[8,4,5,6,7,2,3,1]=>[4,2,1,1]=>90
[7,5,6,4,8,2,3,1]=>[3,2,1,1,1]=>64
[6,5,7,4,8,2,3,1]=>[3,2,1,1,1]=>64
[4,5,6,7,8,2,3,1]=>[5,2,1]=>64
[8,7,6,5,3,2,4,1]=>[2,1,1,1,1,1,1]=>7
[7,8,6,5,3,2,4,1]=>[2,2,1,1,1,1]=>20
[8,6,7,5,3,2,4,1]=>[2,2,1,1,1,1]=>20
[6,7,8,5,3,2,4,1]=>[3,2,1,1,1]=>64
[8,7,5,6,3,2,4,1]=>[2,2,1,1,1,1]=>20
[8,6,5,7,3,2,4,1]=>[2,2,1,1,1,1]=>20
[8,5,6,7,3,2,4,1]=>[3,2,1,1,1]=>64
[5,6,7,8,3,2,4,1]=>[4,2,1,1]=>90
[8,7,6,5,2,3,4,1]=>[3,1,1,1,1,1]=>21
[8,6,7,5,2,3,4,1]=>[3,2,1,1,1]=>64
[6,7,8,5,2,3,4,1]=>[3,3,1,1]=>56
[8,7,5,6,2,3,4,1]=>[3,2,1,1,1]=>64
[7,8,5,6,2,3,4,1]=>[3,2,2,1]=>70
[8,6,5,7,2,3,4,1]=>[3,2,1,1,1]=>64
[8,5,6,7,2,3,4,1]=>[3,3,1,1]=>56
[6,7,5,8,2,3,4,1]=>[3,3,1,1]=>56
[6,5,7,8,2,3,4,1]=>[3,3,1,1]=>56
[5,6,7,8,2,3,4,1]=>[4,3,1]=>70
[8,7,6,3,4,2,5,1]=>[3,1,1,1,1,1]=>21
[7,8,6,3,4,2,5,1]=>[3,2,1,1,1]=>64
[8,6,7,3,4,2,5,1]=>[3,2,1,1,1]=>64
[7,6,8,3,4,2,5,1]=>[3,2,1,1,1]=>64
[6,7,8,3,4,2,5,1]=>[3,3,1,1]=>56
[6,7,8,4,2,3,5,1]=>[3,3,1,1]=>56
[7,8,6,3,2,4,5,1]=>[3,2,1,1,1]=>64
[8,6,7,3,2,4,5,1]=>[3,2,1,1,1]=>64
[6,7,8,3,2,4,5,1]=>[3,3,1,1]=>56
[8,7,6,2,3,4,5,1]=>[4,1,1,1,1]=>35
[7,8,6,2,3,4,5,1]=>[4,2,1,1]=>90
[8,6,7,2,3,4,5,1]=>[4,2,1,1]=>90
[7,6,8,2,3,4,5,1]=>[4,2,1,1]=>90
[6,7,8,2,3,4,5,1]=>[4,3,1]=>70
[7,8,5,4,3,2,6,1]=>[2,2,1,1,1,1]=>20
[8,7,5,3,4,2,6,1]=>[3,1,1,1,1,1]=>21
[7,8,5,3,4,2,6,1]=>[3,2,1,1,1]=>64
[8,7,5,3,2,4,6,1]=>[3,1,1,1,1,1]=>21
[7,8,4,3,2,5,6,1]=>[3,2,1,1,1]=>64
[7,8,3,4,2,5,6,1]=>[4,2,1,1]=>90
[7,8,4,2,3,5,6,1]=>[4,2,1,1]=>90
[7,8,3,2,4,5,6,1]=>[4,2,1,1]=>90
[8,7,2,3,4,5,6,1]=>[5,1,1,1]=>35
[7,8,2,3,4,5,6,1]=>[5,2,1]=>64
[8,6,5,4,3,2,7,1]=>[2,1,1,1,1,1,1]=>7
[8,5,6,3,4,2,7,1]=>[3,2,1,1,1]=>64
[8,6,4,3,5,2,7,1]=>[3,1,1,1,1,1]=>21
[8,4,5,3,6,2,7,1]=>[4,1,1,1,1]=>35
[8,4,3,5,6,2,7,1]=>[4,1,1,1,1]=>35
[8,6,5,3,2,4,7,1]=>[3,1,1,1,1,1]=>21
[8,6,4,2,3,5,7,1]=>[4,1,1,1,1]=>35
[8,6,2,3,4,5,7,1]=>[5,1,1,1]=>35
[8,5,4,3,2,6,7,1]=>[3,1,1,1,1,1]=>21
[8,5,3,4,2,6,7,1]=>[4,1,1,1,1]=>35
[8,3,4,5,2,6,7,1]=>[5,1,1,1]=>35
[8,5,4,2,3,6,7,1]=>[4,1,1,1,1]=>35
[8,4,3,2,5,6,7,1]=>[4,1,1,1,1]=>35
[8,3,4,2,5,6,7,1]=>[5,1,1,1]=>35
[8,4,2,3,5,6,7,1]=>[5,1,1,1]=>35
[8,3,2,4,5,6,7,1]=>[5,1,1,1]=>35
[8,2,3,4,5,6,7,1]=>[6,1,1]=>21
[7,6,5,4,3,2,8,1]=>[2,1,1,1,1,1,1]=>7
[6,7,5,4,3,2,8,1]=>[3,1,1,1,1,1]=>21
[6,5,7,4,3,2,8,1]=>[3,1,1,1,1,1]=>21
[7,6,4,5,3,2,8,1]=>[3,1,1,1,1,1]=>21
[6,7,4,5,3,2,8,1]=>[3,2,1,1,1]=>64
[7,4,5,6,3,2,8,1]=>[4,1,1,1,1]=>35
[6,4,5,7,3,2,8,1]=>[4,1,1,1,1]=>35
[4,5,6,7,3,2,8,1]=>[5,1,1,1]=>35
[7,5,6,3,4,2,8,1]=>[3,2,1,1,1]=>64
[6,5,7,3,4,2,8,1]=>[3,2,1,1,1]=>64
[7,6,4,3,5,2,8,1]=>[3,1,1,1,1,1]=>21
[7,6,3,4,5,2,8,1]=>[4,1,1,1,1]=>35
[7,5,4,3,6,2,8,1]=>[3,1,1,1,1,1]=>21
[7,4,5,3,6,2,8,1]=>[4,1,1,1,1]=>35
[7,5,3,4,6,2,8,1]=>[4,1,1,1,1]=>35
[6,5,4,3,7,2,8,1]=>[3,1,1,1,1,1]=>21
[6,4,5,3,7,2,8,1]=>[4,1,1,1,1]=>35
[5,4,6,3,7,2,8,1]=>[4,1,1,1,1]=>35
[4,5,6,3,7,2,8,1]=>[5,1,1,1]=>35
[6,5,3,4,7,2,8,1]=>[4,1,1,1,1]=>35
[5,6,3,4,7,2,8,1]=>[4,2,1,1]=>90
[6,4,3,5,7,2,8,1]=>[4,1,1,1,1]=>35
[6,3,4,5,7,2,8,1]=>[5,1,1,1]=>35
[4,5,3,6,7,2,8,1]=>[5,1,1,1]=>35
[3,4,5,6,7,2,8,1]=>[6,1,1]=>21
[6,7,5,4,2,3,8,1]=>[3,2,1,1,1]=>64
[7,5,6,4,2,3,8,1]=>[3,2,1,1,1]=>64
[6,5,7,4,2,3,8,1]=>[3,2,1,1,1]=>64
[5,6,7,4,2,3,8,1]=>[4,2,1,1]=>90
[7,6,4,5,2,3,8,1]=>[3,2,1,1,1]=>64
[6,7,4,5,2,3,8,1]=>[3,2,2,1]=>70
[7,4,5,6,2,3,8,1]=>[4,2,1,1]=>90
[6,5,4,7,2,3,8,1]=>[3,2,1,1,1]=>64
[5,6,4,7,2,3,8,1]=>[4,2,1,1]=>90
[5,4,6,7,2,3,8,1]=>[4,2,1,1]=>90
[4,5,6,7,2,3,8,1]=>[5,2,1]=>64
[6,7,5,3,2,4,8,1]=>[3,2,1,1,1]=>64
[6,5,7,3,2,4,8,1]=>[3,2,1,1,1]=>64
[7,6,5,2,3,4,8,1]=>[4,1,1,1,1]=>35
[7,5,6,2,3,4,8,1]=>[4,2,1,1]=>90
[5,6,7,2,3,4,8,1]=>[4,3,1]=>70
[6,7,4,3,2,5,8,1]=>[3,2,1,1,1]=>64
[7,6,4,2,3,5,8,1]=>[4,1,1,1,1]=>35
[7,6,3,2,4,5,8,1]=>[4,1,1,1,1]=>35
[6,7,3,2,4,5,8,1]=>[4,2,1,1]=>90
[7,6,2,3,4,5,8,1]=>[5,1,1,1]=>35
[6,7,2,3,4,5,8,1]=>[5,2,1]=>64
[7,4,3,5,2,6,8,1]=>[4,1,1,1,1]=>35
[7,5,4,2,3,6,8,1]=>[4,1,1,1,1]=>35
[7,4,5,2,3,6,8,1]=>[4,2,1,1]=>90
[7,5,3,2,4,6,8,1]=>[4,1,1,1,1]=>35
[7,5,2,3,4,6,8,1]=>[5,1,1,1]=>35
[7,3,2,4,5,6,8,1]=>[5,1,1,1]=>35
[7,2,3,4,5,6,8,1]=>[6,1,1]=>21
[6,5,4,3,2,7,8,1]=>[3,1,1,1,1,1]=>21
[4,5,6,3,2,7,8,1]=>[5,1,1,1]=>35
[6,5,3,4,2,7,8,1]=>[4,1,1,1,1]=>35
[5,4,3,6,2,7,8,1]=>[4,1,1,1,1]=>35
[3,4,5,6,2,7,8,1]=>[6,1,1]=>21
[6,4,5,2,3,7,8,1]=>[4,2,1,1]=>90
[4,5,6,2,3,7,8,1]=>[5,2,1]=>64
[6,5,2,3,4,7,8,1]=>[5,1,1,1]=>35
[6,2,3,4,5,7,8,1]=>[6,1,1]=>21
[5,4,3,2,6,7,8,1]=>[4,1,1,1,1]=>35
[4,5,3,2,6,7,8,1]=>[5,1,1,1]=>35
[4,3,5,2,6,7,8,1]=>[5,1,1,1]=>35
[3,4,5,2,6,7,8,1]=>[6,1,1]=>21
[5,4,2,3,6,7,8,1]=>[5,1,1,1]=>35
[4,5,2,3,6,7,8,1]=>[5,2,1]=>64
[5,2,3,4,6,7,8,1]=>[6,1,1]=>21
[4,3,2,5,6,7,8,1]=>[5,1,1,1]=>35
[3,4,2,5,6,7,8,1]=>[6,1,1]=>21
[4,2,3,5,6,7,8,1]=>[6,1,1]=>21
[3,2,4,5,6,7,8,1]=>[6,1,1]=>21
[2,3,4,5,6,7,8,1]=>[7,1]=>7
[8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1]=>7
[7,8,6,5,4,3,1,2]=>[2,2,1,1,1,1]=>20
[8,6,7,5,4,3,1,2]=>[2,2,1,1,1,1]=>20
[7,6,8,5,4,3,1,2]=>[2,2,1,1,1,1]=>20
[6,7,8,5,4,3,1,2]=>[3,2,1,1,1]=>64
[8,7,5,6,4,3,1,2]=>[2,2,1,1,1,1]=>20
[7,8,5,6,4,3,1,2]=>[2,2,2,1,1]=>28
[7,6,5,8,4,3,1,2]=>[2,2,1,1,1,1]=>20
[6,7,5,8,4,3,1,2]=>[3,2,1,1,1]=>64
[7,5,6,8,4,3,1,2]=>[3,2,1,1,1]=>64
[6,5,7,8,4,3,1,2]=>[3,2,1,1,1]=>64
[5,6,7,8,4,3,1,2]=>[4,2,1,1]=>90
[8,7,6,4,5,3,1,2]=>[2,2,1,1,1,1]=>20
[7,8,6,4,5,3,1,2]=>[2,2,2,1,1]=>28
[8,6,7,4,5,3,1,2]=>[2,2,2,1,1]=>28
[6,7,8,4,5,3,1,2]=>[3,2,2,1]=>70
[8,7,5,4,6,3,1,2]=>[2,2,1,1,1,1]=>20
[8,5,6,4,7,3,1,2]=>[3,2,1,1,1]=>64
[8,6,4,5,7,3,1,2]=>[3,2,1,1,1]=>64
[8,5,4,6,7,3,1,2]=>[3,2,1,1,1]=>64
[7,6,5,4,8,3,1,2]=>[2,2,1,1,1,1]=>20
[7,5,6,4,8,3,1,2]=>[3,2,1,1,1]=>64
[6,5,7,4,8,3,1,2]=>[3,2,1,1,1]=>64
[7,6,4,5,8,3,1,2]=>[3,2,1,1,1]=>64
[6,7,4,5,8,3,1,2]=>[3,2,2,1]=>70
[5,6,4,7,8,3,1,2]=>[4,2,1,1]=>90
[4,5,6,7,8,3,1,2]=>[5,2,1]=>64
[8,7,6,5,3,4,1,2]=>[2,2,1,1,1,1]=>20
[7,8,6,5,3,4,1,2]=>[2,2,2,1,1]=>28
[7,6,8,5,3,4,1,2]=>[2,2,2,1,1]=>28
[6,7,8,5,3,4,1,2]=>[3,2,2,1]=>70
[8,7,5,6,3,4,1,2]=>[2,2,2,1,1]=>28
[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>14
[8,6,5,7,3,4,1,2]=>[2,2,2,1,1]=>28
[8,5,6,7,3,4,1,2]=>[3,2,2,1]=>70
[7,5,6,8,3,4,1,2]=>[3,2,2,1]=>70
[5,6,7,8,3,4,1,2]=>[4,2,2]=>56
[6,7,8,4,3,5,1,2]=>[3,2,2,1]=>70
[8,7,6,3,4,5,1,2]=>[3,2,1,1,1]=>64
[8,6,7,3,4,5,1,2]=>[3,2,2,1]=>70
[7,8,5,4,3,6,1,2]=>[2,2,2,1,1]=>28
[8,7,4,5,3,6,1,2]=>[3,2,1,1,1]=>64
[7,8,4,5,3,6,1,2]=>[3,2,2,1]=>70
[8,7,4,3,5,6,1,2]=>[3,2,1,1,1]=>64
[7,8,4,3,5,6,1,2]=>[3,2,2,1]=>70
[8,7,3,4,5,6,1,2]=>[4,2,1,1]=>90
[7,8,3,4,5,6,1,2]=>[4,2,2]=>56
[8,5,4,3,6,7,1,2]=>[3,2,1,1,1]=>64
[8,5,3,4,6,7,1,2]=>[4,2,1,1]=>90
[8,4,3,5,6,7,1,2]=>[4,2,1,1]=>90
[8,3,4,5,6,7,1,2]=>[5,2,1]=>64
[7,6,5,4,3,8,1,2]=>[2,2,1,1,1,1]=>20
[5,6,7,4,3,8,1,2]=>[4,2,1,1]=>90
[6,7,4,5,3,8,1,2]=>[3,2,2,1]=>70
[4,5,6,7,3,8,1,2]=>[5,2,1]=>64
[7,6,5,3,4,8,1,2]=>[3,2,1,1,1]=>64
[7,6,4,3,5,8,1,2]=>[3,2,1,1,1]=>64
[7,6,3,4,5,8,1,2]=>[4,2,1,1]=>90
[7,5,4,3,6,8,1,2]=>[3,2,1,1,1]=>64
[7,5,3,4,6,8,1,2]=>[4,2,1,1]=>90
[7,3,4,5,6,8,1,2]=>[5,2,1]=>64
[6,5,4,3,7,8,1,2]=>[3,2,1,1,1]=>64
[5,4,6,3,7,8,1,2]=>[4,2,1,1]=>90
[5,6,3,4,7,8,1,2]=>[4,2,2]=>56
[6,4,3,5,7,8,1,2]=>[4,2,1,1]=>90
[6,3,4,5,7,8,1,2]=>[5,2,1]=>64
[5,4,3,6,7,8,1,2]=>[4,2,1,1]=>90
[4,5,3,6,7,8,1,2]=>[5,2,1]=>64
[4,3,5,6,7,8,1,2]=>[5,2,1]=>64
[3,4,5,6,7,8,1,2]=>[6,2]=>20
[8,7,6,5,4,2,1,3]=>[2,1,1,1,1,1,1]=>7
[7,8,6,5,4,2,1,3]=>[2,2,1,1,1,1]=>20
[8,6,7,5,4,2,1,3]=>[2,2,1,1,1,1]=>20
[7,6,8,5,4,2,1,3]=>[2,2,1,1,1,1]=>20
[6,7,8,5,4,2,1,3]=>[3,2,1,1,1]=>64
[8,7,5,6,4,2,1,3]=>[2,2,1,1,1,1]=>20
[7,8,5,6,4,2,1,3]=>[2,2,2,1,1]=>28
[6,7,5,8,4,2,1,3]=>[3,2,1,1,1]=>64
[7,5,6,8,4,2,1,3]=>[3,2,1,1,1]=>64
[6,5,7,8,4,2,1,3]=>[3,2,1,1,1]=>64
[5,6,7,8,4,2,1,3]=>[4,2,1,1]=>90
[8,7,6,4,5,2,1,3]=>[2,2,1,1,1,1]=>20
[7,6,8,4,5,2,1,3]=>[2,2,2,1,1]=>28
[8,4,5,6,7,2,1,3]=>[4,2,1,1]=>90
[7,6,5,4,8,2,1,3]=>[2,2,1,1,1,1]=>20
[6,7,5,4,8,2,1,3]=>[3,2,1,1,1]=>64
[6,5,7,4,8,2,1,3]=>[3,2,1,1,1]=>64
[5,6,7,4,8,2,1,3]=>[4,2,1,1]=>90
[7,6,4,5,8,2,1,3]=>[3,2,1,1,1]=>64
[7,4,5,6,8,2,1,3]=>[4,2,1,1]=>90
[4,5,6,7,8,2,1,3]=>[5,2,1]=>64
[8,7,6,5,4,1,2,3]=>[3,1,1,1,1,1]=>21
[7,8,6,5,4,1,2,3]=>[3,2,1,1,1]=>64
[7,6,8,5,4,1,2,3]=>[3,2,1,1,1]=>64
[6,7,8,5,4,1,2,3]=>[3,3,1,1]=>56
[7,8,5,6,4,1,2,3]=>[3,2,2,1]=>70
[8,6,5,7,4,1,2,3]=>[3,2,1,1,1]=>64
[8,5,6,7,4,1,2,3]=>[3,3,1,1]=>56
[6,7,5,8,4,1,2,3]=>[3,3,1,1]=>56
[7,5,6,8,4,1,2,3]=>[3,3,1,1]=>56
[6,5,7,8,4,1,2,3]=>[3,3,1,1]=>56
[5,6,7,8,4,1,2,3]=>[4,3,1]=>70
[8,6,7,4,5,1,2,3]=>[3,2,2,1]=>70
[6,7,8,4,5,1,2,3]=>[3,3,2]=>42
[8,7,5,4,6,1,2,3]=>[3,2,1,1,1]=>64
[7,8,5,4,6,1,2,3]=>[3,2,2,1]=>70
[8,7,4,5,6,1,2,3]=>[3,3,1,1]=>56
[8,5,6,4,7,1,2,3]=>[3,3,1,1]=>56
[8,6,4,5,7,1,2,3]=>[3,3,1,1]=>56
[8,4,5,6,7,1,2,3]=>[4,3,1]=>70
[7,6,5,4,8,1,2,3]=>[3,2,1,1,1]=>64
[6,7,5,4,8,1,2,3]=>[3,3,1,1]=>56
[5,6,7,4,8,1,2,3]=>[4,3,1]=>70
[6,7,4,5,8,1,2,3]=>[3,3,2]=>42
[7,5,4,6,8,1,2,3]=>[3,3,1,1]=>56
[6,5,4,7,8,1,2,3]=>[3,3,1,1]=>56
[5,6,4,7,8,1,2,3]=>[4,3,1]=>70
[5,4,6,7,8,1,2,3]=>[4,3,1]=>70
[4,5,6,7,8,1,2,3]=>[5,3]=>28
[8,7,6,5,3,2,1,4]=>[2,1,1,1,1,1,1]=>7
[8,6,7,5,3,2,1,4]=>[2,2,1,1,1,1]=>20
[6,7,8,5,3,2,1,4]=>[3,2,1,1,1]=>64
[7,8,5,6,3,2,1,4]=>[2,2,2,1,1]=>28
[8,5,6,7,3,2,1,4]=>[3,2,1,1,1]=>64
[7,6,5,8,3,2,1,4]=>[2,2,1,1,1,1]=>20
[6,7,5,8,3,2,1,4]=>[3,2,1,1,1]=>64
[7,5,6,8,3,2,1,4]=>[3,2,1,1,1]=>64
[5,6,7,8,3,2,1,4]=>[4,2,1,1]=>90
[8,7,6,5,2,3,1,4]=>[3,1,1,1,1,1]=>21
[7,8,6,5,2,3,1,4]=>[3,2,1,1,1]=>64
[8,6,7,5,2,3,1,4]=>[3,2,1,1,1]=>64
[7,6,8,5,2,3,1,4]=>[3,2,1,1,1]=>64
[8,7,5,6,2,3,1,4]=>[3,2,1,1,1]=>64
[7,8,5,6,2,3,1,4]=>[3,2,2,1]=>70
[8,5,6,7,2,3,1,4]=>[3,3,1,1]=>56
[7,6,5,8,2,3,1,4]=>[3,2,1,1,1]=>64
[7,5,6,8,2,3,1,4]=>[3,3,1,1]=>56
[5,6,7,8,2,3,1,4]=>[4,3,1]=>70
[8,7,6,5,3,1,2,4]=>[3,1,1,1,1,1]=>21
[7,8,6,5,3,1,2,4]=>[3,2,1,1,1]=>64
[8,6,7,5,3,1,2,4]=>[3,2,1,1,1]=>64
[7,6,8,5,3,1,2,4]=>[3,2,1,1,1]=>64
[8,7,5,6,3,1,2,4]=>[3,2,1,1,1]=>64
[6,7,5,8,3,1,2,4]=>[3,3,1,1]=>56
[6,5,7,8,3,1,2,4]=>[3,3,1,1]=>56
[5,6,7,8,3,1,2,4]=>[4,3,1]=>70
[8,7,6,5,2,1,3,4]=>[3,1,1,1,1,1]=>21
[7,8,6,5,2,1,3,4]=>[3,2,1,1,1]=>64
[7,6,8,5,2,1,3,4]=>[3,2,1,1,1]=>64
[6,7,8,5,2,1,3,4]=>[3,3,1,1]=>56
[8,7,5,6,2,1,3,4]=>[3,2,1,1,1]=>64
[8,6,5,7,2,1,3,4]=>[3,2,1,1,1]=>64
[8,5,6,7,2,1,3,4]=>[3,3,1,1]=>56
[7,6,5,8,2,1,3,4]=>[3,2,1,1,1]=>64
[6,7,5,8,2,1,3,4]=>[3,3,1,1]=>56
[7,5,6,8,2,1,3,4]=>[3,3,1,1]=>56
[6,5,7,8,2,1,3,4]=>[3,3,1,1]=>56
[5,6,7,8,2,1,3,4]=>[4,3,1]=>70
[8,7,6,5,1,2,3,4]=>[4,1,1,1,1]=>35
[7,8,6,5,1,2,3,4]=>[4,2,1,1]=>90
[8,6,7,5,1,2,3,4]=>[4,2,1,1]=>90
[7,6,8,5,1,2,3,4]=>[4,2,1,1]=>90
[6,7,8,5,1,2,3,4]=>[4,3,1]=>70
[8,7,5,6,1,2,3,4]=>[4,2,1,1]=>90
[7,8,5,6,1,2,3,4]=>[4,2,2]=>56
[8,6,5,7,1,2,3,4]=>[4,2,1,1]=>90
[8,5,6,7,1,2,3,4]=>[4,3,1]=>70
[7,6,5,8,1,2,3,4]=>[4,2,1,1]=>90
[6,7,5,8,1,2,3,4]=>[4,3,1]=>70
[7,5,6,8,1,2,3,4]=>[4,3,1]=>70
[6,5,7,8,1,2,3,4]=>[4,3,1]=>70
[5,6,7,8,1,2,3,4]=>[4,4]=>14
[8,7,6,4,3,2,1,5]=>[2,1,1,1,1,1,1]=>7
[7,8,6,4,3,2,1,5]=>[2,2,1,1,1,1]=>20
[8,6,7,4,3,2,1,5]=>[2,2,1,1,1,1]=>20
[7,6,8,4,3,2,1,5]=>[2,2,1,1,1,1]=>20
[6,7,8,4,3,2,1,5]=>[3,2,1,1,1]=>64
[8,7,6,3,4,2,1,5]=>[3,1,1,1,1,1]=>21
[7,8,6,3,4,2,1,5]=>[3,2,1,1,1]=>64
[6,7,8,3,4,2,1,5]=>[3,3,1,1]=>56
[8,7,6,4,2,3,1,5]=>[3,1,1,1,1,1]=>21
[6,7,8,4,2,3,1,5]=>[3,3,1,1]=>56
[8,7,6,3,2,4,1,5]=>[3,1,1,1,1,1]=>21
[8,6,7,3,2,4,1,5]=>[3,2,1,1,1]=>64
[6,7,8,3,2,4,1,5]=>[3,3,1,1]=>56
[8,7,6,2,3,4,1,5]=>[4,1,1,1,1]=>35
[8,6,7,2,3,4,1,5]=>[4,2,1,1]=>90
[7,6,8,2,3,4,1,5]=>[4,2,1,1]=>90
[6,7,8,2,3,4,1,5]=>[4,3,1]=>70
[8,7,6,4,3,1,2,5]=>[3,1,1,1,1,1]=>21
[6,7,8,4,3,1,2,5]=>[3,3,1,1]=>56
[8,7,6,3,4,1,2,5]=>[3,2,1,1,1]=>64
[7,8,6,3,4,1,2,5]=>[3,2,2,1]=>70
[8,6,7,3,4,1,2,5]=>[3,2,2,1]=>70
[6,7,8,3,4,1,2,5]=>[3,3,2]=>42
[8,7,6,4,2,1,3,5]=>[3,1,1,1,1,1]=>21
[7,8,6,4,2,1,3,5]=>[3,2,1,1,1]=>64
[8,6,7,4,2,1,3,5]=>[3,2,1,1,1]=>64
[6,7,8,4,2,1,3,5]=>[3,3,1,1]=>56
[8,7,6,4,1,2,3,5]=>[4,1,1,1,1]=>35
[7,8,6,4,1,2,3,5]=>[4,2,1,1]=>90
[7,6,8,4,1,2,3,5]=>[4,2,1,1]=>90
[6,7,8,4,1,2,3,5]=>[4,3,1]=>70
[8,7,6,3,2,1,4,5]=>[3,1,1,1,1,1]=>21
[8,6,7,3,2,1,4,5]=>[3,2,1,1,1]=>64
[6,7,8,3,2,1,4,5]=>[3,3,1,1]=>56
[8,7,6,2,3,1,4,5]=>[4,1,1,1,1]=>35
[7,8,6,2,3,1,4,5]=>[4,2,1,1]=>90
[8,6,7,2,3,1,4,5]=>[4,2,1,1]=>90
[6,7,8,2,3,1,4,5]=>[4,3,1]=>70
[8,7,6,3,1,2,4,5]=>[4,1,1,1,1]=>35
[7,8,6,3,1,2,4,5]=>[4,2,1,1]=>90
[8,6,7,3,1,2,4,5]=>[4,2,1,1]=>90
[7,6,8,3,1,2,4,5]=>[4,2,1,1]=>90
[6,7,8,3,1,2,4,5]=>[4,3,1]=>70
[8,7,6,2,1,3,4,5]=>[4,1,1,1,1]=>35
[8,6,7,2,1,3,4,5]=>[4,2,1,1]=>90
[6,7,8,2,1,3,4,5]=>[4,3,1]=>70
[8,7,6,1,2,3,4,5]=>[5,1,1,1]=>35
[7,8,6,1,2,3,4,5]=>[5,2,1]=>64
[8,6,7,1,2,3,4,5]=>[5,2,1]=>64
[7,6,8,1,2,3,4,5]=>[5,2,1]=>64
[6,7,8,1,2,3,4,5]=>[5,3]=>28
[8,7,5,4,3,2,1,6]=>[2,1,1,1,1,1,1]=>7
[7,8,5,4,3,2,1,6]=>[2,2,1,1,1,1]=>20
[7,8,4,5,3,2,1,6]=>[3,2,1,1,1]=>64
[8,7,5,3,4,2,1,6]=>[3,1,1,1,1,1]=>21
[7,8,3,4,5,2,1,6]=>[4,2,1,1]=>90
[8,7,4,5,2,3,1,6]=>[3,2,1,1,1]=>64
[7,8,4,5,2,3,1,6]=>[3,2,2,1]=>70
[8,7,5,3,2,4,1,6]=>[3,1,1,1,1,1]=>21
[7,8,5,2,3,4,1,6]=>[4,2,1,1]=>90
[8,7,4,3,2,5,1,6]=>[3,1,1,1,1,1]=>21
[7,8,4,3,2,5,1,6]=>[3,2,1,1,1]=>64
[8,7,3,4,2,5,1,6]=>[4,1,1,1,1]=>35
[7,8,3,4,2,5,1,6]=>[4,2,1,1]=>90
[8,7,2,3,4,5,1,6]=>[5,1,1,1]=>35
[7,8,2,3,4,5,1,6]=>[5,2,1]=>64
[8,7,5,4,3,1,2,6]=>[3,1,1,1,1,1]=>21
[7,8,5,4,3,1,2,6]=>[3,2,1,1,1]=>64
[8,7,5,3,4,1,2,6]=>[3,2,1,1,1]=>64
[8,7,3,4,5,1,2,6]=>[4,2,1,1]=>90
[7,8,3,4,5,1,2,6]=>[4,2,2]=>56
[7,8,5,4,2,1,3,6]=>[3,2,1,1,1]=>64
[7,8,5,4,1,2,3,6]=>[4,2,1,1]=>90
[7,8,4,5,1,2,3,6]=>[4,2,2]=>56
[8,7,5,3,2,1,4,6]=>[3,1,1,1,1,1]=>21
[7,8,5,3,2,1,4,6]=>[3,2,1,1,1]=>64
[8,7,5,3,1,2,4,6]=>[4,1,1,1,1]=>35
[7,8,5,3,1,2,4,6]=>[4,2,1,1]=>90
[8,7,5,2,1,3,4,6]=>[4,1,1,1,1]=>35
[7,8,5,2,1,3,4,6]=>[4,2,1,1]=>90
[8,7,5,1,2,3,4,6]=>[5,1,1,1]=>35
[7,8,5,1,2,3,4,6]=>[5,2,1]=>64
[7,8,4,3,2,1,5,6]=>[3,2,1,1,1]=>64
[8,7,3,4,2,1,5,6]=>[4,1,1,1,1]=>35
[7,8,3,4,2,1,5,6]=>[4,2,1,1]=>90
[7,8,4,2,3,1,5,6]=>[4,2,1,1]=>90
[8,7,3,2,4,1,5,6]=>[4,1,1,1,1]=>35
[7,8,3,2,4,1,5,6]=>[4,2,1,1]=>90
[8,7,2,3,4,1,5,6]=>[5,1,1,1]=>35
[7,8,2,3,4,1,5,6]=>[5,2,1]=>64
[7,8,4,3,1,2,5,6]=>[4,2,1,1]=>90
[8,7,3,4,1,2,5,6]=>[4,2,1,1]=>90
[7,8,3,4,1,2,5,6]=>[4,2,2]=>56
[8,7,4,2,1,3,5,6]=>[4,1,1,1,1]=>35
[7,8,4,2,1,3,5,6]=>[4,2,1,1]=>90
[8,7,4,1,2,3,5,6]=>[5,1,1,1]=>35
[8,7,3,2,1,4,5,6]=>[4,1,1,1,1]=>35
[7,8,3,2,1,4,5,6]=>[4,2,1,1]=>90
[8,7,2,3,1,4,5,6]=>[5,1,1,1]=>35
[7,8,2,3,1,4,5,6]=>[5,2,1]=>64
[8,7,2,1,3,4,5,6]=>[5,1,1,1]=>35
[7,8,2,1,3,4,5,6]=>[5,2,1]=>64
[8,7,1,2,3,4,5,6]=>[6,1,1]=>21
[7,8,1,2,3,4,5,6]=>[6,2]=>20
[8,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,1]=>7
[8,5,6,4,3,2,1,7]=>[3,1,1,1,1,1]=>21
[8,6,4,5,3,2,1,7]=>[3,1,1,1,1,1]=>21
[8,4,5,6,3,2,1,7]=>[4,1,1,1,1]=>35
[8,6,5,3,4,2,1,7]=>[3,1,1,1,1,1]=>21
[8,5,6,3,4,2,1,7]=>[3,2,1,1,1]=>64
[8,4,5,3,6,2,1,7]=>[4,1,1,1,1]=>35
[8,4,3,5,6,2,1,7]=>[4,1,1,1,1]=>35
[8,3,4,5,6,2,1,7]=>[5,1,1,1]=>35
[8,6,5,4,2,3,1,7]=>[3,1,1,1,1,1]=>21
[8,5,6,4,2,3,1,7]=>[3,2,1,1,1]=>64
[8,4,5,6,2,3,1,7]=>[4,2,1,1]=>90
[8,6,5,3,2,4,1,7]=>[3,1,1,1,1,1]=>21
[8,6,5,2,3,4,1,7]=>[4,1,1,1,1]=>35
[8,5,6,2,3,4,1,7]=>[4,2,1,1]=>90
[8,6,4,2,3,5,1,7]=>[4,1,1,1,1]=>35
[8,6,3,2,4,5,1,7]=>[4,1,1,1,1]=>35
[8,4,3,5,2,6,1,7]=>[4,1,1,1,1]=>35
[8,5,4,2,3,6,1,7]=>[4,1,1,1,1]=>35
[8,4,5,2,3,6,1,7]=>[4,2,1,1]=>90
[8,5,3,2,4,6,1,7]=>[4,1,1,1,1]=>35
[8,5,2,3,4,6,1,7]=>[5,1,1,1]=>35
[8,3,2,4,5,6,1,7]=>[5,1,1,1]=>35
[8,2,3,4,5,6,1,7]=>[6,1,1]=>21
[8,6,5,4,3,1,2,7]=>[3,1,1,1,1,1]=>21
[8,6,4,5,3,1,2,7]=>[3,2,1,1,1]=>64
[8,6,5,3,4,1,2,7]=>[3,2,1,1,1]=>64
[8,5,6,3,4,1,2,7]=>[3,2,2,1]=>70
[8,5,4,3,6,1,2,7]=>[3,2,1,1,1]=>64
[8,5,3,4,6,1,2,7]=>[4,2,1,1]=>90
[8,4,3,5,6,1,2,7]=>[4,2,1,1]=>90
[8,3,4,5,6,1,2,7]=>[5,2,1]=>64
[8,6,5,4,2,1,3,7]=>[3,1,1,1,1,1]=>21
[8,5,6,4,2,1,3,7]=>[3,2,1,1,1]=>64
[8,4,5,6,2,1,3,7]=>[4,2,1,1]=>90
[8,5,6,4,1,2,3,7]=>[4,2,1,1]=>90
[8,6,4,5,1,2,3,7]=>[4,2,1,1]=>90
[8,4,5,6,1,2,3,7]=>[4,3,1]=>70
[8,6,5,3,2,1,4,7]=>[3,1,1,1,1,1]=>21
[8,5,6,3,2,1,4,7]=>[3,2,1,1,1]=>64
[8,6,5,2,3,1,4,7]=>[4,1,1,1,1]=>35
[8,5,6,2,3,1,4,7]=>[4,2,1,1]=>90
[8,5,6,3,1,2,4,7]=>[4,2,1,1]=>90
[8,6,5,2,1,3,4,7]=>[4,1,1,1,1]=>35
[8,5,6,2,1,3,4,7]=>[4,2,1,1]=>90
[8,6,5,1,2,3,4,7]=>[5,1,1,1]=>35
[8,5,6,1,2,3,4,7]=>[5,2,1]=>64
[8,6,4,3,2,1,5,7]=>[3,1,1,1,1,1]=>21
[8,6,3,4,2,1,5,7]=>[4,1,1,1,1]=>35
[8,6,4,2,3,1,5,7]=>[4,1,1,1,1]=>35
[8,6,3,2,4,1,5,7]=>[4,1,1,1,1]=>35
[8,6,2,3,4,1,5,7]=>[5,1,1,1]=>35
[8,6,4,3,1,2,5,7]=>[4,1,1,1,1]=>35
[8,6,3,4,1,2,5,7]=>[4,2,1,1]=>90
[8,6,4,2,1,3,5,7]=>[4,1,1,1,1]=>35
[8,6,4,1,2,3,5,7]=>[5,1,1,1]=>35
[8,6,3,2,1,4,5,7]=>[4,1,1,1,1]=>35
[8,6,1,2,3,4,5,7]=>[6,1,1]=>21
[8,5,4,3,2,1,6,7]=>[3,1,1,1,1,1]=>21
[8,4,5,3,2,1,6,7]=>[4,1,1,1,1]=>35
[8,4,3,5,2,1,6,7]=>[4,1,1,1,1]=>35
[8,3,4,5,2,1,6,7]=>[5,1,1,1]=>35
[8,4,5,2,3,1,6,7]=>[4,2,1,1]=>90
[8,5,2,3,4,1,6,7]=>[5,1,1,1]=>35
[8,4,2,3,5,1,6,7]=>[5,1,1,1]=>35
[8,2,3,4,5,1,6,7]=>[6,1,1]=>21
[8,5,3,4,1,2,6,7]=>[4,2,1,1]=>90
[8,3,4,5,1,2,6,7]=>[5,2,1]=>64
[8,5,4,2,1,3,6,7]=>[4,1,1,1,1]=>35
[8,5,4,1,2,3,6,7]=>[5,1,1,1]=>35
[8,4,5,1,2,3,6,7]=>[5,2,1]=>64
[8,5,3,2,1,4,6,7]=>[4,1,1,1,1]=>35
[8,5,3,1,2,4,6,7]=>[5,1,1,1]=>35
[8,5,1,2,3,4,6,7]=>[6,1,1]=>21
[8,4,3,2,1,5,6,7]=>[4,1,1,1,1]=>35
[8,3,4,2,1,5,6,7]=>[5,1,1,1]=>35
[8,4,2,3,1,5,6,7]=>[5,1,1,1]=>35
[8,2,3,4,1,5,6,7]=>[6,1,1]=>21
[8,3,4,1,2,5,6,7]=>[5,2,1]=>64
[8,4,2,1,3,5,6,7]=>[5,1,1,1]=>35
[8,4,1,2,3,5,6,7]=>[6,1,1]=>21
[8,3,2,1,4,5,6,7]=>[5,1,1,1]=>35
[8,2,3,1,4,5,6,7]=>[6,1,1]=>21
[8,3,1,2,4,5,6,7]=>[6,1,1]=>21
[8,2,1,3,4,5,6,7]=>[6,1,1]=>21
[8,1,2,3,4,5,6,7]=>[7,1]=>7
[7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1]=>7
[6,7,5,4,3,2,1,8]=>[3,1,1,1,1,1]=>21
[7,5,6,4,3,2,1,8]=>[3,1,1,1,1,1]=>21
[6,5,7,4,3,2,1,8]=>[3,1,1,1,1,1]=>21
[5,6,7,4,3,2,1,8]=>[4,1,1,1,1]=>35
[7,6,4,5,3,2,1,8]=>[3,1,1,1,1,1]=>21
[6,7,4,5,3,2,1,8]=>[3,2,1,1,1]=>64
[7,5,4,6,3,2,1,8]=>[3,1,1,1,1,1]=>21
[7,4,5,6,3,2,1,8]=>[4,1,1,1,1]=>35
[6,5,4,7,3,2,1,8]=>[3,1,1,1,1,1]=>21
[5,6,4,7,3,2,1,8]=>[4,1,1,1,1]=>35
[4,5,6,7,3,2,1,8]=>[5,1,1,1]=>35
[7,6,5,3,4,2,1,8]=>[3,1,1,1,1,1]=>21
[6,7,5,3,4,2,1,8]=>[3,2,1,1,1]=>64
[7,5,6,3,4,2,1,8]=>[3,2,1,1,1]=>64
[6,5,7,3,4,2,1,8]=>[3,2,1,1,1]=>64
[5,6,7,3,4,2,1,8]=>[4,2,1,1]=>90
[7,6,4,3,5,2,1,8]=>[3,1,1,1,1,1]=>21
[6,7,4,3,5,2,1,8]=>[3,2,1,1,1]=>64
[7,6,3,4,5,2,1,8]=>[4,1,1,1,1]=>35
[7,5,4,3,6,2,1,8]=>[3,1,1,1,1,1]=>21
[6,5,4,3,7,2,1,8]=>[3,1,1,1,1,1]=>21
[5,6,4,3,7,2,1,8]=>[4,1,1,1,1]=>35
[5,4,6,3,7,2,1,8]=>[4,1,1,1,1]=>35
[5,4,3,6,7,2,1,8]=>[4,1,1,1,1]=>35
[3,4,5,6,7,2,1,8]=>[6,1,1]=>21
[6,7,5,4,2,3,1,8]=>[3,2,1,1,1]=>64
[7,5,6,4,2,3,1,8]=>[3,2,1,1,1]=>64
[5,6,7,4,2,3,1,8]=>[4,2,1,1]=>90
[7,6,4,5,2,3,1,8]=>[3,2,1,1,1]=>64
[6,7,4,5,2,3,1,8]=>[3,2,2,1]=>70
[7,5,4,6,2,3,1,8]=>[3,2,1,1,1]=>64
[6,5,4,7,2,3,1,8]=>[3,2,1,1,1]=>64
[5,6,4,7,2,3,1,8]=>[4,2,1,1]=>90
[5,4,6,7,2,3,1,8]=>[4,2,1,1]=>90
[4,5,6,7,2,3,1,8]=>[5,2,1]=>64
[7,6,5,3,2,4,1,8]=>[3,1,1,1,1,1]=>21
[6,5,7,3,2,4,1,8]=>[3,2,1,1,1]=>64
[5,6,7,3,2,4,1,8]=>[4,2,1,1]=>90
[7,6,5,2,3,4,1,8]=>[4,1,1,1,1]=>35
[6,7,5,2,3,4,1,8]=>[4,2,1,1]=>90
[7,5,6,2,3,4,1,8]=>[4,2,1,1]=>90
[6,5,7,2,3,4,1,8]=>[4,2,1,1]=>90
[5,6,7,2,3,4,1,8]=>[4,3,1]=>70
[6,7,4,3,2,5,1,8]=>[3,2,1,1,1]=>64
[7,6,4,2,3,5,1,8]=>[4,1,1,1,1]=>35
[6,7,4,2,3,5,1,8]=>[4,2,1,1]=>90
[7,6,3,2,4,5,1,8]=>[4,1,1,1,1]=>35
[6,7,3,2,4,5,1,8]=>[4,2,1,1]=>90
[7,5,4,3,2,6,1,8]=>[3,1,1,1,1,1]=>21
[7,4,5,3,2,6,1,8]=>[4,1,1,1,1]=>35
[7,4,3,5,2,6,1,8]=>[4,1,1,1,1]=>35
[7,5,3,2,4,6,1,8]=>[4,1,1,1,1]=>35
[7,4,2,3,5,6,1,8]=>[5,1,1,1]=>35
[7,2,3,4,5,6,1,8]=>[6,1,1]=>21
[6,5,4,3,2,7,1,8]=>[3,1,1,1,1,1]=>21
[6,3,4,5,2,7,1,8]=>[5,1,1,1]=>35
[4,5,3,6,2,7,1,8]=>[5,1,1,1]=>35
[5,3,4,6,2,7,1,8]=>[5,1,1,1]=>35
[4,3,5,6,2,7,1,8]=>[5,1,1,1]=>35
[3,4,5,6,2,7,1,8]=>[6,1,1]=>21
[5,4,6,2,3,7,1,8]=>[4,2,1,1]=>90
[6,5,3,2,4,7,1,8]=>[4,1,1,1,1]=>35
[6,4,2,3,5,7,1,8]=>[5,1,1,1]=>35
[5,4,3,2,6,7,1,8]=>[4,1,1,1,1]=>35
[4,5,2,3,6,7,1,8]=>[5,2,1]=>64
[5,2,3,4,6,7,1,8]=>[6,1,1]=>21
[4,3,2,5,6,7,1,8]=>[5,1,1,1]=>35
[3,4,2,5,6,7,1,8]=>[6,1,1]=>21
[4,2,3,5,6,7,1,8]=>[6,1,1]=>21
[3,2,4,5,6,7,1,8]=>[6,1,1]=>21
[2,3,4,5,6,7,1,8]=>[7,1]=>7
[7,6,5,4,3,1,2,8]=>[3,1,1,1,1,1]=>21
[6,7,5,4,3,1,2,8]=>[3,2,1,1,1]=>64
[7,5,6,4,3,1,2,8]=>[3,2,1,1,1]=>64
[7,6,4,5,3,1,2,8]=>[3,2,1,1,1]=>64
[5,4,6,7,3,1,2,8]=>[4,2,1,1]=>90
[4,5,6,7,3,1,2,8]=>[5,2,1]=>64
[7,6,5,3,4,1,2,8]=>[3,2,1,1,1]=>64
[6,5,4,3,7,1,2,8]=>[3,2,1,1,1]=>64
[6,3,4,5,7,1,2,8]=>[5,2,1]=>64
[4,3,5,6,7,1,2,8]=>[5,2,1]=>64
[3,4,5,6,7,1,2,8]=>[6,2]=>20
[7,6,5,4,2,1,3,8]=>[3,1,1,1,1,1]=>21
[6,5,7,4,2,1,3,8]=>[3,2,1,1,1]=>64
[7,6,4,5,2,1,3,8]=>[3,2,1,1,1]=>64
[5,4,6,7,2,1,3,8]=>[4,2,1,1]=>90
[4,5,6,7,2,1,3,8]=>[5,2,1]=>64
[7,6,5,4,1,2,3,8]=>[4,1,1,1,1]=>35
[5,6,7,4,1,2,3,8]=>[4,3,1]=>70
[7,4,5,6,1,2,3,8]=>[4,3,1]=>70
[5,4,6,7,1,2,3,8]=>[4,3,1]=>70
[4,5,6,7,1,2,3,8]=>[5,3]=>28
[7,6,5,3,2,1,4,8]=>[3,1,1,1,1,1]=>21
[7,6,5,2,3,1,4,8]=>[4,1,1,1,1]=>35
[6,7,5,2,3,1,4,8]=>[4,2,1,1]=>90
[7,5,6,2,3,1,4,8]=>[4,2,1,1]=>90
[6,5,7,2,3,1,4,8]=>[4,2,1,1]=>90
[5,6,7,2,3,1,4,8]=>[4,3,1]=>70
[7,6,5,2,1,3,4,8]=>[4,1,1,1,1]=>35
[7,5,6,2,1,3,4,8]=>[4,2,1,1]=>90
[5,6,7,2,1,3,4,8]=>[4,3,1]=>70
[7,6,5,1,2,3,4,8]=>[5,1,1,1]=>35
[6,7,5,1,2,3,4,8]=>[5,2,1]=>64
[7,5,6,1,2,3,4,8]=>[5,2,1]=>64
[6,5,7,1,2,3,4,8]=>[5,2,1]=>64
[5,6,7,1,2,3,4,8]=>[5,3]=>28
[7,6,4,3,2,1,5,8]=>[3,1,1,1,1,1]=>21
[6,7,4,3,2,1,5,8]=>[3,2,1,1,1]=>64
[7,6,3,4,2,1,5,8]=>[4,1,1,1,1]=>35
[6,7,3,4,2,1,5,8]=>[4,2,1,1]=>90
[7,6,4,2,3,1,5,8]=>[4,1,1,1,1]=>35
[7,6,3,2,4,1,5,8]=>[4,1,1,1,1]=>35
[7,6,2,3,4,1,5,8]=>[5,1,1,1]=>35
[6,7,2,3,4,1,5,8]=>[5,2,1]=>64
[7,6,4,3,1,2,5,8]=>[4,1,1,1,1]=>35
[7,6,4,2,1,3,5,8]=>[4,1,1,1,1]=>35
[7,6,3,2,1,4,5,8]=>[4,1,1,1,1]=>35
[6,7,3,2,1,4,5,8]=>[4,2,1,1]=>90
[7,6,2,3,1,4,5,8]=>[5,1,1,1]=>35
[6,7,2,3,1,4,5,8]=>[5,2,1]=>64
[6,7,3,1,2,4,5,8]=>[5,2,1]=>64
[6,7,1,2,3,4,5,8]=>[6,2]=>20
[7,5,4,3,2,1,6,8]=>[3,1,1,1,1,1]=>21
[7,4,5,3,2,1,6,8]=>[4,1,1,1,1]=>35
[7,4,3,5,2,1,6,8]=>[4,1,1,1,1]=>35
[7,3,4,5,2,1,6,8]=>[5,1,1,1]=>35
[7,5,4,2,3,1,6,8]=>[4,1,1,1,1]=>35
[7,5,3,2,4,1,6,8]=>[4,1,1,1,1]=>35
[7,5,2,3,4,1,6,8]=>[5,1,1,1]=>35
[7,4,2,3,5,1,6,8]=>[5,1,1,1]=>35
[7,2,3,4,5,1,6,8]=>[6,1,1]=>21
[7,4,5,1,2,3,6,8]=>[5,2,1]=>64
[7,5,3,2,1,4,6,8]=>[4,1,1,1,1]=>35
[7,5,2,3,1,4,6,8]=>[5,1,1,1]=>35
[7,5,3,1,2,4,6,8]=>[5,1,1,1]=>35
[7,5,1,2,3,4,6,8]=>[6,1,1]=>21
[7,2,3,4,1,5,6,8]=>[6,1,1]=>21
[7,4,3,1,2,5,6,8]=>[5,1,1,1]=>35
[7,3,4,1,2,5,6,8]=>[5,2,1]=>64
[7,3,2,1,4,5,6,8]=>[5,1,1,1]=>35
[7,3,1,2,4,5,6,8]=>[6,1,1]=>21
[7,2,1,3,4,5,6,8]=>[6,1,1]=>21
[7,1,2,3,4,5,6,8]=>[7,1]=>7
[6,5,4,3,2,1,7,8]=>[3,1,1,1,1,1]=>21
[5,6,4,3,2,1,7,8]=>[4,1,1,1,1]=>35
[5,4,6,3,2,1,7,8]=>[4,1,1,1,1]=>35
[4,5,6,3,2,1,7,8]=>[5,1,1,1]=>35
[5,6,3,4,2,1,7,8]=>[4,2,1,1]=>90
[5,4,6,2,3,1,7,8]=>[4,2,1,1]=>90
[5,6,3,2,4,1,7,8]=>[4,2,1,1]=>90
[6,5,2,3,4,1,7,8]=>[5,1,1,1]=>35
[5,6,2,3,4,1,7,8]=>[5,2,1]=>64
[6,4,3,2,5,1,7,8]=>[4,1,1,1,1]=>35
[6,2,3,4,5,1,7,8]=>[6,1,1]=>21
[5,4,3,2,6,1,7,8]=>[4,1,1,1,1]=>35
[4,3,5,2,6,1,7,8]=>[5,1,1,1]=>35
[3,4,5,2,6,1,7,8]=>[6,1,1]=>21
[5,2,3,4,6,1,7,8]=>[6,1,1]=>21
[4,3,2,5,6,1,7,8]=>[5,1,1,1]=>35
[4,2,3,5,6,1,7,8]=>[6,1,1]=>21
[3,2,4,5,6,1,7,8]=>[6,1,1]=>21
[2,3,4,5,6,1,7,8]=>[7,1]=>7
[6,5,4,3,1,2,7,8]=>[4,1,1,1,1]=>35
[3,4,5,6,1,2,7,8]=>[6,2]=>20
[6,5,4,2,1,3,7,8]=>[4,1,1,1,1]=>35
[6,4,5,2,1,3,7,8]=>[4,2,1,1]=>90
[4,5,6,1,2,3,7,8]=>[5,3]=>28
[6,4,3,2,1,5,7,8]=>[4,1,1,1,1]=>35
[6,3,4,2,1,5,7,8]=>[5,1,1,1]=>35
[6,4,3,1,2,5,7,8]=>[5,1,1,1]=>35
[6,4,2,1,3,5,7,8]=>[5,1,1,1]=>35
[6,4,1,2,3,5,7,8]=>[6,1,1]=>21
[6,2,3,1,4,5,7,8]=>[6,1,1]=>21
[6,3,1,2,4,5,7,8]=>[6,1,1]=>21
[6,1,2,3,4,5,7,8]=>[7,1]=>7
[5,4,3,2,1,6,7,8]=>[4,1,1,1,1]=>35
[4,5,3,2,1,6,7,8]=>[5,1,1,1]=>35
[5,3,4,2,1,6,7,8]=>[5,1,1,1]=>35
[4,3,5,2,1,6,7,8]=>[5,1,1,1]=>35
[3,4,5,2,1,6,7,8]=>[6,1,1]=>21
[5,4,2,3,1,6,7,8]=>[5,1,1,1]=>35
[4,5,2,3,1,6,7,8]=>[5,2,1]=>64
[5,3,2,4,1,6,7,8]=>[5,1,1,1]=>35
[5,2,3,4,1,6,7,8]=>[6,1,1]=>21
[4,3,2,5,1,6,7,8]=>[5,1,1,1]=>35
[3,4,2,5,1,6,7,8]=>[6,1,1]=>21
[4,2,3,5,1,6,7,8]=>[6,1,1]=>21
[3,2,4,5,1,6,7,8]=>[6,1,1]=>21
[2,3,4,5,1,6,7,8]=>[7,1]=>7
[3,4,5,1,2,6,7,8]=>[6,2]=>20
[4,5,1,2,3,6,7,8]=>[6,2]=>20
[5,3,2,1,4,6,7,8]=>[5,1,1,1]=>35
[5,2,3,1,4,6,7,8]=>[6,1,1]=>21
[5,3,1,2,4,6,7,8]=>[6,1,1]=>21
[5,1,2,3,4,6,7,8]=>[7,1]=>7
[4,3,2,1,5,6,7,8]=>[5,1,1,1]=>35
[3,4,2,1,5,6,7,8]=>[6,1,1]=>21
[4,2,3,1,5,6,7,8]=>[6,1,1]=>21
[3,2,4,1,5,6,7,8]=>[6,1,1]=>21
[2,3,4,1,5,6,7,8]=>[7,1]=>7
[4,3,1,2,5,6,7,8]=>[6,1,1]=>21
[3,4,1,2,5,6,7,8]=>[6,2]=>20
[4,2,1,3,5,6,7,8]=>[6,1,1]=>21
[4,1,2,3,5,6,7,8]=>[7,1]=>7
[3,2,1,4,5,6,7,8]=>[6,1,1]=>21
[2,3,1,4,5,6,7,8]=>[7,1]=>7
[3,1,2,4,5,6,7,8]=>[7,1]=>7
[2,1,3,4,5,6,7,8]=>[7,1]=>7
[1,2,3,4,5,6,7,8]=>[8]=>1
[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]=>21
[6,5,8,7,4,3,2,1]=>[2,2,1,1,1,1]=>20
[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]=>21
[5,7,6,8,4,3,2,1]=>[3,1,1,1,1,1]=>21
[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>7
[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]=>21
[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]=>21
[4,7,6,8,5,3,2,1]=>[3,1,1,1,1,1]=>21
[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]=>21
[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]=>35
[5,7,6,4,8,3,2,1]=>[3,1,1,1,1,1]=>21
[4,7,6,5,8,3,2,1]=>[3,1,1,1,1,1]=>21
[4,6,7,5,8,3,2,1]=>[4,1,1,1,1]=>35
[5,4,7,6,8,3,2,1]=>[3,2,1,1,1]=>64
[4,5,7,6,8,3,2,1]=>[4,1,1,1,1]=>35
[4,6,5,7,8,3,2,1]=>[4,1,1,1,1]=>35
[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>7
[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]=>21
[3,6,8,7,5,4,2,1]=>[3,1,1,1,1,1]=>21
[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]=>21
[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]=>35
[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]=>35
[3,7,6,5,8,4,2,1]=>[3,1,1,1,1,1]=>21
[3,5,7,6,8,4,2,1]=>[4,1,1,1,1]=>35
[3,5,6,7,8,4,2,1]=>[5,1,1,1]=>35
[4,3,8,7,6,5,2,1]=>[2,2,1,1,1,1]=>20
[3,4,6,7,8,5,2,1]=>[5,1,1,1]=>35
[5,4,3,8,7,6,2,1]=>[2,2,2,1,1]=>28
[5,4,3,7,8,6,2,1]=>[3,2,1,1,1]=>64
[3,5,4,7,8,6,2,1]=>[4,2,1,1]=>90
[3,4,5,7,8,6,2,1]=>[5,1,1,1]=>35
[6,5,4,3,8,7,2,1]=>[2,2,1,1,1,1]=>20
[5,6,4,3,8,7,2,1]=>[3,2,1,1,1]=>64
[4,3,6,5,8,7,2,1]=>[3,3,1,1]=>56
[5,4,3,6,8,7,2,1]=>[3,2,1,1,1]=>64
[4,5,3,6,8,7,2,1]=>[4,2,1,1]=>90
[3,4,5,6,8,7,2,1]=>[5,1,1,1]=>35
[5,7,6,4,3,8,2,1]=>[3,1,1,1,1,1]=>21
[5,4,7,6,3,8,2,1]=>[3,2,1,1,1]=>64
[3,7,6,5,4,8,2,1]=>[3,1,1,1,1,1]=>21
[3,5,7,6,4,8,2,1]=>[4,1,1,1,1]=>35
[3,5,6,7,4,8,2,1]=>[5,1,1,1]=>35
[4,3,7,6,5,8,2,1]=>[3,2,1,1,1]=>64
[3,4,7,6,5,8,2,1]=>[4,1,1,1,1]=>35
[3,4,6,7,5,8,2,1]=>[5,1,1,1]=>35
[3,5,4,7,6,8,2,1]=>[4,2,1,1]=>90
[3,4,5,7,6,8,2,1]=>[5,1,1,1]=>35
[3,5,6,4,7,8,2,1]=>[5,1,1,1]=>35
[4,3,6,5,7,8,2,1]=>[4,2,1,1]=>90
[3,4,6,5,7,8,2,1]=>[5,1,1,1]=>35
[3,5,4,6,7,8,2,1]=>[5,1,1,1]=>35
[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]=>7
[2,7,8,6,5,4,3,1]=>[3,1,1,1,1,1]=>21
[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]=>21
[2,7,6,8,5,4,3,1]=>[3,1,1,1,1,1]=>21
[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]=>35
[2,5,8,7,6,4,3,1]=>[3,1,1,1,1,1]=>21
[2,6,7,5,8,4,3,1]=>[4,1,1,1,1]=>35
[2,5,6,7,8,4,3,1]=>[5,1,1,1]=>35
[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]=>21
[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]=>35
[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]=>35
[2,4,6,7,8,5,3,1]=>[5,1,1,1]=>35
[2,5,4,8,7,6,3,1]=>[3,2,1,1,1]=>64
[2,5,4,7,8,6,3,1]=>[4,2,1,1]=>90
[2,4,5,7,8,6,3,1]=>[5,1,1,1]=>35
[2,6,5,4,8,7,3,1]=>[3,2,1,1,1]=>64
[2,5,6,4,8,7,3,1]=>[4,2,1,1]=>90
[2,4,6,5,8,7,3,1]=>[4,2,1,1]=>90
[2,4,5,6,8,7,3,1]=>[5,1,1,1]=>35
[2,7,6,5,4,8,3,1]=>[3,1,1,1,1,1]=>21
[2,5,6,7,4,8,3,1]=>[5,1,1,1]=>35
[2,4,6,7,5,8,3,1]=>[5,1,1,1]=>35
[2,5,4,7,6,8,3,1]=>[4,2,1,1]=>90
[2,6,5,4,7,8,3,1]=>[4,1,1,1,1]=>35
[2,5,6,4,7,8,3,1]=>[5,1,1,1]=>35
[2,4,6,5,7,8,3,1]=>[5,1,1,1]=>35
[2,5,4,6,7,8,3,1]=>[5,1,1,1]=>35
[2,4,5,6,7,8,3,1]=>[6,1,1]=>21
[3,2,8,7,6,5,4,1]=>[2,2,1,1,1,1]=>20
[3,2,6,8,7,5,4,1]=>[3,2,1,1,1]=>64
[3,2,5,7,8,6,4,1]=>[4,2,1,1]=>90
[3,2,5,7,6,8,4,1]=>[4,2,1,1]=>90
[3,2,5,6,7,8,4,1]=>[5,2,1]=>64
[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]=>21
[2,3,6,7,8,5,4,1]=>[5,1,1,1]=>35
[2,3,5,7,8,6,4,1]=>[5,1,1,1]=>35
[2,3,6,5,8,7,4,1]=>[4,2,1,1]=>90
[2,3,5,6,8,7,4,1]=>[5,1,1,1]=>35
[2,3,7,6,5,8,4,1]=>[4,1,1,1,1]=>35
[2,3,5,7,6,8,4,1]=>[5,1,1,1]=>35
[2,3,5,6,7,8,4,1]=>[6,1,1]=>21
[4,3,2,8,7,6,5,1]=>[2,2,2,1,1]=>28
[4,3,2,7,8,6,5,1]=>[3,2,2,1]=>70
[3,4,2,8,7,6,5,1]=>[3,2,1,1,1]=>64
[3,4,2,7,8,6,5,1]=>[4,2,1,1]=>90
[2,4,3,8,7,6,5,1]=>[3,2,1,1,1]=>64
[2,4,3,6,8,7,5,1]=>[4,2,1,1]=>90
[2,4,3,6,7,8,5,1]=>[5,2,1]=>64
[3,2,4,8,7,6,5,1]=>[3,2,1,1,1]=>64
[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]=>35
[2,3,4,6,8,7,5,1]=>[5,1,1,1]=>35
[2,3,4,7,6,8,5,1]=>[5,1,1,1]=>35
[2,3,4,6,7,8,5,1]=>[6,1,1]=>21
[5,4,3,2,8,7,6,1]=>[2,2,2,1,1]=>28
[5,4,3,2,7,8,6,1]=>[3,2,1,1,1]=>64
[3,5,4,2,7,8,6,1]=>[4,2,1,1]=>90
[3,4,5,2,7,8,6,1]=>[5,2,1]=>64
[2,5,4,3,8,7,6,1]=>[3,2,2,1]=>70
[2,5,4,3,7,8,6,1]=>[4,2,1,1]=>90
[2,4,5,3,7,8,6,1]=>[5,2,1]=>64
[3,2,5,4,7,8,6,1]=>[4,3,1]=>70
[2,3,5,4,7,8,6,1]=>[5,2,1]=>64
[4,3,2,5,8,7,6,1]=>[3,2,2,1]=>70
[4,3,2,5,7,8,6,1]=>[4,2,1,1]=>90
[3,4,2,5,8,7,6,1]=>[4,2,1,1]=>90
[3,4,2,5,7,8,6,1]=>[5,2,1]=>64
[3,2,4,5,7,8,6,1]=>[5,2,1]=>64
[2,3,4,5,8,7,6,1]=>[5,1,1,1]=>35
[2,3,4,5,7,8,6,1]=>[6,1,1]=>21
[6,5,4,3,2,8,7,1]=>[2,2,1,1,1,1]=>20
[4,6,5,3,2,8,7,1]=>[3,2,1,1,1]=>64
[5,4,6,3,2,8,7,1]=>[3,2,1,1,1]=>64
[3,5,6,4,2,8,7,1]=>[4,2,1,1]=>90
[4,3,6,5,2,8,7,1]=>[3,3,1,1]=>56
[5,4,3,6,2,8,7,1]=>[3,2,1,1,1]=>64
[4,5,3,6,2,8,7,1]=>[4,2,1,1]=>90
[2,6,5,4,3,8,7,1]=>[3,2,1,1,1]=>64
[2,4,6,5,3,8,7,1]=>[4,2,1,1]=>90
[2,4,5,6,3,8,7,1]=>[5,2,1]=>64
[3,2,6,5,4,8,7,1]=>[3,3,1,1]=>56
[2,3,5,6,4,8,7,1]=>[5,2,1]=>64
[4,3,2,6,5,8,7,1]=>[3,3,1,1]=>56
[2,4,3,6,5,8,7,1]=>[4,3,1]=>70
[3,2,4,6,5,8,7,1]=>[4,3,1]=>70
[2,3,4,6,5,8,7,1]=>[5,2,1]=>64
[5,4,3,2,6,8,7,1]=>[3,2,1,1,1]=>64
[2,4,5,3,6,8,7,1]=>[5,2,1]=>64
[3,2,5,4,6,8,7,1]=>[4,3,1]=>70
[4,3,2,5,6,8,7,1]=>[4,2,1,1]=>90
[3,4,2,5,6,8,7,1]=>[5,2,1]=>64
[2,4,3,5,6,8,7,1]=>[5,2,1]=>64
[3,2,4,5,6,8,7,1]=>[5,2,1]=>64
[2,3,4,5,6,8,7,1]=>[6,1,1]=>21
[5,7,6,4,3,2,8,1]=>[3,1,1,1,1,1]=>21
[4,7,6,5,3,2,8,1]=>[3,1,1,1,1,1]=>21
[4,6,7,5,3,2,8,1]=>[4,1,1,1,1]=>35
[4,6,5,7,3,2,8,1]=>[4,1,1,1,1]=>35
[3,5,7,6,4,2,8,1]=>[4,1,1,1,1]=>35
[3,5,6,7,4,2,8,1]=>[5,1,1,1]=>35
[4,3,7,6,5,2,8,1]=>[3,2,1,1,1]=>64
[3,4,7,6,5,2,8,1]=>[4,1,1,1,1]=>35
[3,4,6,7,5,2,8,1]=>[5,1,1,1]=>35
[5,4,3,7,6,2,8,1]=>[3,2,1,1,1]=>64
[3,5,4,7,6,2,8,1]=>[4,2,1,1]=>90
[3,4,5,7,6,2,8,1]=>[5,1,1,1]=>35
[4,6,5,3,7,2,8,1]=>[4,1,1,1,1]=>35
[3,6,5,4,7,2,8,1]=>[4,1,1,1,1]=>35
[3,5,6,4,7,2,8,1]=>[5,1,1,1]=>35
[4,3,6,5,7,2,8,1]=>[4,2,1,1]=>90
[3,4,6,5,7,2,8,1]=>[5,1,1,1]=>35
[3,5,4,6,7,2,8,1]=>[5,1,1,1]=>35
[2,7,6,5,4,3,8,1]=>[3,1,1,1,1,1]=>21
[2,6,5,7,4,3,8,1]=>[4,1,1,1,1]=>35
[2,5,6,7,4,3,8,1]=>[5,1,1,1]=>35
[2,4,6,7,5,3,8,1]=>[5,1,1,1]=>35
[2,4,6,5,7,3,8,1]=>[5,1,1,1]=>35
[2,5,4,6,7,3,8,1]=>[5,1,1,1]=>35
[2,4,5,6,7,3,8,1]=>[6,1,1]=>21
[3,2,7,6,5,4,8,1]=>[3,2,1,1,1]=>64
[3,2,6,7,5,4,8,1]=>[4,2,1,1]=>90
[3,2,5,7,6,4,8,1]=>[4,2,1,1]=>90
[3,2,6,5,7,4,8,1]=>[4,2,1,1]=>90
[3,2,5,6,7,4,8,1]=>[5,2,1]=>64
[2,3,7,6,5,4,8,1]=>[4,1,1,1,1]=>35
[2,3,5,7,6,4,8,1]=>[5,1,1,1]=>35
[2,3,5,6,7,4,8,1]=>[6,1,1]=>21
[4,3,2,7,6,5,8,1]=>[3,2,2,1]=>70
[3,4,2,6,7,5,8,1]=>[5,2,1]=>64
[2,4,3,6,7,5,8,1]=>[5,2,1]=>64
[2,3,4,7,6,5,8,1]=>[5,1,1,1]=>35
[2,3,4,6,7,5,8,1]=>[6,1,1]=>21
[5,4,3,2,7,6,8,1]=>[3,2,1,1,1]=>64
[3,5,4,2,7,6,8,1]=>[4,2,1,1]=>90
[4,3,5,2,7,6,8,1]=>[4,2,1,1]=>90
[3,4,5,2,7,6,8,1]=>[5,2,1]=>64
[3,2,5,4,7,6,8,1]=>[4,3,1]=>70
[2,3,5,4,7,6,8,1]=>[5,2,1]=>64
[4,3,2,5,7,6,8,1]=>[4,2,1,1]=>90
[3,4,2,5,7,6,8,1]=>[5,2,1]=>64
[3,2,4,5,7,6,8,1]=>[5,2,1]=>64
[2,3,4,5,7,6,8,1]=>[6,1,1]=>21
[3,5,6,4,2,7,8,1]=>[5,1,1,1]=>35
[3,4,6,5,2,7,8,1]=>[5,1,1,1]=>35
[3,5,4,6,2,7,8,1]=>[5,1,1,1]=>35
[2,6,5,4,3,7,8,1]=>[4,1,1,1,1]=>35
[2,5,6,4,3,7,8,1]=>[5,1,1,1]=>35
[2,4,6,5,3,7,8,1]=>[5,1,1,1]=>35
[2,4,5,6,3,7,8,1]=>[6,1,1]=>21
[3,2,5,6,4,7,8,1]=>[5,2,1]=>64
[2,3,6,5,4,7,8,1]=>[5,1,1,1]=>35
[2,3,5,6,4,7,8,1]=>[6,1,1]=>21
[3,4,2,6,5,7,8,1]=>[5,2,1]=>64
[2,4,3,6,5,7,8,1]=>[5,2,1]=>64
[2,3,4,6,5,7,8,1]=>[6,1,1]=>21
[3,5,4,2,6,7,8,1]=>[5,1,1,1]=>35
[2,4,5,3,6,7,8,1]=>[6,1,1]=>21
[3,2,5,4,6,7,8,1]=>[5,2,1]=>64
[2,3,5,4,6,7,8,1]=>[6,1,1]=>21
[2,4,3,5,6,7,8,1]=>[6,1,1]=>21
[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>7
[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]=>21
[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]=>21
[1,7,6,8,5,4,3,2]=>[3,1,1,1,1,1]=>21
[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]=>35
[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]=>21
[1,6,5,8,7,4,3,2]=>[3,2,1,1,1]=>64
[1,7,6,5,8,4,3,2]=>[3,1,1,1,1,1]=>21
[1,6,7,5,8,4,3,2]=>[4,1,1,1,1]=>35
[1,5,7,6,8,4,3,2]=>[4,1,1,1,1]=>35
[1,5,6,7,8,4,3,2]=>[5,1,1,1]=>35
[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]=>21
[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]=>35
[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]=>35
[1,4,6,7,8,5,3,2]=>[5,1,1,1]=>35
[1,5,4,7,8,6,3,2]=>[4,2,1,1]=>90
[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]=>35
[1,4,6,5,8,7,3,2]=>[4,2,1,1]=>90
[1,7,6,5,4,8,3,2]=>[3,1,1,1,1,1]=>21
[1,4,7,6,5,8,3,2]=>[4,1,1,1,1]=>35
[1,4,6,7,5,8,3,2]=>[5,1,1,1]=>35
[1,6,5,4,7,8,3,2]=>[4,1,1,1,1]=>35
[1,4,5,6,7,8,3,2]=>[6,1,1]=>21
[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]=>21
[1,3,7,8,6,5,4,2]=>[4,1,1,1,1]=>35
[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]=>35
[1,3,6,7,8,5,4,2]=>[5,1,1,1]=>35
[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]=>35
[1,3,5,7,8,6,4,2]=>[5,1,1,1]=>35
[1,3,5,6,8,7,4,2]=>[5,1,1,1]=>35
[1,3,6,7,5,8,4,2]=>[5,1,1,1]=>35
[1,3,6,5,7,8,4,2]=>[5,1,1,1]=>35
[1,3,5,6,7,8,4,2]=>[6,1,1]=>21
[1,4,3,8,7,6,5,2]=>[3,2,1,1,1]=>64
[1,4,3,7,8,6,5,2]=>[4,2,1,1]=>90
[1,4,3,6,8,7,5,2]=>[4,2,1,1]=>90
[1,4,3,6,7,8,5,2]=>[5,2,1]=>64
[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]=>35
[1,3,4,7,6,8,5,2]=>[5,1,1,1]=>35
[1,3,4,6,7,8,5,2]=>[6,1,1]=>21
[1,5,4,3,8,7,6,2]=>[3,2,2,1]=>70
[1,4,5,3,8,7,6,2]=>[4,2,1,1]=>90
[1,4,5,3,7,8,6,2]=>[5,2,1]=>64
[1,4,3,5,7,8,6,2]=>[5,2,1]=>64
[1,3,4,5,8,7,6,2]=>[5,1,1,1]=>35
[1,3,4,5,7,8,6,2]=>[6,1,1]=>21
[1,6,5,4,3,8,7,2]=>[3,2,1,1,1]=>64
[1,5,6,4,3,8,7,2]=>[4,2,1,1]=>90
[1,4,6,5,3,8,7,2]=>[4,2,1,1]=>90
[1,4,5,6,3,8,7,2]=>[5,2,1]=>64
[1,4,3,6,5,8,7,2]=>[4,3,1]=>70
[1,5,4,3,6,8,7,2]=>[4,2,1,1]=>90
[1,4,5,3,6,8,7,2]=>[5,2,1]=>64
[1,3,4,5,6,8,7,2]=>[6,1,1]=>21
[1,7,6,5,4,3,8,2]=>[3,1,1,1,1,1]=>21
[1,6,7,5,4,3,8,2]=>[4,1,1,1,1]=>35
[1,6,5,7,4,3,8,2]=>[4,1,1,1,1]=>35
[1,4,6,7,5,3,8,2]=>[5,1,1,1]=>35
[1,5,6,4,7,3,8,2]=>[5,1,1,1]=>35
[1,4,6,5,7,3,8,2]=>[5,1,1,1]=>35
[1,5,4,6,7,3,8,2]=>[5,1,1,1]=>35
[1,4,5,6,7,3,8,2]=>[6,1,1]=>21
[1,3,6,5,7,4,8,2]=>[5,1,1,1]=>35
[1,3,5,6,7,4,8,2]=>[6,1,1]=>21
[1,3,4,6,7,5,8,2]=>[6,1,1]=>21
[1,3,5,4,7,6,8,2]=>[5,2,1]=>64
[1,3,4,5,7,6,8,2]=>[6,1,1]=>21
[1,5,4,6,3,7,8,2]=>[5,1,1,1]=>35
[1,4,3,6,5,7,8,2]=>[5,2,1]=>64
[1,3,4,6,5,7,8,2]=>[6,1,1]=>21
[1,5,4,3,6,7,8,2]=>[5,1,1,1]=>35
[1,4,5,3,6,7,8,2]=>[6,1,1]=>21
[1,4,3,5,6,7,8,2]=>[6,1,1]=>21
[1,3,4,5,6,7,8,2]=>[7,1]=>7
[2,1,8,7,6,5,4,3]=>[2,2,1,1,1,1]=>20
[2,1,7,8,6,5,4,3]=>[3,2,1,1,1]=>64
[2,1,6,8,7,5,4,3]=>[3,2,1,1,1]=>64
[2,1,7,6,8,5,4,3]=>[3,2,1,1,1]=>64
[2,1,6,7,8,5,4,3]=>[4,2,1,1]=>90
[2,1,5,8,7,6,4,3]=>[3,2,1,1,1]=>64
[2,1,5,7,8,6,4,3]=>[4,2,1,1]=>90
[2,1,6,5,8,7,4,3]=>[3,3,1,1]=>56
[2,1,5,6,8,7,4,3]=>[4,2,1,1]=>90
[2,1,7,6,5,8,4,3]=>[3,2,1,1,1]=>64
[2,1,6,7,5,8,4,3]=>[4,2,1,1]=>90
[2,1,5,7,6,8,4,3]=>[4,2,1,1]=>90
[2,1,6,5,7,8,4,3]=>[4,2,1,1]=>90
[2,1,5,6,7,8,4,3]=>[5,2,1]=>64
[2,1,4,8,7,6,5,3]=>[3,2,1,1,1]=>64
[2,1,4,7,8,6,5,3]=>[4,2,1,1]=>90
[2,1,4,6,8,7,5,3]=>[4,2,1,1]=>90
[2,1,4,6,7,8,5,3]=>[5,2,1]=>64
[2,1,5,4,8,7,6,3]=>[3,3,1,1]=>56
[2,1,5,4,7,8,6,3]=>[4,3,1]=>70
[2,1,4,5,8,7,6,3]=>[4,2,1,1]=>90
[2,1,4,5,7,8,6,3]=>[5,2,1]=>64
[2,1,6,5,4,8,7,3]=>[3,3,1,1]=>56
[2,1,5,6,4,8,7,3]=>[4,3,1]=>70
[2,1,4,6,5,8,7,3]=>[4,3,1]=>70
[2,1,5,4,6,8,7,3]=>[4,3,1]=>70
[2,1,4,5,6,8,7,3]=>[5,2,1]=>64
[2,1,7,6,5,4,8,3]=>[3,2,1,1,1]=>64
[2,1,6,7,5,4,8,3]=>[4,2,1,1]=>90
[2,1,5,7,6,4,8,3]=>[4,2,1,1]=>90
[2,1,6,5,7,4,8,3]=>[4,2,1,1]=>90
[2,1,5,6,7,4,8,3]=>[5,2,1]=>64
[2,1,4,7,6,5,8,3]=>[4,2,1,1]=>90
[2,1,4,6,7,5,8,3]=>[5,2,1]=>64
[2,1,5,4,7,6,8,3]=>[4,3,1]=>70
[2,1,5,6,4,7,8,3]=>[5,2,1]=>64
[2,1,5,4,6,7,8,3]=>[5,2,1]=>64
[2,1,4,5,6,7,8,3]=>[6,2]=>20
[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]=>21
[1,2,7,8,6,5,4,3]=>[4,1,1,1,1]=>35
[1,2,6,7,8,5,4,3]=>[5,1,1,1]=>35
[1,2,6,5,8,7,4,3]=>[4,2,1,1]=>90
[1,2,5,6,8,7,4,3]=>[5,1,1,1]=>35
[1,2,7,6,5,8,4,3]=>[4,1,1,1,1]=>35
[1,2,5,7,6,8,4,3]=>[5,1,1,1]=>35
[1,2,6,5,7,8,4,3]=>[5,1,1,1]=>35
[1,2,5,6,7,8,4,3]=>[6,1,1]=>21
[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]=>35
[1,2,4,6,8,7,5,3]=>[5,1,1,1]=>35
[1,2,4,6,7,8,5,3]=>[6,1,1]=>21
[1,2,5,4,8,7,6,3]=>[4,2,1,1]=>90
[1,2,4,5,8,7,6,3]=>[5,1,1,1]=>35
[1,2,4,5,7,8,6,3]=>[6,1,1]=>21
[1,2,5,4,6,8,7,3]=>[5,2,1]=>64
[1,2,4,5,6,8,7,3]=>[6,1,1]=>21
[1,2,7,6,5,4,8,3]=>[4,1,1,1,1]=>35
[1,2,5,7,6,4,8,3]=>[5,1,1,1]=>35
[1,2,5,6,7,4,8,3]=>[6,1,1]=>21
[1,2,4,7,6,5,8,3]=>[5,1,1,1]=>35
[1,2,5,4,7,6,8,3]=>[5,2,1]=>64
[1,2,6,5,4,7,8,3]=>[5,1,1,1]=>35
[1,2,5,4,6,7,8,3]=>[6,1,1]=>21
[1,2,4,5,6,7,8,3]=>[7,1]=>7
[3,2,1,8,7,6,5,4]=>[2,2,2,1,1]=>28
[3,2,1,7,8,6,5,4]=>[3,2,2,1]=>70
[3,2,1,6,8,7,5,4]=>[3,2,2,1]=>70
[3,2,1,7,6,8,5,4]=>[3,2,2,1]=>70
[3,2,1,6,7,8,5,4]=>[4,2,2]=>56
[3,2,1,5,8,7,6,4]=>[3,2,2,1]=>70
[3,2,1,5,7,8,6,4]=>[4,2,2]=>56
[3,2,1,6,5,8,7,4]=>[3,3,2]=>42
[3,2,1,5,6,8,7,4]=>[4,2,2]=>56
[3,2,1,7,6,5,8,4]=>[3,2,2,1]=>70
[3,2,1,6,7,5,8,4]=>[4,2,2]=>56
[3,2,1,5,7,6,8,4]=>[4,2,2]=>56
[3,2,1,6,5,7,8,4]=>[4,2,2]=>56
[3,2,1,5,6,7,8,4]=>[5,2,1]=>64
[2,3,1,8,7,6,5,4]=>[3,2,1,1,1]=>64
[2,3,1,6,8,7,5,4]=>[4,2,1,1]=>90
[2,3,1,7,6,8,5,4]=>[4,2,1,1]=>90
[2,3,1,6,7,8,5,4]=>[5,2,1]=>64
[2,3,1,5,7,8,6,4]=>[5,2,1]=>64
[2,3,1,6,5,8,7,4]=>[4,3,1]=>70
[2,3,1,7,6,5,8,4]=>[4,2,1,1]=>90
[2,3,1,6,7,5,8,4]=>[5,2,1]=>64
[2,3,1,5,7,6,8,4]=>[5,2,1]=>64
[2,3,1,5,6,7,8,4]=>[6,2]=>20
[1,3,2,8,7,6,5,4]=>[3,2,1,1,1]=>64
[1,3,2,6,8,7,5,4]=>[4,2,1,1]=>90
[1,3,2,7,6,8,5,4]=>[4,2,1,1]=>90
[1,3,2,6,7,8,5,4]=>[5,2,1]=>64
[1,3,2,5,8,7,6,4]=>[4,2,1,1]=>90
[1,3,2,5,7,8,6,4]=>[5,2,1]=>64
[1,3,2,6,5,8,7,4]=>[4,3,1]=>70
[1,3,2,5,6,8,7,4]=>[5,2,1]=>64
[1,3,2,7,6,5,8,4]=>[4,2,1,1]=>90
[1,3,2,6,7,5,8,4]=>[5,2,1]=>64
[1,3,2,6,5,7,8,4]=>[5,2,1]=>64
[1,3,2,5,6,7,8,4]=>[6,2]=>20
[2,1,3,8,7,6,5,4]=>[3,2,1,1,1]=>64
[2,1,3,7,8,6,5,4]=>[4,2,1,1]=>90
[2,1,3,6,8,7,5,4]=>[4,2,1,1]=>90
[2,1,3,6,5,8,7,4]=>[4,3,1]=>70
[2,1,3,5,6,7,8,4]=>[6,2]=>20
[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]=>35
[1,2,3,7,8,6,5,4]=>[5,1,1,1]=>35
[1,2,3,6,8,7,5,4]=>[5,1,1,1]=>35
[1,2,3,7,6,8,5,4]=>[5,1,1,1]=>35
[1,2,3,6,7,8,5,4]=>[6,1,1]=>21
[1,2,3,5,8,7,6,4]=>[5,1,1,1]=>35
[1,2,3,5,7,8,6,4]=>[6,1,1]=>21
[1,2,3,6,5,8,7,4]=>[5,2,1]=>64
[1,2,3,5,6,8,7,4]=>[6,1,1]=>21
[1,2,3,7,6,5,8,4]=>[5,1,1,1]=>35
[1,2,3,6,7,5,8,4]=>[6,1,1]=>21
[1,2,3,5,7,6,8,4]=>[6,1,1]=>21
[1,2,3,6,5,7,8,4]=>[6,1,1]=>21
[1,2,3,5,6,7,8,4]=>[7,1]=>7
[4,3,2,1,8,7,6,5]=>[2,2,2,2]=>14
[4,3,2,1,7,8,6,5]=>[3,2,2,1]=>70
[4,3,2,1,6,8,7,5]=>[3,2,2,1]=>70
[4,3,2,1,7,6,8,5]=>[3,2,2,1]=>70
[4,3,2,1,6,7,8,5]=>[4,2,1,1]=>90
[3,4,2,1,8,7,6,5]=>[3,2,2,1]=>70
[3,4,2,1,7,8,6,5]=>[4,2,2]=>56
[3,4,2,1,6,8,7,5]=>[4,2,2]=>56
[3,4,2,1,7,6,8,5]=>[4,2,2]=>56
[3,4,2,1,6,7,8,5]=>[5,2,1]=>64
[2,4,3,1,8,7,6,5]=>[3,2,2,1]=>70
[2,4,3,1,7,8,6,5]=>[4,2,2]=>56
[2,4,3,1,6,8,7,5]=>[4,2,2]=>56
[2,4,3,1,7,6,8,5]=>[4,2,2]=>56
[2,4,3,1,6,7,8,5]=>[5,2,1]=>64
[3,2,4,1,8,7,6,5]=>[3,2,2,1]=>70
[3,2,4,1,7,8,6,5]=>[4,2,2]=>56
[3,2,4,1,6,8,7,5]=>[4,2,2]=>56
[3,2,4,1,7,6,8,5]=>[4,2,2]=>56
[3,2,4,1,6,7,8,5]=>[5,2,1]=>64
[2,3,4,1,8,7,6,5]=>[4,2,1,1]=>90
[2,3,4,1,7,8,6,5]=>[5,2,1]=>64
[2,3,4,1,6,8,7,5]=>[5,2,1]=>64
[2,3,4,1,7,6,8,5]=>[5,2,1]=>64
[2,3,4,1,6,7,8,5]=>[6,2]=>20
[1,4,3,2,8,7,6,5]=>[3,2,2,1]=>70
[1,4,3,2,6,8,7,5]=>[4,2,2]=>56
[1,4,3,2,7,6,8,5]=>[4,2,2]=>56
[1,4,3,2,6,7,8,5]=>[5,2,1]=>64
[1,3,4,2,8,7,6,5]=>[4,2,1,1]=>90
[1,3,4,2,7,8,6,5]=>[5,2,1]=>64
[1,3,4,2,6,8,7,5]=>[5,2,1]=>64
[1,3,4,2,7,6,8,5]=>[5,2,1]=>64
[1,3,4,2,6,7,8,5]=>[6,2]=>20
[2,1,4,3,8,7,6,5]=>[3,3,1,1]=>56
[2,1,4,3,7,8,6,5]=>[4,3,1]=>70
[2,1,4,3,6,8,7,5]=>[4,3,1]=>70
[2,1,4,3,7,6,8,5]=>[4,3,1]=>70
[2,1,4,3,6,7,8,5]=>[5,3]=>28
[1,2,4,3,8,7,6,5]=>[4,2,1,1]=>90
[1,2,4,3,7,8,6,5]=>[5,2,1]=>64
[1,2,4,3,7,6,8,5]=>[5,2,1]=>64
[1,2,4,3,6,7,8,5]=>[6,2]=>20
[3,2,1,4,8,7,6,5]=>[3,2,2,1]=>70
[3,2,1,4,7,8,6,5]=>[4,2,2]=>56
[3,2,1,4,6,8,7,5]=>[4,2,2]=>56
[3,2,1,4,7,6,8,5]=>[4,2,2]=>56
[3,2,1,4,6,7,8,5]=>[5,2,1]=>64
[2,3,1,4,8,7,6,5]=>[4,2,1,1]=>90
[2,3,1,4,7,8,6,5]=>[5,2,1]=>64
[2,3,1,4,7,6,8,5]=>[5,2,1]=>64
[2,3,1,4,6,7,8,5]=>[6,2]=>20
[1,3,2,4,8,7,6,5]=>[4,2,1,1]=>90
[1,3,2,4,6,8,7,5]=>[5,2,1]=>64
[1,3,2,4,7,6,8,5]=>[5,2,1]=>64
[1,3,2,4,6,7,8,5]=>[6,2]=>20
[2,1,3,4,8,7,6,5]=>[4,2,1,1]=>90
[2,1,3,4,7,8,6,5]=>[5,2,1]=>64
[2,1,3,4,7,6,8,5]=>[5,2,1]=>64
[2,1,3,4,6,7,8,5]=>[6,2]=>20
[1,2,3,4,8,7,6,5]=>[5,1,1,1]=>35
[1,2,3,4,7,8,6,5]=>[6,1,1]=>21
[1,2,3,4,6,8,7,5]=>[6,1,1]=>21
[1,2,3,4,7,6,8,5]=>[6,1,1]=>21
[1,2,3,4,6,7,8,5]=>[7,1]=>7
[5,4,3,2,1,8,7,6]=>[2,2,2,1,1]=>28
[5,4,3,2,1,7,8,6]=>[3,2,1,1,1]=>64
[4,5,3,2,1,8,7,6]=>[3,2,2,1]=>70
[3,5,4,2,1,8,7,6]=>[3,2,2,1]=>70
[3,5,4,2,1,7,8,6]=>[4,2,1,1]=>90
[4,3,5,2,1,8,7,6]=>[3,2,2,1]=>70
[3,4,5,2,1,8,7,6]=>[4,2,2]=>56
[2,5,4,3,1,8,7,6]=>[3,2,2,1]=>70
[2,4,5,3,1,8,7,6]=>[4,2,2]=>56
[2,4,5,3,1,7,8,6]=>[5,2,1]=>64
[3,2,5,4,1,8,7,6]=>[3,3,2]=>42
[3,2,5,4,1,7,8,6]=>[4,3,1]=>70
[2,3,5,4,1,8,7,6]=>[4,2,2]=>56
[4,3,2,5,1,8,7,6]=>[3,2,2,1]=>70
[4,3,2,5,1,7,8,6]=>[4,2,1,1]=>90
[3,4,2,5,1,8,7,6]=>[4,2,2]=>56
[3,4,2,5,1,7,8,6]=>[5,2,1]=>64
[2,4,3,5,1,8,7,6]=>[4,2,2]=>56
[2,4,3,5,1,7,8,6]=>[5,2,1]=>64
[3,2,4,5,1,8,7,6]=>[4,2,2]=>56
[2,3,4,5,1,8,7,6]=>[5,2,1]=>64
[2,3,4,5,1,7,8,6]=>[6,2]=>20
[1,5,4,3,2,8,7,6]=>[3,2,2,1]=>70
[1,5,4,3,2,7,8,6]=>[4,2,1,1]=>90
[1,4,5,3,2,8,7,6]=>[4,2,2]=>56
[1,4,5,3,2,7,8,6]=>[5,2,1]=>64
[1,3,5,4,2,7,8,6]=>[5,2,1]=>64
[1,3,4,5,2,8,7,6]=>[5,2,1]=>64
[1,3,4,5,2,7,8,6]=>[6,2]=>20
[2,1,4,5,3,8,7,6]=>[4,3,1]=>70
[1,2,5,4,3,7,8,6]=>[5,2,1]=>64
[1,2,4,5,3,8,7,6]=>[5,2,1]=>64
[1,2,4,5,3,7,8,6]=>[6,2]=>20
[1,3,2,5,4,8,7,6]=>[4,3,1]=>70
[1,3,2,5,4,7,8,6]=>[5,3]=>28
[2,1,3,5,4,8,7,6]=>[4,3,1]=>70
[2,1,3,5,4,7,8,6]=>[5,3]=>28
[1,2,3,5,4,8,7,6]=>[5,2,1]=>64
[1,2,3,5,4,7,8,6]=>[6,2]=>20
[4,3,2,1,5,7,8,6]=>[4,2,1,1]=>90
[2,4,3,1,5,8,7,6]=>[4,2,2]=>56
[3,2,4,1,5,8,7,6]=>[4,2,2]=>56
[3,2,4,1,5,7,8,6]=>[5,2,1]=>64
[2,3,4,1,5,8,7,6]=>[5,2,1]=>64
[2,3,4,1,5,7,8,6]=>[6,2]=>20
[1,4,3,2,5,8,7,6]=>[4,2,2]=>56
[1,4,3,2,5,7,8,6]=>[5,2,1]=>64
[1,3,4,2,5,7,8,6]=>[6,2]=>20
[2,1,4,3,5,8,7,6]=>[4,3,1]=>70
[2,1,4,3,5,7,8,6]=>[5,3]=>28
[1,2,4,3,5,8,7,6]=>[5,2,1]=>64
[1,2,4,3,5,7,8,6]=>[6,2]=>20
[3,2,1,4,5,8,7,6]=>[4,2,2]=>56
[3,2,1,4,5,7,8,6]=>[5,2,1]=>64
[2,3,1,4,5,7,8,6]=>[6,2]=>20
[1,3,2,4,5,8,7,6]=>[5,2,1]=>64
[1,3,2,4,5,7,8,6]=>[6,2]=>20
[2,1,3,4,5,8,7,6]=>[5,2,1]=>64
[2,1,3,4,5,7,8,6]=>[6,2]=>20
[1,2,3,4,5,8,7,6]=>[6,1,1]=>21
[1,2,3,4,5,7,8,6]=>[7,1]=>7
[6,5,4,3,2,1,8,7]=>[2,2,1,1,1,1]=>20
[5,6,4,3,2,1,8,7]=>[3,2,1,1,1]=>64
[4,6,5,3,2,1,8,7]=>[3,2,1,1,1]=>64
[5,4,6,3,2,1,8,7]=>[3,2,1,1,1]=>64
[4,5,6,3,2,1,8,7]=>[4,2,1,1]=>90
[3,6,5,4,2,1,8,7]=>[3,2,1,1,1]=>64
[3,5,6,4,2,1,8,7]=>[4,2,1,1]=>90
[4,3,6,5,2,1,8,7]=>[3,3,1,1]=>56
[3,4,6,5,2,1,8,7]=>[4,2,1,1]=>90
[5,4,3,6,2,1,8,7]=>[3,2,1,1,1]=>64
[4,5,3,6,2,1,8,7]=>[4,2,1,1]=>90
[4,3,5,6,2,1,8,7]=>[4,2,1,1]=>90
[2,6,5,4,3,1,8,7]=>[3,2,1,1,1]=>64
[2,5,6,4,3,1,8,7]=>[4,2,1,1]=>90
[2,4,6,5,3,1,8,7]=>[4,2,1,1]=>90
[3,2,6,5,4,1,8,7]=>[3,3,1,1]=>56
[3,2,5,6,4,1,8,7]=>[4,3,1]=>70
[2,3,6,5,4,1,8,7]=>[4,2,1,1]=>90
[2,3,5,6,4,1,8,7]=>[5,2,1]=>64
[4,3,2,6,5,1,8,7]=>[3,3,1,1]=>56
[3,4,2,6,5,1,8,7]=>[4,3,1]=>70
[2,4,3,6,5,1,8,7]=>[4,3,1]=>70
[5,4,3,2,6,1,8,7]=>[3,2,1,1,1]=>64
[4,3,5,2,6,1,8,7]=>[4,2,1,1]=>90
[3,4,5,2,6,1,8,7]=>[5,2,1]=>64
[2,5,4,3,6,1,8,7]=>[4,2,1,1]=>90
[2,4,5,3,6,1,8,7]=>[5,2,1]=>64
[3,2,5,4,6,1,8,7]=>[4,3,1]=>70
[4,3,2,5,6,1,8,7]=>[4,2,1,1]=>90
[3,4,2,5,6,1,8,7]=>[5,2,1]=>64
[2,4,3,5,6,1,8,7]=>[5,2,1]=>64
[2,3,4,5,6,1,8,7]=>[6,2]=>20
[1,6,5,4,3,2,8,7]=>[3,2,1,1,1]=>64
[1,5,4,6,3,2,8,7]=>[4,2,1,1]=>90
[1,3,6,5,4,2,8,7]=>[4,2,1,1]=>90
[1,3,4,5,6,2,8,7]=>[6,2]=>20
[2,1,6,5,4,3,8,7]=>[3,3,1,1]=>56
[2,1,5,6,4,3,8,7]=>[4,3,1]=>70
[2,1,4,6,5,3,8,7]=>[4,3,1]=>70
[2,1,5,4,6,3,8,7]=>[4,3,1]=>70
[2,1,4,5,6,3,8,7]=>[5,3]=>28
[1,2,4,5,6,3,8,7]=>[6,2]=>20
[2,3,1,6,5,4,8,7]=>[4,3,1]=>70
[1,3,2,6,5,4,8,7]=>[4,3,1]=>70
[1,3,2,5,6,4,8,7]=>[5,3]=>28
[2,1,3,5,6,4,8,7]=>[5,3]=>28
[1,2,3,6,5,4,8,7]=>[5,2,1]=>64
[1,2,3,5,6,4,8,7]=>[6,2]=>20
[4,3,2,1,6,5,8,7]=>[3,3,1,1]=>56
[3,4,2,1,6,5,8,7]=>[4,3,1]=>70
[2,4,3,1,6,5,8,7]=>[4,3,1]=>70
[3,2,4,1,6,5,8,7]=>[4,3,1]=>70
[2,3,4,1,6,5,8,7]=>[5,3]=>28
[1,3,4,2,6,5,8,7]=>[5,3]=>28
[2,1,4,3,6,5,8,7]=>[4,4]=>14
[1,2,4,3,6,5,8,7]=>[5,3]=>28
[2,3,1,4,6,5,8,7]=>[5,3]=>28
[1,3,2,4,6,5,8,7]=>[5,3]=>28
[2,1,3,4,6,5,8,7]=>[5,3]=>28
[1,2,3,4,6,5,8,7]=>[6,2]=>20
[5,4,3,2,1,6,8,7]=>[3,2,1,1,1]=>64
[4,5,3,2,1,6,8,7]=>[4,2,1,1]=>90
[3,5,4,2,1,6,8,7]=>[4,2,1,1]=>90
[4,3,5,2,1,6,8,7]=>[4,2,1,1]=>90
[3,4,5,2,1,6,8,7]=>[5,2,1]=>64
[2,5,4,3,1,6,8,7]=>[4,2,1,1]=>90
[2,4,5,3,1,6,8,7]=>[5,2,1]=>64
[3,2,5,4,1,6,8,7]=>[4,3,1]=>70
[2,3,5,4,1,6,8,7]=>[5,2,1]=>64
[2,3,4,5,1,6,8,7]=>[6,2]=>20
[1,4,5,3,2,6,8,7]=>[5,2,1]=>64
[1,3,5,4,2,6,8,7]=>[5,2,1]=>64
[2,1,4,5,3,6,8,7]=>[5,3]=>28
[1,2,5,4,3,6,8,7]=>[5,2,1]=>64
[1,2,3,5,4,6,8,7]=>[6,2]=>20
[3,2,4,1,5,6,8,7]=>[5,2,1]=>64
[2,3,4,1,5,6,8,7]=>[6,2]=>20
[1,4,3,2,5,6,8,7]=>[5,2,1]=>64
[1,3,4,2,5,6,8,7]=>[6,2]=>20
[1,2,4,3,5,6,8,7]=>[6,2]=>20
[3,2,1,4,5,6,8,7]=>[5,2,1]=>64
[2,3,1,4,5,6,8,7]=>[6,2]=>20
[1,3,2,4,5,6,8,7]=>[6,2]=>20
[2,1,3,4,5,6,8,7]=>[6,2]=>20
[1,2,3,4,5,6,8,7]=>[7,1]=>7
[5,7,6,4,3,2,1,8]=>[3,1,1,1,1,1]=>21
[4,7,6,5,3,2,1,8]=>[3,1,1,1,1,1]=>21
[5,4,7,6,3,2,1,8]=>[3,2,1,1,1]=>64
[4,5,7,6,3,2,1,8]=>[4,1,1,1,1]=>35
[4,6,5,7,3,2,1,8]=>[4,1,1,1,1]=>35
[3,5,7,6,4,2,1,8]=>[4,1,1,1,1]=>35
[3,5,6,7,4,2,1,8]=>[5,1,1,1]=>35
[4,3,7,6,5,2,1,8]=>[3,2,1,1,1]=>64
[3,4,7,6,5,2,1,8]=>[4,1,1,1,1]=>35
[5,4,3,7,6,2,1,8]=>[3,2,1,1,1]=>64
[3,5,4,7,6,2,1,8]=>[4,2,1,1]=>90
[3,6,5,4,7,2,1,8]=>[4,1,1,1,1]=>35
[3,5,6,4,7,2,1,8]=>[5,1,1,1]=>35
[4,3,6,5,7,2,1,8]=>[4,2,1,1]=>90
[2,7,6,5,4,3,1,8]=>[3,1,1,1,1,1]=>21
[2,6,7,5,4,3,1,8]=>[4,1,1,1,1]=>35
[2,5,7,6,4,3,1,8]=>[4,1,1,1,1]=>35
[2,5,6,7,4,3,1,8]=>[5,1,1,1]=>35
[2,4,6,7,5,3,1,8]=>[5,1,1,1]=>35
[2,5,6,4,7,3,1,8]=>[5,1,1,1]=>35
[2,5,4,6,7,3,1,8]=>[5,1,1,1]=>35
[2,4,5,6,7,3,1,8]=>[6,1,1]=>21
[3,2,7,6,5,4,1,8]=>[3,2,1,1,1]=>64
[3,2,6,7,5,4,1,8]=>[4,2,1,1]=>90
[3,2,5,7,6,4,1,8]=>[4,2,1,1]=>90
[3,2,6,5,7,4,1,8]=>[4,2,1,1]=>90
[3,2,5,6,7,4,1,8]=>[5,2,1]=>64
[2,3,7,6,5,4,1,8]=>[4,1,1,1,1]=>35
[2,3,6,7,5,4,1,8]=>[5,1,1,1]=>35
[2,3,5,7,6,4,1,8]=>[5,1,1,1]=>35
[2,3,6,5,7,4,1,8]=>[5,1,1,1]=>35
[2,3,5,6,7,4,1,8]=>[6,1,1]=>21
[4,3,2,6,7,5,1,8]=>[4,2,1,1]=>90
[3,4,2,6,7,5,1,8]=>[5,2,1]=>64
[3,2,4,6,7,5,1,8]=>[5,2,1]=>64
[2,3,4,7,6,5,1,8]=>[5,1,1,1]=>35
[2,3,4,6,7,5,1,8]=>[6,1,1]=>21
[5,4,3,2,7,6,1,8]=>[3,2,1,1,1]=>64
[4,5,3,2,7,6,1,8]=>[4,2,1,1]=>90
[3,5,4,2,7,6,1,8]=>[4,2,1,1]=>90
[4,3,5,2,7,6,1,8]=>[4,2,1,1]=>90
[3,4,5,2,7,6,1,8]=>[5,2,1]=>64
[3,2,5,4,7,6,1,8]=>[4,3,1]=>70
[4,3,2,5,7,6,1,8]=>[4,2,1,1]=>90
[3,4,2,5,7,6,1,8]=>[5,2,1]=>64
[2,3,4,5,7,6,1,8]=>[6,1,1]=>21
[3,5,6,4,2,7,1,8]=>[5,1,1,1]=>35
[3,5,4,6,2,7,1,8]=>[5,1,1,1]=>35
[2,5,4,6,3,7,1,8]=>[5,1,1,1]=>35
[3,2,6,5,4,7,1,8]=>[4,2,1,1]=>90
[2,3,5,6,4,7,1,8]=>[6,1,1]=>21
[2,4,3,6,5,7,1,8]=>[5,2,1]=>64
[2,3,4,6,5,7,1,8]=>[6,1,1]=>21
[2,3,5,4,6,7,1,8]=>[6,1,1]=>21
[1,7,6,5,4,3,2,8]=>[3,1,1,1,1,1]=>21
[1,6,7,5,4,3,2,8]=>[4,1,1,1,1]=>35
[1,6,5,7,4,3,2,8]=>[4,1,1,1,1]=>35
[1,5,6,7,4,3,2,8]=>[5,1,1,1]=>35
[1,4,7,6,5,3,2,8]=>[4,1,1,1,1]=>35
[1,4,6,7,5,3,2,8]=>[5,1,1,1]=>35
[1,5,6,4,7,3,2,8]=>[5,1,1,1]=>35
[1,5,4,6,7,3,2,8]=>[5,1,1,1]=>35
[1,3,6,7,5,4,2,8]=>[5,1,1,1]=>35
[1,3,5,7,6,4,2,8]=>[5,1,1,1]=>35
[1,3,6,5,7,4,2,8]=>[5,1,1,1]=>35
[1,3,5,6,7,4,2,8]=>[6,1,1]=>21
[1,3,4,6,7,5,2,8]=>[6,1,1]=>21
[1,3,5,4,7,6,2,8]=>[5,2,1]=>64
[1,4,3,5,7,6,2,8]=>[5,2,1]=>64
[1,3,4,5,7,6,2,8]=>[6,1,1]=>21
[1,5,4,6,3,7,2,8]=>[5,1,1,1]=>35
[1,3,6,5,4,7,2,8]=>[5,1,1,1]=>35
[1,5,4,3,6,7,2,8]=>[5,1,1,1]=>35
[1,4,5,3,6,7,2,8]=>[6,1,1]=>21
[1,3,4,5,6,7,2,8]=>[7,1]=>7
[2,1,7,6,5,4,3,8]=>[3,2,1,1,1]=>64
[2,1,5,6,7,4,3,8]=>[5,2,1]=>64
[2,1,4,5,6,7,3,8]=>[6,2]=>20
[1,2,7,6,5,4,3,8]=>[4,1,1,1,1]=>35
[1,2,6,7,5,4,3,8]=>[5,1,1,1]=>35
[1,2,5,7,6,4,3,8]=>[5,1,1,1]=>35
[1,2,5,6,7,4,3,8]=>[6,1,1]=>21
[1,2,4,6,7,5,3,8]=>[6,1,1]=>21
[1,2,5,6,4,7,3,8]=>[6,1,1]=>21
[1,2,5,4,6,7,3,8]=>[6,1,1]=>21
[1,2,4,5,6,7,3,8]=>[7,1]=>7
[3,2,1,7,6,5,4,8]=>[3,2,2,1]=>70
[3,2,1,5,7,6,4,8]=>[4,2,2]=>56
[2,3,1,6,7,5,4,8]=>[5,2,1]=>64
[2,3,1,5,6,7,4,8]=>[6,2]=>20
[1,3,2,7,6,5,4,8]=>[4,2,1,1]=>90
[1,3,2,6,7,5,4,8]=>[5,2,1]=>64
[1,3,2,5,7,6,4,8]=>[5,2,1]=>64
[1,3,2,5,6,7,4,8]=>[6,2]=>20
[2,1,3,6,7,5,4,8]=>[5,2,1]=>64
[1,2,3,7,6,5,4,8]=>[5,1,1,1]=>35
[1,2,3,6,7,5,4,8]=>[6,1,1]=>21
[1,2,3,5,7,6,4,8]=>[6,1,1]=>21
[1,2,3,6,5,7,4,8]=>[6,1,1]=>21
[1,2,3,5,6,7,4,8]=>[7,1]=>7
[3,2,4,1,7,6,5,8]=>[4,2,2]=>56
[3,2,4,1,6,7,5,8]=>[5,2,1]=>64
[2,3,4,1,7,6,5,8]=>[5,2,1]=>64
[2,3,4,1,6,7,5,8]=>[6,2]=>20
[1,4,3,2,7,6,5,8]=>[4,2,2]=>56
[1,4,3,2,6,7,5,8]=>[5,2,1]=>64
[1,3,4,2,6,7,5,8]=>[6,2]=>20
[1,2,4,3,6,7,5,8]=>[6,2]=>20
[3,2,1,4,7,6,5,8]=>[4,2,2]=>56
[2,3,1,4,6,7,5,8]=>[6,2]=>20
[1,3,2,4,7,6,5,8]=>[5,2,1]=>64
[1,2,3,4,7,6,5,8]=>[6,1,1]=>21
[1,2,3,4,6,7,5,8]=>[7,1]=>7
[5,4,3,2,1,7,6,8]=>[3,2,1,1,1]=>64
[4,5,3,2,1,7,6,8]=>[4,2,1,1]=>90
[3,5,4,2,1,7,6,8]=>[4,2,1,1]=>90
[3,4,5,2,1,7,6,8]=>[5,2,1]=>64
[2,4,5,3,1,7,6,8]=>[5,2,1]=>64
[3,2,5,4,1,7,6,8]=>[4,3,1]=>70
[2,3,4,5,1,7,6,8]=>[6,2]=>20
[1,5,4,3,2,7,6,8]=>[4,2,1,1]=>90
[1,4,5,3,2,7,6,8]=>[5,2,1]=>64
[1,3,5,4,2,7,6,8]=>[5,2,1]=>64
[1,3,4,5,2,7,6,8]=>[6,2]=>20
[2,1,5,4,3,7,6,8]=>[4,3,1]=>70
[1,2,4,5,3,7,6,8]=>[6,2]=>20
[3,2,1,5,4,7,6,8]=>[4,3,1]=>70
[2,3,1,5,4,7,6,8]=>[5,3]=>28
[1,3,2,5,4,7,6,8]=>[5,3]=>28
[1,2,3,5,4,7,6,8]=>[6,2]=>20
[3,2,4,1,5,7,6,8]=>[5,2,1]=>64
[2,3,4,1,5,7,6,8]=>[6,2]=>20
[1,4,3,2,5,7,6,8]=>[5,2,1]=>64
[1,3,4,2,5,7,6,8]=>[6,2]=>20
[1,2,4,3,5,7,6,8]=>[6,2]=>20
[2,3,1,4,5,7,6,8]=>[6,2]=>20
[1,3,2,4,5,7,6,8]=>[6,2]=>20
[2,1,3,4,5,7,6,8]=>[6,2]=>20
[1,2,3,4,5,7,6,8]=>[7,1]=>7
[3,6,5,4,2,1,7,8]=>[4,1,1,1,1]=>35
[4,3,6,5,2,1,7,8]=>[4,2,1,1]=>90
[2,4,6,5,3,1,7,8]=>[5,1,1,1]=>35
[2,4,5,6,3,1,7,8]=>[6,1,1]=>21
[2,3,5,6,4,1,7,8]=>[6,1,1]=>21
[4,3,2,6,5,1,7,8]=>[4,2,1,1]=>90
[2,4,3,6,5,1,7,8]=>[5,2,1]=>64
[1,6,5,4,3,2,7,8]=>[4,1,1,1,1]=>35
[1,5,6,4,3,2,7,8]=>[5,1,1,1]=>35
[1,4,6,5,3,2,7,8]=>[5,1,1,1]=>35
[1,5,4,6,3,2,7,8]=>[5,1,1,1]=>35
[1,4,5,6,3,2,7,8]=>[6,1,1]=>21
[1,3,5,6,4,2,7,8]=>[6,1,1]=>21
[1,4,3,6,5,2,7,8]=>[5,2,1]=>64
[1,5,4,3,6,2,7,8]=>[5,1,1,1]=>35
[1,4,5,3,6,2,7,8]=>[6,1,1]=>21
[1,4,3,5,6,2,7,8]=>[6,1,1]=>21
[1,3,4,5,6,2,7,8]=>[7,1]=>7
[2,1,5,6,4,3,7,8]=>[5,2,1]=>64
[2,1,4,6,5,3,7,8]=>[5,2,1]=>64
[1,2,6,5,4,3,7,8]=>[5,1,1,1]=>35
[1,2,4,6,5,3,7,8]=>[6,1,1]=>21
[1,2,4,5,6,3,7,8]=>[7,1]=>7
[3,2,1,5,6,4,7,8]=>[5,2,1]=>64
[2,3,1,6,5,4,7,8]=>[5,2,1]=>64
[2,3,1,5,6,4,7,8]=>[6,2]=>20
[1,3,2,6,5,4,7,8]=>[5,2,1]=>64
[1,3,2,5,6,4,7,8]=>[6,2]=>20
[1,2,3,6,5,4,7,8]=>[6,1,1]=>21
[1,2,3,5,6,4,7,8]=>[7,1]=>7
[2,4,3,1,6,5,7,8]=>[5,2,1]=>64
[3,2,4,1,6,5,7,8]=>[5,2,1]=>64
[2,3,4,1,6,5,7,8]=>[6,2]=>20
[2,1,4,3,6,5,7,8]=>[5,3]=>28
[1,2,4,3,6,5,7,8]=>[6,2]=>20
[1,3,2,4,6,5,7,8]=>[6,2]=>20
[2,1,3,4,6,5,7,8]=>[6,2]=>20
[1,2,3,4,6,5,7,8]=>[7,1]=>7
[3,5,4,2,1,6,7,8]=>[5,1,1,1]=>35
[2,5,4,3,1,6,7,8]=>[5,1,1,1]=>35
[2,4,5,3,1,6,7,8]=>[6,1,1]=>21
[3,2,5,4,1,6,7,8]=>[5,2,1]=>64
[2,3,5,4,1,6,7,8]=>[6,1,1]=>21
[2,4,3,5,1,6,7,8]=>[6,1,1]=>21
[1,5,4,3,2,6,7,8]=>[5,1,1,1]=>35
[1,4,5,3,2,6,7,8]=>[6,1,1]=>21
[1,3,4,5,2,6,7,8]=>[7,1]=>7
[2,1,5,4,3,6,7,8]=>[5,2,1]=>64
[2,1,4,5,3,6,7,8]=>[6,2]=>20
[1,2,5,4,3,6,7,8]=>[6,1,1]=>21
[2,3,1,5,4,6,7,8]=>[6,2]=>20
[1,3,2,5,4,6,7,8]=>[6,2]=>20
[1,2,3,5,4,6,7,8]=>[7,1]=>7
[2,4,3,1,5,6,7,8]=>[6,1,1]=>21
[1,4,3,2,5,6,7,8]=>[6,1,1]=>21
[1,3,4,2,5,6,7,8]=>[7,1]=>7
[2,1,4,3,5,6,7,8]=>[6,2]=>20
[1,2,4,3,5,6,7,8]=>[7,1]=>7
[1,3,2,4,5,6,7,8]=>[7,1]=>7
[1,2,3,4,8,6,7,5]=>[6,1,1]=>21
[1,2,3,5,8,6,7,4]=>[6,1,1]=>21
[1,2,3,7,5,6,4,8]=>[6,1,1]=>21
[1,2,3,7,5,6,8,4]=>[6,1,1]=>21
[1,2,3,8,5,6,7,4]=>[6,1,1]=>21
[1,2,3,8,5,7,6,4]=>[5,1,1,1]=>35
[1,2,3,8,6,5,7,4]=>[5,1,1,1]=>35
[1,2,3,8,6,7,5,4]=>[5,1,1,1]=>35
[1,2,4,5,8,6,7,3]=>[6,1,1]=>21
[1,2,4,7,5,6,8,3]=>[6,1,1]=>21
[1,2,4,8,5,6,7,3]=>[6,1,1]=>21
[1,2,4,8,6,5,7,3]=>[5,1,1,1]=>35
[1,2,6,4,5,7,8,3]=>[6,1,1]=>21
[1,2,7,4,5,6,8,3]=>[6,1,1]=>21
[1,2,8,4,5,6,7,3]=>[6,1,1]=>21
[1,2,8,4,6,7,5,3]=>[5,1,1,1]=>35
[1,2,8,4,7,6,5,3]=>[4,1,1,1,1]=>35
[1,2,8,5,4,6,7,3]=>[5,1,1,1]=>35
[1,2,8,5,6,4,7,3]=>[5,1,1,1]=>35
[1,2,8,5,6,7,4,3]=>[5,1,1,1]=>35
[1,2,8,6,5,4,7,3]=>[4,1,1,1,1]=>35
[1,2,8,7,5,6,4,3]=>[4,1,1,1,1]=>35
[1,3,2,7,5,6,8,4]=>[5,2,1]=>64
[1,3,2,8,5,7,6,4]=>[4,2,1,1]=>90
[1,3,2,8,6,5,7,4]=>[4,2,1,1]=>90
[1,3,2,8,6,7,5,4]=>[4,2,1,1]=>90
[1,3,4,2,8,6,7,5]=>[5,2,1]=>64
[1,3,4,5,8,6,7,2]=>[6,1,1]=>21
[1,3,4,8,5,6,7,2]=>[6,1,1]=>21
[1,3,6,4,5,2,8,7]=>[5,2,1]=>64
[1,3,6,4,5,7,8,2]=>[6,1,1]=>21
[1,3,7,4,5,6,2,8]=>[6,1,1]=>21
[1,3,7,4,5,6,8,2]=>[6,1,1]=>21
[1,3,8,4,5,6,7,2]=>[6,1,1]=>21
[1,3,8,4,6,5,7,2]=>[5,1,1,1]=>35
[1,3,8,5,4,6,7,2]=>[5,1,1,1]=>35
[1,3,8,5,4,7,6,2]=>[4,2,1,1]=>90
[1,3,8,5,6,7,4,2]=>[5,1,1,1]=>35
[1,3,8,5,7,6,4,2]=>[4,1,1,1,1]=>35
[1,3,8,6,5,7,4,2]=>[4,1,1,1,1]=>35
[1,3,8,7,5,6,4,2]=>[4,1,1,1,1]=>35
[1,4,3,5,8,6,7,2]=>[5,2,1]=>64
[1,4,3,8,5,6,7,2]=>[5,2,1]=>64
[1,4,3,8,5,7,6,2]=>[4,2,1,1]=>90
[1,4,3,8,6,5,7,2]=>[4,2,1,1]=>90
[1,4,3,8,6,7,5,2]=>[4,2,1,1]=>90
[1,5,3,4,2,6,7,8]=>[6,1,1]=>21
[1,5,3,4,2,7,8,6]=>[5,2,1]=>64
[1,5,3,4,2,8,7,6]=>[4,2,2]=>56
[1,5,3,4,6,2,8,7]=>[5,2,1]=>64
[1,5,3,4,6,7,2,8]=>[6,1,1]=>21
[1,5,3,4,6,7,8,2]=>[6,1,1]=>21
[1,6,3,4,5,8,7,2]=>[5,2,1]=>64
[1,7,3,4,5,6,8,2]=>[6,1,1]=>21
[1,8,3,4,5,6,7,2]=>[6,1,1]=>21
[1,8,3,4,6,7,5,2]=>[5,1,1,1]=>35
[1,6,3,5,4,2,7,8]=>[5,1,1,1]=>35
[1,6,3,5,4,8,7,2]=>[4,2,1,1]=>90
[1,7,3,5,4,6,2,8]=>[5,1,1,1]=>35
[1,8,3,5,4,7,6,2]=>[4,2,1,1]=>90
[1,8,3,5,6,4,7,2]=>[5,1,1,1]=>35
[1,8,3,5,6,7,4,2]=>[5,1,1,1]=>35
[1,8,3,5,7,6,4,2]=>[4,1,1,1,1]=>35
[1,7,3,6,5,4,8,2]=>[4,1,1,1,1]=>35
[1,8,3,6,5,4,7,2]=>[4,1,1,1,1]=>35
[1,8,3,7,5,6,4,2]=>[4,1,1,1,1]=>35
[1,8,3,7,6,5,4,2]=>[3,1,1,1,1,1]=>21
[1,6,4,3,5,2,7,8]=>[5,1,1,1]=>35
[1,6,4,3,5,8,7,2]=>[4,2,1,1]=>90
[1,8,4,3,5,6,7,2]=>[5,1,1,1]=>35
[1,8,4,3,5,7,6,2]=>[4,2,1,1]=>90
[1,7,4,3,6,5,8,2]=>[4,2,1,1]=>90
[1,8,4,3,6,5,7,2]=>[4,2,1,1]=>90
[1,8,4,3,6,7,5,2]=>[4,2,1,1]=>90
[1,6,4,5,3,2,7,8]=>[5,1,1,1]=>35
[1,6,4,5,3,2,8,7]=>[4,2,1,1]=>90
[1,6,4,5,3,8,7,2]=>[4,2,1,1]=>90
[1,7,4,5,3,6,8,2]=>[5,1,1,1]=>35
[1,8,4,5,3,6,7,2]=>[5,1,1,1]=>35
[1,7,4,5,6,3,8,2]=>[5,1,1,1]=>35
[1,8,4,5,6,7,3,2]=>[5,1,1,1]=>35
[1,7,4,6,5,3,2,8]=>[4,1,1,1,1]=>35
[1,8,4,6,5,3,7,2]=>[4,1,1,1,1]=>35
[1,8,4,6,5,7,3,2]=>[4,1,1,1,1]=>35
[1,8,4,7,6,5,3,2]=>[3,1,1,1,1,1]=>21
[1,8,5,4,3,6,7,2]=>[4,1,1,1,1]=>35
[1,8,5,4,3,7,6,2]=>[3,2,1,1,1]=>64
[1,8,5,4,6,3,7,2]=>[4,1,1,1,1]=>35
[1,8,5,4,6,7,3,2]=>[4,1,1,1,1]=>35
[1,8,5,4,7,6,3,2]=>[3,2,1,1,1]=>64
[1,7,6,4,5,3,2,8]=>[4,1,1,1,1]=>35
[1,8,6,4,5,7,3,2]=>[4,1,1,1,1]=>35
[1,8,7,4,5,6,3,2]=>[4,1,1,1,1]=>35
[1,8,7,4,6,5,3,2]=>[3,1,1,1,1,1]=>21
[1,8,6,5,4,3,7,2]=>[3,1,1,1,1,1]=>21
[1,8,6,5,4,7,3,2]=>[3,1,1,1,1,1]=>21
[1,8,7,5,4,6,3,2]=>[3,1,1,1,1,1]=>21
[1,8,7,5,6,4,3,2]=>[3,1,1,1,1,1]=>21
[2,1,3,4,8,6,7,5]=>[5,2,1]=>64
[2,1,3,5,8,6,7,4]=>[5,2,1]=>64
[2,1,3,8,5,6,7,4]=>[5,2,1]=>64
[2,1,3,8,5,7,6,4]=>[4,2,1,1]=>90
[2,1,3,8,6,5,7,4]=>[4,2,1,1]=>90
[2,1,3,8,6,7,5,4]=>[4,2,1,1]=>90
[2,1,4,3,8,6,7,5]=>[4,3,1]=>70
[2,1,4,5,8,6,7,3]=>[5,2,1]=>64
[2,1,4,8,5,6,7,3]=>[5,2,1]=>64
[2,1,4,8,5,7,6,3]=>[4,2,1,1]=>90
[2,1,4,8,6,5,7,3]=>[4,2,1,1]=>90
[2,1,4,8,6,7,5,3]=>[4,2,1,1]=>90
[2,1,5,4,8,6,7,3]=>[4,3,1]=>70
[2,1,6,4,5,3,8,7]=>[4,3,1]=>70
[2,1,6,4,5,7,8,3]=>[5,2,1]=>64
[2,1,6,4,5,8,7,3]=>[4,3,1]=>70
[2,1,8,4,5,6,7,3]=>[5,2,1]=>64
[2,1,8,4,5,7,6,3]=>[4,2,1,1]=>90
[2,1,7,4,6,5,8,3]=>[4,2,1,1]=>90
[2,1,8,4,6,5,7,3]=>[4,2,1,1]=>90
[2,1,8,4,6,7,5,3]=>[4,2,1,1]=>90
[2,1,8,4,7,6,5,3]=>[3,2,1,1,1]=>64
[2,1,8,5,4,7,6,3]=>[3,3,1,1]=>56
[2,1,7,5,6,4,8,3]=>[4,2,1,1]=>90
[2,1,8,5,6,4,7,3]=>[4,2,1,1]=>90
[2,1,8,5,6,7,4,3]=>[4,2,1,1]=>90
[2,1,8,5,7,6,4,3]=>[3,2,1,1,1]=>64
[2,1,8,6,5,4,7,3]=>[3,2,1,1,1]=>64
[2,1,8,6,5,7,4,3]=>[3,2,1,1,1]=>64
[2,1,8,7,5,6,4,3]=>[3,2,1,1,1]=>64
[2,3,1,7,5,6,4,8]=>[5,2,1]=>64
[2,3,1,8,5,6,7,4]=>[5,2,1]=>64
[2,3,1,8,6,7,5,4]=>[4,2,1,1]=>90
[2,3,4,1,8,6,7,5]=>[5,2,1]=>64
[2,3,4,5,8,6,7,1]=>[6,1,1]=>21
[2,3,4,7,5,6,1,8]=>[6,1,1]=>21
[2,3,4,7,5,6,8,1]=>[6,1,1]=>21
[2,3,4,8,5,6,7,1]=>[6,1,1]=>21
[2,3,4,8,5,7,6,1]=>[5,1,1,1]=>35
[2,3,4,8,6,5,7,1]=>[5,1,1,1]=>35
[2,3,4,8,6,7,5,1]=>[5,1,1,1]=>35
[2,3,5,4,8,6,7,1]=>[5,2,1]=>64
[2,3,6,4,5,1,7,8]=>[6,1,1]=>21
[2,3,6,4,5,1,8,7]=>[5,2,1]=>64
[2,3,6,4,5,8,7,1]=>[5,2,1]=>64
[2,3,7,4,5,6,8,1]=>[6,1,1]=>21
[2,3,8,4,5,6,7,1]=>[6,1,1]=>21
[2,3,7,4,6,5,8,1]=>[5,1,1,1]=>35
[2,3,8,4,6,7,5,1]=>[5,1,1,1]=>35
[2,3,7,5,4,6,1,8]=>[5,1,1,1]=>35
[2,3,7,5,4,6,8,1]=>[5,1,1,1]=>35
[2,3,8,5,4,6,7,1]=>[5,1,1,1]=>35
[2,3,7,5,6,4,1,8]=>[5,1,1,1]=>35
[2,3,7,5,6,4,8,1]=>[5,1,1,1]=>35
[2,3,8,5,6,4,7,1]=>[5,1,1,1]=>35
[2,3,8,5,6,7,4,1]=>[5,1,1,1]=>35
[2,3,8,5,7,6,4,1]=>[4,1,1,1,1]=>35
[2,3,8,6,5,4,7,1]=>[4,1,1,1,1]=>35
[2,4,3,5,8,6,7,1]=>[5,2,1]=>64
[2,4,3,7,5,6,8,1]=>[5,2,1]=>64
[2,4,3,8,5,6,7,1]=>[5,2,1]=>64
[2,4,3,8,5,7,6,1]=>[4,2,1,1]=>90
[2,4,3,8,6,5,7,1]=>[4,2,1,1]=>90
[2,5,3,4,1,6,7,8]=>[6,1,1]=>21
[2,5,3,4,1,8,7,6]=>[4,2,2]=>56
[2,5,3,4,6,7,8,1]=>[6,1,1]=>21
[2,5,3,4,6,8,7,1]=>[5,2,1]=>64
[2,5,3,4,7,6,8,1]=>[5,2,1]=>64
[2,5,3,4,8,6,7,1]=>[5,2,1]=>64
[2,6,3,4,5,1,7,8]=>[6,1,1]=>21
[2,6,3,4,5,8,7,1]=>[5,2,1]=>64
[2,7,3,4,5,6,1,8]=>[6,1,1]=>21
[2,8,3,4,5,6,7,1]=>[6,1,1]=>21
[2,8,3,4,5,7,6,1]=>[5,1,1,1]=>35
[2,6,3,5,4,1,8,7]=>[4,2,1,1]=>90
[2,6,3,5,4,8,7,1]=>[4,2,1,1]=>90
[2,7,3,5,4,6,8,1]=>[5,1,1,1]=>35
[2,8,3,5,4,7,6,1]=>[4,2,1,1]=>90
[2,7,3,5,6,4,8,1]=>[5,1,1,1]=>35
[2,8,3,5,6,7,4,1]=>[5,1,1,1]=>35
[2,8,3,5,7,6,4,1]=>[4,1,1,1,1]=>35
[2,7,3,6,5,4,1,8]=>[4,1,1,1,1]=>35
[2,8,3,7,5,6,4,1]=>[4,1,1,1,1]=>35
[2,8,3,7,6,5,4,1]=>[3,1,1,1,1,1]=>21
[2,5,4,3,8,6,7,1]=>[4,2,1,1]=>90
[2,6,4,3,5,1,8,7]=>[4,2,1,1]=>90
[2,6,4,3,5,8,7,1]=>[4,2,1,1]=>90
[2,7,4,3,5,6,8,1]=>[5,1,1,1]=>35
[2,8,4,3,5,6,7,1]=>[5,1,1,1]=>35
[2,8,4,3,5,7,6,1]=>[4,2,1,1]=>90
[2,7,4,3,6,5,8,1]=>[4,2,1,1]=>90
[2,8,4,3,6,5,7,1]=>[4,2,1,1]=>90
[2,8,4,3,6,7,5,1]=>[4,2,1,1]=>90
[2,8,4,3,7,6,5,1]=>[3,2,1,1,1]=>64
[2,8,4,5,3,6,7,1]=>[5,1,1,1]=>35
[2,7,4,5,6,3,1,8]=>[5,1,1,1]=>35
[2,7,4,5,6,3,8,1]=>[5,1,1,1]=>35
[2,8,4,5,6,3,7,1]=>[5,1,1,1]=>35
[2,8,4,5,6,7,3,1]=>[5,1,1,1]=>35
[2,7,4,6,5,3,1,8]=>[4,1,1,1,1]=>35
[2,7,4,6,5,3,8,1]=>[4,1,1,1,1]=>35
[2,8,4,6,5,3,7,1]=>[4,1,1,1,1]=>35
[2,8,4,7,6,5,3,1]=>[3,1,1,1,1,1]=>21
[2,7,5,4,3,6,8,1]=>[4,1,1,1,1]=>35
[2,8,5,4,3,6,7,1]=>[4,1,1,1,1]=>35
[2,8,5,4,3,7,6,1]=>[3,2,1,1,1]=>64
[2,7,5,4,6,3,8,1]=>[4,1,1,1,1]=>35
[2,8,5,4,6,7,3,1]=>[4,1,1,1,1]=>35
[2,8,5,4,7,6,3,1]=>[3,2,1,1,1]=>64
[2,7,6,4,5,3,8,1]=>[4,1,1,1,1]=>35
[2,8,7,4,5,6,3,1]=>[4,1,1,1,1]=>35
[2,8,7,4,6,5,3,1]=>[3,1,1,1,1,1]=>21
[2,8,7,5,4,6,3,1]=>[3,1,1,1,1,1]=>21
[2,8,7,5,6,4,3,1]=>[3,1,1,1,1,1]=>21
[3,2,1,4,8,6,7,5]=>[4,2,2]=>56
[3,2,1,5,8,6,7,4]=>[4,2,2]=>56
[3,2,1,7,5,6,8,4]=>[4,2,2]=>56
[3,2,1,8,5,6,7,4]=>[4,2,2]=>56
[3,2,1,8,5,7,6,4]=>[3,2,2,1]=>70
[3,2,1,8,6,5,7,4]=>[3,2,2,1]=>70
[3,2,1,8,6,7,5,4]=>[3,2,2,1]=>70
[3,2,4,1,8,6,7,5]=>[4,2,2]=>56
[3,2,4,5,8,6,7,1]=>[5,2,1]=>64
[3,2,4,7,5,6,8,1]=>[5,2,1]=>64
[3,2,4,8,5,6,7,1]=>[5,2,1]=>64
[3,2,4,8,6,7,5,1]=>[4,2,1,1]=>90
[3,2,5,4,8,6,7,1]=>[4,3,1]=>70
[3,2,6,4,5,1,8,7]=>[4,3,1]=>70
[3,2,7,4,5,6,1,8]=>[5,2,1]=>64
[3,2,8,4,5,6,7,1]=>[5,2,1]=>64
[3,2,7,4,6,5,1,8]=>[4,2,1,1]=>90
[3,2,7,4,6,5,8,1]=>[4,2,1,1]=>90
[3,2,8,4,6,5,7,1]=>[4,2,1,1]=>90
[3,2,7,5,4,6,1,8]=>[4,2,1,1]=>90
[3,2,8,5,4,6,7,1]=>[4,2,1,1]=>90
[3,2,8,5,4,7,6,1]=>[3,3,1,1]=>56
[3,2,7,5,6,4,1,8]=>[4,2,1,1]=>90
[3,2,7,5,6,4,8,1]=>[4,2,1,1]=>90
[3,2,8,5,6,4,7,1]=>[4,2,1,1]=>90
[3,2,8,5,7,6,4,1]=>[3,2,1,1,1]=>64
[3,2,8,6,5,7,4,1]=>[3,2,1,1,1]=>64
[3,2,8,7,5,6,4,1]=>[3,2,1,1,1]=>64
[4,2,3,1,5,7,8,6]=>[5,2,1]=>64
[4,2,3,1,6,5,8,7]=>[4,3,1]=>70
[4,2,3,1,6,7,8,5]=>[5,2,1]=>64
[4,2,3,1,6,8,7,5]=>[4,2,2]=>56
[4,2,3,1,7,6,8,5]=>[4,2,2]=>56
[4,2,3,1,8,6,7,5]=>[4,2,2]=>56
[4,2,3,1,8,7,6,5]=>[3,2,2,1]=>70
[4,2,3,5,1,8,7,6]=>[4,2,2]=>56
[4,2,3,5,6,1,8,7]=>[5,2,1]=>64
[4,2,3,5,6,8,7,1]=>[5,2,1]=>64
[4,2,3,5,8,7,6,1]=>[4,2,1,1]=>90
[4,2,3,6,5,8,7,1]=>[4,3,1]=>70
[4,2,3,7,5,6,8,1]=>[5,2,1]=>64
[4,2,3,8,5,6,7,1]=>[5,2,1]=>64
[4,2,3,8,5,7,6,1]=>[4,2,1,1]=>90
[4,2,3,7,6,5,8,1]=>[4,2,1,1]=>90
[4,2,3,8,7,6,5,1]=>[3,2,1,1,1]=>64
[5,2,3,4,1,6,8,7]=>[5,2,1]=>64
[5,2,3,4,1,7,8,6]=>[5,2,1]=>64
[5,2,3,4,1,8,7,6]=>[4,2,2]=>56
[5,2,3,4,6,1,8,7]=>[5,2,1]=>64
[5,2,3,4,7,6,1,8]=>[5,2,1]=>64
[5,2,3,4,8,6,7,1]=>[5,2,1]=>64
[6,2,3,4,5,1,8,7]=>[5,2,1]=>64
[6,2,3,4,5,8,7,1]=>[5,2,1]=>64
[8,2,3,4,5,7,6,1]=>[5,1,1,1]=>35
[8,2,3,4,7,6,5,1]=>[4,1,1,1,1]=>35
[6,2,3,5,4,1,8,7]=>[4,2,1,1]=>90
[6,2,3,5,4,7,8,1]=>[5,1,1,1]=>35
[8,2,3,5,4,6,7,1]=>[5,1,1,1]=>35
[8,2,3,5,4,7,6,1]=>[4,2,1,1]=>90
[7,2,3,5,6,4,1,8]=>[5,1,1,1]=>35
[8,2,3,5,6,7,4,1]=>[5,1,1,1]=>35
[8,2,3,5,7,6,4,1]=>[4,1,1,1,1]=>35
[8,2,3,7,5,6,4,1]=>[4,1,1,1,1]=>35
[8,2,3,7,6,5,4,1]=>[3,1,1,1,1,1]=>21
[5,2,4,3,1,6,7,8]=>[5,1,1,1]=>35
[5,2,4,3,1,6,8,7]=>[4,2,1,1]=>90
[5,2,4,3,1,7,6,8]=>[4,2,1,1]=>90
[5,2,4,3,1,8,7,6]=>[3,2,2,1]=>70
[5,2,4,3,6,1,8,7]=>[4,2,1,1]=>90
[5,2,4,3,7,6,1,8]=>[4,2,1,1]=>90
[5,2,4,3,7,6,8,1]=>[4,2,1,1]=>90
[5,2,4,3,8,7,6,1]=>[3,2,2,1]=>70
[6,2,4,3,5,1,8,7]=>[4,2,1,1]=>90
[7,2,4,3,6,5,1,8]=>[4,2,1,1]=>90
[7,2,4,3,6,5,8,1]=>[4,2,1,1]=>90
[8,2,4,3,6,5,7,1]=>[4,2,1,1]=>90
[8,2,4,3,6,7,5,1]=>[4,2,1,1]=>90
[8,2,4,3,7,6,5,1]=>[3,2,1,1,1]=>64
[7,2,4,5,3,6,1,8]=>[5,1,1,1]=>35
[7,2,4,5,3,6,8,1]=>[5,1,1,1]=>35
[8,2,4,5,3,7,6,1]=>[4,2,1,1]=>90
[8,2,4,5,6,7,3,1]=>[5,1,1,1]=>35
[8,2,4,5,7,6,3,1]=>[4,1,1,1,1]=>35
[7,2,4,6,5,3,1,8]=>[4,1,1,1,1]=>35
[7,2,4,6,5,3,8,1]=>[4,1,1,1,1]=>35
[8,2,4,7,5,6,3,1]=>[4,1,1,1,1]=>35
[8,2,4,7,6,5,3,1]=>[3,1,1,1,1,1]=>21
[6,2,5,4,3,1,8,7]=>[3,2,1,1,1]=>64
[6,2,5,4,3,7,1,8]=>[4,1,1,1,1]=>35
[6,2,5,4,3,7,8,1]=>[4,1,1,1,1]=>35
[7,2,5,4,3,6,1,8]=>[4,1,1,1,1]=>35
[8,2,5,4,3,6,7,1]=>[4,1,1,1,1]=>35
[8,2,5,4,3,7,6,1]=>[3,2,1,1,1]=>64
[7,2,5,4,6,3,8,1]=>[4,1,1,1,1]=>35
[7,2,6,4,5,3,8,1]=>[4,1,1,1,1]=>35
[8,2,6,4,5,3,7,1]=>[4,1,1,1,1]=>35
[8,2,6,4,5,7,3,1]=>[4,1,1,1,1]=>35
[8,2,7,4,5,6,3,1]=>[4,1,1,1,1]=>35
[8,2,7,4,6,5,3,1]=>[3,1,1,1,1,1]=>21
[7,2,6,5,4,3,1,8]=>[3,1,1,1,1,1]=>21
[7,2,6,5,4,3,8,1]=>[3,1,1,1,1,1]=>21
[8,2,6,5,4,3,7,1]=>[3,1,1,1,1,1]=>21
[8,2,6,5,4,7,3,1]=>[3,1,1,1,1,1]=>21
[8,2,7,5,4,6,3,1]=>[3,1,1,1,1,1]=>21
[8,2,7,5,6,4,3,1]=>[3,1,1,1,1,1]=>21
[8,2,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]=>7
[4,3,2,1,8,6,7,5]=>[3,2,2,1]=>70
[4,3,2,7,5,6,8,1]=>[4,2,1,1]=>90
[4,3,2,8,5,6,7,1]=>[4,2,1,1]=>90
[4,3,2,8,5,7,6,1]=>[3,2,2,1]=>70
[4,3,2,8,6,7,5,1]=>[3,2,2,1]=>70
[5,3,2,4,1,6,8,7]=>[4,2,1,1]=>90
[5,3,2,4,1,7,6,8]=>[4,2,1,1]=>90
[5,3,2,4,1,8,7,6]=>[3,2,2,1]=>70
[5,3,2,4,7,6,1,8]=>[4,2,1,1]=>90
[8,3,2,4,6,5,7,1]=>[4,2,1,1]=>90
[8,3,2,4,6,7,5,1]=>[4,2,1,1]=>90
[8,3,2,4,7,6,5,1]=>[3,2,1,1,1]=>64
[6,3,2,5,4,1,8,7]=>[3,3,1,1]=>56
[6,3,2,5,4,7,1,8]=>[4,2,1,1]=>90
[6,3,2,5,4,7,8,1]=>[4,2,1,1]=>90
[6,3,2,5,4,8,7,1]=>[3,3,1,1]=>56
[7,3,2,5,4,6,1,8]=>[4,2,1,1]=>90
[8,3,2,5,4,7,6,1]=>[3,3,1,1]=>56
[7,3,2,5,6,4,8,1]=>[4,2,1,1]=>90
[8,3,2,5,6,7,4,1]=>[4,2,1,1]=>90
[8,3,2,5,7,6,4,1]=>[3,2,1,1,1]=>64
[8,3,2,6,5,7,4,1]=>[3,2,1,1,1]=>64
[8,3,2,7,5,6,4,1]=>[3,2,1,1,1]=>64
[8,3,2,7,6,5,4,1]=>[2,2,1,1,1,1]=>20
[5,3,4,2,1,6,8,7]=>[4,2,1,1]=>90
[5,3,4,2,1,7,8,6]=>[4,2,1,1]=>90
[5,3,4,2,1,8,7,6]=>[3,2,2,1]=>70
[5,3,4,2,6,1,8,7]=>[4,2,1,1]=>90
[5,3,4,2,7,6,1,8]=>[4,2,1,1]=>90
[5,3,4,2,7,6,8,1]=>[4,2,1,1]=>90
[5,3,4,2,8,6,7,1]=>[4,2,1,1]=>90
[6,3,4,2,5,1,8,7]=>[4,2,1,1]=>90
[7,3,4,2,6,5,8,1]=>[4,2,1,1]=>90
[6,3,4,5,2,1,8,7]=>[4,2,1,1]=>90
[6,3,4,5,2,8,7,1]=>[4,2,1,1]=>90
[8,3,4,5,2,7,6,1]=>[4,2,1,1]=>90
[8,3,4,5,7,6,2,1]=>[4,1,1,1,1]=>35
[8,3,4,7,6,5,2,1]=>[3,1,1,1,1,1]=>21
[6,3,5,4,2,1,8,7]=>[3,2,1,1,1]=>64
[6,3,5,4,2,7,1,8]=>[4,1,1,1,1]=>35
[6,3,5,4,2,7,8,1]=>[4,1,1,1,1]=>35
[6,3,5,4,2,8,7,1]=>[3,2,1,1,1]=>64
[7,3,5,4,2,6,1,8]=>[4,1,1,1,1]=>35
[8,3,5,4,2,6,7,1]=>[4,1,1,1,1]=>35
[8,3,5,4,2,7,6,1]=>[3,2,1,1,1]=>64
[7,3,5,4,6,2,1,8]=>[4,1,1,1,1]=>35
[7,3,5,4,6,2,8,1]=>[4,1,1,1,1]=>35
[8,3,5,4,6,7,2,1]=>[4,1,1,1,1]=>35
[8,3,5,4,7,6,2,1]=>[3,2,1,1,1]=>64
[7,3,6,4,5,2,1,8]=>[4,1,1,1,1]=>35
[7,3,6,4,5,2,8,1]=>[4,1,1,1,1]=>35
[8,3,6,4,5,2,7,1]=>[4,1,1,1,1]=>35
[8,3,7,4,5,6,2,1]=>[4,1,1,1,1]=>35
[8,3,7,4,6,5,2,1]=>[3,1,1,1,1,1]=>21
[7,3,6,5,4,2,1,8]=>[3,1,1,1,1,1]=>21
[7,3,6,5,4,2,8,1]=>[3,1,1,1,1,1]=>21
[8,3,6,5,4,7,2,1]=>[3,1,1,1,1,1]=>21
[8,3,7,5,4,6,2,1]=>[3,1,1,1,1,1]=>21
[8,3,7,5,6,4,2,1]=>[3,1,1,1,1,1]=>21
[8,3,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>7
[5,4,3,2,8,6,7,1]=>[3,2,1,1,1]=>64
[6,4,3,2,5,1,8,7]=>[3,2,1,1,1]=>64
[6,4,3,2,5,8,7,1]=>[3,2,1,1,1]=>64
[8,4,3,2,5,7,6,1]=>[3,2,1,1,1]=>64
[7,4,3,2,6,5,1,8]=>[3,2,1,1,1]=>64
[7,4,3,2,6,5,8,1]=>[3,2,1,1,1]=>64
[8,4,3,2,6,5,7,1]=>[3,2,1,1,1]=>64
[8,4,3,2,7,6,5,1]=>[2,2,2,1,1]=>28
[6,4,3,5,2,1,8,7]=>[3,2,1,1,1]=>64
[8,4,3,5,2,7,6,1]=>[3,2,1,1,1]=>64
[8,4,3,5,7,6,2,1]=>[3,2,1,1,1]=>64
[7,4,3,6,5,2,1,8]=>[3,2,1,1,1]=>64
[7,4,3,6,5,2,8,1]=>[3,2,1,1,1]=>64
[8,4,3,7,5,6,2,1]=>[3,2,1,1,1]=>64
[8,4,3,7,6,5,2,1]=>[2,2,1,1,1,1]=>20
[6,5,3,4,2,1,8,7]=>[3,2,1,1,1]=>64
[8,5,3,4,2,7,6,1]=>[3,2,1,1,1]=>64
[8,5,3,4,7,6,2,1]=>[3,2,1,1,1]=>64
[8,7,3,4,6,5,2,1]=>[3,1,1,1,1,1]=>21
[7,6,3,5,4,2,1,8]=>[3,1,1,1,1,1]=>21
[7,6,3,5,4,2,8,1]=>[3,1,1,1,1,1]=>21
[8,6,3,5,4,2,7,1]=>[3,1,1,1,1,1]=>21
[8,6,3,5,4,7,2,1]=>[3,1,1,1,1,1]=>21
[8,7,3,5,4,6,2,1]=>[3,1,1,1,1,1]=>21
[8,7,3,5,6,4,2,1]=>[3,1,1,1,1,1]=>21
[8,7,3,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>7
[8,5,4,3,2,7,6,1]=>[2,2,1,1,1,1]=>20
[8,5,4,3,7,6,2,1]=>[2,2,1,1,1,1]=>20
[8,7,4,3,6,5,2,1]=>[2,2,1,1,1,1]=>20
[8,7,4,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>7
[2,4,1,3,6,5,8,7]=>[4,4]=>14
[2,1,4,6,3,5,8,7]=>[4,4]=>14
[2,4,1,6,3,5,8,7]=>[4,4]=>14
[2,4,6,1,3,5,8,7]=>[4,4]=>14
[2,1,4,3,6,8,5,7]=>[4,4]=>14
[2,4,1,3,6,8,5,7]=>[4,4]=>14
[2,1,4,6,3,8,5,7]=>[4,4]=>14
[2,4,1,6,3,8,5,7]=>[4,4]=>14
[2,4,6,1,3,8,5,7]=>[4,4]=>14
[2,1,4,6,8,3,5,7]=>[4,4]=>14
[2,4,1,6,8,3,5,7]=>[4,4]=>14
[2,4,6,1,8,3,5,7]=>[4,4]=>14
[2,4,6,8,1,3,5,7]=>[4,4]=>14
[2,4,1,3,6,5,7,8]=>[5,3]=>28
[2,1,4,6,3,5,7,8]=>[5,3]=>28
[2,4,1,6,3,5,7,8]=>[5,3]=>28
[2,4,6,1,3,5,7,8]=>[5,3]=>28
[2,1,4,6,3,7,5,8]=>[5,3]=>28
[2,4,1,6,3,7,5,8]=>[5,3]=>28
[2,4,6,7,1,3,5,8]=>[5,3]=>28
[2,4,1,3,6,7,8,5]=>[5,3]=>28
[2,1,4,6,3,7,8,5]=>[5,3]=>28
[2,4,1,6,3,7,8,5]=>[5,3]=>28
[2,1,4,6,7,3,8,5]=>[5,3]=>28
[2,4,1,6,7,3,8,5]=>[5,3]=>28
[2,4,6,1,7,3,8,5]=>[5,3]=>28
[2,4,6,7,1,3,8,5]=>[5,3]=>28
[2,1,4,6,7,8,3,5]=>[5,3]=>28
[2,4,1,6,7,8,3,5]=>[5,3]=>28
[2,4,6,7,8,1,3,5]=>[5,3]=>28
[2,1,4,3,7,5,8,6]=>[4,4]=>14
[2,4,1,3,7,5,8,6]=>[4,4]=>14
[2,1,4,7,3,5,8,6]=>[4,4]=>14
[2,4,1,7,3,5,8,6]=>[4,4]=>14
[2,1,4,3,7,8,5,6]=>[4,4]=>14
[2,4,1,3,7,8,5,6]=>[4,4]=>14
[2,4,1,7,3,8,5,6]=>[4,4]=>14
[2,1,4,7,8,3,5,6]=>[4,4]=>14
[2,4,1,7,8,3,5,6]=>[4,4]=>14
[2,4,7,1,8,3,5,6]=>[4,4]=>14
[2,4,1,5,3,7,6,8]=>[5,3]=>28
[2,4,5,1,3,7,6,8]=>[5,3]=>28
[2,4,5,1,7,3,6,8]=>[5,3]=>28
[2,4,1,5,3,7,8,6]=>[5,3]=>28
[2,4,5,1,3,7,8,6]=>[5,3]=>28
[2,1,4,5,7,3,8,6]=>[5,3]=>28
[2,4,1,5,7,3,8,6]=>[5,3]=>28
[2,4,5,1,7,3,8,6]=>[5,3]=>28
[2,4,5,1,7,8,3,6]=>[5,3]=>28
[2,4,5,7,8,1,3,6]=>[5,3]=>28
[2,1,4,3,8,5,6,7]=>[5,3]=>28
[2,4,1,3,8,5,6,7]=>[5,3]=>28
[2,1,4,8,3,5,6,7]=>[5,3]=>28
[2,4,1,8,3,5,6,7]=>[5,3]=>28
[2,4,8,1,3,5,6,7]=>[5,3]=>28
[2,1,4,3,5,8,6,7]=>[5,3]=>28
[2,4,1,5,3,8,6,7]=>[5,3]=>28
[2,1,4,5,8,3,6,7]=>[5,3]=>28
[2,4,1,5,8,3,6,7]=>[5,3]=>28
[2,4,5,1,8,3,6,7]=>[5,3]=>28
[2,4,1,5,3,6,8,7]=>[5,3]=>28
[2,4,1,5,6,3,8,7]=>[5,3]=>28
[2,4,5,1,6,3,8,7]=>[5,3]=>28
[2,4,5,6,1,3,8,7]=>[5,3]=>28
[2,1,4,5,6,8,3,7]=>[5,3]=>28
[2,4,1,5,6,8,3,7]=>[5,3]=>28
[2,4,5,1,6,8,3,7]=>[5,3]=>28
[2,4,5,6,1,8,3,7]=>[5,3]=>28
[2,4,5,6,8,1,3,7]=>[5,3]=>28
[2,4,1,3,5,6,7,8]=>[6,2]=>20
[2,4,1,5,3,6,7,8]=>[6,2]=>20
[2,4,5,1,3,6,7,8]=>[6,2]=>20
[2,4,1,5,6,3,7,8]=>[6,2]=>20
[2,4,5,1,6,3,7,8]=>[6,2]=>20
[2,4,5,6,1,3,7,8]=>[6,2]=>20
[2,4,1,5,6,7,3,8]=>[6,2]=>20
[2,4,5,6,1,7,3,8]=>[6,2]=>20
[2,4,5,6,7,1,3,8]=>[6,2]=>20
[2,4,1,5,6,7,8,3]=>[6,2]=>20
[2,4,5,1,6,7,8,3]=>[6,2]=>20
[2,4,5,6,1,7,8,3]=>[6,2]=>20
[2,4,5,6,7,1,8,3]=>[6,2]=>20
[2,4,5,6,7,8,1,3]=>[6,2]=>20
[2,1,5,3,6,4,8,7]=>[4,4]=>14
[2,5,1,3,6,4,8,7]=>[4,4]=>14
[2,1,5,6,3,4,8,7]=>[4,4]=>14
[2,5,1,6,3,4,8,7]=>[4,4]=>14
[2,5,6,1,3,4,8,7]=>[4,4]=>14
[2,1,5,3,6,8,4,7]=>[4,4]=>14
[2,5,1,3,6,8,4,7]=>[4,4]=>14
[2,5,6,1,3,8,4,7]=>[4,4]=>14
[2,1,5,6,8,3,4,7]=>[4,4]=>14
[2,5,1,6,8,3,4,7]=>[4,4]=>14
[2,5,1,3,6,4,7,8]=>[5,3]=>28
[2,1,5,3,6,7,4,8]=>[5,3]=>28
[2,1,5,6,3,7,4,8]=>[5,3]=>28
[2,5,1,6,3,7,4,8]=>[5,3]=>28
[2,5,6,1,3,7,4,8]=>[5,3]=>28
[2,1,5,6,7,3,4,8]=>[5,3]=>28
[2,1,5,3,6,7,8,4]=>[5,3]=>28
[2,5,1,3,6,7,8,4]=>[5,3]=>28
[2,1,5,6,3,7,8,4]=>[5,3]=>28
[2,5,1,6,3,7,8,4]=>[5,3]=>28
[2,5,6,1,3,7,8,4]=>[5,3]=>28
[2,1,5,6,7,3,8,4]=>[5,3]=>28
[2,5,1,6,7,3,8,4]=>[5,3]=>28
[2,5,6,7,1,3,8,4]=>[5,3]=>28
[2,1,5,6,7,8,3,4]=>[5,3]=>28
[2,5,1,6,7,8,3,4]=>[5,3]=>28
[2,5,6,1,7,8,3,4]=>[5,3]=>28
[2,5,6,7,1,8,3,4]=>[5,3]=>28
[2,5,6,7,8,1,3,4]=>[5,3]=>28
[2,1,5,3,7,4,8,6]=>[4,4]=>14
[2,5,1,3,7,4,8,6]=>[4,4]=>14
[2,5,1,7,3,4,8,6]=>[4,4]=>14
[2,5,7,1,3,4,8,6]=>[4,4]=>14
[2,1,5,3,7,8,4,6]=>[4,4]=>14
[2,5,1,3,7,8,4,6]=>[4,4]=>14
[2,1,5,7,3,8,4,6]=>[4,4]=>14
[2,1,5,7,8,3,4,6]=>[4,4]=>14
[2,5,1,7,8,3,4,6]=>[4,4]=>14
[2,5,7,1,8,3,4,6]=>[4,4]=>14
[2,5,7,8,1,3,4,6]=>[4,4]=>14
[2,3,5,1,4,7,6,8]=>[5,3]=>28
[2,3,5,7,1,4,6,8]=>[5,3]=>28
[2,3,5,1,7,4,8,6]=>[5,3]=>28
[2,3,1,5,7,8,4,6]=>[5,3]=>28
[2,3,5,7,8,1,4,6]=>[5,3]=>28
[2,1,5,3,8,4,6,7]=>[5,3]=>28
[2,5,1,3,8,4,6,7]=>[5,3]=>28
[2,1,5,8,3,4,6,7]=>[5,3]=>28
[2,3,5,1,4,8,6,7]=>[5,3]=>28
[2,1,3,5,8,4,6,7]=>[5,3]=>28
[2,3,5,1,8,4,6,7]=>[5,3]=>28
[2,1,5,3,4,6,8,7]=>[5,3]=>28
[2,3,5,1,6,4,8,7]=>[5,3]=>28
[2,1,3,5,6,8,4,7]=>[5,3]=>28
[2,3,1,5,6,8,4,7]=>[5,3]=>28
[2,3,5,1,6,8,4,7]=>[5,3]=>28
[2,3,5,6,1,8,4,7]=>[5,3]=>28
[2,3,5,6,8,1,4,7]=>[5,3]=>28
[2,1,5,3,4,6,7,8]=>[6,2]=>20
[2,5,1,3,4,6,7,8]=>[6,2]=>20
[2,3,5,1,4,6,7,8]=>[6,2]=>20
[2,3,5,6,1,4,7,8]=>[6,2]=>20
[2,3,5,6,7,1,4,8]=>[6,2]=>20
[2,3,5,1,6,7,8,4]=>[6,2]=>20
[2,3,5,6,7,8,1,4]=>[6,2]=>20
[2,1,6,3,7,4,8,5]=>[4,4]=>14
[2,6,1,3,7,4,8,5]=>[4,4]=>14
[2,1,6,7,3,4,8,5]=>[4,4]=>14
[2,6,1,7,3,4,8,5]=>[4,4]=>14
[2,6,7,1,3,4,8,5]=>[4,4]=>14
[2,1,6,3,7,8,4,5]=>[4,4]=>14
[2,6,1,3,7,8,4,5]=>[4,4]=>14
[2,6,7,1,3,8,4,5]=>[4,4]=>14
[2,1,6,7,8,3,4,5]=>[4,4]=>14
[2,6,1,7,8,3,4,5]=>[4,4]=>14
[2,6,7,1,8,3,4,5]=>[4,4]=>14
[2,6,7,8,1,3,4,5]=>[4,4]=>14
[2,6,1,7,3,4,5,8]=>[5,3]=>28
[2,6,1,3,4,7,5,8]=>[5,3]=>28
[2,3,1,6,4,7,5,8]=>[5,3]=>28
[2,1,6,3,4,7,8,5]=>[5,3]=>28
[2,6,1,3,4,7,8,5]=>[5,3]=>28
[2,3,6,1,4,7,8,5]=>[5,3]=>28
[2,1,3,6,7,4,8,5]=>[5,3]=>28
[2,1,3,6,7,8,4,5]=>[5,3]=>28
[2,3,1,6,7,8,4,5]=>[5,3]=>28
[2,3,6,1,7,8,4,5]=>[5,3]=>28
[2,3,6,7,1,8,4,5]=>[5,3]=>28
[2,3,6,7,8,1,4,5]=>[5,3]=>28
[2,1,6,3,8,4,5,7]=>[5,3]=>28
[2,6,1,3,8,4,5,7]=>[5,3]=>28
[2,1,6,8,3,4,5,7]=>[5,3]=>28
[2,6,1,8,3,4,5,7]=>[5,3]=>28
[2,6,8,1,3,4,5,7]=>[5,3]=>28
[2,1,6,3,4,8,5,7]=>[5,3]=>28
[2,6,1,3,4,8,5,7]=>[5,3]=>28
[2,3,1,6,4,8,5,7]=>[5,3]=>28
[2,3,6,1,4,8,5,7]=>[5,3]=>28
[2,3,1,6,8,4,5,7]=>[5,3]=>28
[2,3,6,1,8,4,5,7]=>[5,3]=>28
[2,1,6,3,4,5,8,7]=>[5,3]=>28
[2,6,1,3,4,5,8,7]=>[5,3]=>28
[2,1,3,6,4,5,8,7]=>[5,3]=>28
[2,3,6,1,4,5,8,7]=>[5,3]=>28
[2,3,4,1,6,8,5,7]=>[5,3]=>28
[2,3,4,6,1,8,5,7]=>[5,3]=>28
[2,3,4,6,8,1,5,7]=>[5,3]=>28
[2,6,1,3,4,5,7,8]=>[6,2]=>20
[2,1,3,6,4,5,7,8]=>[6,2]=>20
[2,3,1,6,4,5,7,8]=>[6,2]=>20
[2,3,6,1,4,5,7,8]=>[6,2]=>20
[2,3,4,6,1,5,7,8]=>[6,2]=>20
[2,3,4,6,7,1,5,8]=>[6,2]=>20
[2,3,4,6,1,7,8,5]=>[6,2]=>20
[2,3,4,6,7,8,1,5]=>[6,2]=>20
[2,1,7,3,8,4,5,6]=>[5,3]=>28
[2,7,1,3,8,4,5,6]=>[5,3]=>28
[2,1,7,8,3,4,5,6]=>[5,3]=>28
[2,7,1,8,3,4,5,6]=>[5,3]=>28
[2,7,8,1,3,4,5,6]=>[5,3]=>28
[2,1,7,3,4,8,5,6]=>[5,3]=>28
[2,1,3,7,4,8,5,6]=>[5,3]=>28
[2,3,1,7,4,8,5,6]=>[5,3]=>28
[2,1,3,7,8,4,5,6]=>[5,3]=>28
[2,3,1,7,8,4,5,6]=>[5,3]=>28
[2,3,7,8,1,4,5,6]=>[5,3]=>28
[2,1,7,3,4,5,8,6]=>[5,3]=>28
[2,7,1,3,4,5,8,6]=>[5,3]=>28
[2,3,1,7,4,5,8,6]=>[5,3]=>28
[2,3,7,1,4,5,8,6]=>[5,3]=>28
[2,1,3,4,7,5,8,6]=>[5,3]=>28
[2,3,4,1,7,5,8,6]=>[5,3]=>28
[2,3,4,7,1,5,8,6]=>[5,3]=>28
[2,1,3,4,7,8,5,6]=>[5,3]=>28
[2,3,1,4,7,8,5,6]=>[5,3]=>28
[2,3,4,1,7,8,5,6]=>[5,3]=>28
[2,3,4,7,1,8,5,6]=>[5,3]=>28
[2,3,4,7,8,1,5,6]=>[5,3]=>28
[2,1,7,3,4,5,6,8]=>[6,2]=>20
[2,7,1,3,4,5,6,8]=>[6,2]=>20
[2,3,7,1,4,5,6,8]=>[6,2]=>20
[2,1,3,4,7,5,6,8]=>[6,2]=>20
[2,3,4,1,7,5,6,8]=>[6,2]=>20
[2,3,4,7,1,5,6,8]=>[6,2]=>20
[2,3,4,5,7,1,6,8]=>[6,2]=>20
[2,3,4,5,7,1,8,6]=>[6,2]=>20
[2,3,4,5,7,8,1,6]=>[6,2]=>20
[2,1,8,3,4,5,6,7]=>[6,2]=>20
[2,8,1,3,4,5,6,7]=>[6,2]=>20
[2,1,3,8,4,5,6,7]=>[6,2]=>20
[2,3,1,8,4,5,6,7]=>[6,2]=>20
[2,3,8,1,4,5,6,7]=>[6,2]=>20
[2,1,3,4,8,5,6,7]=>[6,2]=>20
[2,3,1,4,8,5,6,7]=>[6,2]=>20
[2,3,4,1,8,5,6,7]=>[6,2]=>20
[2,3,4,8,1,5,6,7]=>[6,2]=>20
[2,1,3,4,5,8,6,7]=>[6,2]=>20
[2,3,1,4,5,8,6,7]=>[6,2]=>20
[2,3,4,1,5,8,6,7]=>[6,2]=>20
[2,3,4,5,1,8,6,7]=>[6,2]=>20
[2,3,4,5,8,1,6,7]=>[6,2]=>20
[2,3,4,5,6,8,1,7]=>[6,2]=>20
[3,1,4,2,6,5,8,7]=>[4,4]=>14
[3,4,1,2,6,5,8,7]=>[4,4]=>14
[3,1,4,6,2,5,8,7]=>[4,4]=>14
[3,4,1,6,2,5,8,7]=>[4,4]=>14
[3,4,6,1,2,5,8,7]=>[4,4]=>14
[3,1,4,2,6,8,5,7]=>[4,4]=>14
[3,4,1,2,6,8,5,7]=>[4,4]=>14
[3,1,4,6,2,8,5,7]=>[4,4]=>14
[3,4,1,6,2,8,5,7]=>[4,4]=>14
[3,1,4,6,8,2,5,7]=>[4,4]=>14
[3,4,1,6,8,2,5,7]=>[4,4]=>14
[3,4,6,8,1,2,5,7]=>[4,4]=>14
[3,4,1,2,6,5,7,8]=>[5,3]=>28
[3,1,4,2,6,7,5,8]=>[5,3]=>28
[3,4,1,2,6,7,5,8]=>[5,3]=>28
[3,4,1,6,2,7,5,8]=>[5,3]=>28
[3,4,1,6,7,2,5,8]=>[5,3]=>28
[3,4,6,7,1,2,5,8]=>[5,3]=>28
[3,1,4,2,6,7,8,5]=>[5,3]=>28
[3,4,1,2,6,7,8,5]=>[5,3]=>28
[3,1,4,6,2,7,8,5]=>[5,3]=>28
[3,4,1,6,2,7,8,5]=>[5,3]=>28
[3,4,6,1,2,7,8,5]=>[5,3]=>28
[3,1,4,6,7,2,8,5]=>[5,3]=>28
[3,4,1,6,7,2,8,5]=>[5,3]=>28
[3,4,6,1,7,2,8,5]=>[5,3]=>28
[3,1,4,6,7,8,2,5]=>[5,3]=>28
[3,4,1,6,7,8,2,5]=>[5,3]=>28
[3,4,6,1,7,8,2,5]=>[5,3]=>28
[3,4,6,7,1,8,2,5]=>[5,3]=>28
[3,4,6,7,8,1,2,5]=>[5,3]=>28
[3,1,4,2,7,5,8,6]=>[4,4]=>14
[3,4,1,2,7,5,8,6]=>[4,4]=>14
[3,1,4,7,2,5,8,6]=>[4,4]=>14
[3,4,7,1,2,5,8,6]=>[4,4]=>14
[3,1,4,2,7,8,5,6]=>[4,4]=>14
[3,4,1,2,7,8,5,6]=>[4,4]=>14
[3,4,7,1,8,2,5,6]=>[4,4]=>14
[3,4,7,8,1,2,5,6]=>[4,4]=>14
[3,1,4,2,7,5,6,8]=>[5,3]=>28
[3,4,1,2,7,5,6,8]=>[5,3]=>28
[3,4,1,2,5,7,6,8]=>[5,3]=>28
[3,1,4,5,2,7,6,8]=>[5,3]=>28
[3,4,1,5,2,7,6,8]=>[5,3]=>28
[3,4,1,5,7,2,6,8]=>[5,3]=>28
[3,4,5,7,1,2,6,8]=>[5,3]=>28
[3,1,4,2,5,7,8,6]=>[5,3]=>28
[3,4,1,2,5,7,8,6]=>[5,3]=>28
[3,1,4,5,2,7,8,6]=>[5,3]=>28
[3,4,5,1,2,7,8,6]=>[5,3]=>28
[3,1,4,5,7,2,8,6]=>[5,3]=>28
[3,4,1,5,7,2,8,6]=>[5,3]=>28
[3,1,4,5,7,8,2,6]=>[5,3]=>28
[3,4,1,5,7,8,2,6]=>[5,3]=>28
[3,4,5,1,7,8,2,6]=>[5,3]=>28
[3,4,5,7,8,1,2,6]=>[5,3]=>28
[3,1,4,2,8,5,6,7]=>[5,3]=>28
[3,4,1,2,8,5,6,7]=>[5,3]=>28
[3,1,4,8,2,5,6,7]=>[5,3]=>28
[3,4,1,8,2,5,6,7]=>[5,3]=>28
[3,4,8,1,2,5,6,7]=>[5,3]=>28
[3,1,4,2,5,8,6,7]=>[5,3]=>28
[3,4,1,2,5,8,6,7]=>[5,3]=>28
[3,4,1,5,2,8,6,7]=>[5,3]=>28
[3,1,4,5,8,2,6,7]=>[5,3]=>28
[3,4,1,5,8,2,6,7]=>[5,3]=>28
[3,4,5,8,1,2,6,7]=>[5,3]=>28
[3,4,1,2,5,6,8,7]=>[5,3]=>28
[3,4,5,1,2,6,8,7]=>[5,3]=>28
[3,1,4,5,6,2,8,7]=>[5,3]=>28
[3,4,1,5,6,2,8,7]=>[5,3]=>28
[3,4,5,1,6,2,8,7]=>[5,3]=>28
[3,4,5,6,1,2,8,7]=>[5,3]=>28
[3,1,4,5,6,8,2,7]=>[5,3]=>28
[3,4,1,5,6,8,2,7]=>[5,3]=>28
[3,4,5,6,1,8,2,7]=>[5,3]=>28
[3,4,5,6,8,1,2,7]=>[5,3]=>28
[3,1,4,2,5,6,7,8]=>[6,2]=>20
[3,1,4,5,2,6,7,8]=>[6,2]=>20
[3,4,1,5,2,6,7,8]=>[6,2]=>20
[3,4,1,5,6,2,7,8]=>[6,2]=>20
[3,4,5,1,6,2,7,8]=>[6,2]=>20
[3,1,4,5,6,7,2,8]=>[6,2]=>20
[3,4,1,5,6,7,2,8]=>[6,2]=>20
[3,4,5,1,6,7,2,8]=>[6,2]=>20
[3,4,5,6,1,7,2,8]=>[6,2]=>20
[3,1,4,5,6,7,8,2]=>[6,2]=>20
[3,4,1,5,6,7,8,2]=>[6,2]=>20
[3,4,5,1,6,7,8,2]=>[6,2]=>20
[3,4,5,6,1,7,8,2]=>[6,2]=>20
[3,4,5,6,7,1,8,2]=>[6,2]=>20
[3,1,5,2,6,4,8,7]=>[4,4]=>14
[3,5,1,2,6,4,8,7]=>[4,4]=>14
[3,5,1,6,2,4,8,7]=>[4,4]=>14
[3,5,6,1,2,4,8,7]=>[4,4]=>14
[3,1,5,2,6,8,4,7]=>[4,4]=>14
[3,5,1,2,6,8,4,7]=>[4,4]=>14
[3,1,5,6,8,2,4,7]=>[4,4]=>14
[3,5,1,6,8,2,4,7]=>[4,4]=>14
[3,5,6,1,8,2,4,7]=>[4,4]=>14
[3,5,6,8,1,2,4,7]=>[4,4]=>14
[3,5,1,6,2,4,7,8]=>[5,3]=>28
[3,5,6,1,2,4,7,8]=>[5,3]=>28
[3,5,1,2,6,7,4,8]=>[5,3]=>28
[3,5,1,6,2,7,4,8]=>[5,3]=>28
[3,5,6,1,2,7,4,8]=>[5,3]=>28
[3,5,1,6,7,2,4,8]=>[5,3]=>28
[3,5,6,7,1,2,4,8]=>[5,3]=>28
[3,1,5,2,6,7,8,4]=>[5,3]=>28
[3,5,1,2,6,7,8,4]=>[5,3]=>28
[3,1,5,6,2,7,8,4]=>[5,3]=>28
[3,5,1,6,2,7,8,4]=>[5,3]=>28
[3,5,6,1,2,7,8,4]=>[5,3]=>28
[3,1,5,6,7,2,8,4]=>[5,3]=>28
[3,5,1,6,7,2,8,4]=>[5,3]=>28
[3,5,6,1,7,2,8,4]=>[5,3]=>28
[3,5,6,7,1,2,8,4]=>[5,3]=>28
[3,1,5,6,7,8,2,4]=>[5,3]=>28
[3,5,1,6,7,8,2,4]=>[5,3]=>28
[3,5,6,1,7,8,2,4]=>[5,3]=>28
[3,5,6,7,1,8,2,4]=>[5,3]=>28
[3,5,6,7,8,1,2,4]=>[5,3]=>28
[3,1,5,2,7,4,8,6]=>[4,4]=>14
[3,5,1,2,7,4,8,6]=>[4,4]=>14
[3,1,5,7,2,4,8,6]=>[4,4]=>14
[3,5,7,1,2,4,8,6]=>[4,4]=>14
[3,1,5,2,7,8,4,6]=>[4,4]=>14
[3,5,1,2,7,8,4,6]=>[4,4]=>14
[3,1,5,7,2,8,4,6]=>[4,4]=>14
[3,5,1,7,2,8,4,6]=>[4,4]=>14
[3,1,5,7,8,2,4,6]=>[4,4]=>14
[3,5,1,7,8,2,4,6]=>[4,4]=>14
[3,5,7,8,1,2,4,6]=>[4,4]=>14
[3,1,5,2,7,4,6,8]=>[5,3]=>28
[3,5,1,2,7,4,6,8]=>[5,3]=>28
[3,1,5,7,2,4,6,8]=>[5,3]=>28
[3,5,1,7,2,4,6,8]=>[5,3]=>28
[3,5,7,1,2,4,6,8]=>[5,3]=>28
[3,1,5,2,4,7,6,8]=>[5,3]=>28
[3,5,1,2,4,7,6,8]=>[5,3]=>28
[3,1,2,5,4,7,6,8]=>[5,3]=>28
[1,3,5,2,4,7,6,8]=>[5,3]=>28
[3,1,2,5,7,4,6,8]=>[5,3]=>28
[1,3,2,5,7,4,6,8]=>[5,3]=>28
[1,3,5,2,7,4,6,8]=>[5,3]=>28
[1,3,5,7,2,4,6,8]=>[5,3]=>28
[3,5,1,2,4,7,8,6]=>[5,3]=>28
[3,1,2,5,7,4,8,6]=>[5,3]=>28
[1,3,5,2,7,4,8,6]=>[5,3]=>28
[1,3,5,7,2,4,8,6]=>[5,3]=>28
[1,3,2,5,7,8,4,6]=>[5,3]=>28
[1,3,5,2,7,8,4,6]=>[5,3]=>28
[1,3,5,7,2,8,4,6]=>[5,3]=>28
[1,3,5,7,8,2,4,6]=>[5,3]=>28
[3,1,5,2,8,4,6,7]=>[5,3]=>28
[3,5,1,2,8,4,6,7]=>[5,3]=>28
[3,1,5,8,2,4,6,7]=>[5,3]=>28
[3,5,1,8,2,4,6,7]=>[5,3]=>28
[3,1,5,2,4,8,6,7]=>[5,3]=>28
[3,5,1,2,4,8,6,7]=>[5,3]=>28
[1,3,2,5,4,8,6,7]=>[5,3]=>28
[1,3,5,2,4,8,6,7]=>[5,3]=>28
[3,1,2,5,8,4,6,7]=>[5,3]=>28
[1,3,2,5,8,4,6,7]=>[5,3]=>28
[1,3,5,2,8,4,6,7]=>[5,3]=>28
[1,3,5,8,2,4,6,7]=>[5,3]=>28
[3,5,1,2,4,6,8,7]=>[5,3]=>28
[3,1,2,5,4,6,8,7]=>[5,3]=>28
[1,3,5,2,4,6,8,7]=>[5,3]=>28
[3,1,2,5,6,8,4,7]=>[5,3]=>28
[1,3,5,2,6,8,4,7]=>[5,3]=>28
[1,3,5,6,2,8,4,7]=>[5,3]=>28
[1,3,5,6,8,2,4,7]=>[5,3]=>28
[3,5,1,2,4,6,7,8]=>[6,2]=>20
[1,3,5,2,4,6,7,8]=>[6,2]=>20
[1,3,5,6,2,4,7,8]=>[6,2]=>20
[3,1,2,5,6,7,4,8]=>[6,2]=>20
[1,3,5,2,6,7,4,8]=>[6,2]=>20
[1,3,5,6,2,7,4,8]=>[6,2]=>20
[1,3,5,6,7,2,4,8]=>[6,2]=>20
[3,1,2,5,6,7,8,4]=>[6,2]=>20
[1,3,5,6,7,2,8,4]=>[6,2]=>20
[1,3,5,6,7,8,2,4]=>[6,2]=>20
[3,1,6,2,7,4,8,5]=>[4,4]=>14
[3,6,1,2,7,4,8,5]=>[4,4]=>14
[3,6,1,7,2,4,8,5]=>[4,4]=>14
[3,6,7,1,2,4,8,5]=>[4,4]=>14
[3,6,1,2,7,8,4,5]=>[4,4]=>14
[3,1,6,7,2,8,4,5]=>[4,4]=>14
[3,6,1,7,2,8,4,5]=>[4,4]=>14
[3,6,7,1,2,8,4,5]=>[4,4]=>14
[3,6,1,7,8,2,4,5]=>[4,4]=>14
[3,6,7,8,1,2,4,5]=>[4,4]=>14
[3,1,6,7,2,4,5,8]=>[5,3]=>28
[3,6,1,2,4,7,5,8]=>[5,3]=>28
[3,1,2,6,4,7,5,8]=>[5,3]=>28
[1,3,2,6,4,7,5,8]=>[5,3]=>28
[1,3,2,6,7,4,5,8]=>[5,3]=>28
[1,3,6,2,7,4,5,8]=>[5,3]=>28
[3,1,6,2,4,7,8,5]=>[5,3]=>28
[3,6,1,2,4,7,8,5]=>[5,3]=>28
[3,1,2,6,4,7,8,5]=>[5,3]=>28
[3,1,2,6,7,4,8,5]=>[5,3]=>28
[1,3,2,6,7,4,8,5]=>[5,3]=>28
[1,3,6,2,7,4,8,5]=>[5,3]=>28
[3,1,2,6,7,8,4,5]=>[5,3]=>28
[1,3,2,6,7,8,4,5]=>[5,3]=>28
[1,3,6,2,7,8,4,5]=>[5,3]=>28
[1,3,6,7,8,2,4,5]=>[5,3]=>28
[3,6,1,2,8,4,5,7]=>[5,3]=>28
[3,1,6,8,2,4,5,7]=>[5,3]=>28
[3,6,1,8,2,4,5,7]=>[5,3]=>28
[3,6,8,1,2,4,5,7]=>[5,3]=>28
[3,1,6,2,4,8,5,7]=>[5,3]=>28
[3,6,1,2,4,8,5,7]=>[5,3]=>28
[1,3,2,6,4,8,5,7]=>[5,3]=>28
[1,3,6,2,4,8,5,7]=>[5,3]=>28
[3,1,2,6,8,4,5,7]=>[5,3]=>28
[1,3,2,6,8,4,5,7]=>[5,3]=>28
[3,1,6,2,4,5,8,7]=>[5,3]=>28
[3,6,1,2,4,5,8,7]=>[5,3]=>28
[3,1,2,6,4,5,8,7]=>[5,3]=>28
[1,3,6,2,4,5,8,7]=>[5,3]=>28
[3,1,2,4,6,5,8,7]=>[5,3]=>28
[1,3,4,6,2,5,8,7]=>[5,3]=>28
[1,3,2,4,6,8,5,7]=>[5,3]=>28
[1,3,4,6,8,2,5,7]=>[5,3]=>28
[3,6,1,2,4,5,7,8]=>[6,2]=>20
[1,3,2,6,4,5,7,8]=>[6,2]=>20
[1,3,6,2,4,5,7,8]=>[6,2]=>20
[1,3,4,6,2,5,7,8]=>[6,2]=>20
[1,3,4,6,2,7,5,8]=>[6,2]=>20
[1,3,4,6,7,2,5,8]=>[6,2]=>20
[3,1,2,4,6,7,8,5]=>[6,2]=>20
[1,3,4,6,7,2,8,5]=>[6,2]=>20
[3,1,7,2,8,4,5,6]=>[5,3]=>28
[3,7,1,2,8,4,5,6]=>[5,3]=>28
[3,1,7,8,2,4,5,6]=>[5,3]=>28
[3,7,1,8,2,4,5,6]=>[5,3]=>28
[3,7,8,1,2,4,5,6]=>[5,3]=>28
[3,7,1,2,4,8,5,6]=>[5,3]=>28
[3,1,2,7,4,8,5,6]=>[5,3]=>28
[1,3,2,7,4,8,5,6]=>[5,3]=>28
[1,3,7,2,4,8,5,6]=>[5,3]=>28
[3,1,2,7,8,4,5,6]=>[5,3]=>28
[1,3,7,2,8,4,5,6]=>[5,3]=>28
[1,3,7,8,2,4,5,6]=>[5,3]=>28
[3,1,7,2,4,5,8,6]=>[5,3]=>28
[3,7,1,2,4,5,8,6]=>[5,3]=>28
[1,3,7,2,4,5,8,6]=>[5,3]=>28
[3,1,2,4,7,5,8,6]=>[5,3]=>28
[1,3,2,4,7,5,8,6]=>[5,3]=>28
[1,3,4,2,7,5,8,6]=>[5,3]=>28
[3,1,2,4,7,8,5,6]=>[5,3]=>28
[1,3,2,4,7,8,5,6]=>[5,3]=>28
[1,3,4,2,7,8,5,6]=>[5,3]=>28
[1,3,4,7,8,2,5,6]=>[5,3]=>28
[3,1,7,2,4,5,6,8]=>[6,2]=>20
[3,7,1,2,4,5,6,8]=>[6,2]=>20
[3,1,2,7,4,5,6,8]=>[6,2]=>20
[1,3,2,7,4,5,6,8]=>[6,2]=>20
[1,3,7,2,4,5,6,8]=>[6,2]=>20
[3,1,2,4,7,5,6,8]=>[6,2]=>20
[1,3,4,7,2,5,6,8]=>[6,2]=>20
[3,1,2,4,5,7,6,8]=>[6,2]=>20
[3,1,2,4,5,7,8,6]=>[6,2]=>20
[1,3,4,5,7,8,2,6]=>[6,2]=>20
[3,1,8,2,4,5,6,7]=>[6,2]=>20
[3,8,1,2,4,5,6,7]=>[6,2]=>20
[3,1,2,8,4,5,6,7]=>[6,2]=>20
[1,3,2,8,4,5,6,7]=>[6,2]=>20
[1,3,8,2,4,5,6,7]=>[6,2]=>20
[3,1,2,4,8,5,6,7]=>[6,2]=>20
[1,3,2,4,8,5,6,7]=>[6,2]=>20
[1,3,4,2,8,5,6,7]=>[6,2]=>20
[1,3,4,8,2,5,6,7]=>[6,2]=>20
[3,1,2,4,5,8,6,7]=>[6,2]=>20
[1,3,2,4,5,8,6,7]=>[6,2]=>20
[1,3,4,2,5,8,6,7]=>[6,2]=>20
[1,3,4,5,2,8,6,7]=>[6,2]=>20
[1,3,4,5,8,2,6,7]=>[6,2]=>20
[3,1,2,4,5,6,8,7]=>[6,2]=>20
[1,3,4,5,6,8,2,7]=>[6,2]=>20
[4,1,5,2,6,3,8,7]=>[4,4]=>14
[4,5,1,2,6,3,8,7]=>[4,4]=>14
[4,1,5,6,2,3,8,7]=>[4,4]=>14
[4,5,1,6,2,3,8,7]=>[4,4]=>14
[4,5,6,1,2,3,8,7]=>[4,4]=>14
[4,1,5,2,6,8,3,7]=>[4,4]=>14
[4,5,1,2,6,8,3,7]=>[4,4]=>14
[4,1,5,6,2,8,3,7]=>[4,4]=>14
[4,5,6,1,2,8,3,7]=>[4,4]=>14
[4,1,5,6,8,2,3,7]=>[4,4]=>14
[4,5,1,6,8,2,3,7]=>[4,4]=>14
[4,5,6,1,8,2,3,7]=>[4,4]=>14
[4,5,6,8,1,2,3,7]=>[4,4]=>14
[4,1,5,2,6,3,7,8]=>[5,3]=>28
[4,1,5,6,2,3,7,8]=>[5,3]=>28
[4,5,1,6,2,3,7,8]=>[5,3]=>28
[4,5,1,2,6,7,3,8]=>[5,3]=>28
[4,5,1,6,2,7,3,8]=>[5,3]=>28
[4,5,6,1,2,7,3,8]=>[5,3]=>28
[4,5,6,1,7,2,3,8]=>[5,3]=>28
[4,1,5,2,6,7,8,3]=>[5,3]=>28
[4,5,1,2,6,7,8,3]=>[5,3]=>28
[4,5,1,6,2,7,8,3]=>[5,3]=>28
[4,5,6,1,2,7,8,3]=>[5,3]=>28
[4,1,5,6,7,2,8,3]=>[5,3]=>28
[4,5,1,6,7,2,8,3]=>[5,3]=>28
[4,5,6,1,7,2,8,3]=>[5,3]=>28
[4,5,6,7,1,2,8,3]=>[5,3]=>28
[4,1,5,6,7,8,2,3]=>[5,3]=>28
[4,5,1,6,7,8,2,3]=>[5,3]=>28
[4,5,6,1,7,8,2,3]=>[5,3]=>28
[4,5,6,7,1,8,2,3]=>[5,3]=>28
[4,1,5,2,7,3,8,6]=>[4,4]=>14
[4,5,1,7,2,3,8,6]=>[4,4]=>14
[4,1,5,2,7,8,3,6]=>[4,4]=>14
[4,5,1,2,7,8,3,6]=>[4,4]=>14
[4,1,5,7,2,8,3,6]=>[4,4]=>14
[4,5,1,7,2,8,3,6]=>[4,4]=>14
[4,5,7,1,2,8,3,6]=>[4,4]=>14
[4,5,7,8,1,2,3,6]=>[4,4]=>14
[4,1,5,2,7,3,6,8]=>[5,3]=>28
[4,5,1,2,7,3,6,8]=>[5,3]=>28
[4,1,5,2,3,7,6,8]=>[5,3]=>28
[4,5,1,2,3,7,6,8]=>[5,3]=>28
[4,1,2,5,3,7,6,8]=>[5,3]=>28
[1,4,2,5,3,7,6,8]=>[5,3]=>28
[1,4,5,2,3,7,6,8]=>[5,3]=>28
[4,1,2,5,7,3,6,8]=>[5,3]=>28
[1,4,5,2,7,3,6,8]=>[5,3]=>28
[1,4,5,7,2,3,6,8]=>[5,3]=>28
[4,1,5,2,3,7,8,6]=>[5,3]=>28
[4,1,2,5,3,7,8,6]=>[5,3]=>28
[1,4,5,2,3,7,8,6]=>[5,3]=>28
[4,1,2,5,7,3,8,6]=>[5,3]=>28
[1,4,2,5,7,3,8,6]=>[5,3]=>28
[1,4,5,2,7,3,8,6]=>[5,3]=>28
[1,4,5,7,2,3,8,6]=>[5,3]=>28
[4,1,2,5,7,8,3,6]=>[5,3]=>28
[1,4,2,5,7,8,3,6]=>[5,3]=>28
[1,4,5,2,7,8,3,6]=>[5,3]=>28
[1,4,5,7,8,2,3,6]=>[5,3]=>28
[4,1,5,2,8,3,6,7]=>[5,3]=>28
[4,5,1,2,8,3,6,7]=>[5,3]=>28
[4,5,1,8,2,3,6,7]=>[5,3]=>28
[4,5,8,1,2,3,6,7]=>[5,3]=>28
[4,1,5,2,3,8,6,7]=>[5,3]=>28
[4,5,1,2,3,8,6,7]=>[5,3]=>28
[4,1,2,5,3,8,6,7]=>[5,3]=>28
[1,4,2,5,3,8,6,7]=>[5,3]=>28
[1,4,5,2,3,8,6,7]=>[5,3]=>28
[4,1,2,5,8,3,6,7]=>[5,3]=>28
[1,4,5,2,8,3,6,7]=>[5,3]=>28
[1,4,2,5,3,6,8,7]=>[5,3]=>28
[4,1,2,5,6,3,8,7]=>[5,3]=>28
[1,4,5,2,6,3,8,7]=>[5,3]=>28
[4,1,2,5,6,8,3,7]=>[5,3]=>28
[1,4,2,5,6,8,3,7]=>[5,3]=>28
[1,4,5,2,6,8,3,7]=>[5,3]=>28
[1,4,5,6,8,2,3,7]=>[5,3]=>28
[4,1,5,2,3,6,7,8]=>[6,2]=>20
[4,1,2,5,3,6,7,8]=>[6,2]=>20
[1,4,2,5,3,6,7,8]=>[6,2]=>20
[1,4,5,2,3,6,7,8]=>[6,2]=>20
[4,1,2,5,6,3,7,8]=>[6,2]=>20
[1,4,5,2,6,3,7,8]=>[6,2]=>20
[1,4,5,6,2,3,7,8]=>[6,2]=>20
[4,1,2,5,6,7,3,8]=>[6,2]=>20
[1,4,2,5,6,7,3,8]=>[6,2]=>20
[1,4,5,2,6,7,3,8]=>[6,2]=>20
[1,4,5,6,2,7,3,8]=>[6,2]=>20
[1,4,5,6,7,2,3,8]=>[6,2]=>20
[4,1,2,5,6,7,8,3]=>[6,2]=>20
[1,4,2,5,6,7,8,3]=>[6,2]=>20
[1,4,5,2,6,7,8,3]=>[6,2]=>20
[1,4,5,6,2,7,8,3]=>[6,2]=>20
[1,4,5,6,7,2,8,3]=>[6,2]=>20
[1,4,5,6,7,8,2,3]=>[6,2]=>20
[4,1,6,2,7,3,8,5]=>[4,4]=>14
[4,1,6,7,2,3,8,5]=>[4,4]=>14
[4,6,7,1,2,3,8,5]=>[4,4]=>14
[4,6,1,2,7,8,3,5]=>[4,4]=>14
[4,6,1,7,2,8,3,5]=>[4,4]=>14
[4,6,7,1,2,8,3,5]=>[4,4]=>14
[4,1,6,7,8,2,3,5]=>[4,4]=>14
[4,6,1,7,8,2,3,5]=>[4,4]=>14
[4,6,7,1,8,2,3,5]=>[4,4]=>14
[4,6,7,8,1,2,3,5]=>[4,4]=>14
[4,1,6,2,7,3,5,8]=>[5,3]=>28
[4,1,6,7,2,3,5,8]=>[5,3]=>28
[4,6,1,7,2,3,5,8]=>[5,3]=>28
[4,6,7,1,2,3,5,8]=>[5,3]=>28
[4,1,6,2,3,7,5,8]=>[5,3]=>28
[4,1,2,6,3,7,5,8]=>[5,3]=>28
[1,4,2,6,3,7,5,8]=>[5,3]=>28
[4,1,2,6,7,3,5,8]=>[5,3]=>28
[1,4,2,6,7,3,5,8]=>[5,3]=>28
[1,4,6,2,7,3,5,8]=>[5,3]=>28
[1,4,6,7,2,3,5,8]=>[5,3]=>28
[4,1,6,2,3,7,8,5]=>[5,3]=>28
[4,1,2,6,3,7,8,5]=>[5,3]=>28
[1,4,6,2,3,7,8,5]=>[5,3]=>28
[4,1,2,6,7,3,8,5]=>[5,3]=>28
[1,4,6,2,7,3,8,5]=>[5,3]=>28
[1,4,2,6,7,8,3,5]=>[5,3]=>28
[1,4,6,2,7,8,3,5]=>[5,3]=>28
[1,4,6,7,2,8,3,5]=>[5,3]=>28
[1,4,6,7,8,2,3,5]=>[5,3]=>28
[4,1,6,2,8,3,5,7]=>[5,3]=>28
[4,6,1,2,8,3,5,7]=>[5,3]=>28
[4,1,6,8,2,3,5,7]=>[5,3]=>28
[4,6,1,8,2,3,5,7]=>[5,3]=>28
[4,6,8,1,2,3,5,7]=>[5,3]=>28
[4,1,6,2,3,8,5,7]=>[5,3]=>28
[4,1,2,6,3,8,5,7]=>[5,3]=>28
[1,4,2,6,3,8,5,7]=>[5,3]=>28
[1,4,6,2,3,8,5,7]=>[5,3]=>28
[1,4,2,6,8,3,5,7]=>[5,3]=>28
[1,4,6,2,8,3,5,7]=>[5,3]=>28
[1,4,6,8,2,3,5,7]=>[5,3]=>28
[4,1,6,2,3,5,8,7]=>[5,3]=>28
[4,6,1,2,3,5,8,7]=>[5,3]=>28
[4,1,2,6,3,5,8,7]=>[5,3]=>28
[1,4,2,6,3,5,8,7]=>[5,3]=>28
[1,4,6,2,3,5,8,7]=>[5,3]=>28
[4,1,2,3,6,5,8,7]=>[5,3]=>28
[1,4,2,3,6,5,8,7]=>[5,3]=>28
[1,2,4,6,3,5,8,7]=>[5,3]=>28
[4,1,2,3,6,8,5,7]=>[5,3]=>28
[1,2,4,6,8,3,5,7]=>[5,3]=>28
[4,1,6,2,3,5,7,8]=>[6,2]=>20
[4,6,1,2,3,5,7,8]=>[6,2]=>20
[1,4,2,6,3,5,7,8]=>[6,2]=>20
[1,4,6,2,3,5,7,8]=>[6,2]=>20
[4,1,2,3,6,5,7,8]=>[6,2]=>20
[1,4,2,3,6,5,7,8]=>[6,2]=>20
[1,2,4,6,3,5,7,8]=>[6,2]=>20
[4,1,2,3,6,7,5,8]=>[6,2]=>20
[1,4,2,3,6,7,5,8]=>[6,2]=>20
[4,1,2,3,6,7,8,5]=>[6,2]=>20
[1,4,2,3,6,7,8,5]=>[6,2]=>20
[4,1,7,2,8,3,5,6]=>[5,3]=>28
[4,7,1,2,8,3,5,6]=>[5,3]=>28
[4,1,7,8,2,3,5,6]=>[5,3]=>28
[4,7,1,8,2,3,5,6]=>[5,3]=>28
[4,1,7,2,3,8,5,6]=>[5,3]=>28
[4,7,1,2,3,8,5,6]=>[5,3]=>28
[1,4,2,7,3,8,5,6]=>[5,3]=>28
[1,4,7,2,3,8,5,6]=>[5,3]=>28
[4,1,2,7,8,3,5,6]=>[5,3]=>28
[1,4,2,7,8,3,5,6]=>[5,3]=>28
[1,4,7,2,8,3,5,6]=>[5,3]=>28
[1,4,7,8,2,3,5,6]=>[5,3]=>28
[4,1,7,2,3,5,8,6]=>[5,3]=>28
[4,7,1,2,3,5,8,6]=>[5,3]=>28
[4,1,2,7,3,5,8,6]=>[5,3]=>28
[1,4,2,7,3,5,8,6]=>[5,3]=>28
[1,4,7,2,3,5,8,6]=>[5,3]=>28
[4,1,2,3,7,5,8,6]=>[5,3]=>28
[1,4,2,3,7,5,8,6]=>[5,3]=>28
[1,2,4,7,3,5,8,6]=>[5,3]=>28
[4,1,2,3,7,8,5,6]=>[5,3]=>28
[1,4,2,3,7,8,5,6]=>[5,3]=>28
[1,2,4,3,7,8,5,6]=>[5,3]=>28
[1,2,4,7,3,8,5,6]=>[5,3]=>28
[1,2,4,7,8,3,5,6]=>[5,3]=>28
[4,1,7,2,3,5,6,8]=>[6,2]=>20
[4,7,1,2,3,5,6,8]=>[6,2]=>20
[4,1,2,7,3,5,6,8]=>[6,2]=>20
[1,4,2,7,3,5,6,8]=>[6,2]=>20
[1,4,7,2,3,5,6,8]=>[6,2]=>20
[4,1,2,3,7,5,6,8]=>[6,2]=>20
[1,4,2,3,7,5,6,8]=>[6,2]=>20
[1,2,4,3,7,5,6,8]=>[6,2]=>20
[1,2,4,7,3,5,6,8]=>[6,2]=>20
[4,1,2,3,5,7,6,8]=>[6,2]=>20
[1,4,2,3,5,7,6,8]=>[6,2]=>20
[1,2,4,5,7,3,6,8]=>[6,2]=>20
[4,1,2,3,5,7,8,6]=>[6,2]=>20
[1,4,2,3,5,7,8,6]=>[6,2]=>20
[1,2,4,5,7,8,3,6]=>[6,2]=>20
[4,1,8,2,3,5,6,7]=>[6,2]=>20
[4,8,1,2,3,5,6,7]=>[6,2]=>20
[4,1,2,8,3,5,6,7]=>[6,2]=>20
[1,4,2,8,3,5,6,7]=>[6,2]=>20
[1,4,8,2,3,5,6,7]=>[6,2]=>20
[4,1,2,3,8,5,6,7]=>[6,2]=>20
[1,4,2,3,8,5,6,7]=>[6,2]=>20
[1,2,4,3,8,5,6,7]=>[6,2]=>20
[1,2,4,8,3,5,6,7]=>[6,2]=>20
[4,1,2,3,5,8,6,7]=>[6,2]=>20
[1,4,2,3,5,8,6,7]=>[6,2]=>20
[1,2,4,3,5,8,6,7]=>[6,2]=>20
[1,2,4,5,3,8,6,7]=>[6,2]=>20
[1,2,4,5,8,3,6,7]=>[6,2]=>20
[4,1,2,3,5,6,8,7]=>[6,2]=>20
[1,4,2,3,5,6,8,7]=>[6,2]=>20
[1,2,4,5,6,8,3,7]=>[6,2]=>20
[1,4,2,3,5,6,7,8]=>[7,1]=>7
[5,1,6,2,7,3,8,4]=>[4,4]=>14
[5,6,1,2,7,3,8,4]=>[4,4]=>14
[5,1,6,7,2,3,8,4]=>[4,4]=>14
[5,6,1,7,2,3,8,4]=>[4,4]=>14
[5,6,7,1,2,3,8,4]=>[4,4]=>14
[5,6,1,2,7,8,3,4]=>[4,4]=>14
[5,1,6,7,2,8,3,4]=>[4,4]=>14
[5,6,7,1,2,8,3,4]=>[4,4]=>14
[5,1,6,7,8,2,3,4]=>[4,4]=>14
[5,6,1,7,8,2,3,4]=>[4,4]=>14
[5,6,7,1,8,2,3,4]=>[4,4]=>14
[5,1,6,2,7,3,4,8]=>[5,3]=>28
[5,6,1,7,2,3,4,8]=>[5,3]=>28
[5,1,6,2,3,7,4,8]=>[5,3]=>28
[5,1,2,6,3,7,4,8]=>[5,3]=>28
[1,5,2,6,3,7,4,8]=>[5,3]=>28
[5,1,2,6,7,3,4,8]=>[5,3]=>28
[1,5,2,6,7,3,4,8]=>[5,3]=>28
[1,5,6,7,2,3,4,8]=>[5,3]=>28
[5,1,6,2,3,7,8,4]=>[5,3]=>28
[5,6,1,2,3,7,8,4]=>[5,3]=>28
[5,1,2,6,3,7,8,4]=>[5,3]=>28
[1,5,2,6,3,7,8,4]=>[5,3]=>28
[1,5,6,2,3,7,8,4]=>[5,3]=>28
[5,1,2,6,7,3,8,4]=>[5,3]=>28
[1,5,6,7,2,3,8,4]=>[5,3]=>28
[5,1,2,6,7,8,3,4]=>[5,3]=>28
[1,5,2,6,7,8,3,4]=>[5,3]=>28
[1,5,6,2,7,8,3,4]=>[5,3]=>28
[1,5,6,7,2,8,3,4]=>[5,3]=>28
[1,5,6,7,8,2,3,4]=>[5,3]=>28
[5,1,6,2,8,3,4,7]=>[5,3]=>28
[5,6,1,2,8,3,4,7]=>[5,3]=>28
[5,6,1,8,2,3,4,7]=>[5,3]=>28
[5,6,8,1,2,3,4,7]=>[5,3]=>28
[5,1,6,2,3,8,4,7]=>[5,3]=>28
[5,6,1,2,3,8,4,7]=>[5,3]=>28
[5,1,2,6,3,8,4,7]=>[5,3]=>28
[1,5,2,6,3,8,4,7]=>[5,3]=>28
[1,5,6,2,3,8,4,7]=>[5,3]=>28
[5,1,2,6,8,3,4,7]=>[5,3]=>28
[1,5,2,6,8,3,4,7]=>[5,3]=>28
[1,5,6,2,8,3,4,7]=>[5,3]=>28
[1,5,6,8,2,3,4,7]=>[5,3]=>28
[5,1,6,2,3,4,8,7]=>[5,3]=>28
[5,6,1,2,3,4,8,7]=>[5,3]=>28
[1,5,2,6,3,4,8,7]=>[5,3]=>28
[1,5,6,2,3,4,8,7]=>[5,3]=>28
[1,5,2,3,6,4,8,7]=>[5,3]=>28
[1,2,5,3,6,4,8,7]=>[5,3]=>28
[5,1,2,3,6,8,4,7]=>[5,3]=>28
[1,5,2,3,6,8,4,7]=>[5,3]=>28
[1,2,5,6,3,8,4,7]=>[5,3]=>28
[5,1,6,2,3,4,7,8]=>[6,2]=>20
[5,1,2,6,3,4,7,8]=>[6,2]=>20
[1,5,2,6,3,4,7,8]=>[6,2]=>20
[1,5,6,2,3,4,7,8]=>[6,2]=>20
[5,1,2,3,6,4,7,8]=>[6,2]=>20
[1,5,2,3,6,4,7,8]=>[6,2]=>20
[1,2,5,3,6,4,7,8]=>[6,2]=>20
[1,2,5,6,3,4,7,8]=>[6,2]=>20
[5,1,2,3,6,7,4,8]=>[6,2]=>20
[1,5,2,3,6,7,4,8]=>[6,2]=>20
[1,2,5,6,3,7,4,8]=>[6,2]=>20
[5,1,2,3,6,7,8,4]=>[6,2]=>20
[1,5,2,3,6,7,8,4]=>[6,2]=>20
[1,2,5,3,6,7,8,4]=>[6,2]=>20
[1,2,5,6,3,7,8,4]=>[6,2]=>20
[1,2,5,6,7,3,8,4]=>[6,2]=>20
[1,2,5,6,7,8,3,4]=>[6,2]=>20
[5,1,7,2,8,3,4,6]=>[5,3]=>28
[5,7,1,2,8,3,4,6]=>[5,3]=>28
[5,1,7,8,2,3,4,6]=>[5,3]=>28
[5,7,1,8,2,3,4,6]=>[5,3]=>28
[5,7,8,1,2,3,4,6]=>[5,3]=>28
[5,1,2,7,3,8,4,6]=>[5,3]=>28
[1,5,2,7,3,8,4,6]=>[5,3]=>28
[1,5,7,2,3,8,4,6]=>[5,3]=>28
[5,1,2,7,8,3,4,6]=>[5,3]=>28
[1,5,2,7,8,3,4,6]=>[5,3]=>28
[1,5,7,2,8,3,4,6]=>[5,3]=>28
[1,5,7,8,2,3,4,6]=>[5,3]=>28
[5,1,7,2,3,4,8,6]=>[5,3]=>28
[5,7,1,2,3,4,8,6]=>[5,3]=>28
[5,1,2,7,3,4,8,6]=>[5,3]=>28
[1,5,2,7,3,4,8,6]=>[5,3]=>28
[1,5,7,2,3,4,8,6]=>[5,3]=>28
[5,1,2,3,7,4,8,6]=>[5,3]=>28
[1,5,2,3,7,4,8,6]=>[5,3]=>28
[1,2,5,3,7,4,8,6]=>[5,3]=>28
[5,1,2,3,7,8,4,6]=>[5,3]=>28
[1,5,2,3,7,8,4,6]=>[5,3]=>28
[1,2,5,7,3,8,4,6]=>[5,3]=>28
[1,2,5,7,8,3,4,6]=>[5,3]=>28
[5,1,7,2,3,4,6,8]=>[6,2]=>20
[5,7,1,2,3,4,6,8]=>[6,2]=>20
[1,5,2,7,3,4,6,8]=>[6,2]=>20
[1,5,2,3,7,4,6,8]=>[6,2]=>20
[1,2,5,3,7,4,6,8]=>[6,2]=>20
[1,2,5,7,3,4,6,8]=>[6,2]=>20
[1,5,2,3,4,7,6,8]=>[6,2]=>20
[1,2,5,3,4,7,6,8]=>[6,2]=>20
[1,2,3,5,7,4,6,8]=>[6,2]=>20
[5,1,2,3,4,7,8,6]=>[6,2]=>20
[1,5,2,3,4,7,8,6]=>[6,2]=>20
[1,2,5,3,4,7,8,6]=>[6,2]=>20
[1,2,3,5,7,4,8,6]=>[6,2]=>20
[1,2,3,5,7,8,4,6]=>[6,2]=>20
[5,8,1,2,3,4,6,7]=>[6,2]=>20
[5,1,2,8,3,4,6,7]=>[6,2]=>20
[1,5,2,8,3,4,6,7]=>[6,2]=>20
[1,5,8,2,3,4,6,7]=>[6,2]=>20
[5,1,2,3,8,4,6,7]=>[6,2]=>20
[1,5,2,3,8,4,6,7]=>[6,2]=>20
[1,2,5,3,8,4,6,7]=>[6,2]=>20
[1,2,5,8,3,4,6,7]=>[6,2]=>20
[5,1,2,3,4,8,6,7]=>[6,2]=>20
[1,5,2,3,4,8,6,7]=>[6,2]=>20
[1,2,5,3,4,8,6,7]=>[6,2]=>20
[1,2,3,5,4,8,6,7]=>[6,2]=>20
[1,2,3,5,8,4,6,7]=>[6,2]=>20
[5,1,2,3,4,6,8,7]=>[6,2]=>20
[1,5,2,3,4,6,8,7]=>[6,2]=>20
[1,2,5,3,4,6,8,7]=>[6,2]=>20
[1,2,3,5,6,8,4,7]=>[6,2]=>20
[1,5,2,3,4,6,7,8]=>[7,1]=>7
[1,2,5,3,4,6,7,8]=>[7,1]=>7
[6,1,7,2,8,3,4,5]=>[5,3]=>28
[6,7,1,2,8,3,4,5]=>[5,3]=>28
[6,1,7,8,2,3,4,5]=>[5,3]=>28
[6,7,1,8,2,3,4,5]=>[5,3]=>28
[6,1,7,2,3,8,4,5]=>[5,3]=>28
[6,7,1,2,3,8,4,5]=>[5,3]=>28
[6,1,2,7,3,8,4,5]=>[5,3]=>28
[1,6,2,7,3,8,4,5]=>[5,3]=>28
[1,6,7,2,3,8,4,5]=>[5,3]=>28
[6,1,2,7,8,3,4,5]=>[5,3]=>28
[1,6,2,7,8,3,4,5]=>[5,3]=>28
[1,6,7,2,8,3,4,5]=>[5,3]=>28
[1,6,7,8,2,3,4,5]=>[5,3]=>28
[6,1,7,2,3,4,8,5]=>[5,3]=>28
[6,7,1,2,3,4,8,5]=>[5,3]=>28
[6,1,2,7,3,4,8,5]=>[5,3]=>28
[1,6,2,7,3,4,8,5]=>[5,3]=>28
[6,1,2,3,7,4,8,5]=>[5,3]=>28
[1,6,2,3,7,4,8,5]=>[5,3]=>28
[1,2,6,3,7,4,8,5]=>[5,3]=>28
[6,1,2,3,7,8,4,5]=>[5,3]=>28
[1,6,2,3,7,8,4,5]=>[5,3]=>28
[1,2,6,3,7,8,4,5]=>[5,3]=>28
[1,2,6,7,3,8,4,5]=>[5,3]=>28
[1,2,6,7,8,3,4,5]=>[5,3]=>28
[6,1,7,2,3,4,5,8]=>[6,2]=>20
[6,1,2,7,3,4,5,8]=>[6,2]=>20
[1,6,2,7,3,4,5,8]=>[6,2]=>20
[1,6,7,2,3,4,5,8]=>[6,2]=>20
[6,1,2,3,7,4,5,8]=>[6,2]=>20
[1,6,2,3,7,4,5,8]=>[6,2]=>20
[1,2,6,3,7,4,5,8]=>[6,2]=>20
[1,2,6,7,3,4,5,8]=>[6,2]=>20
[6,1,2,3,4,7,5,8]=>[6,2]=>20
[1,6,2,3,4,7,5,8]=>[6,2]=>20
[1,2,6,3,4,7,5,8]=>[6,2]=>20
[1,2,3,6,4,7,5,8]=>[6,2]=>20
[1,2,3,6,7,4,5,8]=>[6,2]=>20
[6,1,2,3,4,7,8,5]=>[6,2]=>20
[1,6,2,3,4,7,8,5]=>[6,2]=>20
[1,2,6,3,4,7,8,5]=>[6,2]=>20
[1,2,3,6,4,7,8,5]=>[6,2]=>20
[1,2,3,6,7,4,8,5]=>[6,2]=>20
[1,2,3,6,7,8,4,5]=>[6,2]=>20
[6,1,8,2,3,4,5,7]=>[6,2]=>20
[6,8,1,2,3,4,5,7]=>[6,2]=>20
[6,1,2,8,3,4,5,7]=>[6,2]=>20
[1,6,2,8,3,4,5,7]=>[6,2]=>20
[1,6,8,2,3,4,5,7]=>[6,2]=>20
[6,1,2,3,8,4,5,7]=>[6,2]=>20
[1,6,2,3,8,4,5,7]=>[6,2]=>20
[1,2,6,3,8,4,5,7]=>[6,2]=>20
[1,2,6,8,3,4,5,7]=>[6,2]=>20
[6,1,2,3,4,8,5,7]=>[6,2]=>20
[1,6,2,3,4,8,5,7]=>[6,2]=>20
[1,2,6,3,4,8,5,7]=>[6,2]=>20
[1,2,3,6,4,8,5,7]=>[6,2]=>20
[1,2,3,6,8,4,5,7]=>[6,2]=>20
[6,1,2,3,4,5,8,7]=>[6,2]=>20
[1,6,2,3,4,5,8,7]=>[6,2]=>20
[1,2,6,3,4,5,8,7]=>[6,2]=>20
[1,2,3,6,4,5,8,7]=>[6,2]=>20
[1,2,3,4,6,8,5,7]=>[6,2]=>20
[1,6,2,3,4,5,7,8]=>[7,1]=>7
[1,2,6,3,4,5,7,8]=>[7,1]=>7
[1,2,3,6,4,5,7,8]=>[7,1]=>7
[7,1,8,2,3,4,5,6]=>[6,2]=>20
[7,1,2,8,3,4,5,6]=>[6,2]=>20
[1,7,2,8,3,4,5,6]=>[6,2]=>20
[1,7,8,2,3,4,5,6]=>[6,2]=>20
[7,1,2,3,8,4,5,6]=>[6,2]=>20
[1,7,2,3,8,4,5,6]=>[6,2]=>20
[1,2,7,3,8,4,5,6]=>[6,2]=>20
[1,2,7,8,3,4,5,6]=>[6,2]=>20
[7,1,2,3,4,8,5,6]=>[6,2]=>20
[1,7,2,3,4,8,5,6]=>[6,2]=>20
[1,2,7,3,4,8,5,6]=>[6,2]=>20
[1,2,3,7,4,8,5,6]=>[6,2]=>20
[1,2,3,7,8,4,5,6]=>[6,2]=>20
[7,1,2,3,4,5,8,6]=>[6,2]=>20
[1,7,2,3,4,5,8,6]=>[6,2]=>20
[1,2,7,3,4,5,8,6]=>[6,2]=>20
[1,2,3,7,4,5,8,6]=>[6,2]=>20
[1,2,3,4,7,5,8,6]=>[6,2]=>20
[1,2,3,4,7,8,5,6]=>[6,2]=>20
[1,7,2,3,4,5,6,8]=>[7,1]=>7
[1,2,7,3,4,5,6,8]=>[7,1]=>7
[1,2,3,7,4,5,6,8]=>[7,1]=>7
[1,2,3,4,7,5,6,8]=>[7,1]=>7
[1,8,2,3,4,5,6,7]=>[7,1]=>7
[1,2,8,3,4,5,6,7]=>[7,1]=>7
[1,2,3,8,4,5,6,7]=>[7,1]=>7
[1,2,3,4,8,5,6,7]=>[7,1]=>7
[1,2,3,4,5,8,6,7]=>[7,1]=>7
[5,3,2,6,1,4,8,7]=>[3,3,1,1]=>56
[7,3,2,5,4,8,1,6]=>[3,3,1,1]=>56
[8,4,5,2,3,7,6,1]=>[3,3,1,1]=>56
[7,4,5,2,3,8,1,6]=>[3,3,1,1]=>56
[6,4,5,2,3,1,8,7]=>[3,3,1,1]=>56
[5,4,6,2,1,3,8,7]=>[3,3,1,1]=>56
[3,6,1,5,4,2,8,7]=>[3,3,1,1]=>56
[4,6,5,1,3,2,8,7]=>[3,3,1,1]=>56
[5,6,4,3,1,2,8,7]=>[3,3,1,1]=>56
[7,5,4,3,2,8,1,6]=>[2,2,1,1,1,1]=>20
[8,6,4,3,7,2,5,1]=>[2,2,1,1,1,1]=>20
[7,6,4,3,8,2,1,5]=>[2,2,1,1,1,1]=>20
[6,7,4,3,8,1,2,5]=>[3,3,1,1]=>56
[5,7,4,3,1,8,2,6]=>[3,3,1,1]=>56
[4,7,5,1,3,8,2,6]=>[3,3,1,1]=>56
[3,7,1,5,4,8,2,6]=>[3,3,1,1]=>56
[2,1,7,5,4,8,3,6]=>[3,3,1,1]=>56
[3,8,1,5,4,7,6,2]=>[3,3,1,1]=>56
[4,8,5,1,3,7,6,2]=>[3,3,1,1]=>56
[5,8,4,3,1,7,6,2]=>[2,2,2,2]=>14
[6,8,4,3,7,1,5,2]=>[2,2,2,2]=>14
[7,8,4,3,6,5,1,2]=>[2,2,2,2]=>14
[6,8,5,7,3,1,4,2]=>[2,2,2,2]=>14
[5,8,6,7,1,3,4,2]=>[3,3,1,1]=>56
[4,8,6,1,7,3,5,2]=>[3,3,1,1]=>56
[3,8,1,6,7,4,5,2]=>[3,3,1,1]=>56
[2,1,8,6,7,4,5,3]=>[3,3,1,1]=>56
[2,1,7,6,8,4,3,5]=>[3,3,1,1]=>56
[3,7,1,6,8,4,2,5]=>[3,3,1,1]=>56
[4,7,6,1,8,3,2,5]=>[3,3,1,1]=>56
[5,7,6,8,1,3,2,4]=>[3,3,1,1]=>56
[5,4,7,2,1,8,3,6]=>[3,3,1,1]=>56
[6,4,7,2,8,1,3,5]=>[3,3,1,1]=>56
[7,4,6,2,8,3,1,5]=>[3,3,1,1]=>56
[8,4,6,2,7,3,5,1]=>[3,3,1,1]=>56
[8,3,2,6,7,4,5,1]=>[3,3,1,1]=>56
[7,3,2,6,8,4,1,5]=>[3,3,1,1]=>56
[6,3,2,7,8,1,4,5]=>[3,3,1,1]=>56
[5,3,2,7,1,8,4,6]=>[3,3,1,1]=>56
[4,3,2,1,7,8,5,6]=>[3,3,1,1]=>56
[3,4,1,2,8,7,6,5]=>[3,3,1,1]=>56
[5,3,2,8,1,7,6,4]=>[2,2,2,2]=>14
[6,3,2,8,7,1,5,4]=>[2,2,2,2]=>14
[7,3,2,8,6,5,1,4]=>[2,2,2,2]=>14
[8,4,7,2,6,5,3,1]=>[2,2,1,1,1,1]=>20
[7,4,8,2,6,5,1,3]=>[2,2,2,2]=>14
[6,4,8,2,7,1,5,3]=>[2,2,2,2]=>14
[5,4,8,2,1,7,6,3]=>[2,2,2,2]=>14
[4,5,8,1,2,7,6,3]=>[3,3,1,1]=>56
[3,5,1,8,2,7,6,4]=>[3,3,1,1]=>56
[2,1,5,8,3,7,6,4]=>[3,3,1,1]=>56
[2,1,6,8,7,3,5,4]=>[3,3,1,1]=>56
[3,6,1,8,7,2,5,4]=>[3,3,1,1]=>56
[4,6,8,1,7,2,5,3]=>[3,3,1,1]=>56
[5,6,8,7,1,2,4,3]=>[3,3,1,1]=>56
[6,5,8,7,2,1,4,3]=>[2,2,2,2]=>14
[7,5,8,6,2,4,1,3]=>[2,2,2,2]=>14
[8,5,7,6,2,4,3,1]=>[2,2,1,1,1,1]=>20
[5,7,8,6,1,4,2,3]=>[3,3,1,1]=>56
[4,7,8,1,6,5,2,3]=>[3,3,1,1]=>56
[3,7,1,8,6,5,2,4]=>[3,3,1,1]=>56
[2,1,7,8,6,5,3,4]=>[3,3,1,1]=>56
[3,8,1,7,6,5,4,2]=>[2,2,1,1,1,1]=>20
[4,8,7,1,6,5,3,2]=>[2,2,1,1,1,1]=>20
[5,8,7,6,1,4,3,2]=>[2,2,1,1,1,1]=>20
[6,8,7,5,4,1,3,2]=>[2,2,1,1,1,1]=>20
[2,1,4,3,6,5,8,7,10,9]=>[5,5]=>42
[3,4,1,2,6,5,8,7,10,9]=>[5,5]=>42
[4,3,2,1,6,5,8,7,10,9]=>[4,4,1,1]=>300
[6,3,2,5,4,1,8,7,10,9]=>[4,4,1,1]=>300
[8,3,2,5,4,7,6,1,10,9]=>[4,4,1,1]=>300
[10,3,2,5,4,7,6,9,8,1]=>[4,4,1,1]=>300
[4,5,6,1,2,3,8,7,10,9]=>[5,5]=>42
[3,5,1,6,2,4,8,7,10,9]=>[5,5]=>42
[2,1,5,6,3,4,8,7,10,9]=>[5,5]=>42
[2,1,6,5,4,3,8,7,10,9]=>[4,4,1,1]=>300
[6,5,4,3,2,1,8,7,10,9]=>[3,3,1,1,1,1]=>225
[8,5,4,3,2,7,6,1,10,9]=>[3,3,1,1,1,1]=>225
[10,5,4,3,2,7,6,9,8,1]=>[3,3,1,1,1,1]=>225
[2,1,8,5,4,7,6,3,10,9]=>[4,4,1,1]=>300
[8,7,4,3,6,5,2,1,10,9]=>[3,3,1,1,1,1]=>225
[10,7,4,3,6,5,2,9,8,1]=>[3,3,1,1,1,1]=>225
[2,1,10,5,4,7,6,9,8,3]=>[4,4,1,1]=>300
[10,9,4,3,6,5,8,7,2,1]=>[3,3,1,1,1,1]=>225
[5,6,7,8,1,2,3,4,10,9]=>[5,5]=>42
[4,6,7,1,8,2,3,5,10,9]=>[5,5]=>42
[3,6,1,7,8,2,4,5,10,9]=>[5,5]=>42
[2,1,6,7,8,3,4,5,10,9]=>[5,5]=>42
[2,1,5,7,3,8,4,6,10,9]=>[5,5]=>42
[3,5,1,7,2,8,4,6,10,9]=>[5,5]=>42
[4,5,7,1,2,8,3,6,10,9]=>[5,5]=>42
[3,4,1,2,7,8,5,6,10,9]=>[5,5]=>42
[2,1,4,3,7,8,5,6,10,9]=>[5,5]=>42
[2,1,4,3,8,7,6,5,10,9]=>[4,4,1,1]=>300
[4,3,2,1,8,7,6,5,10,9]=>[3,3,2,2]=>252
[8,3,2,7,6,5,4,1,10,9]=>[3,3,1,1,1,1]=>225
[10,3,2,7,6,5,4,9,8,1]=>[3,3,1,1,1,1]=>225
[2,1,8,7,6,5,4,3,10,9]=>[3,3,1,1,1,1]=>225
[8,7,6,5,4,3,2,1,10,9]=>[2,2,1,1,1,1,1,1]=>35
[10,7,6,5,4,3,2,9,8,1]=>[2,2,1,1,1,1,1,1]=>35
[2,1,10,7,6,5,4,9,8,3]=>[3,3,1,1,1,1]=>225
[10,9,6,5,4,3,8,7,2,1]=>[2,2,1,1,1,1,1,1]=>35
[2,1,4,3,10,7,6,9,8,5]=>[4,4,1,1]=>300
[4,3,2,1,10,7,6,9,8,5]=>[3,3,2,2]=>252
[10,3,2,9,6,5,8,7,4,1]=>[3,3,1,1,1,1]=>225
[2,1,10,9,6,5,8,7,4,3]=>[3,3,1,1,1,1]=>225
[10,9,8,5,4,7,6,3,2,1]=>[2,2,1,1,1,1,1,1]=>35
[2,1,7,8,9,10,3,4,5,6]=>[5,5]=>42
[3,7,1,8,9,10,2,4,5,6]=>[5,5]=>42
[4,7,8,1,9,10,2,3,5,6]=>[5,5]=>42
[5,7,8,9,1,10,2,3,4,6]=>[5,5]=>42
[6,7,8,9,10,1,2,3,4,5]=>[5,5]=>42
[5,6,8,9,1,2,10,3,4,7]=>[5,5]=>42
[4,6,8,1,9,2,10,3,5,7]=>[5,5]=>42
[3,6,1,8,9,2,10,4,5,7]=>[5,5]=>42
[2,1,6,8,9,3,10,4,5,7]=>[5,5]=>42
[2,1,5,8,3,9,10,4,6,7]=>[5,5]=>42
[3,5,1,8,2,9,10,4,6,7]=>[5,5]=>42
[4,5,8,1,2,9,10,3,6,7]=>[5,5]=>42
[3,4,1,2,8,9,10,5,6,7]=>[5,5]=>42
[2,1,4,3,8,9,10,5,6,7]=>[5,5]=>42
[2,1,4,3,7,9,5,10,6,8]=>[5,5]=>42
[3,4,1,2,7,9,5,10,6,8]=>[5,5]=>42
[4,5,7,1,2,9,3,10,6,8]=>[5,5]=>42
[3,5,1,7,2,9,4,10,6,8]=>[5,5]=>42
[2,1,5,7,3,9,4,10,6,8]=>[5,5]=>42
[2,1,6,7,9,3,4,10,5,8]=>[5,5]=>42
[3,6,1,7,9,2,4,10,5,8]=>[5,5]=>42
[4,6,7,1,9,2,3,10,5,8]=>[5,5]=>42
[5,6,7,9,1,2,3,10,4,8]=>[5,5]=>42
[2,1,5,6,3,4,9,10,7,8]=>[5,5]=>42
[3,5,1,6,2,4,9,10,7,8]=>[5,5]=>42
[4,5,6,1,2,3,9,10,7,8]=>[5,5]=>42
[3,4,1,2,6,5,9,10,7,8]=>[5,5]=>42
[2,1,4,3,6,5,9,10,7,8]=>[5,5]=>42
[2,1,4,3,6,5,10,9,8,7]=>[4,4,1,1]=>300
[4,3,2,1,6,5,10,9,8,7]=>[3,3,2,2]=>252
[6,3,2,5,4,1,10,9,8,7]=>[3,3,2,2]=>252
[10,3,2,5,4,9,8,7,6,1]=>[3,3,1,1,1,1]=>225
[2,1,6,5,4,3,10,9,8,7]=>[3,3,2,2]=>252
[6,5,4,3,2,1,10,9,8,7]=>[2,2,2,2,1,1]=>90
[10,5,4,3,2,9,8,7,6,1]=>[2,2,2,2,1,1]=>90
[2,1,10,5,4,9,8,7,6,3]=>[3,3,1,1,1,1]=>225
[10,9,4,3,8,7,6,5,2,1]=>[2,2,1,1,1,1,1,1]=>35
[2,1,4,3,10,9,8,7,6,5]=>[3,3,1,1,1,1]=>225
[4,3,2,1,10,9,8,7,6,5]=>[2,2,2,2,1,1]=>90
[10,3,2,9,8,7,6,5,4,1]=>[2,2,1,1,1,1,1,1]=>35
[2,1,10,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1,1]=>35
[9,10,8,7,6,5,4,3,1,2]=>[2,2,1,1,1,1,1,1]=>35
[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>1
[4,2,5,1,3,6,7,8]=>[5,2,1]=>64
[4,2,6,1,3,5,7,8]=>[5,2,1]=>64
[5,3,6,1,2,4,7,8]=>[5,2,1]=>64
[6,2,4,1,3,5,7,8]=>[5,2,1]=>64
[6,3,5,1,2,4,7,8]=>[5,2,1]=>64
[5,3,7,1,2,4,6,8]=>[5,2,1]=>64
[5,4,7,1,2,3,6,8]=>[5,2,1]=>64
[6,2,7,1,3,4,5,8]=>[5,2,1]=>64
[6,3,7,1,2,4,5,8]=>[5,2,1]=>64
[6,4,7,1,2,3,5,8]=>[5,2,1]=>64
[7,3,5,1,2,4,6,8]=>[5,2,1]=>64
[7,3,6,1,2,4,5,8]=>[5,2,1]=>64
[7,4,6,1,2,3,5,8]=>[5,2,1]=>64
[3,2,8,1,4,5,6,7]=>[5,2,1]=>64
[4,2,8,1,3,5,6,7]=>[5,2,1]=>64
[5,4,8,1,2,3,6,7]=>[5,2,1]=>64
[6,2,8,1,3,4,5,7]=>[5,2,1]=>64
[6,3,8,1,2,4,5,7]=>[5,2,1]=>64
[6,4,8,1,2,3,5,7]=>[5,2,1]=>64
[6,5,8,1,2,3,4,7]=>[5,2,1]=>64
[7,2,8,1,3,4,5,6]=>[5,2,1]=>64
[7,3,8,1,2,4,5,6]=>[5,2,1]=>64
[7,4,8,1,2,3,5,6]=>[5,2,1]=>64
[7,5,8,1,2,3,4,6]=>[5,2,1]=>64
[8,2,4,1,3,5,6,7]=>[5,2,1]=>64
[8,3,5,1,2,4,6,7]=>[5,2,1]=>64
[8,3,6,1,2,4,5,7]=>[5,2,1]=>64
[8,3,7,1,2,4,5,6]=>[5,2,1]=>64
[8,4,7,1,2,3,5,6]=>[5,2,1]=>64
[8,5,7,1,2,3,4,6]=>[5,2,1]=>64
[3,2,5,7,1,4,6,8]=>[4,3,1]=>70
[4,2,5,7,1,3,6,8]=>[4,3,1]=>70
[5,2,4,7,1,3,6,8]=>[4,3,1]=>70
[4,2,6,7,1,3,5,8]=>[4,3,1]=>70
[5,2,6,7,1,3,4,8]=>[4,3,1]=>70
[6,2,5,7,1,3,4,8]=>[4,3,1]=>70
[4,2,5,8,1,3,6,7]=>[4,3,1]=>70
[5,2,4,8,1,3,6,7]=>[4,3,1]=>70
[4,2,6,8,1,3,5,7]=>[4,3,1]=>70
[5,2,6,8,1,3,4,7]=>[4,3,1]=>70
[6,2,4,8,1,3,5,7]=>[4,3,1]=>70
[6,3,4,8,1,2,5,7]=>[4,3,1]=>70
[6,3,5,8,1,2,4,7]=>[4,3,1]=>70
[6,4,5,8,1,2,3,7]=>[4,3,1]=>70
[3,2,7,8,1,4,5,6]=>[4,3,1]=>70
[5,4,7,8,1,2,3,6]=>[4,3,1]=>70
[6,2,7,8,1,3,4,5]=>[4,3,1]=>70
[6,3,7,8,1,2,4,5]=>[4,3,1]=>70
[6,4,7,8,1,2,3,5]=>[4,3,1]=>70
[7,2,4,8,1,3,5,6]=>[4,3,1]=>70
[7,3,4,8,1,2,5,6]=>[4,3,1]=>70
[7,3,5,8,1,2,4,6]=>[4,3,1]=>70
[7,4,5,8,1,2,3,6]=>[4,3,1]=>70
[7,4,6,8,1,2,3,5]=>[4,3,1]=>70
[8,3,4,6,1,2,5,7]=>[4,3,1]=>70
[8,3,5,6,1,2,4,7]=>[4,3,1]=>70
[8,3,5,7,1,2,4,6]=>[4,3,1]=>70
[8,2,6,7,1,3,4,5]=>[4,3,1]=>70
[8,4,6,7,1,2,3,5]=>[4,3,1]=>70
[4,6,2,5,1,3,7,8]=>[4,2,2]=>56
[4,6,3,5,1,2,7,8]=>[4,2,2]=>56
[3,7,2,5,1,4,6,8]=>[4,2,2]=>56
[4,7,3,5,1,2,6,8]=>[4,2,2]=>56
[3,7,2,6,1,4,5,8]=>[4,2,2]=>56
[4,7,3,6,1,2,5,8]=>[4,2,2]=>56
[5,7,2,6,1,3,4,8]=>[4,2,2]=>56
[6,7,2,5,1,3,4,8]=>[4,2,2]=>56
[4,8,2,5,1,3,6,7]=>[4,2,2]=>56
[5,8,2,4,1,3,6,7]=>[4,2,2]=>56
[5,8,3,4,1,2,6,7]=>[4,2,2]=>56
[5,8,3,6,1,2,4,7]=>[4,2,2]=>56
[5,8,4,6,1,2,3,7]=>[4,2,2]=>56
[6,8,3,5,1,2,4,7]=>[4,2,2]=>56
[3,8,2,7,1,4,5,6]=>[4,2,2]=>56
[4,8,2,7,1,3,5,6]=>[4,2,2]=>56
[4,8,3,7,1,2,5,6]=>[4,2,2]=>56
[5,8,2,7,1,3,4,6]=>[4,2,2]=>56
[5,8,3,7,1,2,4,6]=>[4,2,2]=>56
[6,8,2,7,1,3,4,5]=>[4,2,2]=>56
[6,8,5,7,1,2,3,4]=>[4,2,2]=>56
[7,8,2,4,1,3,5,6]=>[4,2,2]=>56
[7,8,2,5,1,3,4,6]=>[4,2,2]=>56
[7,8,3,5,1,2,4,6]=>[4,2,2]=>56
[7,8,4,6,1,2,3,5]=>[4,2,2]=>56
[4,3,2,6,1,5,7,8]=>[4,2,1,1]=>90
[5,3,2,6,1,4,7,8]=>[4,2,1,1]=>90
[6,3,2,5,1,4,7,8]=>[4,2,1,1]=>90
[6,5,2,4,1,3,7,8]=>[4,2,1,1]=>90
[4,3,2,7,1,5,6,8]=>[4,2,1,1]=>90
[5,3,2,7,1,4,6,8]=>[4,2,1,1]=>90
[6,3,2,7,1,4,5,8]=>[4,2,1,1]=>90
[6,4,2,7,1,3,5,8]=>[4,2,1,1]=>90
[6,4,3,7,1,2,5,8]=>[4,2,1,1]=>90
[6,5,2,7,1,3,4,8]=>[4,2,1,1]=>90
[6,5,3,7,1,2,4,8]=>[4,2,1,1]=>90
[7,3,2,5,1,4,6,8]=>[4,2,1,1]=>90
[7,4,2,5,1,3,6,8]=>[4,2,1,1]=>90
[7,3,2,6,1,4,5,8]=>[4,2,1,1]=>90
[7,4,3,6,1,2,5,8]=>[4,2,1,1]=>90
[7,5,2,6,1,3,4,8]=>[4,2,1,1]=>90
[7,5,3,6,1,2,4,8]=>[4,2,1,1]=>90
[4,3,2,8,1,5,6,7]=>[4,2,1,1]=>90
[6,4,2,8,1,3,5,7]=>[4,2,1,1]=>90
[6,4,3,8,1,2,5,7]=>[4,2,1,1]=>90
[6,5,2,8,1,3,4,7]=>[4,2,1,1]=>90
[6,5,3,8,1,2,4,7]=>[4,2,1,1]=>90
[7,3,2,8,1,4,5,6]=>[4,2,1,1]=>90
[7,4,2,8,1,3,5,6]=>[4,2,1,1]=>90
[7,4,3,8,1,2,5,6]=>[4,2,1,1]=>90
[7,5,3,8,1,2,4,6]=>[4,2,1,1]=>90
[7,5,4,8,1,2,3,6]=>[4,2,1,1]=>90
[7,6,2,8,1,3,4,5]=>[4,2,1,1]=>90
[8,3,2,5,1,4,6,7]=>[4,2,1,1]=>90
[8,4,2,5,1,3,6,7]=>[4,2,1,1]=>90
[8,3,2,6,1,4,5,7]=>[4,2,1,1]=>90
[8,4,2,6,1,3,5,7]=>[4,2,1,1]=>90
[8,5,3,6,1,2,4,7]=>[4,2,1,1]=>90
[8,6,2,4,1,3,5,7]=>[4,2,1,1]=>90
[8,6,2,5,1,3,4,7]=>[4,2,1,1]=>90
[8,3,2,7,1,4,5,6]=>[4,2,1,1]=>90
[8,4,2,7,1,3,5,6]=>[4,2,1,1]=>90
[8,4,3,7,1,2,5,6]=>[4,2,1,1]=>90
[8,5,2,7,1,3,4,6]=>[4,2,1,1]=>90
[8,5,3,7,1,2,4,6]=>[4,2,1,1]=>90
[8,6,3,7,1,2,4,5]=>[4,2,1,1]=>90
[8,7,2,4,1,3,5,6]=>[4,2,1,1]=>90
[8,7,2,5,1,3,4,6]=>[4,2,1,1]=>90
[8,7,3,5,1,2,4,6]=>[4,2,1,1]=>90
[8,7,2,6,1,3,4,5]=>[4,2,1,1]=>90
[8,7,3,6,1,2,4,5]=>[4,2,1,1]=>90
[8,7,4,6,1,2,3,5]=>[4,2,1,1]=>90
[5,6,2,4,8,1,3,7]=>[3,3,2]=>42
[4,7,2,5,8,1,3,6]=>[3,3,2]=>42
[4,7,3,5,8,1,2,6]=>[3,3,2]=>42
[5,7,2,4,8,1,3,6]=>[3,3,2]=>42
[5,7,3,4,8,1,2,6]=>[3,3,2]=>42
[4,7,3,6,8,1,2,5]=>[3,3,2]=>42
[5,7,2,6,8,1,3,4]=>[3,3,2]=>42
[5,7,4,6,8,1,2,3]=>[3,3,2]=>42
[6,7,3,4,8,1,2,5]=>[3,3,2]=>42
[6,7,3,5,8,1,2,4]=>[3,3,2]=>42
[3,8,2,5,7,1,4,6]=>[3,3,2]=>42
[4,8,3,5,7,1,2,6]=>[3,3,2]=>42
[5,8,2,4,7,1,3,6]=>[3,3,2]=>42
[3,8,2,6,7,1,4,5]=>[3,3,2]=>42
[5,8,2,6,7,1,3,4]=>[3,3,2]=>42
[5,8,3,6,7,1,2,4]=>[3,3,2]=>42
[6,8,2,5,7,1,3,4]=>[3,3,2]=>42
[7,8,2,4,6,1,3,5]=>[3,3,2]=>42
[7,8,2,5,6,1,3,4]=>[3,3,2]=>42
[7,8,3,5,6,1,2,4]=>[3,3,2]=>42
[4,3,2,6,8,1,5,7]=>[3,3,1,1]=>56
[5,3,2,6,8,1,4,7]=>[3,3,1,1]=>56
[5,4,3,6,8,1,2,7]=>[3,3,1,1]=>56
[6,3,2,5,8,1,4,7]=>[3,3,1,1]=>56
[6,4,3,5,8,1,2,7]=>[3,3,1,1]=>56
[6,5,2,4,8,1,3,7]=>[3,3,1,1]=>56
[4,3,2,7,8,1,5,6]=>[3,3,1,1]=>56
[5,3,2,7,8,1,4,6]=>[3,3,1,1]=>56
[5,4,2,7,8,1,3,6]=>[3,3,1,1]=>56
[5,4,3,7,8,1,2,6]=>[3,3,1,1]=>56
[6,4,2,7,8,1,3,5]=>[3,3,1,1]=>56
[6,4,3,7,8,1,2,5]=>[3,3,1,1]=>56
[7,4,2,5,8,1,3,6]=>[3,3,1,1]=>56
[7,4,3,5,8,1,2,6]=>[3,3,1,1]=>56
[7,5,2,6,8,1,3,4]=>[3,3,1,1]=>56
[7,5,3,6,8,1,2,4]=>[3,3,1,1]=>56
[7,6,2,4,8,1,3,5]=>[3,3,1,1]=>56
[8,4,2,5,7,1,3,6]=>[3,3,1,1]=>56
[8,5,2,4,7,1,3,6]=>[3,3,1,1]=>56
[8,3,2,6,7,1,4,5]=>[3,3,1,1]=>56
[8,5,2,6,7,1,3,4]=>[3,3,1,1]=>56
[8,5,3,6,7,1,2,4]=>[3,3,1,1]=>56
[8,6,2,4,7,1,3,5]=>[3,3,1,1]=>56
[8,7,2,4,6,1,3,5]=>[3,3,1,1]=>56
[8,7,3,4,6,1,2,5]=>[3,3,1,1]=>56
[8,7,2,5,6,1,3,4]=>[3,3,1,1]=>56
[4,3,7,2,6,1,5,8]=>[3,2,2,1]=>70
[4,3,8,2,6,1,5,7]=>[3,2,2,1]=>70
[5,3,8,2,6,1,4,7]=>[3,2,2,1]=>70
[5,4,8,2,6,1,3,7]=>[3,2,2,1]=>70
[5,4,8,3,6,1,2,7]=>[3,2,2,1]=>70
[6,4,8,2,5,1,3,7]=>[3,2,2,1]=>70
[6,4,8,3,5,1,2,7]=>[3,2,2,1]=>70
[6,5,8,2,4,1,3,7]=>[3,2,2,1]=>70
[6,5,8,3,4,1,2,7]=>[3,2,2,1]=>70
[4,3,8,2,7,1,5,6]=>[3,2,2,1]=>70
[5,3,8,2,7,1,4,6]=>[3,2,2,1]=>70
[5,4,8,2,7,1,3,6]=>[3,2,2,1]=>70
[5,4,8,3,7,1,2,6]=>[3,2,2,1]=>70
[6,3,8,2,7,1,4,5]=>[3,2,2,1]=>70
[6,4,8,2,7,1,3,5]=>[3,2,2,1]=>70
[7,3,8,2,5,1,4,6]=>[3,2,2,1]=>70
[7,4,8,3,5,1,2,6]=>[3,2,2,1]=>70
[7,5,8,2,4,1,3,6]=>[3,2,2,1]=>70
[7,5,8,2,6,1,3,4]=>[3,2,2,1]=>70
[7,5,8,4,6,1,2,3]=>[3,2,2,1]=>70
[7,6,8,2,5,1,3,4]=>[3,2,2,1]=>70
[7,6,8,3,5,1,2,4]=>[3,2,2,1]=>70
[8,5,6,2,4,1,3,7]=>[3,2,2,1]=>70
[8,4,7,3,5,1,2,6]=>[3,2,2,1]=>70
[8,5,7,2,4,1,3,6]=>[3,2,2,1]=>70
[8,3,7,2,6,1,4,5]=>[3,2,2,1]=>70
[8,4,7,2,6,1,3,5]=>[3,2,2,1]=>70
[8,4,7,3,6,1,2,5]=>[3,2,2,1]=>70
[8,5,7,2,6,1,3,4]=>[3,2,2,1]=>70
[8,6,7,2,4,1,3,5]=>[3,2,2,1]=>70
[8,6,7,2,5,1,3,4]=>[3,2,2,1]=>70
[8,6,7,3,5,1,2,4]=>[3,2,2,1]=>70
[5,4,3,2,7,1,6,8]=>[3,2,1,1,1]=>64
[6,4,3,2,7,1,5,8]=>[3,2,1,1,1]=>64
[6,5,3,2,7,1,4,8]=>[3,2,1,1,1]=>64
[6,5,4,2,7,1,3,8]=>[3,2,1,1,1]=>64
[7,5,3,2,6,1,4,8]=>[3,2,1,1,1]=>64
[7,5,4,2,6,1,3,8]=>[3,2,1,1,1]=>64
[5,4,3,2,8,1,6,7]=>[3,2,1,1,1]=>64
[6,5,3,2,8,1,4,7]=>[3,2,1,1,1]=>64
[6,5,4,3,8,1,2,7]=>[3,2,1,1,1]=>64
[7,5,3,2,8,1,4,6]=>[3,2,1,1,1]=>64
[7,5,4,2,8,1,3,6]=>[3,2,1,1,1]=>64
[7,6,3,2,8,1,4,5]=>[3,2,1,1,1]=>64
[7,6,4,3,8,1,2,5]=>[3,2,1,1,1]=>64
[7,6,5,2,8,1,3,4]=>[3,2,1,1,1]=>64
[8,5,3,2,6,1,4,7]=>[3,2,1,1,1]=>64
[8,5,4,2,6,1,3,7]=>[3,2,1,1,1]=>64
[8,6,5,2,4,1,3,7]=>[3,2,1,1,1]=>64
[8,5,3,2,7,1,4,6]=>[3,2,1,1,1]=>64
[8,6,3,2,7,1,4,5]=>[3,2,1,1,1]=>64
[8,6,4,3,7,1,2,5]=>[3,2,1,1,1]=>64
[8,7,3,2,6,1,4,5]=>[3,2,1,1,1]=>64
[8,7,4,2,6,1,3,5]=>[3,2,1,1,1]=>64
[8,7,4,3,6,1,2,5]=>[3,2,1,1,1]=>64
[8,7,5,2,6,1,3,4]=>[3,2,1,1,1]=>64
[8,7,6,2,4,1,3,5]=>[3,2,1,1,1]=>64
[8,7,6,2,5,1,3,4]=>[3,2,1,1,1]=>64
[8,7,6,3,5,1,2,4]=>[3,2,1,1,1]=>64
[4,8,3,7,2,6,1,5]=>[2,2,2,2]=>14
[5,8,3,7,2,6,1,4]=>[2,2,2,2]=>14
[5,8,4,7,3,6,1,2]=>[2,2,2,2]=>14
[6,8,3,7,2,5,1,4]=>[2,2,2,2]=>14
[6,8,4,7,2,5,1,3]=>[2,2,2,2]=>14
[6,8,5,7,2,4,1,3]=>[2,2,2,2]=>14
[7,8,4,6,3,5,1,2]=>[2,2,2,2]=>14
[7,8,5,6,2,4,1,3]=>[2,2,2,2]=>14
[5,4,3,8,2,7,1,6]=>[2,2,2,1,1]=>28
[6,4,3,8,2,7,1,5]=>[2,2,2,1,1]=>28
[6,5,3,8,2,7,1,4]=>[2,2,2,1,1]=>28
[6,5,4,8,3,7,1,2]=>[2,2,2,1,1]=>28
[7,4,3,8,2,6,1,5]=>[2,2,2,1,1]=>28
[7,5,3,8,2,6,1,4]=>[2,2,2,1,1]=>28
[7,5,4,8,2,6,1,3]=>[2,2,2,1,1]=>28
[7,6,3,8,2,5,1,4]=>[2,2,2,1,1]=>28
[7,6,4,8,2,5,1,3]=>[2,2,2,1,1]=>28
[8,4,3,7,2,6,1,5]=>[2,2,2,1,1]=>28
[8,5,3,7,2,6,1,4]=>[2,2,2,1,1]=>28
[8,5,4,7,2,6,1,3]=>[2,2,2,1,1]=>28
[8,5,4,7,3,6,1,2]=>[2,2,2,1,1]=>28
[8,6,3,7,2,5,1,4]=>[2,2,2,1,1]=>28
[8,6,4,7,2,5,1,3]=>[2,2,2,1,1]=>28
[8,6,4,7,3,5,1,2]=>[2,2,2,1,1]=>28
[8,6,5,7,2,4,1,3]=>[2,2,2,1,1]=>28
[8,7,3,6,2,5,1,4]=>[2,2,2,1,1]=>28
[8,7,4,6,2,5,1,3]=>[2,2,2,1,1]=>28
[8,7,4,6,3,5,1,2]=>[2,2,2,1,1]=>28
[8,7,5,6,2,4,1,3]=>[2,2,2,1,1]=>28
[6,5,4,3,2,8,1,7]=>[2,2,1,1,1,1]=>20
[7,6,5,4,2,8,1,3]=>[2,2,1,1,1,1]=>20
[8,5,4,3,2,7,1,6]=>[2,2,1,1,1,1]=>20
[8,7,4,3,2,6,1,5]=>[2,2,1,1,1,1]=>20
[8,7,5,3,2,6,1,4]=>[2,2,1,1,1,1]=>20
[8,7,5,4,2,6,1,3]=>[2,2,1,1,1,1]=>20
[8,7,6,3,2,5,1,4]=>[2,2,1,1,1,1]=>20
[8,7,6,4,2,5,1,3]=>[2,2,1,1,1,1]=>20
[8,7,6,5,2,4,1,3]=>[2,2,1,1,1,1]=>20
[8,1,2,3,4,7,5,6]=>[6,1,1]=>21
[8,1,2,3,6,4,5,7]=>[6,1,1]=>21
[8,1,2,3,7,4,5,6]=>[6,1,1]=>21
[7,1,2,3,6,4,8,5]=>[5,2,1]=>64
[5,1,2,3,8,7,4,6]=>[5,2,1]=>64
[8,1,2,3,6,7,4,5]=>[5,2,1]=>64
[4,1,2,8,3,7,5,6]=>[5,2,1]=>64
[8,1,2,5,3,4,6,7]=>[6,1,1]=>21
[7,1,2,5,3,4,8,6]=>[5,2,1]=>64
[8,1,2,6,3,4,5,7]=>[6,1,1]=>21
[7,1,2,6,3,4,8,5]=>[5,2,1]=>64
[6,1,2,5,3,8,4,7]=>[5,2,1]=>64
[8,1,2,5,3,7,4,6]=>[5,2,1]=>64
[8,1,2,6,3,7,4,5]=>[5,2,1]=>64
[6,1,2,5,3,7,8,4]=>[5,2,1]=>64
[4,1,2,8,6,3,5,7]=>[5,2,1]=>64
[4,1,2,8,7,3,5,6]=>[5,2,1]=>64
[4,1,2,7,6,3,8,5]=>[4,3,1]=>70
[8,1,2,5,6,3,4,7]=>[5,2,1]=>64
[8,1,2,5,7,3,4,6]=>[5,2,1]=>64
[8,1,2,7,6,3,4,5]=>[5,1,1,1]=>35
[7,1,2,5,6,3,8,4]=>[5,2,1]=>64
[4,1,2,5,8,7,3,6]=>[4,3,1]=>70
[4,1,2,8,6,7,3,5]=>[4,3,1]=>70
[8,1,2,5,6,7,3,4]=>[5,2,1]=>64
[3,1,8,2,4,7,5,6]=>[5,2,1]=>64
[3,1,8,2,6,4,5,7]=>[5,2,1]=>64
[3,1,8,2,7,4,5,6]=>[5,2,1]=>64
[3,1,7,2,6,4,8,5]=>[4,3,1]=>70
[3,1,5,2,8,7,4,6]=>[4,3,1]=>70
[3,1,8,2,6,7,4,5]=>[4,3,1]=>70
[8,1,4,2,3,5,6,7]=>[6,1,1]=>21
[7,1,4,2,3,5,8,6]=>[5,2,1]=>64
[6,1,4,2,3,8,5,7]=>[5,2,1]=>64
[8,1,4,2,3,7,5,6]=>[5,2,1]=>64
[6,1,4,2,3,7,8,5]=>[5,2,1]=>64
[8,1,5,2,3,4,6,7]=>[6,1,1]=>21
[7,1,5,2,3,4,8,6]=>[5,2,1]=>64
[8,1,7,2,3,4,5,6]=>[6,1,1]=>21
[6,1,5,2,3,8,4,7]=>[5,2,1]=>64
[8,1,5,2,3,7,4,6]=>[5,2,1]=>64
[6,1,8,2,3,7,4,5]=>[5,2,1]=>64
[6,1,5,2,3,7,8,4]=>[5,2,1]=>64
[5,1,4,2,8,3,6,7]=>[5,2,1]=>64
[5,1,4,2,7,3,8,6]=>[4,3,1]=>70
[8,1,4,2,6,3,5,7]=>[5,2,1]=>64
[8,1,4,2,7,3,5,6]=>[5,2,1]=>64
[7,1,4,2,6,3,8,5]=>[4,3,1]=>70
[8,1,5,2,6,3,4,7]=>[5,2,1]=>64
[8,1,5,2,7,3,4,6]=>[5,2,1]=>64
[7,1,8,2,6,3,4,5]=>[5,2,1]=>64
[7,1,5,2,6,3,8,4]=>[4,3,1]=>70
[5,1,4,2,6,8,3,7]=>[4,3,1]=>70
[5,1,4,2,8,7,3,6]=>[4,2,2]=>56
[8,1,4,2,6,7,3,5]=>[4,3,1]=>70
[8,1,5,2,6,7,3,4]=>[4,3,1]=>70
[5,1,4,2,6,7,8,3]=>[5,2,1]=>64
[3,1,4,8,2,7,5,6]=>[4,3,1]=>70
[3,1,8,5,2,4,6,7]=>[5,2,1]=>64
[3,1,7,5,2,4,8,6]=>[4,3,1]=>70
[3,1,8,6,2,4,5,7]=>[5,2,1]=>64
[3,1,7,6,2,4,8,5]=>[4,3,1]=>70
[3,1,6,5,2,8,4,7]=>[4,3,1]=>70
[3,1,8,5,2,7,4,6]=>[4,3,1]=>70
[3,1,8,6,2,7,4,5]=>[4,3,1]=>70
[3,1,6,5,2,7,8,4]=>[4,3,1]=>70
[8,1,4,5,2,3,6,7]=>[5,2,1]=>64
[7,1,4,5,2,3,8,6]=>[4,3,1]=>70
[8,1,4,6,2,3,5,7]=>[5,2,1]=>64
[7,1,4,8,2,3,5,6]=>[5,2,1]=>64
[7,1,4,6,2,3,8,5]=>[4,3,1]=>70
[8,1,6,5,2,3,4,7]=>[5,1,1,1]=>35
[7,1,8,5,2,3,4,6]=>[5,2,1]=>64
[7,1,8,6,2,3,4,5]=>[5,2,1]=>64
[7,1,6,5,2,3,8,4]=>[4,2,1,1]=>90
[6,1,4,5,2,8,3,7]=>[4,3,1]=>70
[8,1,4,5,2,7,3,6]=>[4,3,1]=>70
[8,1,4,6,2,7,3,5]=>[4,3,1]=>70
[8,1,6,5,2,7,3,4]=>[4,2,1,1]=>90
[6,1,4,5,2,7,8,3]=>[5,2,1]=>64
[3,1,4,8,6,2,5,7]=>[4,3,1]=>70
[3,1,4,8,7,2,5,6]=>[4,3,1]=>70
[3,1,4,7,6,2,8,5]=>[4,3,1]=>70
[3,1,8,5,6,2,4,7]=>[4,3,1]=>70
[3,1,8,5,7,2,4,6]=>[4,3,1]=>70
[3,1,8,7,6,2,4,5]=>[4,2,1,1]=>90
[3,1,7,5,6,2,8,4]=>[4,3,1]=>70
[8,1,4,5,6,2,3,7]=>[5,2,1]=>64
[8,1,4,5,7,2,3,6]=>[4,3,1]=>70
[8,1,4,7,6,2,3,5]=>[4,2,1,1]=>90
[8,1,7,5,6,2,3,4]=>[4,2,1,1]=>90
[7,1,4,5,6,2,8,3]=>[5,2,1]=>64
[3,1,4,5,8,7,2,6]=>[4,3,1]=>70
[3,1,4,8,6,7,2,5]=>[4,3,1]=>70
[3,1,8,5,6,7,2,4]=>[4,3,1]=>70
[8,1,4,5,6,7,2,3]=>[5,2,1]=>64
[2,8,1,3,4,7,5,6]=>[5,2,1]=>64
[2,8,1,3,6,4,5,7]=>[5,2,1]=>64
[2,8,1,3,7,4,5,6]=>[5,2,1]=>64
[2,7,1,3,6,4,8,5]=>[4,3,1]=>70
[2,5,1,3,8,7,4,6]=>[4,3,1]=>70
[2,8,1,3,6,7,4,5]=>[4,3,1]=>70
[2,4,1,8,3,7,5,6]=>[4,3,1]=>70
[2,8,1,5,3,4,6,7]=>[5,2,1]=>64
[2,7,1,5,3,4,8,6]=>[4,3,1]=>70
[2,8,1,6,3,4,5,7]=>[5,2,1]=>64
[2,7,1,6,3,4,8,5]=>[4,3,1]=>70
[2,6,1,5,3,8,4,7]=>[4,3,1]=>70
[2,8,1,5,3,7,4,6]=>[4,3,1]=>70
[2,6,1,5,3,7,8,4]=>[4,3,1]=>70
[2,4,1,8,6,3,5,7]=>[4,3,1]=>70
[2,4,1,8,7,3,5,6]=>[4,3,1]=>70
[2,4,1,7,6,3,8,5]=>[4,3,1]=>70
[2,8,1,5,6,3,4,7]=>[4,3,1]=>70
[2,8,1,5,7,3,4,6]=>[4,3,1]=>70
[2,8,1,7,6,3,4,5]=>[4,2,1,1]=>90
[2,7,1,5,6,3,8,4]=>[4,3,1]=>70
[2,4,1,5,8,7,3,6]=>[4,3,1]=>70
[2,4,1,8,6,7,3,5]=>[4,3,1]=>70
[2,8,1,5,6,7,3,4]=>[4,3,1]=>70
[7,3,1,2,4,5,8,6]=>[5,2,1]=>64
[6,3,1,2,4,8,5,7]=>[5,2,1]=>64
[8,3,1,2,4,7,5,6]=>[5,2,1]=>64
[6,3,1,2,4,7,8,5]=>[5,2,1]=>64
[5,3,1,2,8,4,6,7]=>[5,2,1]=>64
[5,3,1,2,7,4,8,6]=>[4,3,1]=>70
[8,3,1,2,6,4,5,7]=>[5,2,1]=>64
[8,3,1,2,7,4,5,6]=>[5,2,1]=>64
[7,3,1,2,6,4,8,5]=>[4,3,1]=>70
[5,3,1,2,6,8,4,7]=>[4,3,1]=>70
[5,3,1,2,8,7,4,6]=>[4,2,2]=>56
[8,3,1,2,6,7,4,5]=>[4,3,1]=>70
[5,3,1,2,6,7,8,4]=>[5,2,1]=>64
[7,4,1,2,3,5,8,6]=>[5,2,1]=>64
[6,4,1,2,3,8,5,7]=>[5,2,1]=>64
[8,4,1,2,3,7,5,6]=>[5,2,1]=>64
[6,4,1,2,3,7,8,5]=>[5,2,1]=>64
[7,6,1,2,3,4,8,5]=>[5,2,1]=>64
[5,8,1,2,3,7,4,6]=>[5,2,1]=>64
[8,6,1,2,3,7,4,5]=>[5,2,1]=>64
[5,4,1,2,8,3,6,7]=>[5,2,1]=>64
[5,4,1,2,7,3,8,6]=>[4,3,1]=>70
[8,4,1,2,6,3,5,7]=>[5,2,1]=>64
[8,4,1,2,7,3,5,6]=>[5,2,1]=>64
[7,4,1,2,6,3,8,5]=>[4,3,1]=>70
[5,8,1,2,6,3,4,7]=>[5,2,1]=>64
[5,8,1,2,7,3,4,6]=>[5,2,1]=>64
[8,7,1,2,6,3,4,5]=>[5,1,1,1]=>35
[5,7,1,2,6,3,8,4]=>[4,3,1]=>70
[5,4,1,2,6,8,3,7]=>[4,3,1]=>70
[5,4,1,2,8,7,3,6]=>[4,2,2]=>56
[8,4,1,2,6,7,3,5]=>[4,3,1]=>70
[5,8,1,2,6,7,3,4]=>[4,3,1]=>70
[5,4,1,2,6,7,8,3]=>[5,2,1]=>64
[4,3,1,8,2,5,6,7]=>[5,2,1]=>64
[4,3,1,7,2,5,8,6]=>[4,3,1]=>70
[4,3,1,6,2,8,5,7]=>[4,3,1]=>70
[4,3,1,8,2,7,5,6]=>[4,2,2]=>56
[4,3,1,6,2,7,8,5]=>[4,3,1]=>70
[8,3,1,5,2,4,6,7]=>[5,2,1]=>64
[7,3,1,5,2,4,8,6]=>[4,3,1]=>70
[8,3,1,6,2,4,5,7]=>[5,2,1]=>64
[7,3,1,8,2,4,5,6]=>[5,2,1]=>64
[7,3,1,6,2,4,8,5]=>[4,3,1]=>70
[6,3,1,5,2,8,4,7]=>[4,3,1]=>70
[8,3,1,5,2,7,4,6]=>[4,3,1]=>70
[8,3,1,6,2,7,4,5]=>[4,3,1]=>70
[6,3,1,5,2,7,8,4]=>[4,3,1]=>70
[8,4,1,5,2,3,6,7]=>[5,2,1]=>64
[7,4,1,5,2,3,8,6]=>[4,3,1]=>70
[8,4,1,6,2,3,5,7]=>[5,2,1]=>64
[7,4,1,8,2,3,5,6]=>[5,2,1]=>64
[7,4,1,6,2,3,8,5]=>[4,3,1]=>70
[6,8,1,5,2,3,4,7]=>[5,2,1]=>64
[8,7,1,5,2,3,4,6]=>[5,1,1,1]=>35
[8,7,1,6,2,3,4,5]=>[5,1,1,1]=>35
[6,7,1,5,2,3,8,4]=>[4,3,1]=>70
[6,4,1,5,2,8,3,7]=>[4,3,1]=>70
[8,4,1,5,2,7,3,6]=>[4,3,1]=>70
[8,4,1,6,2,7,3,5]=>[4,3,1]=>70
[6,8,1,5,2,7,3,4]=>[4,2,2]=>56
[6,4,1,5,2,7,8,3]=>[4,3,1]=>70
[4,3,1,5,8,2,6,7]=>[4,3,1]=>70
[4,3,1,5,7,2,8,6]=>[4,3,1]=>70
[4,3,1,8,6,2,5,7]=>[4,2,2]=>56
[4,3,1,8,7,2,5,6]=>[4,2,2]=>56
[4,3,1,7,6,2,8,5]=>[3,3,2]=>42
[8,3,1,5,6,2,4,7]=>[4,3,1]=>70
[8,3,1,5,7,2,4,6]=>[4,3,1]=>70
[8,3,1,7,6,2,4,5]=>[4,2,1,1]=>90
[7,3,1,5,6,2,8,4]=>[4,3,1]=>70
[8,4,1,5,6,2,3,7]=>[4,3,1]=>70
[8,4,1,5,7,2,3,6]=>[4,3,1]=>70
[8,4,1,7,6,2,3,5]=>[4,2,1,1]=>90
[7,8,1,5,6,2,3,4]=>[4,2,2]=>56
[7,4,1,5,6,2,8,3]=>[4,3,1]=>70
[4,3,1,5,6,8,2,7]=>[4,3,1]=>70
[4,3,1,5,8,7,2,6]=>[3,3,2]=>42
[4,3,1,8,6,7,2,5]=>[3,3,2]=>42
[8,3,1,5,6,7,2,4]=>[4,3,1]=>70
[8,4,1,5,6,7,2,3]=>[4,3,1]=>70
[4,3,1,5,6,7,8,2]=>[5,2,1]=>64
[2,3,8,1,4,7,5,6]=>[5,2,1]=>64
[2,3,8,1,6,4,5,7]=>[5,2,1]=>64
[2,3,8,1,7,4,5,6]=>[5,2,1]=>64
[2,3,7,1,6,4,8,5]=>[4,3,1]=>70
[2,3,5,1,8,7,4,6]=>[4,3,1]=>70
[2,3,8,1,6,7,4,5]=>[4,3,1]=>70
[2,8,4,1,3,5,6,7]=>[5,2,1]=>64
[2,7,4,1,3,5,8,6]=>[4,3,1]=>70
[2,6,4,1,3,8,5,7]=>[4,3,1]=>70
[2,8,4,1,3,7,5,6]=>[4,3,1]=>70
[2,6,4,1,3,7,8,5]=>[4,3,1]=>70
[2,8,5,1,3,4,6,7]=>[5,2,1]=>64
[2,7,5,1,3,4,8,6]=>[4,3,1]=>70
[2,8,7,1,3,4,5,6]=>[5,2,1]=>64
[2,6,5,1,3,8,4,7]=>[4,3,1]=>70
[2,8,5,1,3,7,4,6]=>[4,3,1]=>70
[2,6,8,1,3,7,4,5]=>[4,3,1]=>70
[2,6,5,1,3,7,8,4]=>[4,3,1]=>70
[2,5,4,1,8,3,6,7]=>[4,3,1]=>70
[2,5,4,1,7,3,8,6]=>[4,3,1]=>70
[2,8,4,1,6,3,5,7]=>[4,3,1]=>70
[2,8,4,1,7,3,5,6]=>[4,3,1]=>70
[2,7,4,1,6,3,8,5]=>[4,3,1]=>70
[2,8,5,1,6,3,4,7]=>[4,3,1]=>70
[2,8,5,1,7,3,4,6]=>[4,3,1]=>70
[2,7,8,1,6,3,4,5]=>[4,3,1]=>70
[2,7,5,1,6,3,8,4]=>[4,3,1]=>70
[2,5,4,1,6,8,3,7]=>[4,3,1]=>70
[2,5,4,1,8,7,3,6]=>[3,3,2]=>42
[2,8,4,1,6,7,3,5]=>[4,3,1]=>70
[2,8,5,1,6,7,3,4]=>[4,3,1]=>70
[2,5,4,1,6,7,8,3]=>[5,2,1]=>64
[7,3,4,1,2,5,8,6]=>[4,3,1]=>70
[6,3,4,1,2,8,5,7]=>[4,3,1]=>70
[8,3,4,1,2,7,5,6]=>[4,3,1]=>70
[6,3,4,1,2,7,8,5]=>[4,3,1]=>70
[7,3,5,1,2,4,8,6]=>[4,3,1]=>70
[6,3,7,1,2,4,8,5]=>[4,3,1]=>70
[6,3,5,1,2,8,4,7]=>[4,3,1]=>70
[8,3,5,1,2,7,4,6]=>[4,3,1]=>70
[6,3,8,1,2,7,4,5]=>[4,2,2]=>56
[6,3,5,1,2,7,8,4]=>[4,3,1]=>70
[7,5,4,1,2,3,8,6]=>[4,2,1,1]=>90
[6,8,4,1,2,3,5,7]=>[5,2,1]=>64
[6,7,4,1,2,3,8,5]=>[4,3,1]=>70
[6,8,5,1,2,3,4,7]=>[5,2,1]=>64
[6,7,5,1,2,3,8,4]=>[4,3,1]=>70
[6,5,4,1,2,8,3,7]=>[4,2,1,1]=>90
[8,5,4,1,2,7,3,6]=>[4,2,1,1]=>90
[6,8,4,1,2,7,3,5]=>[4,2,2]=>56
[6,8,5,1,2,7,3,4]=>[4,2,2]=>56
[6,5,4,1,2,7,8,3]=>[4,2,1,1]=>90
[5,3,4,1,8,2,6,7]=>[4,3,1]=>70
[5,3,4,1,7,2,8,6]=>[4,3,1]=>70
[8,3,4,1,6,2,5,7]=>[4,3,1]=>70
[8,3,4,1,7,2,5,6]=>[4,3,1]=>70
[7,3,4,1,6,2,8,5]=>[4,3,1]=>70
[8,3,5,1,6,2,4,7]=>[4,3,1]=>70
[8,3,5,1,7,2,4,6]=>[4,3,1]=>70
[7,3,8,1,6,2,4,5]=>[4,2,2]=>56
[7,3,5,1,6,2,8,4]=>[4,3,1]=>70
[8,5,4,1,6,2,3,7]=>[4,2,1,1]=>90
[8,5,4,1,7,2,3,6]=>[4,2,1,1]=>90
[7,8,4,1,6,2,3,5]=>[4,2,2]=>56
[7,8,5,1,6,2,3,4]=>[4,2,2]=>56
[7,5,4,1,6,2,8,3]=>[3,3,1,1]=>56
[5,3,4,1,6,8,2,7]=>[4,3,1]=>70
[5,3,4,1,8,7,2,6]=>[3,3,2]=>42
[8,3,4,1,6,7,2,5]=>[4,3,1]=>70
[8,3,5,1,6,7,2,4]=>[4,3,1]=>70
[8,5,4,1,6,7,2,3]=>[3,3,1,1]=>56
[5,3,4,1,6,7,8,2]=>[5,2,1]=>64
[2,3,4,8,1,7,5,6]=>[5,2,1]=>64
[2,3,8,5,1,4,6,7]=>[5,2,1]=>64
[2,3,7,5,1,4,8,6]=>[4,3,1]=>70
[2,3,8,6,1,4,5,7]=>[5,2,1]=>64
[2,3,7,6,1,4,8,5]=>[4,3,1]=>70
[2,3,6,5,1,8,4,7]=>[4,3,1]=>70
[2,3,8,5,1,7,4,6]=>[4,3,1]=>70
[2,3,8,6,1,7,4,5]=>[4,3,1]=>70
[2,3,6,5,1,7,8,4]=>[5,2,1]=>64
[2,8,4,5,1,3,6,7]=>[5,2,1]=>64
[2,7,4,5,1,3,8,6]=>[4,3,1]=>70
[2,8,4,6,1,3,5,7]=>[4,3,1]=>70
[2,7,4,8,1,3,5,6]=>[4,3,1]=>70
[2,7,4,6,1,3,8,5]=>[4,3,1]=>70
[2,8,6,5,1,3,4,7]=>[4,2,1,1]=>90
[2,7,8,5,1,3,4,6]=>[4,3,1]=>70
[2,7,8,6,1,3,4,5]=>[4,3,1]=>70
[2,7,6,5,1,3,8,4]=>[3,3,1,1]=>56
[2,6,4,5,1,8,3,7]=>[4,3,1]=>70
[2,8,4,5,1,7,3,6]=>[4,3,1]=>70
[2,8,4,6,1,7,3,5]=>[4,3,1]=>70
[2,8,6,5,1,7,3,4]=>[3,3,1,1]=>56
[2,6,4,5,1,7,8,3]=>[5,2,1]=>64
[7,3,4,5,1,2,8,6]=>[4,3,1]=>70
[7,3,4,6,1,2,8,5]=>[4,3,1]=>70
[8,3,6,5,1,2,4,7]=>[4,2,1,1]=>90
[7,3,8,5,1,2,4,6]=>[4,2,2]=>56
[7,3,8,6,1,2,4,5]=>[4,2,2]=>56
[7,3,6,5,1,2,8,4]=>[3,3,1,1]=>56
[7,6,4,5,1,2,8,3]=>[3,3,1,1]=>56
[6,3,4,5,1,8,2,7]=>[4,3,1]=>70
[8,3,4,5,1,7,2,6]=>[4,3,1]=>70
[8,3,4,6,1,7,2,5]=>[4,3,1]=>70
[8,3,6,5,1,7,2,4]=>[3,3,1,1]=>56
[8,6,4,5,1,7,2,3]=>[3,3,1,1]=>56
[6,3,4,5,1,7,8,2]=>[5,2,1]=>64
[2,3,4,8,6,1,5,7]=>[5,2,1]=>64
[2,3,4,8,7,1,5,6]=>[5,2,1]=>64
[2,3,4,7,6,1,8,5]=>[5,2,1]=>64
[2,3,8,5,6,1,4,7]=>[5,2,1]=>64
[2,3,8,5,7,1,4,6]=>[4,3,1]=>70
[2,3,8,7,6,1,4,5]=>[4,2,1,1]=>90
[2,3,7,5,6,1,8,4]=>[5,2,1]=>64
[2,8,4,5,6,1,3,7]=>[5,2,1]=>64
[2,8,4,5,7,1,3,6]=>[4,3,1]=>70
[2,8,4,7,6,1,3,5]=>[3,3,1,1]=>56
[2,8,7,5,6,1,3,4]=>[3,3,1,1]=>56
[2,7,4,5,6,1,8,3]=>[5,2,1]=>64
[8,3,4,5,7,1,2,6]=>[4,3,1]=>70
[8,3,4,7,6,1,2,5]=>[3,3,1,1]=>56
[8,3,7,5,6,1,2,4]=>[3,3,1,1]=>56
[7,3,4,5,6,1,8,2]=>[5,2,1]=>64
[2,3,4,5,8,7,1,6]=>[5,2,1]=>64
[2,3,4,8,6,7,1,5]=>[5,2,1]=>64
[2,3,8,5,6,7,1,4]=>[5,2,1]=>64
[2,8,4,5,6,7,1,3]=>[5,2,1]=>64
[9,1,2,3,4,5,6,7,8]=>[8,1]=>8
[8,1,2,3,4,5,6,9,7]=>[7,2]=>27
[7,1,2,3,4,5,9,6,8]=>[7,2]=>27
[9,1,2,3,4,5,8,6,7]=>[7,1,1]=>28
[7,1,2,3,4,5,8,9,6]=>[7,2]=>27
[6,1,2,3,4,9,5,7,8]=>[7,2]=>27
[6,1,2,3,4,8,5,9,7]=>[6,3]=>48
[9,1,2,3,4,7,5,6,8]=>[7,1,1]=>28
[9,1,2,3,4,8,5,6,7]=>[7,1,1]=>28
[8,1,2,3,4,7,5,9,6]=>[6,2,1]=>105
[6,1,2,3,4,7,9,5,8]=>[6,3]=>48
[6,1,2,3,4,9,8,5,7]=>[6,2,1]=>105
[9,1,2,3,4,7,8,5,6]=>[6,2,1]=>105
[6,1,2,3,4,7,8,9,5]=>[7,2]=>27
[5,1,2,3,9,4,6,7,8]=>[7,2]=>27
[5,1,2,3,8,4,6,9,7]=>[6,3]=>48
[8,1,2,3,9,4,5,6,7]=>[7,2]=>27
[5,1,2,3,9,8,4,6,7]=>[6,2,1]=>105
[9,1,2,3,6,8,4,5,7]=>[6,2,1]=>105
[5,1,2,3,6,9,8,4,7]=>[5,3,1]=>162
[5,1,2,3,6,7,8,9,4]=>[7,2]=>27
[4,1,2,8,3,5,6,9,7]=>[6,3]=>48
[4,1,2,9,3,5,8,6,7]=>[6,2,1]=>105
[4,1,2,9,3,8,5,6,7]=>[6,2,1]=>105
[9,1,2,8,3,4,5,6,7]=>[7,1,1]=>28
[7,1,2,8,3,4,5,9,6]=>[6,3]=>48
[4,1,2,5,9,3,6,7,8]=>[6,3]=>48
[4,1,2,8,9,3,5,6,7]=>[6,3]=>48
[8,1,2,5,9,3,4,6,7]=>[6,2,1]=>105
[8,1,2,9,6,3,4,5,7]=>[6,2,1]=>105
[4,1,2,5,9,8,3,6,7]=>[5,3,1]=>162
[9,1,2,8,6,7,3,4,5]=>[5,2,1,1]=>189
[4,1,2,5,6,7,9,3,8]=>[6,3]=>48
[4,1,2,9,6,7,8,3,5]=>[5,3,1]=>162
[9,1,2,5,6,7,8,3,4]=>[6,2,1]=>105
[4,1,2,5,6,7,8,9,3]=>[7,2]=>27
[3,1,9,2,4,5,6,7,8]=>[7,2]=>27
[3,1,8,2,4,5,6,9,7]=>[6,3]=>48
[3,1,9,2,4,5,8,6,7]=>[6,2,1]=>105
[8,1,4,2,3,5,6,9,7]=>[6,2,1]=>105
[9,1,4,2,3,5,8,6,7]=>[6,2,1]=>105
[6,1,4,2,3,7,8,9,5]=>[6,2,1]=>105
[9,1,8,2,3,4,5,6,7]=>[7,1,1]=>28
[8,1,7,2,3,4,5,9,6]=>[6,2,1]=>105
[3,1,4,9,2,5,6,7,8]=>[6,3]=>48
[3,1,4,9,2,5,8,6,7]=>[5,3,1]=>162
[3,1,9,8,2,4,5,6,7]=>[6,2,1]=>105
[9,1,4,5,2,3,6,7,8]=>[6,2,1]=>105
[7,1,4,5,2,3,8,9,6]=>[5,3,1]=>162
[7,1,4,9,2,3,5,6,8]=>[6,2,1]=>105
[9,1,4,8,2,3,5,6,7]=>[6,2,1]=>105
[9,1,6,5,2,3,4,7,8]=>[6,1,1,1]=>56
[7,1,9,6,2,3,4,5,8]=>[6,2,1]=>105
[9,1,8,6,2,3,4,5,7]=>[6,1,1,1]=>56
[7,1,8,9,2,3,4,5,6]=>[6,3]=>48
[3,1,4,8,9,2,5,6,7]=>[5,4]=>42
[3,1,8,9,7,2,4,5,6]=>[5,3,1]=>162
[8,1,4,5,6,2,3,9,7]=>[5,3,1]=>162
[8,1,4,9,7,2,3,5,6]=>[5,2,2]=>120
[8,1,9,5,6,2,3,4,7]=>[5,2,2]=>120
[8,1,9,7,6,2,3,4,5]=>[5,2,1,1]=>189
[7,1,4,5,6,2,8,9,3]=>[6,2,1]=>105
[3,1,4,5,6,9,2,7,8]=>[6,3]=>48
[3,1,4,5,6,8,2,9,7]=>[6,3]=>48
[3,1,4,9,8,7,2,5,6]=>[4,3,1,1]=>216
[3,1,9,8,6,7,2,4,5]=>[4,3,1,1]=>216
[9,1,4,5,6,7,2,3,8]=>[6,2,1]=>105
[9,1,4,8,6,7,2,3,5]=>[4,3,1,1]=>216
[9,1,8,5,6,7,2,3,4]=>[4,3,1,1]=>216
[8,1,4,5,6,7,2,9,3]=>[6,2,1]=>105
[3,1,4,5,6,7,9,2,8]=>[6,3]=>48
[3,1,4,9,6,7,8,2,5]=>[5,3,1]=>162
[3,1,9,5,6,7,8,2,4]=>[5,3,1]=>162
[9,1,4,5,6,7,8,2,3]=>[6,2,1]=>105
[3,1,4,5,6,7,8,9,2]=>[7,2]=>27
[2,9,1,3,4,5,6,7,8]=>[7,2]=>27
[2,8,1,3,4,5,6,9,7]=>[6,3]=>48
[2,7,1,3,4,5,9,6,8]=>[6,3]=>48
[2,9,1,3,4,5,8,6,7]=>[6,2,1]=>105
[2,7,1,3,4,5,8,9,6]=>[6,3]=>48
[2,6,1,3,4,9,5,7,8]=>[6,3]=>48
[2,9,1,3,4,8,5,6,7]=>[6,2,1]=>105
[2,8,1,3,9,4,5,6,7]=>[6,3]=>48
[2,9,1,3,8,7,4,5,6]=>[5,2,1,1]=>189
[2,9,1,3,6,7,8,4,5]=>[5,3,1]=>162
[2,5,1,3,6,7,8,9,4]=>[6,3]=>48
[2,4,1,6,3,8,5,9,7]=>[5,4]=>42
[2,9,1,8,3,4,5,6,7]=>[6,2,1]=>105
[2,7,1,6,3,4,8,9,5]=>[5,3,1]=>162
[2,6,1,5,3,7,8,9,4]=>[5,3,1]=>162
[2,4,1,5,9,3,6,7,8]=>[6,3]=>48
[2,4,1,8,9,3,5,6,7]=>[5,4]=>42
[2,8,1,9,7,3,4,5,6]=>[5,3,1]=>162
[2,9,1,8,6,7,3,4,5]=>[4,3,1,1]=>216
[2,4,1,5,6,7,9,3,8]=>[6,3]=>48
[2,4,1,5,6,9,8,3,7]=>[5,3,1]=>162
[2,9,1,5,6,7,8,3,4]=>[5,3,1]=>162
[2,4,1,5,6,7,8,9,3]=>[7,2]=>27
[9,3,1,2,4,5,6,7,8]=>[7,1,1]=>28
[8,3,1,2,4,5,6,9,7]=>[6,2,1]=>105
[9,3,1,2,4,5,8,6,7]=>[6,2,1]=>105
[6,3,1,2,4,7,8,9,5]=>[6,2,1]=>105
[9,3,1,2,6,7,8,4,5]=>[5,3,1]=>162
[5,3,1,2,6,7,8,9,4]=>[6,2,1]=>105
[9,4,1,2,3,5,6,7,8]=>[7,1,1]=>28
[7,4,1,2,3,5,8,9,6]=>[6,2,1]=>105
[6,4,1,2,3,7,8,9,5]=>[6,2,1]=>105
[5,9,1,2,3,4,6,7,8]=>[7,2]=>27
[5,8,1,2,3,4,6,9,7]=>[6,3]=>48
[5,7,1,2,3,4,8,9,6]=>[6,3]=>48
[9,6,1,2,3,4,5,7,8]=>[7,1,1]=>28
[8,6,1,2,3,4,5,9,7]=>[6,2,1]=>105
[9,7,1,2,3,4,5,6,8]=>[7,1,1]=>28
[8,9,1,2,3,4,5,6,7]=>[7,2]=>27
[8,7,1,2,3,4,5,9,6]=>[6,2,1]=>105
[9,6,1,2,3,4,8,5,7]=>[6,2,1]=>105
[9,7,1,2,3,4,8,5,6]=>[6,2,1]=>105
[7,6,1,2,3,4,8,9,5]=>[6,2,1]=>105
[5,9,1,2,3,8,4,6,7]=>[6,2,1]=>105
[9,8,1,2,3,7,4,5,6]=>[6,1,1,1]=>56
[8,6,1,2,3,7,4,9,5]=>[5,3,1]=>162
[9,6,1,2,3,7,8,4,5]=>[5,3,1]=>162
[5,6,1,2,3,7,8,9,4]=>[6,3]=>48
[5,4,1,2,9,3,6,7,8]=>[6,2,1]=>105
[8,4,1,2,9,3,5,6,7]=>[6,2,1]=>105
[5,8,1,2,9,3,4,6,7]=>[6,3]=>48
[9,7,1,2,6,3,8,4,5]=>[5,2,1,1]=>189
[9,8,1,2,6,7,3,4,5]=>[5,2,1,1]=>189
[5,4,1,2,6,7,9,3,8]=>[5,3,1]=>162
[5,4,1,2,6,7,8,9,3]=>[6,2,1]=>105
[4,3,1,9,2,5,6,7,8]=>[6,2,1]=>105
[9,3,1,8,2,4,5,6,7]=>[6,2,1]=>105
[9,4,1,8,2,3,5,6,7]=>[6,2,1]=>105
[6,9,1,5,2,3,4,7,8]=>[6,2,1]=>105
[9,7,1,6,2,3,4,5,8]=>[6,1,1,1]=>56
[8,7,1,9,2,3,4,5,6]=>[6,2,1]=>105
[8,7,1,6,2,3,4,9,5]=>[5,2,1,1]=>189
[9,8,1,6,2,7,3,4,5]=>[5,2,1,1]=>189
[9,8,1,7,6,2,3,4,5]=>[5,1,1,1,1]=>70
[4,3,1,5,6,8,2,9,7]=>[5,3,1]=>162
[4,3,1,5,9,8,2,6,7]=>[4,3,2]=>168
[4,3,1,5,8,7,2,9,6]=>[4,3,2]=>168
[8,9,1,5,6,7,2,3,4]=>[4,3,2]=>168
[4,3,1,5,6,7,9,2,8]=>[5,3,1]=>162
[4,3,1,5,6,9,8,2,7]=>[4,3,2]=>168
[9,3,1,5,6,7,8,2,4]=>[5,3,1]=>162
[9,4,1,5,6,7,8,2,3]=>[5,3,1]=>162
[4,3,1,5,6,7,8,9,2]=>[6,2,1]=>105
[2,3,9,1,4,5,6,7,8]=>[7,2]=>27
[2,3,8,1,4,5,6,9,7]=>[6,3]=>48
[2,3,9,1,4,5,8,6,7]=>[6,2,1]=>105
[2,3,9,1,4,7,8,5,6]=>[5,3,1]=>162
[2,3,9,1,8,7,4,5,6]=>[5,2,1,1]=>189
[2,3,8,1,6,7,4,9,5]=>[5,3,1]=>162
[2,3,5,1,6,7,9,4,8]=>[6,3]=>48
[2,3,9,1,6,7,8,4,5]=>[5,3,1]=>162
[2,3,5,1,6,7,8,9,4]=>[7,2]=>27
[2,9,4,1,3,5,6,7,8]=>[6,2,1]=>105
[2,6,4,1,3,7,8,9,5]=>[5,3,1]=>162
[2,9,5,1,3,4,6,7,8]=>[6,2,1]=>105
[2,6,9,1,3,4,5,7,8]=>[6,3]=>48
[2,9,7,1,3,4,5,6,8]=>[6,2,1]=>105
[2,9,8,1,3,4,5,6,7]=>[6,2,1]=>105
[2,6,7,1,3,4,8,9,5]=>[5,4]=>42
[2,9,4,1,6,3,5,7,8]=>[5,3,1]=>162
[2,8,4,1,9,3,5,6,7]=>[5,3,1]=>162
[2,9,4,1,6,3,8,5,7]=>[4,4,1]=>84
[2,9,8,1,7,3,4,5,6]=>[5,2,1,1]=>189
[2,9,5,1,6,7,8,3,4]=>[5,3,1]=>162
[9,3,4,1,2,5,6,7,8]=>[6,2,1]=>105
[6,3,4,1,2,7,8,9,5]=>[5,3,1]=>162
[9,3,7,1,2,4,5,6,8]=>[6,2,1]=>105
[9,3,8,1,2,4,5,6,7]=>[6,2,1]=>105
[9,5,4,1,2,3,6,7,8]=>[6,1,1,1]=>56
[8,5,4,1,2,3,6,9,7]=>[5,2,1,1]=>189
[6,9,4,1,2,3,5,7,8]=>[6,2,1]=>105
[6,8,4,1,2,3,5,9,7]=>[5,3,1]=>162
[9,7,4,1,2,3,5,6,8]=>[6,1,1,1]=>56
[9,8,4,1,2,3,5,6,7]=>[6,1,1,1]=>56
[6,9,5,1,2,3,4,7,8]=>[6,2,1]=>105
[6,8,5,1,2,3,4,9,7]=>[5,3,1]=>162
[8,7,5,1,2,3,4,9,6]=>[5,2,1,1]=>189
[6,7,9,1,2,3,4,5,8]=>[6,3]=>48
[6,9,8,1,2,3,4,5,7]=>[6,2,1]=>105
[9,7,8,1,2,3,4,5,6]=>[6,2,1]=>105
[6,7,8,1,2,3,4,9,5]=>[5,4]=>42
[6,5,4,1,2,8,3,9,7]=>[4,3,1,1]=>216
[7,8,9,1,6,2,3,4,5]=>[5,3,1]=>162
[7,8,5,1,6,2,3,9,4]=>[4,3,2]=>168
[5,3,4,1,6,8,2,9,7]=>[5,3,1]=>162
[9,3,4,1,8,7,2,5,6]=>[4,3,1,1]=>216
[8,3,4,1,6,7,2,9,5]=>[5,3,1]=>162
[8,5,4,1,6,7,2,9,3]=>[4,3,1,1]=>216
[5,3,4,1,9,7,8,2,6]=>[4,3,2]=>168
[9,3,5,1,6,7,8,2,4]=>[5,3,1]=>162
[9,5,4,1,6,7,8,2,3]=>[4,3,1,1]=>216
[5,3,4,1,6,7,8,9,2]=>[6,2,1]=>105
[2,3,4,9,1,5,6,7,8]=>[7,2]=>27
[2,3,4,9,1,5,8,6,7]=>[6,2,1]=>105
[2,3,4,9,1,7,8,5,6]=>[5,3,1]=>162
[2,3,4,6,1,7,8,9,5]=>[7,2]=>27
[2,3,9,5,1,4,6,7,8]=>[6,2,1]=>105
[2,3,9,6,1,4,5,7,8]=>[6,2,1]=>105
[2,3,7,9,1,4,5,6,8]=>[6,3]=>48
[2,3,9,8,1,4,5,6,7]=>[6,2,1]=>105
[2,3,9,5,1,7,4,6,8]=>[5,3,1]=>162
[2,3,9,6,1,7,8,4,5]=>[5,3,1]=>162
[2,9,4,5,1,3,6,7,8]=>[6,2,1]=>105
[2,7,4,5,1,3,8,9,6]=>[5,3,1]=>162
[2,9,8,6,1,3,4,5,7]=>[5,2,1,1]=>189
[2,7,8,9,1,3,4,5,6]=>[5,4]=>42
[2,8,9,6,1,7,3,4,5]=>[4,3,2]=>168
[2,9,6,5,1,7,8,3,4]=>[4,3,1,1]=>216
[7,3,4,5,1,2,8,9,6]=>[5,3,1]=>162
[9,3,4,8,1,2,5,6,7]=>[5,3,1]=>162
[7,3,4,8,1,2,5,9,6]=>[4,4,1]=>84
[7,3,8,9,1,2,4,5,6]=>[5,3,1]=>162
[9,8,4,5,1,2,3,6,7]=>[5,2,1,1]=>189
[7,8,4,6,1,2,3,9,5]=>[4,3,2]=>168
[9,8,6,5,1,2,3,4,7]=>[5,1,1,1,1]=>70
[7,8,9,6,1,2,3,4,5]=>[5,3,1]=>162
[7,8,6,5,1,2,3,9,4]=>[4,3,1,1]=>216
[8,3,9,6,1,7,2,4,5]=>[4,3,2]=>168
[8,3,6,5,1,7,2,9,4]=>[4,3,1,1]=>216
[8,6,4,5,1,7,2,9,3]=>[4,3,1,1]=>216
[6,3,4,5,1,7,9,2,8]=>[5,3,1]=>162
[6,3,4,5,1,9,8,2,7]=>[4,3,2]=>168
[9,3,4,6,1,7,8,2,5]=>[5,3,1]=>162
[6,3,4,5,1,7,8,9,2]=>[6,2,1]=>105
[2,3,4,5,9,1,6,7,8]=>[7,2]=>27
[2,3,4,5,8,1,6,9,7]=>[6,3]=>48
[2,3,4,5,9,1,8,6,7]=>[6,2,1]=>105
[2,3,4,5,7,1,8,9,6]=>[7,2]=>27
[2,3,4,9,6,1,5,7,8]=>[6,2,1]=>105
[2,3,4,9,7,1,5,6,8]=>[6,2,1]=>105
[2,3,4,9,6,1,8,5,7]=>[5,3,1]=>162
[2,3,4,9,7,1,8,5,6]=>[5,3,1]=>162
[2,3,9,5,6,1,4,7,8]=>[6,2,1]=>105
[2,3,8,5,6,1,4,9,7]=>[5,3,1]=>162
[2,3,9,5,6,1,8,4,7]=>[5,3,1]=>162
[2,8,4,5,6,1,3,9,7]=>[5,3,1]=>162
[2,8,9,5,7,1,3,4,6]=>[4,3,2]=>168
[2,8,9,7,6,1,3,4,5]=>[4,3,1,1]=>216
[2,9,7,5,6,1,8,3,4]=>[4,3,1,1]=>216
[8,3,4,5,6,1,2,9,7]=>[5,3,1]=>162
[8,3,4,7,6,1,2,9,5]=>[4,3,1,1]=>216
[8,3,9,7,6,1,2,4,5]=>[4,2,2,1]=>216
[8,3,7,5,6,1,2,9,4]=>[4,3,1,1]=>216
[9,7,4,5,6,1,2,3,8]=>[4,3,1,1]=>216
[8,9,4,5,6,1,2,3,7]=>[4,3,2]=>168
[8,9,7,5,6,1,2,3,4]=>[4,2,2,1]=>216
[8,7,4,5,6,1,2,9,3]=>[4,3,1,1]=>216
[7,3,4,5,6,1,9,2,8]=>[5,3,1]=>162
[9,3,4,5,6,1,8,2,7]=>[5,3,1]=>162
[9,3,7,5,6,1,8,2,4]=>[4,3,1,1]=>216
[7,3,4,5,6,1,8,9,2]=>[6,2,1]=>105
[2,3,4,5,6,9,1,7,8]=>[7,2]=>27
[2,3,4,5,6,8,1,9,7]=>[7,2]=>27
[2,3,4,5,9,7,1,6,8]=>[6,2,1]=>105
[2,3,4,5,9,8,1,6,7]=>[6,2,1]=>105
[2,3,4,9,6,7,1,5,8]=>[6,2,1]=>105
[2,3,9,5,6,7,1,4,8]=>[6,2,1]=>105
[2,3,9,5,6,8,1,4,7]=>[5,3,1]=>162
[2,9,4,5,6,7,1,3,8]=>[6,2,1]=>105
[2,9,4,5,6,8,1,3,7]=>[5,3,1]=>162
[2,9,4,5,8,7,1,3,6]=>[4,3,1,1]=>216
[2,9,4,8,6,7,1,3,5]=>[4,3,1,1]=>216
[2,9,8,5,6,7,1,3,4]=>[4,3,1,1]=>216
[2,8,4,5,6,7,1,9,3]=>[6,2,1]=>105
[9,3,4,5,6,7,1,2,8]=>[6,2,1]=>105
[9,3,4,5,6,8,1,2,7]=>[5,3,1]=>162
[9,8,4,5,6,7,1,2,3]=>[4,3,1,1]=>216
[8,3,4,5,6,7,1,9,2]=>[6,2,1]=>105
[2,3,4,5,6,7,9,1,8]=>[7,2]=>27
[2,3,4,5,6,9,8,1,7]=>[6,2,1]=>105
[2,3,4,5,9,7,8,1,6]=>[6,2,1]=>105
[2,3,4,9,6,7,8,1,5]=>[6,2,1]=>105
[2,3,9,5,6,7,8,1,4]=>[6,2,1]=>105
[2,9,4,5,6,7,8,1,3]=>[6,2,1]=>105
[9,3,4,5,6,7,8,1,2]=>[6,2,1]=>105
[2,3,4,5,6,7,8,9,1]=>[8,1]=>8
[]=>[]=>1
[3,5,2,6,1,4,8,7]=>[4,3,1]=>70
[3,5,2,6,4,1,8,7]=>[4,3,1]=>70
[3,5,2,7,4,8,1,6]=>[4,3,1]=>70
[3,5,2,7,4,8,6,1]=>[4,3,1]=>70
[4,5,7,2,3,8,6,1]=>[4,3,1]=>70
[4,5,7,2,3,8,1,6]=>[4,3,1]=>70
[4,5,6,2,3,1,8,7]=>[4,3,1]=>70
[4,5,6,2,1,3,8,7]=>[4,3,1]=>70
[3,5,1,6,4,2,8,7]=>[4,3,1]=>70
[4,5,6,1,3,2,8,7]=>[4,3,1]=>70
[4,5,6,3,1,2,8,7]=>[4,3,1]=>70
[4,5,7,3,2,8,1,6]=>[4,2,1,1]=>90
[4,5,7,3,2,8,6,1]=>[4,2,1,1]=>90
[4,6,7,3,8,2,5,1]=>[4,2,1,1]=>90
[4,6,7,3,8,2,1,5]=>[4,2,1,1]=>90
[4,6,7,3,8,1,2,5]=>[4,3,1]=>70
[4,5,7,3,1,8,2,6]=>[4,3,1]=>70
[4,5,7,1,3,8,2,6]=>[4,3,1]=>70
[3,5,1,7,4,8,2,6]=>[4,3,1]=>70
[2,1,5,7,4,8,3,6]=>[4,3,1]=>70
[2,1,5,7,4,8,6,3]=>[4,3,1]=>70
[3,5,1,7,4,8,6,2]=>[4,3,1]=>70
[4,5,7,1,3,8,6,2]=>[4,3,1]=>70
[4,5,7,3,1,8,6,2]=>[4,2,2]=>56
[4,6,7,3,8,1,5,2]=>[4,2,2]=>56
[4,6,7,3,8,5,1,2]=>[4,2,2]=>56
[4,6,7,3,8,5,2,1]=>[4,2,1,1]=>90
[5,6,7,8,3,1,4,2]=>[4,2,2]=>56
[5,6,7,8,1,3,4,2]=>[4,3,1]=>70
[4,6,7,1,8,3,5,2]=>[4,3,1]=>70
[3,6,1,7,8,4,5,2]=>[4,3,1]=>70
[2,1,6,7,8,4,5,3]=>[4,3,1]=>70
[2,1,6,7,8,4,3,5]=>[4,3,1]=>70
[3,6,1,7,8,4,2,5]=>[4,3,1]=>70
[4,6,7,1,8,3,2,5]=>[4,3,1]=>70
[5,6,7,8,1,3,2,4]=>[4,3,1]=>70
[4,5,7,2,1,8,3,6]=>[4,3,1]=>70
[4,6,7,2,8,1,3,5]=>[4,3,1]=>70
[4,6,7,2,8,3,1,5]=>[4,3,1]=>70
[4,6,7,2,8,3,5,1]=>[4,3,1]=>70
[3,6,2,7,8,4,5,1]=>[4,3,1]=>70
[3,6,2,7,8,4,1,5]=>[4,3,1]=>70
[3,6,2,7,8,1,4,5]=>[4,3,1]=>70
[3,5,2,7,1,8,4,6]=>[4,3,1]=>70
[3,4,2,1,7,8,5,6]=>[4,3,1]=>70
[3,4,1,2,7,8,6,5]=>[4,3,1]=>70
[3,5,2,7,1,8,6,4]=>[4,2,2]=>56
[3,6,2,7,8,1,5,4]=>[4,2,2]=>56
[3,6,2,7,8,5,1,4]=>[4,2,2]=>56
[3,6,2,7,8,5,4,1]=>[4,2,1,1]=>90
[4,6,7,2,8,5,3,1]=>[4,2,1,1]=>90
[4,6,7,2,8,5,1,3]=>[4,2,2]=>56
[4,6,7,2,8,1,5,3]=>[4,2,2]=>56
[4,5,7,2,1,8,6,3]=>[4,2,2]=>56
[4,5,7,1,2,8,6,3]=>[4,3,1]=>70
[3,5,1,7,2,8,6,4]=>[4,3,1]=>70
[2,1,5,7,3,8,6,4]=>[4,3,1]=>70
[2,1,6,7,8,3,5,4]=>[4,3,1]=>70
[3,6,1,7,8,2,5,4]=>[4,3,1]=>70
[4,6,7,1,8,2,5,3]=>[4,3,1]=>70
[5,6,7,8,1,2,4,3]=>[4,3,1]=>70
[5,6,7,8,2,1,4,3]=>[4,2,2]=>56
[5,6,7,8,2,4,1,3]=>[4,2,2]=>56
[5,6,7,8,2,4,3,1]=>[4,2,1,1]=>90
[5,6,7,8,1,4,2,3]=>[4,3,1]=>70
[4,6,7,1,8,5,2,3]=>[4,3,1]=>70
[3,6,1,7,8,5,2,4]=>[4,3,1]=>70
[2,1,6,7,8,5,3,4]=>[4,3,1]=>70
[3,6,1,7,8,5,4,2]=>[4,2,1,1]=>90
[4,6,7,1,8,5,3,2]=>[4,2,1,1]=>90
[5,6,7,8,1,4,3,2]=>[4,2,1,1]=>90
[5,6,7,8,4,1,3,2]=>[4,2,1,1]=>90
[3,4,2,1,6,5,8,7,10,9]=>[5,4,1]=>288
[3,5,2,6,4,1,8,7,10,9]=>[5,4,1]=>288
[3,5,2,7,4,8,6,1,10,9]=>[5,4,1]=>288
[3,5,2,7,4,9,6,10,8,1]=>[5,4,1]=>288
[2,1,5,6,4,3,8,7,10,9]=>[5,4,1]=>288
[4,5,6,3,2,1,8,7,10,9]=>[5,3,1,1]=>567
[4,5,7,3,2,8,6,1,10,9]=>[5,3,1,1]=>567
[4,5,7,3,2,9,6,10,8,1]=>[5,3,1,1]=>567
[2,1,5,7,4,8,6,3,10,9]=>[5,4,1]=>288
[4,6,7,3,8,5,2,1,10,9]=>[5,3,1,1]=>567
[4,6,7,3,9,5,2,10,8,1]=>[5,3,1,1]=>567
[2,1,5,7,4,9,6,10,8,3]=>[5,4,1]=>288
[4,6,8,3,9,5,10,7,2,1]=>[5,3,1,1]=>567
[2,1,4,3,7,8,6,5,10,9]=>[5,4,1]=>288
[3,4,2,1,7,8,6,5,10,9]=>[5,3,2]=>450
[3,6,2,7,8,5,4,1,10,9]=>[5,3,1,1]=>567
[3,6,2,7,9,5,4,10,8,1]=>[5,3,1,1]=>567
[2,1,6,7,8,5,4,3,10,9]=>[5,3,1,1]=>567
[5,6,7,8,4,3,2,1,10,9]=>[5,2,1,1,1]=>448
[5,6,7,9,4,3,2,10,8,1]=>[5,2,1,1,1]=>448
[2,1,6,7,9,5,4,10,8,3]=>[5,3,1,1]=>567
[5,6,8,9,4,3,10,7,2,1]=>[5,2,1,1,1]=>448
[2,1,4,3,7,9,6,10,8,5]=>[5,4,1]=>288
[3,4,2,1,7,9,6,10,8,5]=>[5,3,2]=>450
[3,6,2,8,9,5,10,7,4,1]=>[5,3,1,1]=>567
[2,1,6,8,9,5,10,7,4,3]=>[5,3,1,1]=>567
[5,7,8,9,4,10,6,3,2,1]=>[5,2,1,1,1]=>448
[6,7,8,9,10,1,4,5,3,2]=>[5,3,1,1]=>567
[6,7,8,9,10,1,4,5,2,3]=>[5,3,2]=>450
[6,7,8,9,10,4,3,2,1,5]=>[5,2,1,1,1]=>448
[6,7,8,9,10,1,3,4,5,2]=>[5,4,1]=>288
[6,7,8,9,10,3,4,1,2,5]=>[5,3,2]=>450
[6,7,8,9,10,3,4,2,1,5]=>[5,3,1,1]=>567
[6,7,8,9,10,2,3,4,1,5]=>[5,4,1]=>288
[2,1,4,3,6,5,9,10,8,7]=>[5,4,1]=>288
[3,4,2,1,6,5,9,10,8,7]=>[5,3,2]=>450
[3,5,2,6,4,1,9,10,8,7]=>[5,3,2]=>450
[3,5,2,8,4,9,10,7,6,1]=>[5,3,1,1]=>567
[2,1,5,6,4,3,9,10,8,7]=>[5,3,2]=>450
[4,5,6,3,2,1,9,10,8,7]=>[5,2,2,1]=>525
[4,5,8,3,2,9,10,7,6,1]=>[5,2,2,1]=>525
[2,1,5,8,4,9,10,7,6,3]=>[5,3,1,1]=>567
[4,7,8,3,9,10,6,5,2,1]=>[5,2,1,1,1]=>448
[2,1,4,3,8,9,10,7,6,5]=>[5,3,1,1]=>567
[3,4,2,1,8,9,10,7,6,5]=>[5,2,2,1]=>525
[3,7,2,8,9,10,6,5,4,1]=>[5,2,1,1,1]=>448
[2,1,7,8,9,10,6,5,4,3]=>[5,2,1,1,1]=>448
[6,7,8,9,10,1,5,4,3,2]=>[5,2,1,1,1]=>448
[6,7,8,9,10,5,4,3,2,1]=>[5,1,1,1,1,1]=>126
[6,5,8,7,3,4,1,2]=>[2,2,2,2]=>14
[3,6,7,4,5,8,1,2]=>[4,2,2]=>56
[1,6,7,4,5,2,3,8]=>[4,2,2]=>56
[1,5,4,7,6,2,3,8]=>[4,2,2]=>56
[3,5,4,7,6,8,1,2]=>[4,2,2]=>56
[4,5,3,7,8,6,1,2]=>[4,2,2]=>56
[5,4,3,8,7,6,1,2]=>[2,2,2,2]=>14
[6,4,8,3,7,5,1,2]=>[2,2,2,2]=>14
[6,3,8,4,5,7,1,2]=>[4,2,2]=>56
[3,2,5,6,1,8,7,4]=>[4,2,2]=>56
[6,2,8,4,5,1,7,3]=>[4,2,2]=>56
[7,8,1,4,5,2,3,6]=>[4,2,2]=>56
[4,1,3,2,8,6,5,7]=>[4,2,2]=>56
[6,2,8,3,1,5,7,4]=>[4,2,2]=>56
[5,2,3,8,1,6,7,4]=>[4,2,2]=>56
[6,3,8,2,1,7,5,4]=>[2,2,2,2]=>14
[7,8,3,2,1,6,5,4]=>[2,2,2,2]=>14
[7,8,4,2,6,1,5,3]=>[2,2,2,2]=>14
[5,4,2,8,7,1,6,3]=>[2,2,2,2]=>14
[4,5,2,7,8,1,6,3]=>[4,2,2]=>56
[2,5,3,7,1,6,8,4]=>[4,2,2]=>56
[1,5,3,7,2,6,4,8]=>[4,2,2]=>56
[1,6,7,3,2,5,4,8]=>[4,2,2]=>56
[2,6,7,3,1,5,8,4]=>[4,2,2]=>56
[3,6,7,2,1,8,5,4]=>[4,2,2]=>56
[7,8,5,6,2,1,4,3]=>[2,2,2,2]=>14
[6,5,8,7,1,2,3,4]=>[4,2,2]=>56
[6,4,8,1,7,2,3,5]=>[4,2,2]=>56
[7,8,3,1,2,6,4,5]=>[4,2,2]=>56
[5,3,1,8,2,7,4,6]=>[4,2,2]=>56
[4,3,1,2,8,7,5,6]=>[4,2,2]=>56
[4,2,1,3,8,5,7,6]=>[4,2,2]=>56
[4,3,1,2,6,5,8,7]=>[4,3,1]=>70
[5,3,1,6,2,4,8,7]=>[4,3,1]=>70
[6,3,1,5,2,4,8,7]=>[4,3,1]=>70
[7,3,1,5,2,8,4,6]=>[4,3,1]=>70
[8,4,5,1,2,7,3,6]=>[4,3,1]=>70
[7,4,5,1,2,8,3,6]=>[4,3,1]=>70
[6,4,5,1,2,3,8,7]=>[4,3,1]=>70
[5,4,6,1,2,3,8,7]=>[4,3,1]=>70
[2,1,6,5,3,4,8,7]=>[4,3,1]=>70
[3,6,1,5,2,4,8,7]=>[4,3,1]=>70
[4,6,5,1,2,3,8,7]=>[4,3,1]=>70
[5,6,4,1,2,3,8,7]=>[4,3,1]=>70
[6,5,4,1,2,3,8,7]=>[4,2,1,1]=>90
[7,5,4,1,2,8,3,6]=>[4,2,1,1]=>90
[8,6,4,1,7,2,3,5]=>[4,2,1,1]=>90
[7,6,4,1,8,2,3,5]=>[4,2,1,1]=>90
[6,7,4,1,8,2,3,5]=>[4,3,1]=>70
[5,7,4,1,2,8,3,6]=>[4,3,1]=>70
[4,7,5,1,2,8,3,6]=>[4,3,1]=>70
[3,7,1,5,2,8,4,6]=>[4,3,1]=>70
[2,1,7,5,3,8,4,6]=>[4,3,1]=>70
[2,1,8,5,3,7,4,6]=>[4,3,1]=>70
[3,8,1,5,2,7,4,6]=>[4,3,1]=>70
[4,8,5,1,2,7,3,6]=>[4,3,1]=>70
[5,8,4,1,2,7,3,6]=>[4,2,2]=>56
[6,8,4,1,7,2,3,5]=>[4,2,2]=>56
[8,7,4,1,6,2,3,5]=>[4,2,1,1]=>90
[5,8,6,7,1,2,3,4]=>[4,3,1]=>70
[4,8,6,1,7,2,3,5]=>[4,3,1]=>70
[3,8,1,6,7,2,4,5]=>[4,3,1]=>70
[2,1,8,6,7,3,4,5]=>[4,3,1]=>70
[2,1,7,6,8,3,4,5]=>[4,3,1]=>70
[3,7,1,6,8,2,4,5]=>[4,3,1]=>70
[4,7,6,1,8,2,3,5]=>[4,3,1]=>70
[5,7,6,8,1,2,3,4]=>[4,3,1]=>70
[5,4,7,1,2,8,3,6]=>[4,3,1]=>70
[6,4,7,1,8,2,3,5]=>[4,3,1]=>70
[7,4,6,1,8,2,3,5]=>[4,3,1]=>70
[8,4,6,1,7,2,3,5]=>[4,3,1]=>70
[8,3,1,6,7,2,4,5]=>[4,3,1]=>70
[7,3,1,6,8,2,4,5]=>[4,3,1]=>70
[6,3,1,7,8,2,4,5]=>[4,3,1]=>70
[5,3,1,7,2,8,4,6]=>[4,3,1]=>70
[4,3,1,2,7,8,5,6]=>[4,3,1]=>70
[2,1,4,3,8,7,5,6]=>[4,3,1]=>70
[3,4,1,2,8,7,5,6]=>[4,3,1]=>70
[6,3,1,8,7,2,4,5]=>[4,2,2]=>56
[7,3,1,8,6,2,4,5]=>[4,2,2]=>56
[8,4,7,1,6,2,3,5]=>[4,2,1,1]=>90
[7,4,8,1,6,2,3,5]=>[4,2,2]=>56
[5,4,8,1,2,7,3,6]=>[4,2,2]=>56
[4,5,8,1,2,7,3,6]=>[4,3,1]=>70
[3,5,1,8,2,7,4,6]=>[4,3,1]=>70
[2,1,5,8,3,7,4,6]=>[4,3,1]=>70
[2,1,6,8,7,3,4,5]=>[4,3,1]=>70
[3,6,1,8,7,2,4,5]=>[4,3,1]=>70
[4,6,8,1,7,2,3,5]=>[4,3,1]=>70
[5,6,8,7,1,2,3,4]=>[4,3,1]=>70
[7,5,8,6,1,2,3,4]=>[4,2,2]=>56
[8,5,7,6,1,2,3,4]=>[4,2,1,1]=>90
[5,7,8,6,1,2,3,4]=>[4,3,1]=>70
[4,7,8,1,6,2,3,5]=>[4,3,1]=>70
[3,7,1,8,6,2,4,5]=>[4,3,1]=>70
[2,1,7,8,6,3,4,5]=>[4,3,1]=>70
[2,1,8,7,6,3,4,5]=>[4,2,1,1]=>90
[3,8,1,7,6,2,4,5]=>[4,2,1,1]=>90
[4,8,7,1,6,2,3,5]=>[4,2,1,1]=>90
[5,8,7,6,1,2,3,4]=>[4,2,1,1]=>90
[6,8,7,5,1,2,3,4]=>[4,2,1,1]=>90
[6,4,7,3,8,5,1,2]=>[3,2,2,1]=>70
[6,4,7,2,5,1,8,3]=>[3,2,2,1]=>70
[5,4,3,7,6,8,1,2]=>[3,2,2,1]=>70
[6,4,8,3,5,7,1,2]=>[3,2,2,1]=>70
[5,4,2,6,7,1,8,3]=>[4,2,1,1]=>90
[5,4,2,8,6,1,7,3]=>[3,2,2,1]=>70
[6,4,8,2,5,1,7,3]=>[3,2,2,1]=>70
[7,8,4,2,5,1,6,3]=>[3,2,2,1]=>70
[4,3,2,1,6,8,5,7]=>[3,3,1,1]=>56
[4,3,2,1,8,6,5,7]=>[3,2,2,1]=>70
[5,3,2,8,1,6,4,7]=>[3,2,2,1]=>70
[7,8,3,2,1,5,4,6]=>[3,2,2,1]=>70
[7,8,3,2,1,5,6,4]=>[3,2,2,1]=>70
[6,3,8,2,1,5,7,4]=>[3,2,2,1]=>70
[5,3,2,7,1,8,6,4]=>[3,2,2,1]=>70
[5,3,2,7,1,6,8,4]=>[3,2,2,1]=>70
[6,3,7,2,1,8,5,4]=>[3,2,2,1]=>70
[6,4,7,2,8,1,5,3]=>[3,2,2,1]=>70
[6,5,7,8,2,1,4,3]=>[3,2,2,1]=>70
[6,5,8,7,2,1,3,4]=>[3,2,2,1]=>70
[6,3,7,2,1,8,4,5]=>[3,3,1,1]=>56
[5,3,2,7,1,4,8,6]=>[3,3,1,1]=>56
[6,3,8,2,1,7,4,5]=>[3,2,2,1]=>70
[5,3,2,8,1,7,4,6]=>[3,2,2,1]=>70
[4,3,2,1,8,7,5,6]=>[3,2,2,1]=>70
[4,3,2,1,8,5,7,6]=>[3,2,2,1]=>70
[6,3,8,2,1,4,7,5]=>[3,2,2,1]=>70
[6,3,8,2,1,4,5,7]=>[4,2,1,1]=>90
[4,3,2,1,8,5,6,7]=>[4,2,1,1]=>90
[4,3,2,1,5,8,6,7]=>[4,2,1,1]=>90
[7,8,4,1,6,2,5,3]=>[3,2,2,1]=>70
[6,1,8,4,7,2,5,3]=>[3,2,2,1]=>70
[1,6,8,4,7,2,5,3]=>[3,2,2,1]=>70
[7,8,1,3,2,6,5,4]=>[3,2,2,1]=>70
[7,8,3,4,6,5,1,2]=>[3,2,2,1]=>70
[7,8,2,4,6,1,5,3]=>[3,2,2,1]=>70
[7,8,1,2,3,6,5,4]=>[4,2,1,1]=>90
[6,1,8,2,3,7,5,4]=>[4,2,1,1]=>90
[1,6,8,2,3,7,5,4]=>[4,2,1,1]=>90
[6,2,8,1,3,7,5,4]=>[3,2,2,1]=>70
[6,2,8,4,7,1,5,3]=>[3,2,2,1]=>70
[6,3,8,4,7,5,1,2]=>[3,2,2,1]=>70
[2,6,8,4,7,1,5,3]=>[3,2,2,1]=>70
[1,2,5,8,3,7,6,4]=>[4,2,1,1]=>90
[2,4,1,3,8,7,6,5]=>[3,3,1,1]=>56
[2,5,3,8,1,7,6,4]=>[3,2,2,1]=>70
[4,2,1,3,8,7,6,5]=>[3,2,2,1]=>70
[4,1,2,3,8,7,6,5]=>[4,2,1,1]=>90
[4,3,1,2,8,7,6,5]=>[3,2,2,1]=>70
[6,3,8,1,2,7,5,4]=>[3,2,2,1]=>70
[5,1,3,8,2,7,6,4]=>[3,2,2,1]=>70
[1,5,4,8,7,2,6,3]=>[3,2,2,1]=>70
[6,4,8,1,7,2,5,3]=>[3,2,2,1]=>70
[5,6,8,7,2,1,4,3]=>[3,2,2,1]=>70
[4,5,1,8,7,2,6,3]=>[3,3,1,1]=>56
[1,4,5,8,7,2,6,3]=>[4,2,1,1]=>90
[4,6,8,2,7,1,5,3]=>[3,2,2,1]=>70
[4,6,8,3,7,5,1,2]=>[3,2,2,1]=>70
[4,5,2,8,7,1,6,3]=>[3,2,2,1]=>70
[3,5,2,8,1,7,6,4]=>[3,2,2,1]=>70
[3,1,2,4,8,7,6,5]=>[4,2,1,1]=>90
[3,4,5,8,7,6,1,2]=>[4,2,1,1]=>90
[4,1,3,2,6,5,8,7]=>[4,3,1]=>70
[5,1,3,2,6,4,8,7]=>[4,3,1]=>70
[6,1,3,2,5,4,8,7]=>[4,3,1]=>70
[7,1,3,2,5,4,8,6]=>[4,3,1]=>70
[8,1,3,2,5,4,7,6]=>[4,3,1]=>70
[8,1,4,2,5,3,7,6]=>[4,3,1]=>70
[7,1,4,2,5,3,8,6]=>[4,3,1]=>70
[6,1,4,2,5,3,8,7]=>[4,3,1]=>70
[5,1,4,2,6,3,8,7]=>[4,3,1]=>70
[2,1,6,3,5,4,8,7]=>[4,3,1]=>70
[3,1,6,2,5,4,8,7]=>[4,3,1]=>70
[4,1,6,2,5,3,8,7]=>[4,3,1]=>70
[6,2,5,1,4,3,8,7]=>[3,3,1,1]=>56
[5,2,6,1,4,3,8,7]=>[3,3,2]=>42
[5,2,7,1,4,3,8,6]=>[3,3,2]=>42
[5,2,8,1,4,3,7,6]=>[3,3,2]=>42
[6,2,8,1,4,3,7,5]=>[3,3,2]=>42
[6,2,7,1,4,3,8,5]=>[3,3,2]=>42
[7,2,6,1,4,3,8,5]=>[3,3,1,1]=>56
[7,2,5,1,4,3,8,6]=>[3,3,1,1]=>56
[4,1,7,2,5,3,8,6]=>[4,3,1]=>70
[3,1,7,2,5,4,8,6]=>[4,3,1]=>70
[2,1,7,3,5,4,8,6]=>[4,3,1]=>70
[2,1,8,3,5,4,7,6]=>[4,3,1]=>70
[3,1,8,2,5,4,7,6]=>[4,3,1]=>70
[4,1,8,2,5,3,7,6]=>[4,3,1]=>70
[8,2,5,1,4,3,7,6]=>[3,3,1,1]=>56
[8,2,6,1,4,3,7,5]=>[3,3,1,1]=>56
[7,1,4,3,8,2,6,5]=>[3,2,2,1]=>70
[8,1,4,3,7,2,6,5]=>[3,2,2,1]=>70
[8,1,5,3,7,2,6,4]=>[3,2,2,1]=>70
[7,1,5,3,8,2,6,4]=>[3,2,2,1]=>70
[8,2,6,1,5,3,7,4]=>[3,3,1,1]=>56
[5,1,8,2,6,3,7,4]=>[4,3,1]=>70
[4,1,8,2,6,3,7,5]=>[4,3,1]=>70
[3,1,8,2,6,4,7,5]=>[4,3,1]=>70
[2,1,8,3,6,4,7,5]=>[4,3,1]=>70
[2,1,7,3,6,4,8,5]=>[4,3,1]=>70
[4,1,7,2,6,3,8,5]=>[4,3,1]=>70
[5,1,7,2,6,3,8,4]=>[4,3,1]=>70
[7,2,6,1,5,3,8,4]=>[3,3,1,1]=>56
[6,2,7,1,5,3,8,4]=>[3,3,2]=>42
[6,2,8,1,5,3,7,4]=>[3,3,2]=>42
[8,1,5,2,6,3,7,4]=>[4,3,1]=>70
[6,1,5,2,7,3,8,4]=>[4,3,1]=>70
[6,1,4,2,7,3,8,5]=>[4,3,1]=>70
[8,1,4,2,6,3,7,5]=>[4,3,1]=>70
[8,1,3,2,6,4,7,5]=>[4,3,1]=>70
[7,1,3,2,6,4,8,5]=>[4,3,1]=>70
[6,1,3,2,7,4,8,5]=>[4,3,1]=>70
[5,1,3,2,7,4,8,6]=>[4,3,1]=>70
[4,1,3,2,7,5,8,6]=>[4,3,1]=>70
[2,1,4,3,8,5,7,6]=>[4,3,1]=>70
[3,1,4,2,8,5,7,6]=>[4,3,1]=>70
[4,1,3,2,8,5,7,6]=>[4,2,2]=>56
[5,1,3,2,8,4,7,6]=>[4,2,2]=>56
[6,1,3,2,8,4,7,5]=>[4,2,2]=>56
[8,4,7,1,3,2,6,5]=>[3,2,2,1]=>70
[7,4,8,1,3,2,6,5]=>[3,2,2,1]=>70
[7,3,8,1,4,2,6,5]=>[3,3,2]=>42
[8,3,7,1,4,2,6,5]=>[3,3,1,1]=>56
[6,1,4,2,8,3,7,5]=>[4,2,2]=>56
[5,1,4,2,8,3,7,6]=>[4,2,2]=>56
[4,1,5,2,8,3,7,6]=>[4,3,1]=>70
[3,1,5,2,8,4,7,6]=>[4,3,1]=>70
[2,1,5,3,8,4,7,6]=>[4,3,1]=>70
[2,1,6,3,8,4,7,5]=>[4,3,1]=>70
[3,1,6,2,8,4,7,5]=>[4,3,1]=>70
[4,1,6,2,8,3,7,5]=>[4,3,1]=>70
[5,1,6,2,8,3,7,4]=>[4,3,1]=>70
[6,1,5,2,8,3,7,4]=>[4,2,2]=>56
[8,3,7,1,5,2,6,4]=>[3,3,1,1]=>56
[7,3,8,1,5,2,6,4]=>[3,3,2]=>42
[6,2,7,3,8,1,5,4]=>[3,3,2]=>42
[6,2,8,3,7,1,5,4]=>[3,2,2,1]=>70
[8,3,7,2,6,1,5,4]=>[2,2,2,1,1]=>28
[5,1,8,3,7,2,6,4]=>[3,2,2,1]=>70
[4,1,8,3,7,2,6,5]=>[3,2,2,1]=>70
[3,1,8,4,7,2,6,5]=>[3,3,1,1]=>56
[2,1,8,4,7,3,6,5]=>[3,3,1,1]=>56
[2,1,7,4,8,3,6,5]=>[3,3,2]=>42
[3,1,7,4,8,2,6,5]=>[3,3,2]=>42
[4,1,7,3,8,2,6,5]=>[3,3,2]=>42
[5,1,7,3,8,2,6,4]=>[3,3,2]=>42
[7,3,8,2,6,1,5,4]=>[2,2,2,2]=>14
[8,2,6,3,7,1,5,4]=>[3,2,2,1]=>70
[7,2,6,3,8,1,5,4]=>[3,2,2,1]=>70
[3,4,2,6,8,1,5,7]=>[4,3,1]=>70
[5,3,6,2,8,1,4,7]=>[3,3,1,1]=>56
[5,3,6,2,4,8,1,7]=>[3,3,1,1]=>56
[5,7,3,8,2,4,1,6]=>[3,3,1,1]=>56
[5,7,3,8,2,4,6,1]=>[3,3,1,1]=>56
[7,4,2,5,8,3,6,1]=>[3,3,1,1]=>56
[7,4,2,5,8,3,1,6]=>[3,3,1,1]=>56
[4,5,2,6,3,8,1,7]=>[4,3,1]=>70
[4,5,2,1,6,8,3,7]=>[4,3,1]=>70
[5,3,1,6,8,2,4,7]=>[4,3,1]=>70
[5,6,2,8,1,3,4,7]=>[4,3,1]=>70
[3,5,6,1,4,8,2,7]=>[4,3,1]=>70
[4,1,5,6,3,8,2,7]=>[4,3,1]=>70
[4,5,1,6,3,8,2,7]=>[4,3,1]=>70
[4,5,6,3,2,8,1,7]=>[4,2,1,1]=>90
[7,4,5,3,8,2,1,6]=>[3,2,1,1,1]=>64
[7,4,5,3,8,2,6,1]=>[3,2,1,1,1]=>64
[6,7,4,8,3,2,5,1]=>[3,2,1,1,1]=>64
[6,7,4,8,3,2,1,5]=>[3,2,1,1,1]=>64
[6,7,4,1,8,3,2,5]=>[3,3,1,1]=>56
[7,4,5,3,1,8,2,6]=>[3,3,1,1]=>56
[4,7,1,5,8,3,2,6]=>[3,3,1,1]=>56
[5,3,7,8,1,4,2,6]=>[3,3,2]=>42
[7,5,8,2,4,6,1,3]=>[3,2,2,1]=>70
[7,3,5,8,1,4,6,2]=>[3,3,1,1]=>56
[4,5,1,7,8,3,6,2]=>[4,3,1]=>70
[7,4,1,5,8,3,6,2]=>[3,3,1,1]=>56
[6,7,4,3,8,1,5,2]=>[3,2,2,1]=>70
[6,7,4,8,3,1,5,2]=>[3,2,2,1]=>70
[6,7,4,8,3,5,2,1]=>[3,2,1,1,1]=>64
[5,6,7,3,8,4,2,1]=>[4,2,1,1]=>90
[5,6,7,3,1,8,4,2]=>[4,2,2]=>56
[5,6,1,7,3,8,4,2]=>[4,3,1]=>70
[5,1,6,7,3,8,4,2]=>[4,3,1]=>70
[6,4,7,1,8,3,5,2]=>[3,3,1,1]=>56
[6,7,8,3,1,4,5,2]=>[3,3,2]=>42
[6,7,2,8,4,5,1,3]=>[3,3,2]=>42
[6,7,2,8,4,1,3,5]=>[3,3,2]=>42
[6,1,7,4,8,3,2,5]=>[3,3,1,1]=>56
[5,1,6,7,3,2,8,4]=>[4,3,1]=>70
[5,6,1,7,3,2,8,4]=>[4,3,1]=>70
[5,6,7,3,2,1,8,4]=>[4,2,1,1]=>90
[5,6,7,3,2,8,4,1]=>[4,2,1,1]=>90
[5,6,2,7,3,8,4,1]=>[4,3,1]=>70
[5,6,2,7,3,1,8,4]=>[4,3,1]=>70
[5,6,2,1,7,3,8,4]=>[4,3,1]=>70
[6,1,7,4,2,8,3,5]=>[4,3,1]=>70
[6,7,2,1,8,3,4,5]=>[4,3,1]=>70
[7,5,8,2,1,3,4,6]=>[4,2,1,1]=>90
[5,7,3,1,8,2,4,6]=>[4,3,1]=>70
[4,7,1,5,2,8,3,6]=>[4,3,1]=>70
[7,4,2,5,1,8,3,6]=>[3,3,1,1]=>56
[6,7,4,2,1,8,3,5]=>[3,3,1,1]=>56
[6,7,4,2,8,3,1,5]=>[3,3,1,1]=>56
[6,7,4,2,8,3,5,1]=>[3,3,1,1]=>56
[3,6,7,2,8,4,5,1]=>[4,3,1]=>70
[3,6,7,2,8,4,1,5]=>[4,3,1]=>70
[3,6,7,2,1,8,4,5]=>[4,3,1]=>70
[5,7,3,8,2,1,4,6]=>[3,3,1,1]=>56
[3,4,7,8,2,1,5,6]=>[4,3,1]=>70
[3,7,8,1,4,6,2,5]=>[3,3,2]=>42
[3,4,7,8,2,6,1,5]=>[4,2,2]=>56
[5,7,3,8,2,6,1,4]=>[3,2,2,1]=>70
[3,6,7,2,8,5,1,4]=>[4,2,2]=>56
[3,6,7,8,5,2,1,4]=>[4,2,1,1]=>90
[3,6,7,8,5,2,4,1]=>[4,2,1,1]=>90
[6,4,7,8,2,5,3,1]=>[3,2,2,1]=>70
[6,4,7,8,2,1,5,3]=>[3,2,2,1]=>70
[4,1,5,7,8,2,6,3]=>[4,3,1]=>70
[5,3,7,8,1,6,2,4]=>[3,3,2]=>42
[6,7,2,8,5,1,3,4]=>[3,3,2]=>42
[6,4,1,7,8,2,5,3]=>[3,3,2]=>42
[5,1,6,2,7,8,4,3]=>[4,3,1]=>70
[5,6,2,1,7,8,4,3]=>[4,2,2]=>56
[5,6,2,7,1,8,4,3]=>[4,2,2]=>56
[5,6,2,7,8,4,3,1]=>[4,2,1,1]=>90
[5,6,7,2,8,4,3,1]=>[4,2,1,1]=>90
[5,6,7,2,1,8,4,3]=>[4,2,2]=>56
[5,6,1,7,2,8,4,3]=>[4,3,1]=>70
[5,1,6,7,2,8,4,3]=>[4,3,1]=>70
[6,4,7,1,8,2,5,3]=>[3,3,2]=>42
[3,6,7,1,8,5,2,4]=>[4,3,1]=>70
[6,7,8,5,2,4,1,3]=>[3,2,2,1]=>70
[6,7,8,3,5,1,4,2]=>[3,2,2,1]=>70
[4,6,7,8,1,5,3,2]=>[4,2,1,1]=>90
[5,1,6,7,8,4,3,2]=>[4,2,1,1]=>90
[5,6,1,7,8,4,3,2]=>[4,2,1,1]=>90
[5,6,7,1,8,4,3,2]=>[4,2,1,1]=>90
[8,6,1,3,4,2,5,7]=>[5,1,1,1]=>35
[8,3,2,5,1,6,4,7]=>[4,2,1,1]=>90
[8,5,3,6,2,4,1,7]=>[3,2,1,1,1]=>64
[5,3,2,7,4,1,8,6]=>[3,3,1,1]=>56
[7,5,3,8,2,4,6,1]=>[3,2,1,1,1]=>64
[7,2,4,5,8,3,6,1]=>[4,2,1,1]=>90
[2,4,5,3,7,1,8,6]=>[5,2,1]=>64
[8,2,4,5,6,3,1,7]=>[5,1,1,1]=>35
[8,2,4,5,6,1,3,7]=>[5,2,1]=>64
[8,1,2,4,5,6,3,7]=>[6,1,1]=>21
[8,2,5,1,3,6,4,7]=>[4,3,1]=>70
[8,5,6,2,1,4,3,7]=>[3,2,2,1]=>70
[8,5,3,6,4,1,2,7]=>[3,2,2,1]=>70
[8,4,1,5,6,3,2,7]=>[4,2,1,1]=>90
[8,1,4,5,6,3,2,7]=>[5,1,1,1]=>35
[4,5,3,7,2,1,8,6]=>[4,2,1,1]=>90
[7,4,5,8,3,2,6,1]=>[3,2,1,1,1]=>64
[4,3,6,7,2,8,5,1]=>[4,2,1,1]=>90
[4,3,6,7,2,8,1,5]=>[4,2,1,1]=>90
[1,4,3,6,7,2,8,5]=>[5,2,1]=>64
[4,5,3,7,1,8,2,6]=>[4,3,1]=>70
[4,1,5,3,7,2,8,6]=>[4,3,1]=>70
[5,3,4,7,1,2,8,6]=>[4,3,1]=>70
[7,5,8,2,1,4,6,3]=>[3,2,2,1]=>70
[7,5,3,8,4,1,6,2]=>[3,2,2,1]=>70
[7,4,5,8,3,6,1,2]=>[3,2,2,1]=>70
[4,3,6,7,8,1,5,2]=>[4,2,2]=>56
[1,6,4,7,8,3,5,2]=>[4,2,1,1]=>90
[6,4,7,8,3,5,2,1]=>[3,2,1,1,1]=>64
[3,5,6,7,8,4,1,2]=>[5,2,1]=>64
[3,1,5,6,7,8,4,2]=>[5,2,1]=>64
[4,6,1,7,8,3,5,2]=>[4,3,1]=>70
[3,6,7,1,4,8,5,2]=>[4,3,1]=>70
[6,2,4,1,7,8,5,3]=>[4,2,2]=>56
[2,6,7,1,4,8,3,5]=>[4,3,1]=>70
[4,3,6,7,8,1,2,5]=>[4,3,1]=>70
[1,5,3,6,7,8,2,4]=>[5,2,1]=>64
[3,5,6,7,8,2,1,4]=>[5,2,1]=>64
[3,5,6,7,8,2,4,1]=>[5,2,1]=>64
[5,2,7,1,3,8,4,6]=>[4,3,1]=>70
[5,3,1,7,8,2,4,6]=>[4,3,1]=>70
[4,5,2,7,8,1,3,6]=>[4,3,1]=>70
[4,2,6,7,8,3,1,5]=>[4,3,1]=>70
[4,2,6,7,8,3,5,1]=>[4,3,1]=>70
[3,6,2,7,4,8,5,1]=>[4,3,1]=>70
[3,6,2,7,4,8,1,5]=>[4,3,1]=>70
[3,2,1,6,4,7,8,5]=>[4,3,1]=>70
[3,7,4,2,1,5,8,6]=>[4,2,1,1]=>90
[1,7,3,4,2,5,8,6]=>[5,2,1]=>64
[4,7,2,1,3,5,8,6]=>[4,3,1]=>70
[7,8,4,2,1,3,6,5]=>[3,2,2,1]=>70
[7,8,1,3,4,2,6,5]=>[4,2,2]=>56
[7,8,3,4,2,1,6,5]=>[3,2,2,1]=>70
[6,3,2,7,1,8,5,4]=>[3,2,2,1]=>70
[3,6,2,7,1,8,5,4]=>[4,2,2]=>56
[6,7,3,8,2,5,4,1]=>[3,2,2,1]=>70
[6,4,7,8,5,2,3,1]=>[3,2,2,1]=>70
[2,6,4,7,8,1,5,3]=>[4,2,2]=>56
[4,6,2,7,8,1,5,3]=>[4,2,2]=>56
[7,4,5,8,6,2,1,3]=>[3,2,2,1]=>70
[7,4,1,5,8,6,2,3]=>[3,3,2]=>42
[7,5,3,8,6,1,2,4]=>[3,2,2,1]=>70
[7,5,8,2,1,6,3,4]=>[3,2,2,1]=>70
[6,2,7,1,3,8,5,4]=>[3,3,2]=>42
[6,3,1,7,8,2,5,4]=>[3,3,2]=>42
[4,6,1,7,8,5,2,3]=>[4,3,1]=>70
[5,1,2,6,7,8,4,3]=>[5,2,1]=>64
[5,2,6,7,8,4,1,3]=>[4,2,2]=>56
[5,2,6,7,8,4,3,1]=>[4,2,1,1]=>90
[2,5,6,7,8,4,1,3]=>[5,2,1]=>64
[1,5,2,6,7,8,4,3]=>[5,2,1]=>64
[1,6,4,7,8,5,2,3]=>[4,2,2]=>56
[2,6,7,1,3,8,5,4]=>[4,3,1]=>70
[6,7,8,2,1,5,4,3]=>[3,2,2,1]=>70
[6,7,3,8,5,1,4,2]=>[3,2,2,1]=>70
[6,4,7,8,5,3,1,2]=>[3,2,2,1]=>70
[4,5,2,3,7,6,1,8]=>[4,3,1]=>70
[6,4,3,7,2,5,1,8]=>[3,2,1,1,1]=>64
[8,4,3,6,5,1,2,7]=>[3,2,2,1]=>70
[1,5,6,3,4,8,7,2]=>[4,3,1]=>70
[4,6,2,7,3,5,1,8]=>[4,3,1]=>70
[3,2,6,7,4,5,1,8]=>[4,3,1]=>70
[4,7,2,6,5,3,1,8]=>[3,2,1,1,1]=>64
[5,7,6,2,4,3,1,8]=>[3,2,1,1,1]=>64
[1,7,5,4,8,3,6,2]=>[3,2,1,1,1]=>64
[8,7,5,4,1,3,2,6]=>[3,1,1,1,1,1]=>21
[6,8,5,4,2,1,3,7]=>[3,2,1,1,1]=>64
[5,8,6,2,4,1,3,7]=>[3,2,2,1]=>70
[4,8,2,6,5,1,3,7]=>[3,2,2,1]=>70
[3,2,8,6,5,1,4,7]=>[3,2,2,1]=>70
[4,1,2,6,5,8,7,3]=>[4,3,1]=>70
[5,1,6,2,4,8,7,3]=>[4,3,1]=>70
[6,1,5,4,2,8,7,3]=>[3,2,2,1]=>70
[7,1,5,4,8,2,6,3]=>[3,2,2,1]=>70
[8,1,5,4,7,6,2,3]=>[3,2,2,1]=>70
[1,8,6,7,4,5,3,2]=>[3,2,1,1,1]=>64
[8,1,6,7,4,5,2,3]=>[3,2,2,1]=>70
[7,1,6,8,4,2,5,3]=>[3,2,2,1]=>70
[6,1,7,8,2,4,5,3]=>[4,3,1]=>70
[5,1,7,2,8,4,6,3]=>[4,3,1]=>70
[4,1,2,7,8,5,6,3]=>[4,3,1]=>70
[3,2,1,7,8,5,6,4]=>[3,3,2]=>42
[3,2,8,7,1,5,4,6]=>[3,2,2,1]=>70
[4,8,2,7,1,5,3,6]=>[3,2,2,1]=>70
[5,8,7,2,1,4,3,6]=>[3,2,2,1]=>70
[6,8,7,1,2,4,3,5]=>[4,2,1,1]=>90
[7,8,6,1,4,2,3,5]=>[4,2,1,1]=>90
[8,7,6,1,4,3,2,5]=>[3,1,1,1,1,1]=>21
[1,7,6,8,4,3,5,2]=>[3,2,1,1,1]=>64
[1,6,7,8,3,4,5,2]=>[4,3,1]=>70
[8,6,7,1,3,4,2,5]=>[4,2,1,1]=>90
[7,6,8,1,3,2,4,5]=>[4,2,1,1]=>90
[5,7,8,2,1,3,4,6]=>[4,3,1]=>70
[4,7,2,8,1,3,5,6]=>[4,3,1]=>70
[3,2,6,8,4,1,5,7]=>[4,3,1]=>70
[4,6,2,8,3,1,5,7]=>[4,3,1]=>70
[5,6,8,2,3,1,4,7]=>[4,3,1]=>70
[6,5,8,3,2,1,4,7]=>[3,2,1,1,1]=>64
[7,5,8,3,1,2,4,6]=>[4,2,1,1]=>90
[8,5,7,3,1,4,2,6]=>[3,2,2,1]=>70
[1,5,7,3,8,4,6,2]=>[4,3,1]=>70
[1,4,3,7,8,5,6,2]=>[4,3,1]=>70
[8,4,3,7,1,5,2,6]=>[3,2,2,1]=>70
[6,4,3,8,2,1,5,7]=>[3,2,1,1,1]=>64
[4,5,2,3,8,1,6,7]=>[4,3,1]=>70
[3,2,5,4,8,1,6,7]=>[4,3,1]=>70
[4,5,2,3,1,8,7,6]=>[3,3,2]=>42
[6,4,3,1,2,8,7,5]=>[3,2,2,1]=>70
[7,4,3,1,8,2,6,5]=>[3,2,2,1]=>70
[8,4,3,1,7,6,2,5]=>[3,2,2,1]=>70
[1,5,8,3,7,6,4,2]=>[3,2,1,1,1]=>64
[8,5,1,3,7,6,2,4]=>[3,2,2,1]=>70
[7,5,1,3,8,2,6,4]=>[3,2,2,1]=>70
[6,5,1,3,2,8,7,4]=>[3,2,2,1]=>70
[5,6,1,2,3,8,7,4]=>[4,3,1]=>70
[4,6,2,1,3,8,7,5]=>[3,3,2]=>42
[3,2,6,1,4,8,7,5]=>[3,3,2]=>42
[3,2,7,1,8,4,6,5]=>[3,3,2]=>42
[4,7,2,1,8,3,6,5]=>[3,3,2]=>42
[5,7,1,2,8,3,6,4]=>[4,3,1]=>70
[6,7,1,8,2,3,5,4]=>[4,3,1]=>70
[7,6,1,8,3,2,5,4]=>[3,2,2,1]=>70
[8,6,1,7,3,5,2,4]=>[3,2,2,1]=>70
[1,6,8,7,3,5,4,2]=>[3,2,1,1,1]=>64
[1,7,8,6,5,3,4,2]=>[3,2,1,1,1]=>64
[8,7,1,6,5,3,2,4]=>[3,1,1,1,1,1]=>21
[7,8,1,6,5,2,3,4]=>[4,2,1,1]=>90
[6,8,1,7,2,5,3,4]=>[4,2,1,1]=>90
[5,8,1,2,7,6,3,4]=>[4,2,1,1]=>90
[4,8,2,1,7,6,3,5]=>[3,2,2,1]=>70
[3,2,8,1,7,6,4,5]=>[3,2,2,1]=>70
[4,1,2,8,7,6,5,3]=>[3,2,1,1,1]=>64
[5,1,8,2,7,6,4,3]=>[3,2,1,1,1]=>64
[6,1,8,7,2,5,4,3]=>[3,2,1,1,1]=>64
[7,1,8,6,5,2,4,3]=>[3,2,1,1,1]=>64
[8,1,7,6,5,4,2,3]=>[3,1,1,1,1,1]=>21
[3,1,2,6,5,8,7,4]=>[4,3,1]=>70
[3,1,6,2,4,8,7,5]=>[4,3,1]=>70
[3,1,5,2,4,8,7,6]=>[4,3,1]=>70
[4,5,1,2,3,8,7,6]=>[4,3,1]=>70
[4,6,1,2,3,8,7,5]=>[4,3,1]=>70
[1,6,5,3,4,8,7,2]=>[4,2,1,1]=>90
[6,1,5,2,4,8,7,3]=>[4,2,1,1]=>90
[6,5,1,2,3,8,7,4]=>[4,2,2]=>56
[6,4,1,2,3,8,7,5]=>[4,2,2]=>56
[5,4,1,2,3,8,7,6]=>[4,2,2]=>56
[5,4,1,2,7,3,6,8]=>[5,2,1]=>64
[6,4,1,7,2,3,5,8]=>[5,2,1]=>64
[6,4,1,8,2,3,5,7]=>[5,2,1]=>64
[7,4,1,2,8,3,6,5]=>[4,2,2]=>56
[7,5,1,2,8,3,6,4]=>[4,2,2]=>56
[7,1,5,2,8,4,6,3]=>[4,2,1,1]=>90
[1,7,5,3,8,4,6,2]=>[4,2,1,1]=>90
[1,8,5,3,7,4,6,2]=>[4,2,1,1]=>90
[8,1,5,2,7,4,6,3]=>[4,2,1,1]=>90
[8,5,1,2,7,3,6,4]=>[4,2,1,1]=>90
[8,4,1,2,7,3,6,5]=>[4,2,1,1]=>90
[8,4,1,7,2,3,5,6]=>[5,2,1]=>64
[7,4,1,6,2,3,5,8]=>[5,2,1]=>64
[8,6,1,7,2,3,5,4]=>[4,2,1,1]=>90
[8,1,6,7,2,4,5,3]=>[4,2,1,1]=>90
[1,8,6,7,3,4,5,2]=>[4,2,1,1]=>90
[1,7,6,8,3,4,5,2]=>[4,2,1,1]=>90
[7,1,6,8,2,4,5,3]=>[4,2,1,1]=>90
[7,6,1,8,2,3,5,4]=>[4,2,1,1]=>90
[4,7,1,2,8,3,6,5]=>[4,3,1]=>70
[3,1,7,2,8,4,6,5]=>[4,3,1]=>70
[3,1,2,7,8,5,6,4]=>[4,3,1]=>70
[1,4,3,8,7,5,6,2]=>[4,2,1,1]=>90
[4,1,2,8,7,5,6,3]=>[4,2,1,1]=>90
[3,1,2,8,7,5,6,4]=>[4,2,1,1]=>90
[3,1,8,2,7,4,6,5]=>[4,2,1,1]=>90
[3,1,8,7,2,4,5,6]=>[5,2,1]=>64
[3,1,7,6,2,4,5,8]=>[5,2,1]=>64
[4,7,1,6,2,3,5,8]=>[5,2,1]=>64
[4,8,1,6,2,3,5,7]=>[5,2,1]=>64
[4,8,1,7,2,3,5,6]=>[5,2,1]=>64
[4,8,1,2,7,3,6,5]=>[4,2,1,1]=>90
[5,8,1,2,7,3,6,4]=>[4,2,1,1]=>90
[5,1,8,2,7,4,6,3]=>[4,2,1,1]=>90
[1,5,8,3,7,4,6,2]=>[4,2,1,1]=>90
[1,6,8,7,3,4,5,2]=>[4,2,1,1]=>90
[6,1,8,7,2,4,5,3]=>[4,2,1,1]=>90
[6,8,1,7,2,3,5,4]=>[4,2,1,1]=>90
[6,8,7,1,2,3,4,5]=>[5,2,1]=>64
[5,8,7,1,2,3,4,6]=>[5,2,1]=>64
[5,8,6,1,2,3,4,7]=>[5,2,1]=>64
[5,7,6,1,2,3,4,8]=>[5,2,1]=>64
[7,8,1,6,2,3,5,4]=>[4,2,1,1]=>90
[7,1,8,6,2,4,5,3]=>[4,2,1,1]=>90
[1,7,8,6,3,4,5,2]=>[4,2,1,1]=>90
[1,8,7,6,3,4,5,2]=>[4,1,1,1,1]=>35
[8,1,7,6,2,4,5,3]=>[4,1,1,1,1]=>35
[8,7,1,6,2,3,5,4]=>[4,1,1,1,1]=>35
[3,2,5,1,6,4,8,7]=>[4,3,1]=>70
[3,2,5,4,7,1,8,6]=>[4,3,1]=>70
[4,2,5,3,7,6,8,1]=>[4,3,1]=>70
[4,2,5,3,7,1,8,6]=>[4,3,1]=>70
[4,2,5,3,6,1,8,7]=>[4,3,1]=>70
[4,2,5,1,6,3,8,7]=>[4,3,1]=>70
[3,1,5,4,6,2,8,7]=>[4,3,1]=>70
[4,1,5,3,6,2,8,7]=>[4,3,1]=>70
[4,3,5,1,6,2,8,7]=>[4,3,1]=>70
[4,3,5,2,7,1,8,6]=>[4,2,1,1]=>90
[4,3,6,2,7,5,8,1]=>[4,2,1,1]=>90
[4,3,6,2,7,1,8,5]=>[4,2,1,1]=>90
[4,3,6,1,7,2,8,5]=>[4,3,1]=>70
[4,3,5,1,7,2,8,6]=>[4,3,1]=>70
[3,1,5,4,7,2,8,6]=>[4,3,1]=>70
[2,1,5,4,7,3,8,6]=>[4,3,1]=>70
[3,1,5,4,7,6,8,2]=>[4,3,1]=>70
[4,1,5,3,7,6,8,2]=>[4,3,1]=>70
[4,3,5,1,7,6,8,2]=>[4,2,2]=>56
[4,3,6,1,7,5,8,2]=>[4,2,2]=>56
[4,3,6,5,7,1,8,2]=>[4,2,2]=>56
[5,3,6,4,7,2,8,1]=>[4,2,1,1]=>90
[5,3,6,4,7,1,8,2]=>[4,2,2]=>56
[5,3,6,1,7,4,8,2]=>[4,2,2]=>56
[5,1,6,3,7,4,8,2]=>[4,3,1]=>70
[4,1,6,3,7,5,8,2]=>[4,3,1]=>70
[3,1,6,4,7,5,8,2]=>[4,3,1]=>70
[2,1,6,4,7,5,8,3]=>[4,3,1]=>70
[2,1,6,4,7,3,8,5]=>[4,3,1]=>70
[3,1,6,4,7,2,8,5]=>[4,3,1]=>70
[4,1,6,3,7,2,8,5]=>[4,3,1]=>70
[5,1,6,3,7,2,8,4]=>[4,3,1]=>70
[5,3,6,1,7,2,8,4]=>[4,3,1]=>70
[5,3,6,2,7,1,8,4]=>[4,2,1,1]=>90
[5,3,6,2,7,4,8,1]=>[4,2,1,1]=>90
[5,2,6,3,7,4,8,1]=>[4,3,1]=>70
[5,2,6,3,7,1,8,4]=>[4,3,1]=>70
[5,2,6,1,7,3,8,4]=>[4,3,1]=>70
[4,2,5,1,7,3,8,6]=>[4,3,1]=>70
[4,2,6,1,7,3,8,5]=>[4,3,1]=>70
[4,2,6,3,7,1,8,5]=>[4,3,1]=>70
[4,2,6,3,7,5,8,1]=>[4,3,1]=>70
[3,2,6,4,7,5,8,1]=>[4,3,1]=>70
[3,2,6,4,7,1,8,5]=>[4,3,1]=>70
[3,2,6,1,7,4,8,5]=>[4,3,1]=>70
[3,2,5,1,7,4,8,6]=>[4,3,1]=>70
[3,2,4,1,7,5,8,6]=>[4,3,1]=>70
[3,1,4,2,7,6,8,5]=>[4,3,1]=>70
[3,2,5,1,7,6,8,4]=>[4,2,2]=>56
[3,2,6,1,7,5,8,4]=>[4,2,2]=>56
[3,2,6,5,7,1,8,4]=>[4,2,2]=>56
[4,2,6,5,7,3,8,1]=>[4,2,1,1]=>90
[4,2,6,5,7,1,8,3]=>[4,2,2]=>56
[4,2,6,1,7,5,8,3]=>[4,2,2]=>56
[4,2,5,1,7,6,8,3]=>[4,2,2]=>56
[4,1,5,2,7,6,8,3]=>[4,3,1]=>70
[3,1,5,2,7,6,8,4]=>[4,3,1]=>70
[2,1,5,3,7,6,8,4]=>[4,3,1]=>70
[2,1,6,3,7,5,8,4]=>[4,3,1]=>70
[3,1,6,2,7,5,8,4]=>[4,3,1]=>70
[4,1,6,2,7,5,8,3]=>[4,3,1]=>70
[5,1,6,2,7,4,8,3]=>[4,3,1]=>70
[5,2,6,1,7,4,8,3]=>[4,2,2]=>56
[5,2,6,4,7,1,8,3]=>[4,2,2]=>56
[5,2,6,4,7,3,8,1]=>[4,2,1,1]=>90
[5,4,6,2,7,3,8,1]=>[4,2,1,1]=>90
[5,4,6,2,7,1,8,3]=>[4,2,1,1]=>90
[5,4,6,1,7,2,8,3]=>[4,3,1]=>70
[5,1,6,4,7,2,8,3]=>[4,3,1]=>70
[4,1,6,5,7,2,8,3]=>[4,3,1]=>70
[3,1,6,5,7,2,8,4]=>[4,3,1]=>70
[2,1,6,5,7,3,8,4]=>[4,3,1]=>70
[3,1,6,5,7,4,8,2]=>[4,2,1,1]=>90
[4,1,6,5,7,3,8,2]=>[4,2,1,1]=>90
[5,1,6,4,7,3,8,2]=>[4,2,1,1]=>90
[5,4,6,1,7,3,8,2]=>[4,2,1,1]=>90
[5,4,6,3,7,1,8,2]=>[4,2,1,1]=>90
[8,3,5,2,1,6,4,7]=>[4,2,1,1]=>90
[8,6,3,5,2,4,1,7]=>[3,2,1,1,1]=>64
[3,7,5,2,4,1,8,6]=>[3,3,1,1]=>56
[8,3,7,5,2,4,6,1]=>[3,2,1,1,1]=>64
[8,2,4,5,7,3,6,1]=>[4,2,1,1]=>90
[2,4,5,7,3,1,8,6]=>[5,2,1]=>64
[8,2,4,6,5,3,1,7]=>[4,1,1,1,1]=>35
[8,2,5,4,6,1,3,7]=>[4,2,1,1]=>90
[8,6,3,5,1,4,2,7]=>[3,2,1,1,1]=>64
[8,6,1,4,5,3,2,7]=>[4,1,1,1,1]=>35
[8,1,5,6,4,3,2,7]=>[4,1,1,1,1]=>35
[5,7,4,3,2,1,8,6]=>[3,2,1,1,1]=>64
[8,5,7,4,3,2,6,1]=>[2,2,1,1,1,1]=>20
[4,6,8,3,2,7,5,1]=>[3,2,2,1]=>70
[4,7,6,3,2,8,1,5]=>[3,2,1,1,1]=>64
[1,4,6,7,3,2,8,5]=>[5,2,1]=>64
[5,4,7,3,1,8,2,6]=>[3,3,1,1]=>56
[1,7,4,5,3,2,8,6]=>[4,2,1,1]=>90
[3,7,5,1,4,2,8,6]=>[3,3,1,1]=>56
[5,7,4,2,1,3,8,6]=>[3,3,1,1]=>56
[8,5,7,4,2,1,6,3]=>[2,2,2,1,1]=>28
[8,3,7,5,1,4,6,2]=>[3,2,1,1,1]=>64
[8,4,1,7,5,3,6,2]=>[3,2,1,1,1]=>64
[4,6,3,8,7,1,5,2]=>[3,2,2,1]=>70
[1,7,4,8,6,3,5,2]=>[3,2,2,1]=>70
[8,4,7,6,3,5,2,1]=>[2,2,1,1,1,1]=>20
[3,6,5,8,7,4,1,2]=>[3,2,2,1]=>70
[3,1,5,8,6,7,4,2]=>[4,2,1,1]=>90
[4,8,1,6,7,3,5,2]=>[3,3,1,1]=>56
[3,6,4,1,8,7,5,2]=>[3,2,2,1]=>70
[8,2,6,1,4,7,5,3]=>[3,3,1,1]=>56
[2,7,6,8,1,4,3,5]=>[3,3,1,1]=>56
[3,7,1,6,4,8,2,5]=>[3,3,1,1]=>56
[1,7,3,5,6,8,2,4]=>[5,2,1]=>64
[1,3,6,7,5,8,2,4]=>[5,2,1]=>64
[3,7,6,5,8,2,1,4]=>[3,2,1,1,1]=>64
[3,6,8,5,7,2,4,1]=>[3,2,2,1]=>70
[2,3,5,7,6,8,1,4]=>[5,2,1]=>64
[2,1,6,5,7,8,3,4]=>[4,3,1]=>70
[4,2,7,6,8,3,1,5]=>[3,3,1,1]=>56
[4,2,6,8,7,3,5,1]=>[3,3,1,1]=>56
[3,8,2,4,6,7,5,1]=>[4,2,1,1]=>90
[3,7,2,6,4,8,1,5]=>[3,3,1,1]=>56
[3,2,6,1,4,7,8,5]=>[4,3,1]=>70
[5,3,7,2,1,8,4,6]=>[3,3,1,1]=>56
[4,7,3,2,1,5,8,6]=>[3,3,1,1]=>56
[8,7,6,1,3,4,2,5]=>[4,1,1,1,1]=>35
[8,5,7,3,2,1,6,4]=>[2,2,2,1,1]=>28
[8,3,6,7,2,1,5,4]=>[3,2,2,1]=>70
[3,7,8,6,2,1,5,4]=>[3,2,2,1]=>70
[8,7,6,3,5,2,4,1]=>[2,2,1,1,1,1]=>20
[2,7,4,8,1,6,5,3]=>[3,2,2,1]=>70
[4,6,8,2,1,7,5,3]=>[3,2,2,1]=>70
[8,4,1,5,7,2,6,3]=>[3,3,1,1]=>56
[8,5,3,7,1,6,2,4]=>[3,2,2,1]=>70
[8,5,7,2,1,3,6,4]=>[3,2,2,1]=>70
[8,2,6,7,1,3,5,4]=>[3,3,1,1]=>56
[8,3,6,1,7,5,2,4]=>[3,3,1,1]=>56
[4,6,1,8,7,2,5,3]=>[3,3,1,1]=>56
[8,1,2,5,6,7,4,3]=>[5,1,1,1]=>35
[8,2,6,5,7,4,1,3]=>[3,2,1,1,1]=>64
[2,1,7,8,5,6,4,3]=>[3,3,1,1]=>56
[8,2,5,7,6,4,3,1]=>[3,1,1,1,1,1]=>21
[2,7,6,8,5,4,1,3]=>[3,2,1,1,1]=>64
[1,7,2,5,8,6,4,3]=>[4,2,1,1]=>90
[1,7,4,8,2,6,5,3]=>[3,2,2,1]=>70
[3,7,8,1,6,5,2,4]=>[3,3,1,1]=>56
[2,7,8,6,1,3,5,4]=>[3,3,1,1]=>56
[8,7,6,3,5,1,4,2]=>[2,2,1,1,1,1]=>20
[8,4,7,6,5,1,3,2]=>[2,2,1,1,1,1]=>20
[8,7,1,5,6,4,3,2]=>[3,1,1,1,1,1]=>21
[8,1,6,7,5,4,3,2]=>[3,1,1,1,1,1]=>21
[6,5,3,1,2,4,8,7]=>[4,2,1,1]=>90
[4,6,3,5,1,2,8,7]=>[3,3,2]=>42
[8,5,3,7,2,1,4,6]=>[3,2,1,1,1]=>64
[6,8,1,4,5,7,3,2]=>[4,2,1,1]=>90
[8,7,2,4,5,1,3,6]=>[4,2,1,1]=>90
[3,6,2,4,5,1,8,7]=>[4,3,1]=>70
[2,6,1,4,5,3,8,7]=>[4,3,1]=>70
[6,1,2,4,5,3,8,7]=>[5,2,1]=>64
[5,6,3,2,1,4,8,7]=>[3,3,1,1]=>56
[5,4,3,6,1,2,8,7]=>[3,3,1,1]=>56
[6,3,1,4,5,2,8,7]=>[4,3,1]=>70
[3,1,6,4,5,2,8,7]=>[4,3,1]=>70
[8,3,7,4,5,1,2,6]=>[4,2,1,1]=>90
[5,8,7,4,2,6,3,1]=>[2,2,2,1,1]=>28
[2,8,7,4,1,6,3,5]=>[3,3,1,1]=>56
[8,1,7,4,2,6,3,5]=>[4,2,1,1]=>90
[3,7,8,4,5,1,2,6]=>[4,2,2]=>56
[2,1,8,7,5,3,4,6]=>[4,2,1,1]=>90
[2,1,6,8,5,7,3,4]=>[3,3,2]=>42
[5,6,3,8,1,7,2,4]=>[3,3,2]=>42
[7,6,1,4,5,8,3,2]=>[4,1,1,1,1]=>35
[3,7,6,4,5,8,2,1]=>[4,1,1,1,1]=>35
[8,5,7,4,1,6,3,2]=>[2,2,2,1,1]=>28
[5,1,8,4,7,6,2,3]=>[3,2,2,1]=>70
[2,5,8,4,7,6,1,3]=>[3,2,2,1]=>70
[2,4,8,3,5,6,7,1]=>[5,2,1]=>64
[4,1,8,3,5,6,7,2]=>[5,2,1]=>64
[3,8,4,2,5,6,7,1]=>[5,1,1,1]=>35
[8,4,1,3,5,6,7,2]=>[5,1,1,1]=>35
[7,5,8,4,3,6,1,2]=>[2,2,2,1,1]=>28
[6,5,3,8,4,1,7,2]=>[3,2,2,1]=>70
[2,1,5,8,4,6,7,3]=>[4,3,1]=>70
[2,1,4,8,3,6,7,5]=>[4,3,1]=>70
[6,4,3,8,2,1,7,5]=>[2,2,2,1,1]=>28
[7,3,8,4,2,6,1,5]=>[3,2,2,1]=>70
[8,3,1,2,5,6,7,4]=>[5,2,1]=>64
[3,1,8,2,5,6,7,4]=>[5,2,1]=>64
[2,3,8,1,5,6,7,4]=>[5,2,1]=>64
[4,3,8,2,5,6,7,1]=>[4,2,1,1]=>90
[4,8,2,3,5,6,7,1]=>[5,2,1]=>64
[3,8,2,1,5,6,7,4]=>[4,2,2]=>56
[2,8,1,3,5,6,7,4]=>[5,2,1]=>64
[8,1,2,3,5,6,7,4]=>[6,1,1]=>21
[7,8,2,4,3,6,1,5]=>[3,2,2,1]=>70
[6,8,3,2,4,1,7,5]=>[3,2,2,1]=>70
[2,1,8,3,4,6,7,5]=>[5,2,1]=>64
[2,1,7,8,5,4,3,6]=>[3,3,1,1]=>56
[5,7,3,8,1,4,2,6]=>[3,3,2]=>42
[7,1,8,4,5,3,2,6]=>[4,2,1,1]=>90
[2,7,8,4,5,3,1,6]=>[4,2,1,1]=>90
[8,7,1,4,3,6,2,5]=>[3,2,1,1,1]=>64
[3,8,7,4,2,6,1,5]=>[3,2,1,1,1]=>64
[5,7,8,4,3,6,2,1]=>[3,2,1,1,1]=>64
[5,6,3,8,4,2,7,1]=>[3,3,1,1]=>56
[4,8,3,6,2,1,7,5]=>[3,2,2,1]=>70
[8,6,3,1,4,2,7,5]=>[3,3,1,1]=>56
[7,5,3,8,2,4,1,6]=>[3,2,1,1,1]=>64
[2,4,3,1,8,5,7,6]=>[4,2,2]=>56
[4,1,3,2,6,8,7,5]=>[4,2,2]=>56
[7,5,3,6,2,8,1,4]=>[3,2,1,1,1]=>64
[8,6,3,5,1,2,7,4]=>[3,3,1,1]=>56
[5,8,3,2,6,1,7,4]=>[3,2,2,1]=>70
[4,5,3,8,6,2,7,1]=>[4,2,1,1]=>90
[3,5,8,4,7,6,2,1]=>[3,2,1,1,1]=>64
[5,8,2,4,7,6,1,3]=>[3,2,2,1]=>70
[8,7,5,4,1,6,2,3]=>[3,2,1,1,1]=>64
[2,7,6,4,5,8,1,3]=>[4,2,1,1]=>90
[7,1,6,4,5,8,2,3]=>[4,2,1,1]=>90
[5,7,3,6,1,8,2,4]=>[3,3,2]=>42
[2,1,7,6,5,8,3,4]=>[3,3,1,1]=>56
[2,1,8,5,3,6,7,4]=>[4,3,1]=>70
[6,8,3,5,2,1,7,4]=>[3,2,2,1]=>70
[7,8,5,4,2,6,1,3]=>[2,2,2,1,1]=>28
[8,1,4,2,5,6,7,3]=>[5,2,1]=>64
[2,8,4,1,5,6,7,3]=>[5,2,1]=>64
[4,8,1,2,5,6,7,3]=>[5,2,1]=>64
[3,4,8,1,5,6,7,2]=>[5,2,1]=>64
[3,4,2,8,5,6,7,1]=>[5,2,1]=>64
[2,4,1,8,5,6,7,3]=>[5,2,1]=>64
[4,1,2,8,5,6,7,3]=>[5,2,1]=>64
[8,4,2,1,5,6,7,3]=>[4,2,1,1]=>90
[7,5,2,4,8,6,1,3]=>[3,2,2,1]=>70
[6,5,3,2,8,1,7,4]=>[2,2,2,1,1]=>28
[2,1,5,3,8,6,7,4]=>[4,3,1]=>70
[6,4,3,5,8,1,7,2]=>[3,2,2,1]=>70
[7,3,5,4,8,6,1,2]=>[3,2,2,1]=>70
[8,3,4,1,5,6,7,2]=>[5,2,1]=>64
[4,3,1,8,5,6,7,2]=>[4,2,2]=>56
[3,1,4,8,5,6,7,2]=>[5,2,1]=>64
[6,5,3,7,2,8,4,1]=>[3,2,1,1,1]=>64
[6,3,7,4,5,8,2,1]=>[4,2,1,1]=>90
[6,7,2,4,5,8,3,1]=>[4,2,1,1]=>90
[5,1,7,4,8,6,3,2]=>[3,3,1,1]=>56
[2,5,7,4,8,6,3,1]=>[4,2,1,1]=>90
[5,6,3,7,1,8,4,2]=>[4,2,2]=>56
[3,8,7,4,5,2,1,6]=>[4,1,1,1,1]=>35
[3,7,5,4,8,6,2,1]=>[3,2,1,1,1]=>64
[5,7,1,4,8,6,2,3]=>[3,3,2]=>42
[5,6,3,1,8,2,7,4]=>[3,3,2]=>42
[4,6,3,5,8,2,7,1]=>[3,3,1,1]=>56
[4,6,3,8,1,2,7,5]=>[3,3,2]=>42
[3,7,8,4,1,6,2,5]=>[3,3,2]=>42
[3,2,5,1,6,8,4,7]=>[4,3,1]=>70
[3,6,2,5,4,8,1,7]=>[3,3,1,1]=>56
[3,5,2,4,7,1,8,6]=>[4,3,1]=>70
[3,5,8,2,4,7,6,1]=>[3,3,1,1]=>56
[4,2,5,8,3,7,6,1]=>[3,3,1,1]=>56
[4,2,6,5,3,8,1,7]=>[3,3,1,1]=>56
[5,4,2,1,6,8,3,7]=>[3,3,1,1]=>56
[6,3,5,1,4,8,2,7]=>[3,3,1,1]=>56
[4,6,1,5,3,8,2,7]=>[3,3,1,1]=>56
[5,1,6,4,3,8,2,7]=>[3,3,1,1]=>56
[5,4,3,2,7,1,8,6]=>[3,2,1,1,1]=>64
[5,4,3,8,2,7,6,1]=>[2,2,2,1,1]=>28
[4,3,6,2,8,7,5,1]=>[3,2,2,1]=>70
[4,3,7,6,2,1,8,5]=>[3,2,2,1]=>70
[6,4,3,1,7,2,8,5]=>[3,3,1,1]=>56
[7,5,4,3,1,8,2,6]=>[3,2,1,1,1]=>64
[1,4,7,5,8,3,2,6]=>[4,2,1,1]=>90
[7,1,3,5,8,4,2,6]=>[4,2,1,1]=>90
[7,2,5,8,4,1,3,6]=>[3,3,1,1]=>56
[2,8,5,7,4,6,1,3]=>[3,2,2,1]=>70
[3,5,8,7,1,4,6,2]=>[3,3,1,1]=>56
[1,4,5,8,7,3,6,2]=>[4,2,1,1]=>90
[1,5,4,8,7,3,6,2]=>[3,2,2,1]=>70
[6,4,3,8,1,7,5,2]=>[2,2,2,2]=>14
[4,3,7,1,8,6,5,2]=>[3,2,2,1]=>70
[4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1]=>20
[5,3,8,7,6,4,2,1]=>[2,2,1,1,1,1]=>20
[7,5,3,1,8,6,4,2]=>[2,2,2,2]=>14
[1,8,6,5,3,7,4,2]=>[3,2,1,1,1]=>64
[1,5,8,6,3,7,4,2]=>[4,2,1,1]=>90
[4,6,1,8,7,3,5,2]=>[3,3,1,1]=>56
[6,8,7,3,1,4,5,2]=>[3,2,2,1]=>70
[6,2,8,7,4,5,1,3]=>[3,2,2,1]=>70
[7,6,2,8,4,1,3,5]=>[3,2,2,1]=>70
[7,3,1,6,8,4,2,5]=>[3,3,1,1]=>56
[1,7,6,4,8,3,2,5]=>[3,2,1,1,1]=>64
[5,7,1,6,3,2,8,4]=>[3,3,1,1]=>56
[6,1,7,5,3,2,8,4]=>[3,3,1,1]=>56
[7,6,5,3,2,1,8,4]=>[2,2,1,1,1,1]=>20
[6,5,3,2,8,7,4,1]=>[2,2,2,1,1]=>28
[5,2,6,3,8,7,4,1]=>[3,3,1,1]=>56
[5,2,7,6,3,1,8,4]=>[3,3,1,1]=>56
[6,5,2,1,7,3,8,4]=>[3,3,1,1]=>56
[5,2,7,4,1,8,3,6]=>[3,3,2]=>42
[4,7,2,6,3,1,8,5]=>[3,3,1,1]=>56
[2,4,8,6,3,7,5,1]=>[4,2,1,1]=>90
[3,8,6,2,4,7,5,1]=>[3,3,1,1]=>56
[7,3,6,2,4,1,8,5]=>[3,3,1,1]=>56
[3,6,7,2,1,4,8,5]=>[4,3,1]=>70
[4,3,7,8,2,1,5,6]=>[3,3,1,1]=>56
[8,3,7,1,4,6,2,5]=>[3,3,1,1]=>56
[3,8,2,5,7,1,6,4]=>[3,2,2,1]=>70
[8,3,6,2,7,1,5,4]=>[3,2,2,1]=>70
[7,8,3,6,2,1,5,4]=>[2,2,2,2]=>14
[8,7,3,6,2,5,4,1]=>[2,2,1,1,1,1]=>20
[4,7,8,2,1,6,5,3]=>[3,2,2,1]=>70
[4,2,6,8,1,7,5,3]=>[3,2,2,1]=>70
[5,4,8,2,7,1,6,3]=>[2,2,2,2]=>14
[4,8,1,5,7,2,6,3]=>[3,3,1,1]=>56
[5,8,3,7,1,6,2,4]=>[3,2,2,1]=>70
[5,8,7,2,6,1,3,4]=>[3,2,2,1]=>70
[8,6,2,7,5,1,3,4]=>[3,2,2,1]=>70
[3,6,8,1,7,5,2,4]=>[3,3,1,1]=>56
[5,1,6,8,2,7,4,3]=>[3,3,1,1]=>56
[6,5,2,8,1,7,4,3]=>[2,2,2,2]=>14
[5,2,7,1,8,6,4,3]=>[3,2,2,1]=>70
[5,8,2,7,6,4,3,1]=>[2,2,1,1,1,1]=>20
[6,2,8,7,5,4,3,1]=>[2,2,1,1,1,1]=>20
[7,6,2,1,8,5,4,3]=>[2,2,2,1,1]=>28
[6,1,7,2,8,5,4,3]=>[3,3,1,1]=>56
[7,5,1,8,2,6,4,3]=>[3,2,2,1]=>70
[4,7,1,8,6,2,5,3]=>[3,3,1,1]=>56
[7,8,3,1,6,5,2,4]=>[3,2,2,1]=>70
[8,7,4,6,1,5,3,2]=>[2,2,1,1,1,1]=>20
[8,5,7,1,6,4,3,2]=>[2,2,1,1,1,1]=>20
[6,8,1,7,5,4,3,2]=>[2,2,1,1,1,1]=>20
[7,1,8,6,5,4,3,2]=>[2,2,1,1,1,1]=>20
[5,4,2,3,7,6,1,8]=>[4,2,1,1]=>90
[6,4,2,7,3,5,1,8]=>[4,2,1,1]=>90
[7,4,2,6,3,5,1,8]=>[4,2,1,1]=>90
[8,4,2,6,3,1,5,7]=>[4,2,1,1]=>90
[3,2,7,6,4,5,1,8]=>[4,2,1,1]=>90
[4,7,2,6,3,5,1,8]=>[4,2,1,1]=>90
[5,7,6,2,3,4,1,8]=>[4,2,1,1]=>90
[1,6,5,2,3,8,4,7]=>[5,2,1]=>64
[1,7,5,2,8,3,4,6]=>[5,2,1]=>64
[6,8,5,2,3,1,4,7]=>[4,2,1,1]=>90
[5,8,6,2,3,1,4,7]=>[4,2,1,1]=>90
[4,8,2,6,3,1,5,7]=>[4,2,1,1]=>90
[3,2,8,6,4,1,5,7]=>[4,2,1,1]=>90
[3,2,1,6,4,8,5,7]=>[4,3,1]=>70
[7,1,5,2,8,3,4,6]=>[5,2,1]=>64
[1,8,5,2,7,3,4,6]=>[5,2,1]=>64
[1,8,6,7,2,3,4,5]=>[5,2,1]=>64
[8,1,6,7,2,3,4,5]=>[5,2,1]=>64
[7,1,6,8,2,3,4,5]=>[5,2,1]=>64
[3,2,1,7,8,4,5,6]=>[4,3,1]=>70
[3,2,8,7,1,4,5,6]=>[4,2,2]=>56
[5,8,7,2,1,3,4,6]=>[4,2,1,1]=>90
[1,7,6,8,2,3,4,5]=>[5,2,1]=>64
[6,5,8,2,3,1,4,7]=>[4,2,1,1]=>90
[8,5,7,2,1,3,4,6]=>[4,2,1,1]=>90
[6,4,2,8,3,1,5,7]=>[4,2,1,1]=>90
[5,4,2,3,8,1,6,7]=>[4,2,1,1]=>90
[3,2,5,4,1,8,6,7]=>[4,3,1]=>70
[4,5,2,3,1,8,6,7]=>[4,3,1]=>70
[5,4,2,3,1,8,6,7]=>[4,2,1,1]=>90
[6,4,2,1,3,8,5,7]=>[4,2,1,1]=>90
[7,4,2,1,8,3,5,6]=>[4,2,1,1]=>90
[8,4,2,1,7,3,5,6]=>[4,2,1,1]=>90
[1,4,2,8,7,3,5,6]=>[5,2,1]=>64
[1,5,8,2,7,3,4,6]=>[5,2,1]=>64
[8,5,1,2,7,3,4,6]=>[5,2,1]=>64
[7,5,1,2,8,3,4,6]=>[5,2,1]=>64
[6,5,1,2,3,8,4,7]=>[5,2,1]=>64
[4,6,2,1,3,8,5,7]=>[4,3,1]=>70
[3,2,6,1,4,8,5,7]=>[4,3,1]=>70
[3,2,7,1,8,4,5,6]=>[4,3,1]=>70
[4,7,2,1,8,3,5,6]=>[4,3,1]=>70
[7,6,1,8,2,3,4,5]=>[5,2,1]=>64
[8,6,1,7,2,3,4,5]=>[5,2,1]=>64
[1,6,8,7,2,3,4,5]=>[5,2,1]=>64
[1,7,8,6,2,3,4,5]=>[5,2,1]=>64
[7,8,1,6,2,3,4,5]=>[5,2,1]=>64
[6,8,1,7,2,3,4,5]=>[5,2,1]=>64
[4,8,2,1,7,3,5,6]=>[4,2,2]=>56
[3,2,8,1,7,4,5,6]=>[4,2,2]=>56
[3,2,1,8,7,4,5,6]=>[4,2,2]=>56
[5,1,8,2,7,3,4,6]=>[5,2,1]=>64
[6,1,8,7,2,3,4,5]=>[5,2,1]=>64
[8,1,7,6,2,3,4,5]=>[5,1,1,1]=>35
[1,8,7,6,2,3,4,5]=>[5,1,1,1]=>35
[6,3,5,1,2,4,8,7]=>[4,3,1]=>70
[4,3,5,6,1,2,8,7]=>[4,3,1]=>70
[8,3,7,5,2,1,4,6]=>[3,2,1,1,1]=>64
[6,3,7,5,1,8,4,2]=>[3,2,2,1]=>70
[6,5,2,7,1,8,3,4]=>[3,3,1,1]=>56
[8,5,2,7,4,1,3,6]=>[3,2,2,1]=>70
[2,6,1,5,4,3,8,7]=>[3,3,1,1]=>56
[6,4,3,5,1,2,8,7]=>[3,3,1,1]=>56
[5,3,1,4,6,2,8,7]=>[4,3,1]=>70
[3,1,4,6,5,2,8,7]=>[4,3,1]=>70
[5,7,4,6,2,8,3,1]=>[3,2,2,1]=>70
[8,1,4,7,2,6,3,5]=>[4,2,1,1]=>90
[3,4,7,8,5,2,1,6]=>[4,2,1,1]=>90
[2,1,8,5,7,3,4,6]=>[4,3,1]=>70
[8,6,3,5,1,7,4,2]=>[3,2,1,1,1]=>64
[5,8,2,4,6,7,3,1]=>[4,2,1,1]=>90
[3,4,8,6,5,7,1,2]=>[4,2,1,1]=>90
[7,5,4,8,1,6,3,2]=>[2,2,2,1,1]=>28
[5,1,4,6,8,2,7,3]=>[4,2,2]=>56
[2,5,4,6,7,1,8,3]=>[5,2,1]=>64
[2,4,6,3,7,5,8,1]=>[5,2,1]=>64
[4,1,6,3,8,5,7,2]=>[4,3,1]=>70
[3,7,4,2,8,6,5,1]=>[3,2,2,1]=>70
[7,4,1,3,5,8,6,2]=>[4,2,1,1]=>90
[6,5,8,4,1,7,3,2]=>[2,2,2,1,1]=>28
[8,5,3,7,4,1,6,2]=>[3,2,2,1]=>70
[2,1,4,8,3,7,6,5]=>[3,3,1,1]=>56
[7,4,3,8,2,1,6,5]=>[2,2,2,1,1]=>28
[6,3,7,4,1,8,2,5]=>[3,3,2]=>42
[8,3,1,2,5,7,6,4]=>[4,2,1,1]=>90
[3,1,8,2,7,6,5,4]=>[3,2,1,1,1]=>64
[2,3,8,1,6,7,5,4]=>[4,2,1,1]=>90
[4,3,7,2,6,8,5,1]=>[3,2,2,1]=>70
[4,7,2,3,8,5,6,1]=>[4,3,1]=>70
[3,8,2,1,7,5,6,4]=>[3,2,2,1]=>70
[2,8,1,3,6,5,7,4]=>[4,2,1,1]=>90
[2,7,8,5,4,3,1,6]=>[3,2,1,1,1]=>64
[8,7,1,6,3,4,2,5]=>[4,1,1,1,1]=>35
[3,8,6,7,2,4,1,5]=>[3,3,1,1]=>56
[5,3,8,7,4,2,6,1]=>[3,2,1,1,1]=>64
[4,3,8,7,2,1,6,5]=>[2,2,2,2]=>14
[8,3,6,1,4,2,7,5]=>[3,3,1,1]=>56
[7,3,5,8,2,4,1,6]=>[3,3,1,1]=>56
[2,3,4,1,8,5,7,6]=>[5,2,1]=>64
[4,1,3,2,6,7,8,5]=>[5,2,1]=>64
[8,3,5,6,2,7,1,4]=>[4,2,1,1]=>90
[5,3,6,1,8,7,2,4]=>[3,3,2]=>42
[5,6,2,8,7,4,1,3]=>[3,2,2,1]=>70
[7,8,5,6,1,4,2,3]=>[3,2,2,1]=>70
[2,8,6,5,4,7,1,3]=>[3,2,1,1,1]=>64
[8,1,6,4,5,7,2,3]=>[4,2,1,1]=>90
[5,8,3,6,1,7,2,4]=>[3,3,2]=>42
[2,1,8,6,5,7,3,4]=>[3,3,1,1]=>56
[2,1,7,5,3,6,8,4]=>[4,3,1]=>70
[6,7,3,5,2,1,8,4]=>[3,2,2,1]=>70
[7,1,4,2,5,6,8,3]=>[5,2,1]=>64
[2,7,4,1,6,5,8,3]=>[4,2,1,1]=>90
[4,6,1,2,8,7,3,5]=>[4,3,1]=>70
[2,4,1,5,8,7,6,3]=>[4,2,1,1]=>90
[4,1,2,5,8,6,7,3]=>[5,2,1]=>64
[6,4,2,1,5,8,7,3]=>[3,2,2,1]=>70
[8,5,2,4,6,1,7,3]=>[4,2,1,1]=>90
[7,5,3,2,6,8,1,4]=>[3,2,1,1,1]=>64
[2,1,5,3,6,8,7,4]=>[4,3,1]=>70
[7,3,5,4,6,1,8,2]=>[4,2,1,1]=>90
[6,3,4,1,5,7,8,2]=>[5,2,1]=>64
[4,3,1,5,7,6,8,2]=>[4,2,2]=>56
[3,1,4,5,6,8,7,2]=>[5,2,1]=>64
[4,5,2,6,3,1,8,7]=>[4,3,1]=>70
[6,5,2,1,4,3,8,7]=>[3,3,1,1]=>56
[6,5,2,7,4,8,3,1]=>[3,2,1,1,1]=>64
[8,5,2,7,4,1,6,3]=>[3,2,2,1]=>70
[8,3,7,5,2,1,6,4]=>[3,2,1,1,1]=>64
[6,3,7,5,2,8,4,1]=>[3,2,2,1]=>70
[3,1,6,5,4,2,8,7]=>[3,3,1,1]=>56
[5,6,3,2,4,1,8,7]=>[3,3,1,1]=>56
[3,6,2,4,1,5,8,7]=>[4,3,1]=>70
[2,6,1,3,5,4,8,7]=>[4,3,1]=>70
[6,7,2,3,4,8,5,1]=>[4,3,1]=>70
[8,7,2,3,4,1,6,5]=>[4,2,1,1]=>90
[5,1,7,3,8,4,6,2]=>[4,3,1]=>70
[2,5,7,3,8,6,4,1]=>[4,2,1,1]=>90
[7,6,1,3,5,8,4,2]=>[4,1,1,1,1]=>35
[3,6,7,4,1,8,5,2]=>[4,2,2]=>56
[5,6,3,7,4,8,1,2]=>[4,2,2]=>56
[2,1,6,7,4,8,5,3]=>[4,3,1]=>70
[2,1,8,7,4,3,6,5]=>[3,3,1,1]=>56
[5,8,3,7,4,2,6,1]=>[3,2,1,1,1]=>64
[3,8,7,4,1,2,6,5]=>[3,3,1,1]=>56
[7,8,1,3,5,2,6,4]=>[4,2,2]=>56
[5,8,7,3,2,6,1,4]=>[2,2,2,1,1]=>28
[2,8,6,3,1,5,7,4]=>[4,2,1,1]=>90
[8,1,6,3,2,5,4,7]=>[4,2,1,1]=>90
[2,8,4,1,6,3,7,5]=>[4,3,1]=>70
[4,8,1,2,7,6,3,5]=>[4,2,1,1]=>90
[3,8,4,2,5,7,1,6]=>[4,2,1,1]=>90
[6,8,3,5,2,7,4,1]=>[3,2,2,1]=>70
[2,1,5,3,8,7,6,4]=>[3,3,1,1]=>56
[6,5,3,2,8,7,1,4]=>[2,2,2,1,1]=>28
[7,5,2,4,8,1,6,3]=>[3,2,2,1]=>70
[3,4,2,8,5,7,6,1]=>[4,2,1,1]=>90
[2,4,1,8,7,6,5,3]=>[3,2,1,1,1]=>64
[8,4,2,1,7,5,3,6]=>[3,2,2,1]=>70
[4,3,1,8,6,7,5,2]=>[3,2,2,1]=>70
[3,1,4,8,6,5,7,2]=>[4,2,1,1]=>90
[7,1,6,5,4,8,2,3]=>[3,2,1,1,1]=>64
[3,7,5,6,8,4,2,1]=>[4,1,1,1,1]=>35
[5,7,1,6,8,2,4,3]=>[3,3,1,1]=>56
[8,6,2,5,1,7,4,3]=>[3,2,1,1,1]=>64
[5,6,2,1,8,7,3,4]=>[3,3,2]=>42
[4,6,2,5,8,3,7,1]=>[3,3,1,1]=>56
[7,5,2,6,3,8,1,4]=>[3,3,1,1]=>56
[4,1,2,3,6,8,7,5]=>[5,2,1]=>64
[2,4,3,1,8,5,6,7]=>[5,2,1]=>64
[7,5,2,8,3,4,6,1]=>[4,2,1,1]=>90
[5,6,2,8,4,3,1,7]=>[3,3,1,1]=>56
[4,7,2,8,1,5,3,6]=>[3,3,2]=>42
[8,7,2,1,4,5,6,3]=>[4,2,1,1]=>90
[3,6,8,7,1,5,4,2]=>[3,2,1,1,1]=>64
[5,7,8,6,3,4,1,2]=>[3,2,2,1]=>70
[7,1,8,5,4,3,6,2]=>[3,2,1,1,1]=>64
[2,7,8,4,5,3,6,1]=>[4,2,1,1]=>90
[5,7,3,8,1,4,6,2]=>[3,3,2]=>42
[2,1,7,8,5,4,6,3]=>[3,3,1,1]=>56
[2,1,5,8,4,6,3,7]=>[4,3,1]=>70
[6,5,3,8,4,1,2,7]=>[3,2,2,1]=>70
[7,5,8,4,3,6,2,1]=>[2,2,1,1,1,1]=>20
[2,4,8,3,5,6,1,7]=>[5,2,1]=>64
[4,1,8,3,6,5,2,7]=>[4,2,1,1]=>90
[3,4,8,1,7,2,5,6]=>[4,3,1]=>70
[8,4,1,3,7,2,6,5]=>[3,2,2,1]=>70
[3,1,8,2,4,7,6,5]=>[4,2,1,1]=>90
[2,3,8,1,4,6,7,5]=>[5,2,1]=>64
[4,3,8,2,5,1,7,6]=>[3,2,2,1]=>70
[6,3,8,4,2,5,7,1]=>[4,2,1,1]=>90
[7,4,3,8,2,5,1,6]=>[3,2,1,1,1]=>64
[2,1,4,8,3,5,7,6]=>[4,3,1]=>70
[6,8,2,4,3,5,1,7]=>[4,2,1,1]=>90
[4,8,2,3,5,1,6,7]=>[5,2,1]=>64
[3,8,2,1,4,6,5,7]=>[4,2,2]=>56
[2,8,1,3,4,5,7,6]=>[5,2,1]=>64
[2,8,4,1,6,5,3,7]=>[4,2,1,1]=>90
[2,8,4,1,6,5,7,3]=>[4,2,1,1]=>90
[2,8,7,6,1,4,3,5]=>[3,2,1,1,1]=>64
[2,8,5,6,7,4,3,1]=>[4,1,1,1,1]=>35
[7,5,8,6,1,4,2,3]=>[3,2,2,1]=>70
[3,5,7,6,1,4,2,8]=>[4,2,1,1]=>90
[3,5,7,2,4,1,6,8]=>[4,3,1]=>70
[7,5,8,2,4,1,6,3]=>[3,2,2,1]=>70
[2,8,5,3,4,7,6,1]=>[4,2,1,1]=>90
[2,8,5,3,4,1,7,6]=>[4,2,1,1]=>90
[2,8,5,3,4,1,6,7]=>[5,1,1,1]=>35
[2,8,7,6,1,4,5,3]=>[3,2,1,1,1]=>64
[2,8,5,3,6,1,7,4]=>[4,2,1,1]=>90
[2,8,5,6,7,4,1,3]=>[4,2,1,1]=>90
[2,8,5,3,4,7,1,6]=>[4,2,1,1]=>90
[2,8,5,3,4,6,1,7]=>[5,1,1,1]=>35
[2,8,5,3,4,6,7,1]=>[5,1,1,1]=>35
[3,5,7,2,4,6,1,8]=>[4,3,1]=>70
[6,5,2,7,3,1,4,8]=>[4,2,1,1]=>90
[6,5,2,8,3,1,7,4]=>[3,2,2,1]=>70
[6,5,2,8,3,1,4,7]=>[4,2,1,1]=>90
[7,5,8,2,4,6,3,1]=>[3,2,1,1,1]=>64
[7,5,8,6,1,4,3,2]=>[2,2,2,1,1]=>28
[6,5,8,2,1,3,7,4]=>[3,2,2,1]=>70
[3,5,6,2,1,8,7,4]=>[4,2,2]=>56
[3,5,7,6,1,4,8,2]=>[4,2,1,1]=>90
[3,5,7,2,4,1,8,6]=>[4,3,1]=>70
[3,5,7,2,4,6,8,1]=>[4,3,1]=>70
[6,5,2,7,3,1,8,4]=>[3,3,1,1]=>56
[4,5,2,6,3,1,7,8]=>[5,2,1]=>64
[4,1,2,3,7,6,8,5]=>[5,2,1]=>64
[6,5,2,7,3,4,8,1]=>[4,2,1,1]=>90
[5,1,6,7,4,3,8,2]=>[4,2,1,1]=>90
[5,1,2,6,4,8,7,3]=>[4,3,1]=>70
[5,1,2,8,6,4,7,3]=>[4,2,1,1]=>90
[5,1,6,8,7,3,4,2]=>[3,3,1,1]=>56
[6,5,2,8,3,7,4,1]=>[3,2,2,1]=>70
[4,1,2,3,8,7,5,6]=>[5,2,1]=>64
[4,1,2,3,8,6,5,7]=>[5,2,1]=>64
[4,1,2,3,8,6,7,5]=>[5,2,1]=>64
[4,1,2,3,7,6,5,8]=>[5,2,1]=>64
[4,1,2,3,8,5,7,6]=>[5,2,1]=>64
[7,1,6,8,4,3,5,2]=>[3,2,1,1,1]=>64
[6,1,2,8,4,5,7,3]=>[5,2,1]=>64
[5,6,8,2,3,1,7,4]=>[3,3,2]=>42
[6,5,8,2,4,3,1,7]=>[3,2,1,1,1]=>64
[6,5,8,2,4,3,7,1]=>[3,2,1,1,1]=>64
[7,5,2,8,3,4,1,6]=>[4,2,1,1]=>90
[6,5,2,8,3,7,1,4]=>[3,2,2,1]=>70
[6,5,2,7,3,4,1,8]=>[4,2,1,1]=>90
[5,1,6,7,4,3,2,8]=>[4,2,1,1]=>90
[5,1,6,8,7,3,2,4]=>[3,3,1,1]=>56
[7,1,6,8,4,3,2,5]=>[3,2,1,1,1]=>64
[5,7,8,6,3,4,2,1]=>[3,2,1,1,1]=>64
[4,1,8,3,6,5,7,2]=>[4,2,1,1]=>90
[4,1,8,3,6,2,7,5]=>[4,2,2]=>56
[3,1,4,8,6,2,7,5]=>[4,3,1]=>70
[3,1,4,8,6,5,2,7]=>[4,2,1,1]=>90
[7,1,6,5,8,3,2,4]=>[3,2,1,1,1]=>64
[4,1,6,7,8,3,2,5]=>[4,3,1]=>70
[4,1,6,5,7,3,2,8]=>[4,2,1,1]=>90
[4,5,2,6,3,7,1,8]=>[5,2,1]=>64
[4,5,2,7,3,8,1,6]=>[4,3,1]=>70
[3,5,6,2,4,8,7,1]=>[4,3,1]=>70
[3,5,6,2,4,8,1,7]=>[4,3,1]=>70
[3,7,5,6,8,4,1,2]=>[4,2,1,1]=>90
[3,6,5,2,8,1,7,4]=>[3,2,2,1]=>70
[6,1,2,5,8,4,7,3]=>[4,2,1,1]=>90
[7,1,6,5,8,3,4,2]=>[3,2,1,1,1]=>64
[7,5,2,6,3,8,4,1]=>[3,3,1,1]=>56
[4,1,2,3,5,8,7,6]=>[5,2,1]=>64
[4,1,2,3,7,8,6,5]=>[5,2,1]=>64
[4,5,2,7,3,8,6,1]=>[4,3,1]=>70
[4,1,6,7,8,3,5,2]=>[4,3,1]=>70
[4,1,2,6,8,5,7,3]=>[4,3,1]=>70
[4,1,2,5,6,8,7,3]=>[5,2,1]=>64
[4,5,2,6,3,7,8,1]=>[5,2,1]=>64
[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]=>28
[7,8,4,2,1,5,3,6]=>[3,2,2,1]=>70
[7,8,2,1,6,5,3,4]=>[3,2,2,1]=>70
[6,4,1,2,5,7,3,8]=>[5,2,1]=>64
[2,4,8,1,5,7,3,6]=>[4,3,1]=>70
[4,3,8,1,7,2,5,6]=>[4,2,2]=>56
[7,8,3,4,5,1,6,2]=>[4,2,2]=>56
[7,8,3,5,4,2,1,6]=>[3,2,1,1,1]=>64
[7,8,3,6,5,4,1,2]=>[2,2,2,1,1]=>28
[7,8,2,6,4,1,3,5]=>[3,2,2,1]=>70
[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]=>20
[2,1,8,7,5,4,3,6]=>[3,2,1,1,1]=>64
[1,3,8,2,6,4,7,5]=>[4,3,1]=>70
[5,3,7,1,6,4,8,2]=>[3,2,2,1]=>70
[5,3,6,2,7,4,1,8]=>[4,2,1,1]=>90
[6,1,2,5,8,7,4,3]=>[4,2,1,1]=>90
[6,3,1,8,4,2,7,5]=>[3,3,2]=>42
[6,4,2,1,5,3,8,7]=>[3,3,1,1]=>56
[6,4,3,7,5,8,1,2]=>[3,2,2,1]=>70
[4,3,8,7,5,6,1,2]=>[3,2,2,1]=>70
[2,4,7,1,5,3,6,8]=>[5,2,1]=>64
[1,3,7,6,4,2,8,5]=>[4,2,1,1]=>90
[3,7,2,8,6,4,1,5]=>[3,3,1,1]=>56
[3,8,1,7,6,4,5,2]=>[3,2,1,1,1]=>64
[1,8,5,7,3,6,4,2]=>[3,2,1,1,1]=>64
[2,7,5,8,3,6,1,4]=>[3,2,2,1]=>70
[1,5,6,8,2,4,7,3]=>[4,3,1]=>70
[5,6,7,3,8,4,1,2]=>[4,2,2]=>56
[4,5,6,7,2,8,1,3]=>[5,2,1]=>64
[4,5,7,6,1,8,3,2]=>[4,2,1,1]=>90
[1,5,8,6,2,7,3,4]=>[4,3,1]=>70
[1,6,5,8,3,2,7,4]=>[3,2,2,1]=>70
[4,6,5,7,1,2,8,3]=>[4,3,1]=>70
[4,7,5,6,3,1,8,2]=>[4,2,1,1]=>90
[5,1,6,3,4,2,8,7]=>[4,3,1]=>70
[5,7,6,4,3,8,1,2]=>[3,2,1,1,1]=>64
[6,3,4,5,8,7,1,2]=>[4,2,2]=>56
[6,2,4,1,8,3,7,5]=>[3,3,2]=>42
[5,1,4,2,7,6,8,3]=>[4,2,2]=>56
[1,6,2,4,7,8,3,5]=>[5,2,1]=>64
[5,7,2,4,1,6,3,8]=>[4,2,2]=>56
[5,8,7,6,3,4,1,2]=>[2,2,2,1,1]=>28
[5,8,7,6,2,3,1,4]=>[3,2,1,1,1]=>64
[4,8,2,1,5,6,3,7]=>[4,2,2]=>56
[4,2,7,8,1,6,3,5]=>[3,3,2]=>42
[2,1,8,7,6,5,3,4]=>[3,2,1,1,1]=>64
[4,8,6,3,5,7,1,2]=>[3,2,2,1]=>70
[3,8,6,5,2,4,1,7]=>[3,2,1,1,1]=>64
[5,3,7,8,2,1,6,4]=>[3,2,2,1]=>70
[5,2,8,7,1,6,4,3]=>[2,2,2,1,1]=>28
[3,6,7,8,5,1,4,2]=>[4,2,1,1]=>90
[3,7,8,5,1,2,4,6]=>[4,3,1]=>70
[4,1,8,6,2,3,5,7]=>[5,2,1]=>64
[3,8,7,6,5,4,1,2]=>[2,2,1,1,1,1]=>20
[2,8,7,5,1,4,3,6]=>[3,2,1,1,1]=>64
[2,8,6,7,5,1,3,4]=>[3,3,1,1]=>56
[2,7,8,6,5,4,1,3]=>[3,2,1,1,1]=>64
[6,4,2,7,1,3,8,5]=>[3,3,1,1]=>56
[7,4,2,5,1,3,8,6]=>[3,3,1,1]=>56
[8,5,3,6,1,7,2,4]=>[3,3,1,1]=>56
[7,3,6,2,4,8,1,5]=>[3,3,1,1]=>56
[5,3,6,7,1,2,8,4]=>[4,3,1]=>70
[6,3,7,4,1,2,8,5]=>[3,3,2]=>42
[4,7,1,5,2,3,8,6]=>[4,3,1]=>70
[7,6,4,2,3,8,1,5]=>[3,2,1,1,1]=>64
[8,6,4,2,3,7,1,5]=>[3,2,1,1,1]=>64
[4,7,6,3,8,1,2,5]=>[3,3,1,1]=>56
[5,7,4,2,3,8,1,6]=>[3,3,1,1]=>56
[3,7,6,1,4,8,2,5]=>[3,3,1,1]=>56
[6,4,7,5,2,8,1,3]=>[3,2,2,1]=>70
[7,4,8,5,2,6,1,3]=>[3,2,2,1]=>70
[3,8,6,2,4,7,1,5]=>[3,3,1,1]=>56
[4,8,6,2,7,1,3,5]=>[3,3,1,1]=>56
[2,6,5,8,1,3,4,7]=>[4,3,1]=>70
[2,5,7,4,8,1,3,6]=>[4,3,1]=>70
[5,4,6,7,2,8,1,3]=>[4,2,1,1]=>90
[3,5,7,1,4,8,2,6]=>[4,3,1]=>70
[5,3,7,2,4,8,1,6]=>[3,3,1,1]=>56
[5,4,7,3,8,1,2,6]=>[3,3,1,1]=>56
[7,4,6,3,8,1,2,5]=>[3,3,1,1]=>56
[8,4,6,3,7,1,2,5]=>[3,3,1,1]=>56
[8,4,1,6,7,2,3,5]=>[4,3,1]=>70
[7,4,1,6,8,2,3,5]=>[4,3,1]=>70
[6,5,3,7,1,8,2,4]=>[3,3,1,1]=>56
[6,5,1,2,7,8,3,4]=>[4,3,1]=>70
[5,3,6,4,7,8,1,2]=>[4,2,2]=>56
[6,3,7,4,8,5,1,2]=>[3,3,2]=>42
[4,7,1,5,8,6,2,3]=>[3,3,2]=>42
[7,5,1,2,8,6,3,4]=>[4,2,2]=>56
[7,6,1,8,5,2,3,4]=>[4,2,1,1]=>90
[8,6,1,7,5,2,3,4]=>[4,2,1,1]=>90
[5,7,2,8,1,6,3,4]=>[3,3,2]=>42
[6,3,7,8,5,1,2,4]=>[3,3,2]=>42
[3,6,8,2,7,1,4,5]=>[3,3,2]=>42
[2,4,8,7,1,3,5,6]=>[4,3,1]=>70
[4,3,8,7,1,2,5,6]=>[4,2,2]=>56
[5,3,8,7,1,2,4,6]=>[4,2,2]=>56
[8,3,7,6,1,2,4,5]=>[4,2,1,1]=>90
[8,4,7,6,1,2,3,5]=>[4,2,1,1]=>90
[3,5,8,7,1,2,4,6]=>[4,3,1]=>70
[2,5,8,7,1,3,4,6]=>[4,3,1]=>70
[6,8,4,7,5,1,2,3]=>[3,2,2,1]=>70
[5,8,7,1,6,2,3,4]=>[4,2,1,1]=>90
[2,8,7,6,1,3,4,5]=>[4,2,1,1]=>90
[3,8,7,6,1,2,4,5]=>[4,2,1,1]=>90
[4,8,7,6,1,2,3,5]=>[4,2,1,1]=>90
[5,6,3,1,4,2,8,7]=>[3,3,2]=>42
[7,5,3,8,2,1,6,4]=>[2,2,2,1,1]=>28
[3,8,7,4,5,1,6,2]=>[4,2,1,1]=>90
[2,1,7,8,5,3,6,4]=>[3,3,2]=>42
[5,7,3,8,1,2,6,4]=>[3,3,2]=>42
[8,7,1,4,5,3,2,6]=>[4,1,1,1,1]=>35
[2,7,8,4,1,6,5,3]=>[3,2,2,1]=>70
[7,1,8,4,2,6,5,3]=>[3,2,2,1]=>70
[7,5,1,4,8,6,3,2]=>[3,2,1,1,1]=>64
[6,5,3,1,8,4,7,2]=>[3,2,2,1]=>70
[8,6,3,1,2,5,7,4]=>[4,2,1,1]=>90
[8,7,1,4,2,6,5,3]=>[3,2,1,1,1]=>64
[2,3,4,5,6,7,8,1,9]=>[8,1]=>8
[2,3,4,5,6,8,9,1,7]=>[7,2]=>27
[2,3,4,5,7,8,9,1,6]=>[7,2]=>27
[2,3,4,6,7,8,9,1,5]=>[7,2]=>27
[2,3,5,6,7,8,9,1,4]=>[7,2]=>27
[2,4,5,6,7,8,9,1,3]=>[7,2]=>27
[3,4,5,6,7,8,9,1,2]=>[7,2]=>27
[2,3,4,5,6,7,8,9,10,1]=>[9,1]=>9
[2,3,4,5,6,7,8,9,1,10]=>[9,1]=>9
[2,3,4,5,6,7,1,8,9]=>[8,1]=>8
[2,3,4,5,6,7,8,10,1,9]=>[8,2]=>35
[2,3,4,5,6,1,9,7,8]=>[7,2]=>27
[2,3,4,5,6,7,9,10,1,8]=>[8,2]=>35
[2,3,4,5,1,8,9,6,7]=>[6,3]=>48
[2,3,4,5,6,8,9,10,1,7]=>[8,2]=>35
[2,3,4,1,7,8,9,5,6]=>[6,3]=>48
[2,3,4,5,7,8,9,10,1,6]=>[8,2]=>35
[2,3,1,6,7,8,9,4,5]=>[6,3]=>48
[2,3,4,6,7,8,9,10,1,5]=>[8,2]=>35
[2,1,5,6,7,8,9,3,4]=>[6,3]=>48
[2,3,5,6,7,8,9,10,1,4]=>[8,2]=>35
[1,4,5,6,7,8,9,2,3]=>[7,2]=>27
[2,4,5,6,7,8,9,10,1,3]=>[8,2]=>35
[3,4,5,6,7,8,9,10,1,2]=>[8,2]=>35
[3,6,4,5,7,2,8,1]=>[5,1,1,1]=>35
[5,3,2,7,4,6,8,1]=>[4,2,1,1]=>90
[7,5,3,6,2,4,8,1]=>[3,2,1,1,1]=>64
[8,5,3,6,2,7,1,4]=>[3,2,1,1,1]=>64
[8,2,6,3,4,7,1,5]=>[4,2,1,1]=>90
[7,2,6,3,4,5,8,1]=>[5,1,1,1]=>35
[6,2,7,3,4,5,8,1]=>[5,2,1]=>64
[5,4,7,6,2,3,8,1]=>[3,2,2,1]=>70
[6,7,3,5,2,4,8,1]=>[3,2,2,1]=>70
[3,7,6,2,4,5,8,1]=>[4,2,1,1]=>90
[2,7,6,3,4,5,8,1]=>[5,1,1,1]=>35
[8,6,5,2,3,7,1,4]=>[3,2,1,1,1]=>64
[8,5,2,1,7,3,4,6]=>[4,2,1,1]=>90
[7,5,2,1,8,3,4,6]=>[4,2,1,1]=>90
[1,6,3,2,8,4,5,7]=>[5,2,1]=>64
[5,4,8,6,2,7,1,3]=>[3,2,2,1]=>70
[6,8,3,5,2,7,1,4]=>[3,2,2,1]=>70
[7,8,5,2,3,6,1,4]=>[3,2,2,1]=>70
[6,8,2,1,7,3,4,5]=>[4,2,2]=>56
[1,8,6,3,7,2,4,5]=>[4,2,1,1]=>90
[1,8,2,7,3,4,5,6]=>[6,1,1]=>21
[2,8,1,7,3,4,5,6]=>[5,2,1]=>64
[3,8,6,1,7,2,4,5]=>[4,3,1]=>70
[4,8,1,5,7,2,3,6]=>[4,3,1]=>70
[4,2,8,3,7,1,5,6]=>[4,2,2]=>56
[8,1,2,7,3,4,5,6]=>[6,1,1]=>21
[3,6,2,7,1,8,4,5]=>[4,3,1]=>70
[6,3,7,1,2,8,4,5]=>[4,3,1]=>70
[7,2,6,1,8,3,4,5]=>[4,3,1]=>70
[3,2,1,5,8,4,6,7]=>[4,3,1]=>70
[4,3,5,1,6,8,2,7]=>[4,3,1]=>70
[5,4,6,3,8,7,1,2]=>[3,2,2,1]=>70
[3,6,4,5,8,7,1,2]=>[4,2,2]=>56
[6,5,3,4,8,7,1,2]=>[3,2,2,1]=>70
[5,3,2,8,7,1,4,6]=>[3,2,2,1]=>70
[5,3,1,8,7,2,4,6]=>[4,2,2]=>56
[8,5,3,7,6,1,2,4]=>[3,2,2,1]=>70
[6,1,8,3,7,2,4,5]=>[4,2,2]=>56
[6,3,8,1,7,2,4,5]=>[4,2,2]=>56
[7,6,8,2,3,5,1,4]=>[3,2,2,1]=>70
[3,7,8,2,4,6,1,5]=>[3,3,2]=>42
[6,7,3,8,2,5,1,4]=>[3,2,2,1]=>70
[5,4,7,8,2,6,1,3]=>[3,2,2,1]=>70
[4,2,5,8,7,1,3,6]=>[3,3,2]=>42
[2,3,8,7,1,4,5,6]=>[5,2,1]=>64
[7,2,8,6,1,3,4,5]=>[4,2,2]=>56
[2,1,8,7,3,4,5,6]=>[5,2,1]=>64
[8,2,7,6,1,3,4,5]=>[4,2,1,1]=>90
[1,2,8,7,3,4,5,6]=>[6,1,1]=>21
[1,3,8,7,2,4,5,6]=>[5,2,1]=>64
[1,7,8,3,6,2,4,5]=>[4,2,2]=>56
[4,1,5,8,7,2,3,6]=>[4,3,1]=>70
[5,4,8,7,6,1,2,3]=>[3,2,2,1]=>70
[6,8,3,7,5,1,2,4]=>[3,2,2,1]=>70
[7,8,6,2,5,1,3,4]=>[3,2,2,1]=>70
[8,1,6,7,3,2,5,4]=>[3,2,2,1]=>70
[8,1,6,7,3,2,4,5]=>[4,2,1,1]=>90
[8,1,5,3,7,2,4,6]=>[4,2,1,1]=>90
[8,1,5,3,6,2,4,7]=>[4,2,1,1]=>90
[7,5,1,3,6,2,4,8]=>[4,2,1,1]=>90
[7,5,8,3,6,2,4,1]=>[2,2,2,1,1]=>28
[7,4,8,3,2,6,5,1]=>[2,2,2,1,1]=>28
[7,4,1,3,2,6,5,8]=>[4,2,1,1]=>90
[8,1,4,3,2,6,5,7]=>[4,2,1,1]=>90
[8,1,4,3,2,7,5,6]=>[4,2,1,1]=>90
[8,1,4,3,2,7,6,5]=>[3,2,2,1]=>70
[8,1,5,4,6,7,2,3]=>[4,2,1,1]=>90
[8,1,5,3,6,2,7,4]=>[4,2,1,1]=>90
[8,1,4,3,2,6,7,5]=>[4,2,1,1]=>90
[8,1,4,3,2,5,7,6]=>[4,2,1,1]=>90
[8,1,4,3,2,5,6,7]=>[5,1,1,1]=>35
[7,4,1,3,2,5,6,8]=>[5,1,1,1]=>35
[7,4,8,3,2,5,6,1]=>[3,2,1,1,1]=>64
[6,4,3,8,2,5,7,1]=>[3,2,1,1,1]=>64
[6,4,3,1,2,5,8,7]=>[4,2,1,1]=>90
[7,4,1,3,2,5,8,6]=>[4,2,1,1]=>90
[7,4,1,3,2,6,8,5]=>[4,2,1,1]=>90
[7,5,1,3,6,2,8,4]=>[4,2,1,1]=>90
[7,5,1,4,6,8,2,3]=>[4,2,1,1]=>90
[7,5,8,3,6,2,1,4]=>[2,2,2,1,1]=>28
[7,4,8,3,2,6,1,5]=>[2,2,2,1,1]=>28
[7,4,8,3,2,5,1,6]=>[3,2,1,1,1]=>64
[6,4,3,8,2,5,1,7]=>[3,2,1,1,1]=>64
[6,4,3,7,2,5,8,1]=>[3,2,1,1,1]=>64
[5,4,3,2,8,6,1,7]=>[3,2,1,1,1]=>64
[5,4,3,2,8,7,1,6]=>[2,2,2,1,1]=>28
[6,5,3,8,7,2,1,4]=>[2,2,2,1,1]=>28
[6,5,4,8,7,1,2,3]=>[3,2,2,1]=>70
[6,5,4,1,7,8,2,3]=>[3,3,1,1]=>56
[6,5,3,1,7,2,8,4]=>[3,3,1,1]=>56
[6,4,3,1,2,7,8,5]=>[4,2,1,1]=>90
[5,4,3,2,1,8,6,7]=>[3,2,1,1,1]=>64
[6,5,3,1,8,2,7,4]=>[3,2,2,1]=>70
[6,5,4,1,8,7,2,3]=>[3,2,2,1]=>70
[7,5,1,4,8,6,2,3]=>[3,2,2,1]=>70
[7,4,1,3,2,8,6,5]=>[3,2,2,1]=>70
[7,4,1,3,2,8,5,6]=>[4,2,1,1]=>90
[6,4,3,1,2,8,5,7]=>[4,2,1,1]=>90
[6,4,3,1,2,7,5,8]=>[4,2,1,1]=>90
[6,4,3,8,2,7,5,1]=>[2,2,2,1,1]=>28
[6,5,3,8,7,2,4,1]=>[2,2,2,1,1]=>28
[6,5,3,1,7,2,4,8]=>[4,2,1,1]=>90
[6,5,3,1,8,2,4,7]=>[4,2,1,1]=>90
[7,5,1,3,8,2,4,6]=>[4,2,1,1]=>90
[7,6,1,8,3,2,4,5]=>[4,2,1,1]=>90
[7,6,1,8,4,5,2,3]=>[3,2,2,1]=>70
[7,6,8,1,4,5,2,3]=>[3,2,2,1]=>70
[7,6,8,1,3,2,5,4]=>[3,2,2,1]=>70
[6,5,3,7,8,2,4,1]=>[3,2,1,1,1]=>64
[6,4,3,7,2,8,5,1]=>[3,2,1,1,1]=>64
[6,4,3,7,2,1,5,8]=>[3,2,1,1,1]=>64
[7,4,8,3,2,1,5,6]=>[3,2,1,1,1]=>64
[7,4,8,3,2,1,6,5]=>[2,2,2,1,1]=>28
[7,5,8,3,1,2,6,4]=>[3,2,2,1]=>70
[7,5,8,4,1,6,2,3]=>[3,2,2,1]=>70
[6,5,4,8,1,7,2,3]=>[3,2,2,1]=>70
[6,5,3,8,1,2,7,4]=>[3,2,2,1]=>70
[5,4,3,2,8,1,7,6]=>[2,2,2,1,1]=>28
[6,4,3,7,2,1,8,5]=>[3,2,1,1,1]=>64
[6,5,3,7,1,2,8,4]=>[3,3,1,1]=>56
[6,5,4,7,1,8,2,3]=>[3,3,1,1]=>56
[6,5,3,7,8,2,1,4]=>[3,2,1,1,1]=>64
[6,4,3,7,2,8,1,5]=>[3,2,1,1,1]=>64
[5,4,3,2,7,8,1,6]=>[3,2,1,1,1]=>64
[5,4,3,2,6,8,1,7]=>[3,2,1,1,1]=>64
[5,6,2,1,3,4,8,7]=>[4,3,1]=>70
[7,6,1,2,5,8,3,4]=>[4,2,1,1]=>90
[2,1,7,8,4,3,5,6]=>[4,3,1]=>70
[7,8,1,2,5,4,6,3]=>[4,2,1,1]=>90
[8,4,1,3,7,6,2,5]=>[3,2,2,1]=>70
[6,5,2,1,8,7,4,3]=>[2,2,2,2]=>14
[4,7,2,8,1,3,6,5]=>[3,3,2]=>42
[3,4,7,1,8,2,6,5]=>[4,3,1]=>70
[1,8,2,4,3,5,6,7]=>[6,1,1]=>21
[1,7,2,4,3,5,6,8]=>[6,1,1]=>21
[1,6,2,4,3,5,7,8]=>[6,1,1]=>21
[1,5,2,4,3,6,7,8]=>[6,1,1]=>21
[1,6,2,5,3,4,7,8]=>[6,1,1]=>21
[1,7,2,5,3,4,6,8]=>[6,1,1]=>21
[1,8,2,5,3,4,6,7]=>[6,1,1]=>21
[1,8,2,6,3,4,5,7]=>[6,1,1]=>21
[1,7,2,6,3,4,5,8]=>[6,1,1]=>21
[1,8,2,7,3,5,4,6]=>[5,1,1,1]=>35
[1,7,2,8,3,5,4,6]=>[5,2,1]=>64
[1,6,2,8,3,5,4,7]=>[5,2,1]=>64
[1,5,2,8,3,6,4,7]=>[5,2,1]=>64
[1,4,2,8,3,6,5,7]=>[5,2,1]=>64
[1,3,2,8,4,6,5,7]=>[5,2,1]=>64
[1,2,3,8,4,6,5,7]=>[6,1,1]=>21
[1,2,3,7,4,6,5,8]=>[6,1,1]=>21
[1,3,2,7,4,6,5,8]=>[5,2,1]=>64
[1,4,2,7,3,6,5,8]=>[5,2,1]=>64
[1,5,2,7,3,6,4,8]=>[5,2,1]=>64
[1,6,2,7,3,5,4,8]=>[5,2,1]=>64
[1,7,2,6,3,5,4,8]=>[5,1,1,1]=>35
[1,8,2,6,3,5,4,7]=>[5,1,1,1]=>35
[1,8,2,5,3,6,4,7]=>[5,2,1]=>64
[1,7,2,5,3,6,4,8]=>[5,2,1]=>64
[1,6,2,5,3,7,4,8]=>[5,2,1]=>64
[1,5,2,4,3,7,6,8]=>[5,2,1]=>64
[1,6,2,4,3,7,5,8]=>[5,2,1]=>64
[1,7,2,4,3,6,5,8]=>[5,2,1]=>64
[1,8,2,4,3,6,5,7]=>[5,2,1]=>64
[1,8,2,3,4,6,5,7]=>[6,1,1]=>21
[1,7,2,3,4,6,5,8]=>[6,1,1]=>21
[1,8,2,3,4,7,5,6]=>[6,1,1]=>21
[1,8,2,4,3,7,5,6]=>[5,2,1]=>64
[1,7,2,4,3,8,5,6]=>[5,2,1]=>64
[1,6,2,4,3,8,5,7]=>[5,2,1]=>64
[1,5,2,4,3,8,6,7]=>[5,2,1]=>64
[1,6,2,5,3,8,4,7]=>[5,2,1]=>64
[1,7,2,5,3,8,4,6]=>[5,2,1]=>64
[1,8,2,5,3,7,4,6]=>[5,2,1]=>64
[1,8,2,6,3,7,4,5]=>[5,2,1]=>64
[1,7,2,6,3,8,4,5]=>[5,2,1]=>64
[1,2,3,8,4,7,5,6]=>[6,1,1]=>21
[1,3,2,8,4,7,5,6]=>[5,2,1]=>64
[1,4,2,8,3,7,5,6]=>[5,2,1]=>64
[1,5,2,8,3,7,4,6]=>[5,2,1]=>64
[1,6,2,8,3,7,4,5]=>[5,2,1]=>64
[1,7,2,8,3,6,4,5]=>[5,2,1]=>64
[1,8,2,7,3,6,4,5]=>[5,1,1,1]=>35
[4,6,3,7,2,5,1,8]=>[4,2,1,1]=>90
[4,6,3,7,5,2,1,8]=>[4,2,1,1]=>90
[4,6,3,8,5,1,7,2]=>[3,3,2]=>42
[4,6,3,8,5,1,2,7]=>[3,3,2]=>42
[5,6,8,3,4,1,2,7]=>[3,3,2]=>42
[5,6,8,3,4,1,7,2]=>[3,3,2]=>42
[4,6,2,7,5,3,1,8]=>[4,2,1,1]=>90
[5,6,7,2,4,3,1,8]=>[4,2,1,1]=>90
[5,6,8,4,3,1,7,2]=>[3,2,2,1]=>70
[5,6,8,4,3,1,2,7]=>[3,3,1,1]=>56
[5,7,8,4,1,6,2,3]=>[3,3,2]=>42
[5,7,8,4,1,6,3,2]=>[3,2,2,1]=>70
[5,7,8,4,1,3,6,2]=>[3,3,1,1]=>56
[5,6,8,4,2,1,7,3]=>[3,2,2,1]=>70
[5,6,8,2,4,1,7,3]=>[3,3,2]=>42
[4,6,2,8,5,1,7,3]=>[3,3,2]=>42
[3,2,6,8,5,1,7,4]=>[3,3,2]=>42
[3,2,6,8,5,1,4,7]=>[3,3,2]=>42
[4,6,2,8,5,1,3,7]=>[3,3,2]=>42
[5,6,8,2,4,1,3,7]=>[3,3,2]=>42
[5,6,8,4,2,1,3,7]=>[3,3,1,1]=>56
[5,7,8,4,1,3,2,6]=>[3,3,1,1]=>56
[5,7,8,4,1,2,6,3]=>[3,3,2]=>42
[5,7,8,4,1,2,3,6]=>[4,3,1]=>70
[6,7,8,1,5,2,3,4]=>[4,3,1]=>70
[6,7,8,1,5,2,4,3]=>[3,3,1,1]=>56
[6,7,8,1,5,3,2,4]=>[3,3,1,1]=>56
[6,7,8,1,3,5,2,4]=>[3,3,2]=>42
[5,7,8,2,1,6,3,4]=>[3,3,2]=>42
[4,7,2,8,1,6,3,5]=>[3,3,2]=>42
[3,2,7,8,1,6,4,5]=>[3,3,2]=>42
[3,2,7,8,1,6,5,4]=>[3,2,2,1]=>70
[4,7,2,8,1,6,5,3]=>[3,2,2,1]=>70
[5,7,8,2,1,6,4,3]=>[3,2,2,1]=>70
[6,7,8,1,3,5,4,2]=>[3,3,1,1]=>56
[6,7,8,1,5,3,4,2]=>[3,3,1,1]=>56
[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]=>64
[6,7,8,1,5,4,2,3]=>[3,3,1,1]=>56
[6,7,8,1,4,5,2,3]=>[3,3,2]=>42
[6,7,8,1,4,5,3,2]=>[3,3,1,1]=>56
[6,7,8,1,4,3,5,2]=>[3,3,1,1]=>56
[6,7,8,1,3,4,5,2]=>[4,3,1]=>70
[5,7,8,2,1,4,6,3]=>[3,3,2]=>42
[4,7,2,8,1,5,6,3]=>[3,3,2]=>42
[3,2,7,8,1,5,6,4]=>[3,3,2]=>42
[3,2,6,8,4,1,7,5]=>[3,3,2]=>42
[4,6,2,8,3,1,7,5]=>[3,3,2]=>42
[5,6,8,3,2,1,7,4]=>[3,2,2,1]=>70
[5,7,8,3,1,4,6,2]=>[3,3,2]=>42
[5,7,8,3,1,6,4,2]=>[3,2,2,1]=>70
[5,7,8,3,1,6,2,4]=>[3,3,2]=>42
[4,7,3,8,1,6,2,5]=>[3,3,2]=>42
[4,7,3,8,1,6,5,2]=>[3,2,2,1]=>70
[4,7,3,8,1,5,6,2]=>[3,3,2]=>42
[4,6,3,8,2,1,7,5]=>[3,2,2,1]=>70
[4,5,3,2,8,1,7,6]=>[3,2,2,1]=>70
[4,5,2,3,8,1,7,6]=>[3,3,2]=>42
[3,2,5,4,8,1,7,6]=>[3,3,2]=>42
[4,5,3,2,8,1,6,7]=>[4,2,1,1]=>90
[4,6,3,8,2,1,5,7]=>[3,3,1,1]=>56
[4,7,3,8,1,5,2,6]=>[3,3,2]=>42
[4,7,3,8,1,2,6,5]=>[3,3,2]=>42
[4,7,3,8,1,2,5,6]=>[4,3,1]=>70
[5,7,8,3,1,2,4,6]=>[4,3,1]=>70
[5,7,8,3,1,2,6,4]=>[3,3,2]=>42
[5,7,8,3,1,4,2,6]=>[3,3,2]=>42
[5,6,8,3,2,1,4,7]=>[3,3,1,1]=>56
[3,2,7,8,1,5,4,6]=>[3,3,2]=>42
[5,7,8,2,1,4,3,6]=>[3,3,2]=>42
[6,7,8,1,3,4,2,5]=>[4,3,1]=>70
[6,7,8,1,4,3,2,5]=>[3,3,1,1]=>56
[6,7,8,1,4,2,5,3]=>[3,3,2]=>42
[6,7,8,1,4,2,3,5]=>[4,3,1]=>70
[6,7,8,1,2,5,3,4]=>[4,3,1]=>70
[6,7,8,1,2,5,4,3]=>[3,3,1,1]=>56
[6,7,8,1,2,4,5,3]=>[4,3,1]=>70
[6,7,8,1,3,2,5,4]=>[3,3,2]=>42
[5,7,8,2,1,3,6,4]=>[3,3,2]=>42
[3,2,7,8,1,4,6,5]=>[3,3,2]=>42
[6,7,8,1,3,2,4,5]=>[4,3,1]=>70
[6,7,8,1,2,4,3,5]=>[4,3,1]=>70
[6,7,8,1,2,3,5,4]=>[4,3,1]=>70
[7,2,8,5,1,6,4,3]=>[3,2,2,1]=>70
[1,3,7,5,2,6,4,8]=>[5,2,1]=>64
[1,3,7,5,4,2,6,8]=>[5,1,1,1]=>35
[7,2,8,5,4,1,6,3]=>[3,2,2,1]=>70
[2,8,5,4,3,1,7,6]=>[3,2,1,1,1]=>64
[2,8,4,5,6,1,7,3]=>[5,2,1]=>64
[2,8,6,5,7,3,1,4]=>[3,2,1,1,1]=>64
[2,8,4,5,3,7,1,6]=>[4,2,1,1]=>90
[2,8,4,3,5,6,1,7]=>[5,1,1,1]=>35
[7,2,8,4,5,6,1,3]=>[4,2,2]=>56
[1,6,3,7,5,2,4,8]=>[4,2,2]=>56
[6,2,3,8,5,1,7,4]=>[4,2,2]=>56
[6,3,2,8,5,1,4,7]=>[3,2,2,1]=>70
[7,4,8,2,5,6,3,1]=>[3,2,2,1]=>70
[7,4,8,5,2,1,3,6]=>[3,2,2,1]=>70
[6,4,8,5,1,3,7,2]=>[3,2,2,1]=>70
[6,3,7,5,2,1,8,4]=>[3,2,2,1]=>70
[4,3,7,5,1,2,8,6]=>[3,3,2]=>42
[4,3,7,1,5,6,8,2]=>[4,2,2]=>56
[3,6,1,7,5,2,8,4]=>[4,3,1]=>70
[3,4,1,2,7,6,8,5]=>[4,3,1]=>70
[3,4,2,1,7,5,8,6]=>[4,3,1]=>70
[3,6,5,7,1,4,8,2]=>[4,2,1,1]=>90
[6,5,2,7,4,1,8,3]=>[3,2,2,1]=>70
[3,5,2,6,4,8,7,1]=>[4,3,1]=>70
[5,3,1,8,6,4,7,2]=>[3,2,2,1]=>70
[5,6,1,8,7,2,4,3]=>[3,3,1,1]=>56
[6,3,5,8,2,7,4,1]=>[3,2,2,1]=>70
[6,5,8,4,2,3,7,1]=>[3,2,1,1,1]=>64
[6,2,5,8,3,7,1,4]=>[3,2,2,1]=>70
[1,6,5,7,3,4,2,8]=>[4,2,1,1]=>90
[1,5,2,7,4,6,3,8]=>[5,2,1]=>64
[5,2,1,8,7,6,3,4]=>[3,2,2,1]=>70
[7,1,3,8,4,6,2,5]=>[4,2,2]=>56
[2,3,4,8,6,1,7,5]=>[5,2,1]=>64
[2,3,4,8,6,5,1,7]=>[5,1,1,1]=>35
[2,7,3,5,8,6,1,4]=>[4,2,2]=>56
[3,2,4,7,8,6,1,5]=>[4,2,2]=>56
[1,5,4,6,2,7,3,8]=>[5,2,1]=>64
[5,2,4,7,1,8,3,6]=>[4,3,1]=>70
[5,3,6,4,1,8,7,2]=>[3,3,2]=>42
[5,3,6,1,4,8,2,7]=>[3,3,2]=>42
[7,3,5,6,8,4,2,1]=>[4,1,1,1,1]=>35
[6,3,5,1,8,2,7,4]=>[3,3,2]=>42
[2,6,1,5,8,4,7,3]=>[3,3,1,1]=>56
[2,7,6,5,8,3,4,1]=>[3,2,1,1,1]=>64
[5,7,1,6,3,8,4,2]=>[3,3,1,1]=>56
[3,2,4,1,7,8,5,6]=>[4,3,1]=>70
[3,1,4,2,7,8,6,5]=>[4,3,1]=>70
[5,1,4,7,2,8,6,3]=>[4,2,2]=>56
[3,6,4,7,8,2,5,1]=>[4,2,1,1]=>90
[3,1,4,6,8,5,7,2]=>[4,3,1]=>70
[6,3,4,5,7,1,8,2]=>[5,2,1]=>64
[2,5,4,6,1,7,8,3]=>[5,2,1]=>64
[7,2,1,4,3,6,5,8]=>[4,3,1]=>70
[7,3,4,1,2,6,5,8]=>[4,3,1]=>70
[7,6,3,2,5,4,1,8]=>[3,2,1,1,1]=>64
[6,7,3,2,5,4,8,1]=>[3,2,2,1]=>70
[1,8,3,2,5,4,7,6]=>[4,3,1]=>70
[1,8,4,5,2,3,7,6]=>[4,3,1]=>70
[7,3,5,1,6,2,4,8]=>[4,3,1]=>70
[7,2,1,5,6,3,4,8]=>[4,3,1]=>70
[1,8,5,4,3,2,7,6]=>[3,2,1,1,1]=>64
[1,8,6,4,3,7,2,5]=>[3,2,1,1,1]=>64
[6,5,7,4,3,1,8,2]=>[3,2,1,1,1]=>64
[6,4,7,5,1,3,8,2]=>[3,2,2,1]=>70
[6,3,7,1,5,4,8,2]=>[3,2,2,1]=>70
[2,5,8,4,3,1,7,6]=>[3,2,2,1]=>70
[2,6,8,4,3,7,1,5]=>[3,2,2,1]=>70
[2,7,8,4,3,6,5,1]=>[3,2,2,1]=>70
[1,8,7,4,3,6,5,2]=>[3,2,1,1,1]=>64
[1,8,7,5,6,3,4,2]=>[3,2,1,1,1]=>64
[2,7,8,5,6,3,4,1]=>[3,2,2,1]=>70
[2,6,8,5,7,3,1,4]=>[3,2,2,1]=>70
[2,5,8,6,7,1,3,4]=>[4,3,1]=>70
[2,4,8,6,1,7,3,5]=>[4,3,1]=>70
[3,2,1,8,6,7,4,5]=>[3,3,2]=>42
[5,3,7,1,6,8,4,2]=>[3,2,2,1]=>70
[5,4,7,6,1,8,3,2]=>[3,2,2,1]=>70
[4,6,7,5,8,3,1,2]=>[4,2,1,1]=>90
[1,8,6,5,7,3,2,4]=>[3,2,1,1,1]=>64
[1,8,5,6,7,2,3,4]=>[4,3,1]=>70
[5,4,6,7,1,8,2,3]=>[4,3,1]=>70
[5,3,6,1,7,8,2,4]=>[4,3,1]=>70
[5,2,1,6,7,8,3,4]=>[4,3,1]=>70
[6,2,1,5,7,3,8,4]=>[4,3,1]=>70
[6,3,5,1,7,2,8,4]=>[4,3,1]=>70
[1,8,4,6,2,7,3,5]=>[4,3,1]=>70
[1,8,3,2,6,7,4,5]=>[4,3,1]=>70
[5,7,3,2,6,8,4,1]=>[3,2,2,1]=>70
[5,6,3,2,7,8,1,4]=>[4,2,1,1]=>90
[6,5,3,2,7,1,8,4]=>[3,2,1,1,1]=>64
[6,2,1,4,3,7,8,5]=>[4,3,1]=>70
[4,6,3,2,8,7,1,5]=>[3,2,2,1]=>70
[4,7,3,2,8,6,5,1]=>[3,2,2,1]=>70
[1,8,3,2,7,6,5,4]=>[3,2,1,1,1]=>64
[1,8,4,7,2,6,5,3]=>[3,2,1,1,1]=>64
[3,6,4,8,2,7,1,5]=>[3,2,2,1]=>70
[3,4,5,8,1,2,7,6]=>[4,3,1]=>70
[4,3,5,1,8,2,7,6]=>[3,3,2]=>42
[3,5,6,8,7,1,2,4]=>[4,3,1]=>70
[3,6,5,8,7,2,1,4]=>[3,2,2,1]=>70
[1,8,5,7,6,2,4,3]=>[3,2,1,1,1]=>64
[1,8,6,7,5,4,2,3]=>[3,2,1,1,1]=>64
[3,6,7,8,5,4,1,2]=>[4,2,1,1]=>90
[3,4,7,8,1,6,5,2]=>[4,2,1,1]=>90
[4,2,1,7,8,6,5,3]=>[3,2,2,1]=>70
[2,4,8,7,1,6,5,3]=>[3,2,1,1,1]=>64
[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]=>132
[2,1,4,3,6,5,8,7,12,11,10,9]=>[5,5,1,1]=>1485
[2,1,4,3,6,5,10,9,8,7,12,11]=>[5,5,1,1]=>1485
[2,1,4,3,6,5,12,9,8,11,10,7]=>[5,5,1,1]=>1485
[2,1,4,3,6,5,12,11,10,9,8,7]=>[4,4,1,1,1,1]=>1925
[2,1,4,3,8,7,6,5,10,9,12,11]=>[5,5,1,1]=>1485
[2,1,4,3,8,7,6,5,12,11,10,9]=>[4,4,2,2]=>2640
[2,1,4,3,10,7,6,9,8,5,12,11]=>[5,5,1,1]=>1485
[2,1,4,3,12,7,6,9,8,11,10,5]=>[5,5,1,1]=>1485
[2,1,4,3,12,7,6,11,10,9,8,5]=>[4,4,1,1,1,1]=>1925
[2,1,4,3,10,9,8,7,6,5,12,11]=>[4,4,1,1,1,1]=>1925
[2,1,4,3,12,9,8,7,6,11,10,5]=>[4,4,1,1,1,1]=>1925
[2,1,4,3,12,11,8,7,10,9,6,5]=>[4,4,1,1,1,1]=>1925
[2,1,4,3,12,11,10,9,8,7,6,5]=>[3,3,1,1,1,1,1,1]=>616
[2,1,6,5,4,3,8,7,10,9,12,11]=>[5,5,1,1]=>1485
[2,1,6,5,4,3,8,7,12,11,10,9]=>[4,4,2,2]=>2640
[2,1,6,5,4,3,10,9,8,7,12,11]=>[4,4,2,2]=>2640
[2,1,6,5,4,3,12,9,8,11,10,7]=>[4,4,2,2]=>2640
[2,1,6,5,4,3,12,11,10,9,8,7]=>[3,3,2,2,1,1]=>2673
[2,1,8,5,4,7,6,3,10,9,12,11]=>[5,5,1,1]=>1485
[2,1,8,5,4,7,6,3,12,11,10,9]=>[4,4,2,2]=>2640
[2,1,10,5,4,7,6,9,8,3,12,11]=>[5,5,1,1]=>1485
[2,1,12,5,4,7,6,9,8,11,10,3]=>[5,5,1,1]=>1485
[2,1,12,5,4,7,6,11,10,9,8,3]=>[4,4,1,1,1,1]=>1925
[2,1,10,5,4,9,8,7,6,3,12,11]=>[4,4,1,1,1,1]=>1925
[2,1,12,5,4,9,8,7,6,11,10,3]=>[4,4,1,1,1,1]=>1925
[2,1,12,5,4,11,8,7,10,9,6,3]=>[4,4,1,1,1,1]=>1925
[2,1,12,5,4,11,10,9,8,7,6,3]=>[3,3,1,1,1,1,1,1]=>616
[2,1,8,7,6,5,4,3,10,9,12,11]=>[4,4,1,1,1,1]=>1925
[2,1,8,7,6,5,4,3,12,11,10,9]=>[3,3,2,2,1,1]=>2673
[2,1,10,7,6,5,4,9,8,3,12,11]=>[4,4,1,1,1,1]=>1925
[2,1,12,7,6,5,4,9,8,11,10,3]=>[4,4,1,1,1,1]=>1925
[2,1,12,7,6,5,4,11,10,9,8,3]=>[3,3,2,2,1,1]=>2673
[2,1,10,9,6,5,8,7,4,3,12,11]=>[4,4,1,1,1,1]=>1925
[2,1,12,9,6,5,8,7,4,11,10,3]=>[4,4,1,1,1,1]=>1925
[2,1,12,11,6,5,8,7,10,9,4,3]=>[4,4,1,1,1,1]=>1925
[2,1,12,11,6,5,10,9,8,7,4,3]=>[3,3,1,1,1,1,1,1]=>616
[2,1,10,9,8,7,6,5,4,3,12,11]=>[3,3,1,1,1,1,1,1]=>616
[2,1,12,9,8,7,6,5,4,11,10,3]=>[3,3,1,1,1,1,1,1]=>616
[2,1,12,11,8,7,6,5,10,9,4,3]=>[3,3,1,1,1,1,1,1]=>616
[2,1,12,11,10,7,6,9,8,5,4,3]=>[3,3,1,1,1,1,1,1]=>616
[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1,1,1,1]=>54
[4,3,2,1,6,5,8,7,10,9,12,11]=>[5,5,1,1]=>1485
[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,4,2,2]=>2640
[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,4,2,2]=>2640
[4,3,2,1,6,5,12,9,8,11,10,7]=>[4,4,2,2]=>2640
[4,3,2,1,6,5,12,11,10,9,8,7]=>[3,3,2,2,1,1]=>2673
[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,4,2,2]=>2640
[4,3,2,1,8,7,6,5,12,11,10,9]=>[3,3,3,3]=>462
[4,3,2,1,10,7,6,9,8,5,12,11]=>[4,4,2,2]=>2640
[4,3,2,1,12,7,6,9,8,11,10,5]=>[4,4,2,2]=>2640
[4,3,2,1,12,7,6,11,10,9,8,5]=>[3,3,2,2,1,1]=>2673
[4,3,2,1,10,9,8,7,6,5,12,11]=>[3,3,2,2,1,1]=>2673
[4,3,2,1,12,9,8,7,6,11,10,5]=>[3,3,2,2,1,1]=>2673
[4,3,2,1,12,11,8,7,10,9,6,5]=>[3,3,2,2,1,1]=>2673
[4,3,2,1,12,11,10,9,8,7,6,5]=>[2,2,2,2,1,1,1,1]=>275
[6,3,2,5,4,1,8,7,10,9,12,11]=>[5,5,1,1]=>1485
[6,3,2,5,4,1,8,7,12,11,10,9]=>[4,4,2,2]=>2640
[6,3,2,5,4,1,10,9,8,7,12,11]=>[4,4,2,2]=>2640
[6,3,2,5,4,1,12,9,8,11,10,7]=>[4,4,2,2]=>2640
[6,3,2,5,4,1,12,11,10,9,8,7]=>[3,3,2,2,1,1]=>2673
[8,3,2,5,4,7,6,1,10,9,12,11]=>[5,5,1,1]=>1485
[8,3,2,5,4,7,6,1,12,11,10,9]=>[4,4,2,2]=>2640
[10,3,2,5,4,7,6,9,8,1,12,11]=>[5,5,1,1]=>1485
[12,3,2,5,4,7,6,9,8,11,10,1]=>[5,5,1,1]=>1485
[12,3,2,5,4,7,6,11,10,9,8,1]=>[4,4,1,1,1,1]=>1925
[10,3,2,5,4,9,8,7,6,1,12,11]=>[4,4,1,1,1,1]=>1925
[12,3,2,5,4,9,8,7,6,11,10,1]=>[4,4,1,1,1,1]=>1925
[12,3,2,5,4,11,8,7,10,9,6,1]=>[4,4,1,1,1,1]=>1925
[12,3,2,5,4,11,10,9,8,7,6,1]=>[3,3,1,1,1,1,1,1]=>616
[8,3,2,7,6,5,4,1,10,9,12,11]=>[4,4,1,1,1,1]=>1925
[8,3,2,7,6,5,4,1,12,11,10,9]=>[3,3,2,2,1,1]=>2673
[10,3,2,7,6,5,4,9,8,1,12,11]=>[4,4,1,1,1,1]=>1925
[12,3,2,7,6,5,4,9,8,11,10,1]=>[4,4,1,1,1,1]=>1925
[12,3,2,7,6,5,4,11,10,9,8,1]=>[3,3,2,2,1,1]=>2673
[10,3,2,9,6,5,8,7,4,1,12,11]=>[4,4,1,1,1,1]=>1925
[12,3,2,9,6,5,8,7,4,11,10,1]=>[4,4,1,1,1,1]=>1925
[12,3,2,11,6,5,8,7,10,9,4,1]=>[4,4,1,1,1,1]=>1925
[12,3,2,11,6,5,10,9,8,7,4,1]=>[3,3,1,1,1,1,1,1]=>616
[10,3,2,9,8,7,6,5,4,1,12,11]=>[3,3,1,1,1,1,1,1]=>616
[12,3,2,9,8,7,6,5,4,11,10,1]=>[3,3,1,1,1,1,1,1]=>616
[12,3,2,11,8,7,6,5,10,9,4,1]=>[3,3,1,1,1,1,1,1]=>616
[12,3,2,11,10,7,6,9,8,5,4,1]=>[3,3,1,1,1,1,1,1]=>616
[12,3,2,11,10,9,8,7,6,5,4,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[6,5,4,3,2,1,8,7,10,9,12,11]=>[4,4,1,1,1,1]=>1925
[6,5,4,3,2,1,8,7,12,11,10,9]=>[3,3,2,2,1,1]=>2673
[6,5,4,3,2,1,10,9,8,7,12,11]=>[3,3,2,2,1,1]=>2673
[6,5,4,3,2,1,12,9,8,11,10,7]=>[3,3,2,2,1,1]=>2673
[6,5,4,3,2,1,12,11,10,9,8,7]=>[2,2,2,2,2,2]=>132
[8,5,4,3,2,7,6,1,10,9,12,11]=>[4,4,1,1,1,1]=>1925
[8,5,4,3,2,7,6,1,12,11,10,9]=>[3,3,2,2,1,1]=>2673
[10,5,4,3,2,7,6,9,8,1,12,11]=>[4,4,1,1,1,1]=>1925
[12,5,4,3,2,7,6,9,8,11,10,1]=>[4,4,1,1,1,1]=>1925
[12,5,4,3,2,7,6,11,10,9,8,1]=>[3,3,2,2,1,1]=>2673
[10,5,4,3,2,9,8,7,6,1,12,11]=>[3,3,2,2,1,1]=>2673
[12,5,4,3,2,9,8,7,6,11,10,1]=>[3,3,2,2,1,1]=>2673
[12,5,4,3,2,11,8,7,10,9,6,1]=>[3,3,2,2,1,1]=>2673
[12,5,4,3,2,11,10,9,8,7,6,1]=>[2,2,2,2,1,1,1,1]=>275
[8,7,4,3,6,5,2,1,10,9,12,11]=>[4,4,1,1,1,1]=>1925
[8,7,4,3,6,5,2,1,12,11,10,9]=>[3,3,2,2,1,1]=>2673
[10,7,4,3,6,5,2,9,8,1,12,11]=>[4,4,1,1,1,1]=>1925
[12,7,4,3,6,5,2,9,8,11,10,1]=>[4,4,1,1,1,1]=>1925
[12,7,4,3,6,5,2,11,10,9,8,1]=>[3,3,2,2,1,1]=>2673
[10,9,4,3,6,5,8,7,2,1,12,11]=>[4,4,1,1,1,1]=>1925
[12,9,4,3,6,5,8,7,2,11,10,1]=>[4,4,1,1,1,1]=>1925
[12,11,4,3,6,5,8,7,10,9,2,1]=>[4,4,1,1,1,1]=>1925
[12,11,4,3,6,5,10,9,8,7,2,1]=>[3,3,1,1,1,1,1,1]=>616
[10,9,4,3,8,7,6,5,2,1,12,11]=>[3,3,1,1,1,1,1,1]=>616
[12,9,4,3,8,7,6,5,2,11,10,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,4,3,8,7,6,5,10,9,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,4,3,10,7,6,9,8,5,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,4,3,10,9,8,7,6,5,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[8,7,6,5,4,3,2,1,10,9,12,11]=>[3,3,1,1,1,1,1,1]=>616
[8,7,6,5,4,3,2,1,12,11,10,9]=>[2,2,2,2,1,1,1,1]=>275
[10,7,6,5,4,3,2,9,8,1,12,11]=>[3,3,1,1,1,1,1,1]=>616
[12,7,6,5,4,3,2,9,8,11,10,1]=>[3,3,1,1,1,1,1,1]=>616
[12,7,6,5,4,3,2,11,10,9,8,1]=>[2,2,2,2,1,1,1,1]=>275
[10,9,6,5,4,3,8,7,2,1,12,11]=>[3,3,1,1,1,1,1,1]=>616
[12,9,6,5,4,3,8,7,2,11,10,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,6,5,4,3,8,7,10,9,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,6,5,4,3,10,9,8,7,2,1]=>[2,2,2,2,1,1,1,1]=>275
[10,9,8,5,4,7,6,3,2,1,12,11]=>[3,3,1,1,1,1,1,1]=>616
[12,9,8,5,4,7,6,3,2,11,10,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,8,5,4,7,6,3,10,9,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,10,5,4,7,6,9,8,3,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,10,5,4,9,8,7,6,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[10,9,8,7,6,5,4,3,2,1,12,11]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,9,8,7,6,5,4,3,2,11,10,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,11,8,7,6,5,4,3,10,9,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,11,10,7,6,5,4,9,8,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,11,10,9,6,5,8,7,4,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[7,4,6,1,8,3,5,2]=>[3,3,1,1]=>56
[8,3,5,1,7,4,6,2]=>[3,3,1,1]=>56
[8,3,4,1,7,5,6,2]=>[4,2,1,1]=>90
[4,8,3,1,7,5,6,2]=>[3,2,2,1]=>70
[4,6,2,1,7,5,8,3]=>[4,2,2]=>56
[1,4,6,2,7,5,8,3]=>[5,2,1]=>64
[1,7,5,2,6,8,4,3]=>[4,2,1,1]=>90
[7,5,2,1,6,8,4,3]=>[3,2,2,1]=>70
[6,8,4,3,1,7,5,2]=>[2,2,2,2]=>14
[3,6,8,4,1,7,5,2]=>[3,2,2,1]=>70
[3,6,7,5,1,8,4,2]=>[4,2,1,1]=>90
[7,5,6,1,8,3,4,2]=>[3,3,1,1]=>56
[3,4,6,5,7,1,8,2]=>[5,2,1]=>64
[4,7,5,6,1,8,3,2]=>[4,2,1,1]=>90
[6,7,5,1,8,4,3,2]=>[3,2,1,1,1]=>64
[6,8,4,1,7,5,3,2]=>[2,2,2,1,1]=>28
[6,7,5,3,1,8,4,2]=>[3,2,2,1]=>70
[8,4,2,1,6,7,5,3]=>[3,2,2,1]=>70
[1,8,4,2,6,7,5,3]=>[4,2,1,1]=>90
[1,5,3,2,7,6,8,4]=>[4,2,2]=>56
[5,3,2,1,7,6,8,4]=>[3,2,2,1]=>70
[2,5,3,1,7,6,8,4]=>[4,2,2]=>56
[2,8,4,1,6,7,5,3]=>[4,2,1,1]=>90
[2,7,5,1,6,8,4,3]=>[4,2,1,1]=>90
[2,4,6,1,7,5,8,3]=>[5,2,1]=>64
[4,7,1,6,5,8,2,3]=>[3,3,1,1]=>56
[4,8,2,6,5,7,1,3]=>[3,2,2,1]=>70
[4,6,1,2,7,5,8,3]=>[4,3,1]=>70
[7,5,1,2,6,8,4,3]=>[4,2,1,1]=>90
[8,4,1,2,6,7,5,3]=>[4,2,1,1]=>90
[5,3,1,2,7,6,8,4]=>[4,2,2]=>56
[1,2,5,3,7,6,8,4]=>[5,2,1]=>64
[4,3,1,2,7,6,8,5]=>[4,2,2]=>56
[3,5,1,2,7,6,8,4]=>[4,3,1]=>70
[6,7,1,5,8,2,3,4]=>[4,3,1]=>70
[2,7,6,1,5,8,3,4]=>[3,3,1,1]=>56
[2,3,5,1,7,6,8,4]=>[5,2,1]=>64
[7,6,1,5,8,3,2,4]=>[3,2,1,1,1]=>64
[3,6,7,1,5,8,2,4]=>[4,3,1]=>70
[7,1,6,5,8,2,4,3]=>[3,2,1,1,1]=>64
[7,5,1,6,8,4,2,3]=>[3,3,1,1]=>56
[8,4,1,6,7,5,2,3]=>[3,3,1,1]=>56
[5,2,3,1,7,6,8,4]=>[4,2,2]=>56
[3,5,2,1,7,6,8,4]=>[4,2,2]=>56
[1,3,5,2,7,6,8,4]=>[5,2,1]=>64
[1,7,6,2,5,8,3,4]=>[4,2,1,1]=>90
[7,6,2,1,5,8,3,4]=>[3,3,1,1]=>56
[8,3,1,5,7,6,2,4]=>[3,3,1,1]=>56
[6,2,4,1,7,5,8,3]=>[4,2,2]=>56
[6,2,5,1,7,4,8,3]=>[4,2,1,1]=>90
[7,1,6,4,8,2,5,3]=>[3,2,2,1]=>70
[8,2,6,4,7,1,5,3]=>[3,2,2,1]=>70
[6,1,5,2,7,4,8,3]=>[4,2,1,1]=>90
[7,6,2,5,8,3,1,4]=>[3,2,1,1,1]=>64
[8,3,5,7,6,2,1,4]=>[3,2,1,1,1]=>64
[1,8,3,5,7,6,2,4]=>[4,2,1,1]=>90
[1,5,2,3,7,6,8,4]=>[5,2,1]=>64
[5,2,1,3,7,6,8,4]=>[4,2,2]=>56
[7,5,2,6,8,4,1,3]=>[3,2,2,1]=>70
[8,4,2,6,7,5,1,3]=>[3,2,2,1]=>70
[6,1,4,2,7,5,8,3]=>[4,2,2]=>56
[8,2,6,5,7,1,4,3]=>[3,2,1,1,1]=>64
[3,6,8,2,5,7,1,4]=>[3,3,2]=>42
[8,3,2,5,7,6,1,4]=>[3,2,2,1]=>70
[5,1,3,2,7,6,8,4]=>[4,2,2]=>56
[4,1,3,2,7,6,8,5]=>[4,2,2]=>56
[4,2,1,3,7,6,8,5]=>[4,2,2]=>56
[1,4,2,3,7,6,8,5]=>[5,2,1]=>64
[2,4,1,3,7,6,8,5]=>[4,3,1]=>70
[2,5,1,3,7,6,8,4]=>[4,3,1]=>70
[2,8,3,5,7,6,1,4]=>[4,2,1,1]=>90
[6,8,2,3,5,7,1,4]=>[4,2,2]=>56
[6,7,1,3,5,8,2,4]=>[4,2,2]=>56
[8,3,5,7,6,1,2,4]=>[3,3,1,1]=>56
[5,1,2,3,7,6,8,4]=>[5,2,1]=>64
[3,1,2,4,7,6,8,5]=>[5,2,1]=>64
[8,5,9,3,6,10,1,2,4,7]=>[4,3,2,1]=>768
[8,4,9,2,5,10,1,3,6,7]=>[4,3,2,1]=>768
[8,1,2,4,3,6,5,7]=>[5,2,1]=>64
[8,1,3,5,6,2,7,4]=>[5,2,1]=>64
[8,1,3,4,2,6,7,5]=>[5,2,1]=>64
[8,1,3,2,4,5,7,6]=>[5,2,1]=>64
[2,7,8,3,4,5,6,1]=>[5,2,1]=>64
[2,6,3,8,4,5,7,1]=>[5,2,1]=>64
[6,3,2,1,4,5,8,7]=>[4,2,1,1]=>90
[7,3,1,4,2,6,8,5]=>[4,3,1]=>70
[7,4,1,5,6,8,2,3]=>[4,3,1]=>70
[4,7,8,5,6,1,2,3]=>[3,3,2]=>42
[3,7,8,5,6,2,1,4]=>[3,2,2,1]=>70
[3,7,8,4,2,6,1,5]=>[3,2,2,1]=>70
[3,7,8,2,4,5,1,6]=>[4,3,1]=>70
[3,6,2,8,4,5,1,7]=>[4,3,1]=>70
[2,3,6,7,4,5,8,1]=>[5,2,1]=>64
[3,5,2,4,8,6,1,7]=>[4,3,1]=>70
[3,5,4,2,8,7,1,6]=>[3,2,2,1]=>70
[4,6,5,8,7,1,2,3]=>[3,3,2]=>42
[6,4,5,1,7,8,2,3]=>[4,3,1]=>70
[7,4,1,2,3,8,5,6]=>[5,2,1]=>64
[6,2,4,1,3,7,5,8]=>[4,3,1]=>70
[2,6,4,8,3,7,5,1]=>[3,2,2,1]=>70
[2,6,5,8,7,3,4,1]=>[3,2,2,1]=>70
[6,2,5,1,7,3,4,8]=>[4,3,1]=>70
[6,5,2,1,8,3,4,7]=>[4,2,1,1]=>90
[2,5,6,7,8,3,4,1]=>[5,2,1]=>64
[2,4,6,7,3,8,5,1]=>[5,2,1]=>64
[4,2,6,7,3,1,5,8]=>[4,3,1]=>70
[4,7,8,2,3,1,5,6]=>[4,3,1]=>70
[4,7,8,3,2,1,6,5]=>[3,2,2,1]=>70
[5,6,4,8,1,7,2,3]=>[3,3,2]=>42
[5,6,3,8,1,2,7,4]=>[3,3,2]=>42
[4,2,5,3,7,1,6,8]=>[4,3,1]=>70
[4,3,6,7,2,1,8,5]=>[4,2,1,1]=>90
[3,4,6,7,2,8,1,5]=>[5,2,1]=>64
[3,4,5,2,7,8,1,6]=>[5,2,1]=>64
[3,4,2,5,6,8,1,7]=>[5,2,1]=>64
[5,2,7,8,6,4,1,3]=>[3,2,2,1]=>70
[5,1,2,7,8,6,4,3]=>[4,2,1,1]=>90
[4,7,1,8,6,5,2,3]=>[3,3,1,1]=>56
[4,7,1,2,8,6,5,3]=>[3,3,1,1]=>56
[4,6,8,1,2,7,5,3]=>[3,3,1,1]=>56
[6,8,7,1,5,3,2,4]=>[3,2,1,1,1]=>64
[6,8,7,3,5,1,2,4]=>[3,2,2,1]=>70
[7,8,1,6,3,5,2,4]=>[3,2,2,1]=>70
[7,8,1,3,6,5,2,4]=>[3,2,2,1]=>70
[7,8,3,6,5,2,1,4]=>[2,2,2,1,1]=>28
[4,7,2,8,6,1,5,3]=>[3,2,2,1]=>70
[1,7,3,4,8,6,5,2]=>[4,2,1,1]=>90
[4,2,7,1,8,6,5,3]=>[3,2,2,1]=>70
[7,8,2,3,6,5,1,4]=>[3,2,2,1]=>70
[8,5,7,1,6,2,3,4]=>[4,2,1,1]=>90
[8,5,7,1,2,6,3,4]=>[4,2,1,1]=>90
[6,8,2,7,1,3,5,4]=>[3,2,2,1]=>70
[6,8,7,2,5,3,1,4]=>[3,2,1,1,1]=>64
[6,2,4,8,7,1,5,3]=>[3,2,2,1]=>70
[1,6,8,3,7,4,5,2]=>[4,2,1,1]=>90
[1,6,8,3,4,7,5,2]=>[4,2,1,1]=>90
[6,2,4,8,1,7,5,3]=>[3,2,2,1]=>70
[6,8,7,2,3,5,1,4]=>[3,2,2,1]=>70
[6,8,2,1,7,3,5,4]=>[3,2,2,1]=>70
[8,5,7,2,1,6,3,4]=>[3,2,2,1]=>70
[8,5,7,1,2,3,6,4]=>[4,2,1,1]=>90
[8,7,6,2,1,4,3,5]=>[3,2,1,1,1]=>64
[8,5,7,2,3,1,6,4]=>[3,2,2,1]=>70
[5,8,4,2,7,1,6,3]=>[2,2,2,2]=>14
[1,8,7,5,3,4,6,2]=>[4,1,1,1,1]=>35
[1,8,7,3,5,4,6,2]=>[4,1,1,1,1]=>35
[8,2,5,4,7,1,6,3]=>[3,2,2,1]=>70
[8,5,2,7,3,1,6,4]=>[3,2,2,1]=>70
[8,7,6,2,4,3,1,5]=>[3,1,1,1,1,1]=>21
[8,7,6,1,2,4,3,5]=>[4,1,1,1,1]=>35
[8,7,6,1,4,2,3,5]=>[4,1,1,1,1]=>35
[8,7,6,4,1,3,2,5]=>[3,1,1,1,1,1]=>21
[5,8,4,7,2,1,6,3]=>[2,2,2,2]=>14
[1,8,7,5,4,3,6,2]=>[3,1,1,1,1,1]=>21
[1,6,8,4,3,7,5,2]=>[3,2,2,1]=>70
[6,8,7,3,2,5,1,4]=>[2,2,2,1,1]=>28
[6,8,1,7,3,2,5,4]=>[3,2,2,1]=>70
[8,5,7,3,1,6,2,4]=>[3,2,2,1]=>70
[8,5,7,1,3,2,6,4]=>[3,2,2,1]=>70
[8,5,7,3,1,2,6,4]=>[3,2,2,1]=>70
[5,8,4,7,1,2,6,3]=>[3,2,2,1]=>70
[5,8,4,1,7,2,6,3]=>[3,2,2,1]=>70
[5,8,4,7,1,6,2,3]=>[3,2,2,1]=>70
[8,1,2,6,5,7,4,3]=>[4,1,1,1,1]=>35
[8,2,5,6,7,4,1,3]=>[4,2,1,1]=>90
[4,8,5,7,1,6,2,3]=>[3,3,1,1]=>56
[4,8,5,7,1,2,6,3]=>[3,3,1,1]=>56
[4,8,5,1,7,2,6,3]=>[3,3,1,1]=>56
[8,5,3,1,7,2,6,4]=>[3,2,2,1]=>70
[8,5,3,7,1,2,6,4]=>[3,2,2,1]=>70
[6,8,1,3,7,2,5,4]=>[3,2,2,1]=>70
[4,6,2,8,1,7,5,3]=>[3,2,2,1]=>70
[1,6,4,8,3,7,5,2]=>[3,2,2,1]=>70
[1,8,7,4,5,3,6,2]=>[4,1,1,1,1]=>35
[4,8,5,7,2,1,6,3]=>[3,2,2,1]=>70
[8,5,3,7,2,1,6,4]=>[2,2,2,1,1]=>28
[8,7,6,3,1,4,2,5]=>[3,2,1,1,1]=>64
[8,7,6,1,3,2,4,5]=>[4,1,1,1,1]=>35
[8,5,3,2,7,1,6,4]=>[2,2,2,1,1]=>28
[4,8,5,2,7,1,6,3]=>[3,2,2,1]=>70
[1,8,7,4,3,5,6,2]=>[4,1,1,1,1]=>35
[1,8,7,3,4,5,6,2]=>[5,1,1,1]=>35
[8,2,4,5,7,1,6,3]=>[4,2,1,1]=>90
[8,5,2,3,7,1,6,4]=>[3,2,2,1]=>70
[6,3,1,5,4,2,8,7]=>[3,3,1,1]=>56
[8,3,1,5,2,7,6,4]=>[3,3,1,1]=>56
[8,5,4,2,1,7,3,6]=>[3,2,1,1,1]=>64
[8,5,4,2,1,7,6,3]=>[2,2,2,1,1]=>28
[6,5,4,2,1,3,8,7]=>[3,2,1,1,1]=>64
[6,5,4,2,3,1,8,7]=>[3,2,1,1,1]=>64
[6,3,2,5,1,4,8,7]=>[3,3,1,1]=>56
[6,5,4,3,1,2,8,7]=>[3,2,1,1,1]=>64
[6,5,4,1,3,2,8,7]=>[3,2,1,1,1]=>64
[8,5,4,1,2,7,6,3]=>[3,2,2,1]=>70
[8,7,4,1,6,3,2,5]=>[3,2,1,1,1]=>64
[8,7,4,1,6,3,5,2]=>[3,2,1,1,1]=>64
[8,7,4,1,6,5,3,2]=>[2,2,1,1,1,1]=>20
[8,5,4,1,3,7,6,2]=>[3,2,1,1,1]=>64
[8,5,4,3,1,7,6,2]=>[2,2,2,1,1]=>28
[8,3,2,5,1,7,6,4]=>[3,2,2,1]=>70
[2,1,8,5,3,7,6,4]=>[3,3,1,1]=>56
[8,3,2,5,1,7,4,6]=>[3,3,1,1]=>56
[8,5,4,3,1,7,2,6]=>[3,2,1,1,1]=>64
[8,5,4,1,3,7,2,6]=>[3,2,1,1,1]=>64
[8,7,4,1,6,5,2,3]=>[3,2,1,1,1]=>64
[8,7,4,1,6,2,5,3]=>[3,2,1,1,1]=>64
[8,7,6,5,2,1,4,3]=>[2,2,1,1,1,1]=>20
[8,7,4,3,6,2,1,5]=>[2,2,1,1,1,1]=>20
[8,3,2,7,6,4,1,5]=>[3,2,1,1,1]=>64
[2,1,8,7,6,4,3,5]=>[3,2,1,1,1]=>64
[2,1,8,7,6,4,5,3]=>[3,2,1,1,1]=>64
[8,3,2,7,6,4,5,1]=>[3,2,1,1,1]=>64
[8,7,4,3,6,2,5,1]=>[2,2,1,1,1,1]=>20
[8,7,6,5,2,4,3,1]=>[2,1,1,1,1,1,1]=>7
[8,5,4,2,3,7,6,1]=>[3,2,1,1,1]=>64
[8,7,4,2,6,5,3,1]=>[2,2,1,1,1,1]=>20
[8,7,4,2,6,3,5,1]=>[3,2,1,1,1]=>64
[8,7,4,2,6,3,1,5]=>[3,2,1,1,1]=>64
[8,3,1,7,6,4,2,5]=>[3,2,1,1,1]=>64
[8,3,1,7,6,4,5,2]=>[3,2,1,1,1]=>64
[8,3,1,7,6,5,4,2]=>[2,2,1,1,1,1]=>20
[8,3,1,5,4,7,6,2]=>[3,3,1,1]=>56
[8,3,1,5,4,7,2,6]=>[3,3,1,1]=>56
[8,3,1,7,6,5,2,4]=>[3,2,1,1,1]=>64
[8,3,1,7,6,2,5,4]=>[3,2,1,1,1]=>64
[8,7,4,2,6,1,5,3]=>[2,2,2,1,1]=>28
[8,7,4,2,6,5,1,3]=>[2,2,2,1,1]=>28
[8,5,4,2,3,7,1,6]=>[3,2,1,1,1]=>64
[8,3,2,5,4,7,1,6]=>[3,3,1,1]=>56
[2,1,8,5,4,7,3,6]=>[3,3,1,1]=>56
[8,3,2,7,6,5,1,4]=>[2,2,2,1,1]=>28
[8,7,4,3,6,5,1,2]=>[2,2,2,1,1]=>28
[8,7,6,5,3,1,4,2]=>[2,2,1,1,1,1]=>20
[8,7,6,5,1,3,2,4]=>[3,1,1,1,1,1]=>21
[8,7,6,5,1,3,4,2]=>[3,1,1,1,1,1]=>21
[8,7,6,5,1,4,3,2]=>[2,1,1,1,1,1,1]=>7
[8,7,6,5,4,1,3,2]=>[2,1,1,1,1,1,1]=>7
[8,7,4,3,6,1,5,2]=>[2,2,2,1,1]=>28
[8,3,2,7,6,1,5,4]=>[2,2,2,1,1]=>28
[2,1,8,7,6,3,5,4]=>[3,2,1,1,1]=>64
[8,3,2,7,6,1,4,5]=>[3,2,2,1]=>70
[8,7,6,5,1,4,2,3]=>[3,1,1,1,1,1]=>21
[8,7,6,5,1,2,4,3]=>[3,1,1,1,1,1]=>21
[7,3,5,1,8,4,6,2]=>[3,3,1,1]=>56
[7,3,4,1,8,5,6,2]=>[4,2,2]=>56
[4,5,6,2,1,8,7,3]=>[4,2,2]=>56
[1,6,5,2,7,4,3,8]=>[4,2,1,1]=>90
[7,4,3,1,8,6,5,2]=>[2,2,2,2]=>14
[7,6,5,1,8,4,3,2]=>[2,2,1,1,1,1]=>20
[7,6,4,1,8,5,3,2]=>[2,2,2,1,1]=>28
[6,4,2,1,8,7,5,3]=>[2,2,2,2]=>14
[1,6,4,2,7,5,3,8]=>[4,2,2]=>56
[1,5,3,2,7,6,4,8]=>[4,2,2]=>56
[5,3,2,1,8,7,6,4]=>[2,2,2,2]=>14
[2,5,3,1,7,8,6,4]=>[4,2,2]=>56
[2,6,4,1,7,8,5,3]=>[4,2,2]=>56
[2,6,5,1,7,8,4,3]=>[4,2,1,1]=>90
[4,5,7,1,6,8,2,3]=>[4,3,1]=>70
[6,5,1,2,8,4,3,7]=>[4,2,1,1]=>90
[6,4,1,2,8,5,3,7]=>[4,2,2]=>56
[5,3,1,2,8,6,4,7]=>[4,2,2]=>56
[4,3,1,2,8,6,5,7]=>[4,2,2]=>56
[6,1,2,5,8,3,4,7]=>[5,2,1]=>64
[7,1,3,4,8,2,5,6]=>[5,2,1]=>64
[7,1,5,6,8,2,3,4]=>[4,3,1]=>70
[2,6,1,5,7,8,3,4]=>[4,3,1]=>70
[7,4,1,6,8,5,2,3]=>[3,3,1,1]=>56
[5,2,3,1,8,6,7,4]=>[4,2,2]=>56
[3,5,2,1,6,8,7,4]=>[4,2,2]=>56
[1,6,2,5,7,3,4,8]=>[5,2,1]=>64
[6,2,1,5,8,7,3,4]=>[3,3,2]=>42
[7,3,1,5,8,6,2,4]=>[3,3,2]=>42
[6,2,4,1,8,5,7,3]=>[4,2,2]=>56
[6,2,5,1,8,4,7,3]=>[3,3,1,1]=>56
[7,3,1,4,8,6,2,5]=>[3,3,2]=>42
[6,2,1,4,8,7,3,5]=>[3,3,2]=>42
[1,6,2,4,7,3,5,8]=>[5,2,1]=>64
[5,2,1,3,8,7,4,6]=>[4,2,2]=>56
[7,4,1,3,8,5,2,6]=>[4,2,1,1]=>90
[7,5,1,3,8,4,2,6]=>[4,2,1,1]=>90
[3,6,7,1,4,8,2,5]=>[4,3,1]=>70
[7,6,1,4,8,3,2,5]=>[3,2,1,1,1]=>64
[4,2,1,3,8,7,5,6]=>[4,2,2]=>56
[2,6,1,4,7,8,3,5]=>[4,3,1]=>70
[7,1,4,6,8,2,3,5]=>[4,3,1]=>70
[7,1,3,5,8,2,4,6]=>[4,3,1]=>70
[6,1,2,4,8,3,5,7]=>[5,2,1]=>64
[5,2,3,1,6,4,8,7]=>[4,3,1]=>70
[7,4,5,2,3,1,8,6]=>[3,3,1,1]=>56
[8,6,7,3,5,2,4,1]=>[2,2,2,1,1]=>28
[7,3,5,2,4,1,8,6]=>[3,3,1,1]=>56
[6,3,5,2,4,1,8,7]=>[3,3,1,1]=>56
[5,2,4,1,6,3,8,7]=>[4,3,1]=>70
[4,1,6,3,5,2,8,7]=>[4,3,1]=>70
[6,3,4,1,5,2,8,7]=>[4,3,1]=>70
[5,2,6,3,4,1,8,7]=>[4,3,1]=>70
[5,2,7,3,4,1,8,6]=>[4,3,1]=>70
[5,2,8,6,7,3,4,1]=>[3,3,1,1]=>56
[6,2,8,5,7,3,4,1]=>[3,2,2,1]=>70
[6,2,7,3,4,1,8,5]=>[4,3,1]=>70
[7,3,4,1,5,2,8,6]=>[4,3,1]=>70
[4,1,7,3,5,2,8,6]=>[4,3,1]=>70
[3,1,7,4,5,2,8,6]=>[4,3,1]=>70
[2,1,7,4,5,3,8,6]=>[4,3,1]=>70
[3,1,8,6,7,4,5,2]=>[3,3,1,1]=>56
[4,1,8,6,7,3,5,2]=>[3,3,1,1]=>56
[8,6,7,3,4,1,5,2]=>[3,2,2,1]=>70
[8,5,7,3,4,1,6,2]=>[3,2,2,1]=>70
[8,5,6,2,7,3,4,1]=>[3,3,1,1]=>56
[8,4,7,3,5,1,6,2]=>[3,2,2,1]=>70
[5,1,8,4,7,3,6,2]=>[3,2,2,1]=>70
[4,1,8,5,7,3,6,2]=>[3,3,1,1]=>56
[3,1,8,5,7,4,6,2]=>[3,3,1,1]=>56
[2,1,8,5,7,4,6,3]=>[3,3,1,1]=>56
[2,1,7,4,6,3,8,5]=>[4,3,1]=>70
[3,1,7,4,6,2,8,5]=>[4,3,1]=>70
[4,1,7,3,6,2,8,5]=>[4,2,2]=>56
[5,1,7,3,6,2,8,4]=>[4,2,2]=>56
[6,2,7,3,5,1,8,4]=>[4,2,2]=>56
[6,2,8,4,7,3,5,1]=>[3,2,2,1]=>70
[8,4,7,3,6,2,5,1]=>[2,2,2,1,1]=>28
[7,3,6,2,5,1,8,4]=>[3,2,2,1]=>70
[6,2,5,1,7,3,8,4]=>[4,3,1]=>70
[5,2,4,1,7,3,8,6]=>[4,3,1]=>70
[6,2,4,1,7,3,8,5]=>[4,3,1]=>70
[8,5,7,3,6,2,4,1]=>[2,2,2,1,1]=>28
[8,5,7,4,6,2,3,1]=>[2,2,2,1,1]=>28
[7,4,6,2,3,1,8,5]=>[3,3,1,1]=>56
[6,2,3,1,7,4,8,5]=>[4,3,1]=>70
[5,2,3,1,7,4,8,6]=>[4,3,1]=>70
[4,2,3,1,7,5,8,6]=>[4,3,1]=>70
[3,1,4,2,8,6,7,5]=>[4,3,1]=>70
[6,2,3,1,8,5,7,4]=>[4,2,2]=>56
[8,5,6,2,3,1,7,4]=>[3,3,1,1]=>56
[7,4,8,5,6,2,3,1]=>[3,2,2,1]=>70
[7,3,8,5,6,2,4,1]=>[3,2,2,1]=>70
[8,5,6,2,4,1,7,3]=>[3,2,2,1]=>70
[5,2,4,1,8,6,7,3]=>[4,2,2]=>56
[4,1,5,2,8,6,7,3]=>[4,3,1]=>70
[3,1,5,2,8,6,7,4]=>[4,3,1]=>70
[2,1,6,3,8,5,7,4]=>[4,3,1]=>70
[3,1,6,2,8,5,7,4]=>[4,3,1]=>70
[4,1,6,2,8,5,7,3]=>[4,3,1]=>70
[5,1,6,2,8,4,7,3]=>[4,3,1]=>70
[8,4,6,2,5,1,7,3]=>[3,2,2,1]=>70
[7,3,8,4,6,2,5,1]=>[3,2,2,1]=>70
[6,2,7,3,8,4,5,1]=>[4,3,1]=>70
[8,4,5,1,6,2,7,3]=>[4,3,1]=>70
[5,1,8,4,6,2,7,3]=>[4,2,2]=>56
[4,1,8,5,6,2,7,3]=>[4,3,1]=>70
[3,1,8,5,6,2,7,4]=>[4,3,1]=>70
[2,1,8,5,6,3,7,4]=>[4,3,1]=>70
[2,1,7,4,8,5,6,3]=>[4,3,1]=>70
[3,1,7,4,8,5,6,2]=>[4,3,1]=>70
[4,1,7,3,8,5,6,2]=>[4,3,1]=>70
[7,3,8,4,5,1,6,2]=>[4,2,2]=>56
[8,4,5,1,7,3,6,2]=>[3,3,1,1]=>56
[7,3,6,2,8,4,5,1]=>[3,3,1,1]=>56
[7,8,5,6,1,3,4,2]=>[3,2,2,1]=>70
[1,3,8,4,7,2,5,6]=>[5,2,1]=>64
[3,6,1,4,7,2,5,8]=>[4,3,1]=>70
[4,6,1,2,5,7,3,8]=>[5,2,1]=>64
[1,4,8,2,5,7,3,6]=>[4,3,1]=>70
[7,8,2,4,5,6,1,3]=>[4,2,2]=>56
[7,8,1,5,4,6,3,2]=>[3,2,1,1,1]=>64
[7,8,2,1,6,3,4,5]=>[4,2,2]=>56
[7,8,4,5,3,1,6,2]=>[3,2,2,1]=>70
[5,6,1,4,3,2,7,8]=>[4,2,1,1]=>90
[1,4,6,8,3,7,5,2]=>[4,2,1,1]=>90
[2,4,8,5,3,1,6,7]=>[5,1,1,1]=>35
[3,5,8,4,7,6,1,2]=>[3,2,2,1]=>70
[1,6,2,4,7,3,8,5]=>[5,2,1]=>64
[5,7,3,6,1,4,8,2]=>[3,2,2,1]=>70
[5,3,6,7,2,1,8,4]=>[4,2,1,1]=>90
[6,1,7,5,2,4,8,3]=>[4,2,1,1]=>90
[6,3,1,2,4,5,8,7]=>[5,2,1]=>64
[1,4,7,2,5,3,8,6]=>[4,3,1]=>70
[1,6,7,5,8,2,4,3]=>[4,2,1,1]=>90
[3,5,6,7,8,1,4,2]=>[5,2,1]=>64
[3,6,5,7,8,2,1,4]=>[4,2,1,1]=>90
[5,2,7,6,1,4,3,8]=>[3,2,2,1]=>70
[2,1,6,8,4,5,3,7]=>[4,3,1]=>70
[2,7,1,8,5,3,4,6]=>[4,3,1]=>70
[5,7,8,6,3,2,1,4]=>[3,2,1,1,1]=>64
[5,7,8,6,1,3,4,2]=>[3,3,1,1]=>56
[7,6,5,8,1,3,4,2]=>[3,2,1,1,1]=>64
[2,6,3,4,5,8,1,7]=>[5,2,1]=>64
[7,2,1,4,8,3,5,6]=>[4,3,1]=>70
[5,6,2,7,3,1,4,8]=>[4,3,1]=>70
[5,7,6,4,1,8,3,2]=>[3,2,1,1,1]=>64
[6,7,1,5,2,8,3,4]=>[4,3,1]=>70
[6,1,5,2,8,3,4,7]=>[5,2,1]=>64
[6,7,5,3,8,4,1,2]=>[3,2,2,1]=>70
[7,1,5,3,4,2,8,6]=>[4,2,1,1]=>90
[7,5,2,4,3,1,6,8]=>[4,1,1,1,1]=>35
[6,8,1,3,7,5,4,2]=>[3,2,1,1,1]=>64
[7,4,2,6,5,1,3,8]=>[3,2,2,1]=>70
[6,8,1,2,3,4,7,5]=>[5,2,1]=>64
[5,8,2,3,7,6,4,1]=>[3,2,1,1,1]=>64
[2,5,3,6,8,4,7,1]=>[4,3,1]=>70
[2,1,4,7,8,5,6,3]=>[4,3,1]=>70
[2,5,7,8,1,4,6,3]=>[4,3,1]=>70
[3,5,7,4,1,6,2,8]=>[4,2,2]=>56
[5,2,8,4,6,1,7,3]=>[4,2,2]=>56
[5,2,1,8,6,3,7,4]=>[3,3,2]=>42
[4,2,8,5,7,6,3,1]=>[3,2,1,1,1]=>64
[1,4,2,7,5,8,6,3]=>[4,3,1]=>70
[4,1,8,6,7,5,3,2]=>[3,2,1,1,1]=>64
[5,3,8,7,6,2,4,1]=>[2,2,2,1,1]=>28
[5,8,4,7,6,2,1,3]=>[2,2,2,1,1]=>28
[5,8,7,4,3,6,1,2]=>[2,2,2,1,1]=>28
[6,4,8,3,1,7,2,5]=>[3,2,2,1]=>70
[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]=>28
[5,8,7,4,1,6,2,3]=>[3,2,2,1]=>70
[6,8,5,3,1,2,7,4]=>[3,2,2,1]=>70
[4,5,1,2,7,6,3,8]=>[4,3,1]=>70
[4,5,1,2,6,8,7,3]=>[4,3,1]=>70
[3,5,6,1,8,4,7,2]=>[4,3,1]=>70
[4,2,6,1,7,3,5,8]=>[4,3,1]=>70
[4,5,3,1,7,6,2,8]=>[4,2,2]=>56
[3,5,2,7,8,1,6,4]=>[4,2,2]=>56
[3,1,4,7,5,6,2,8]=>[5,2,1]=>64
[4,2,5,6,1,8,7,3]=>[4,2,2]=>56
[4,5,3,1,6,8,7,2]=>[4,2,2]=>56
[2,1,7,5,8,6,4,3]=>[3,3,1,1]=>56
[1,2,7,5,3,8,6,4]=>[4,2,2]=>56
[4,1,2,7,3,8,6,5]=>[4,3,1]=>70
[6,4,1,7,5,2,3,8]=>[4,2,2]=>56
[6,1,3,7,5,2,4,8]=>[4,2,2]=>56
[3,1,2,6,8,5,4,7]=>[4,3,1]=>70
[3,7,1,2,5,4,8,6]=>[4,3,1]=>70
[1,3,7,2,4,8,6,5]=>[4,3,1]=>70
[2,4,1,7,8,6,5,3]=>[4,2,1,1]=>90
[3,4,7,5,1,8,6,2]=>[4,2,2]=>56
[2,7,4,1,5,8,6,3]=>[4,2,2]=>56
[2,3,7,1,5,8,6,4]=>[4,3,1]=>70
[5,2,8,1,3,7,4,6]=>[4,2,2]=>56
[2,1,6,8,3,4,7,5]=>[4,3,1]=>70
[2,6,8,3,1,5,7,4]=>[4,2,2]=>56
[2,8,6,4,1,5,7,3]=>[4,2,1,1]=>90
[3,6,4,8,5,1,7,2]=>[4,2,2]=>56
[6,3,7,4,5,1,8,2]=>[4,2,2]=>56
[2,6,3,7,5,8,1,4]=>[4,2,2]=>56
[5,2,1,7,8,3,4,6]=>[4,3,1]=>70
[4,7,2,3,6,8,1,5]=>[4,2,2]=>56
[5,2,7,3,6,8,1,4]=>[4,2,2]=>56
[5,7,4,6,2,8,1,3]=>[3,2,2,1]=>70
[5,7,3,4,6,1,8,2]=>[4,2,2]=>56
[5,3,8,4,6,1,7,2]=>[4,2,2]=>56
[8,5,2,4,1,6,7,3]=>[4,2,1,1]=>90
[8,2,3,5,1,6,7,4]=>[5,2,1]=>64
[4,2,8,3,6,7,1,5]=>[4,2,2]=>56
[2,4,8,1,7,3,5,6]=>[4,3,1]=>70
[8,4,1,3,6,2,5,7]=>[4,2,1,1]=>90
[4,8,3,1,7,2,5,6]=>[4,2,2]=>56
[5,2,8,4,7,1,6,3]=>[3,2,2,1]=>70
[5,8,4,7,3,1,6,2]=>[2,2,2,2]=>14
[4,6,8,3,1,7,5,2]=>[3,2,2,1]=>70
[6,3,8,2,7,1,5,4]=>[2,2,2,2]=>14
[6,3,1,8,2,4,7,5]=>[4,2,2]=>56
[5,3,8,1,2,6,4,7]=>[4,2,2]=>56
[5,7,4,1,6,2,3,8]=>[4,2,2]=>56
[8,5,4,1,2,6,3,7]=>[4,2,1,1]=>90
[5,1,8,4,2,7,3,6]=>[4,2,2]=>56
[1,6,2,8,5,3,7,4]=>[4,2,2]=>56
[6,8,5,3,1,7,4,2]=>[2,2,2,2]=>14
[8,4,5,1,2,6,3,7]=>[4,3,1]=>70
[5,6,3,7,1,2,4,8]=>[4,3,1]=>70
[1,6,3,7,2,8,4,5]=>[4,3,1]=>70
[6,3,2,7,8,5,1,4]=>[3,2,2,1]=>70
[4,5,7,8,3,1,6,2]=>[4,2,2]=>56
[4,7,2,5,8,1,6,3]=>[3,3,2]=>42
[8,1,3,4,6,2,5,7]=>[5,2,1]=>64
[3,8,2,4,6,7,1,5]=>[4,2,2]=>56
[3,5,6,8,2,7,1,4]=>[4,2,2]=>56
[2,4,5,6,8,1,7,3]=>[5,2,1]=>64
[4,8,3,5,6,1,7,2]=>[4,2,2]=>56
[5,6,2,3,7,8,1,4]=>[4,3,1]=>70
[5,8,7,3,4,1,2,6]=>[3,2,2,1]=>70
[6,8,7,3,4,1,2,5]=>[3,2,2,1]=>70
[6,8,4,7,1,5,3,2]=>[2,2,2,1,1]=>28
[6,8,4,7,2,5,3,1]=>[2,2,2,1,1]=>28
[5,4,8,7,2,6,3,1]=>[2,2,2,1,1]=>28
[5,4,8,7,1,6,3,2]=>[2,2,2,1,1]=>28
[5,3,8,7,6,1,2,4]=>[3,2,2,1]=>70
[4,3,8,7,6,1,2,5]=>[3,2,2,1]=>70
[4,8,3,7,5,1,2,6]=>[3,2,2,1]=>70
[8,3,4,6,5,1,2,7]=>[4,2,1,1]=>90
[3,8,4,7,5,1,2,6]=>[4,2,1,1]=>90
[3,4,8,7,6,1,2,5]=>[3,3,1,1]=>56
[3,5,8,7,6,1,2,4]=>[3,3,1,1]=>56
[4,5,8,7,6,1,2,3]=>[3,3,1,1]=>56
[4,5,8,7,1,6,3,2]=>[3,2,1,1,1]=>64
[4,5,8,7,2,6,3,1]=>[3,2,1,1,1]=>64
[3,5,8,2,7,6,4,1]=>[3,2,1,1,1]=>64
[3,5,8,1,7,6,4,2]=>[3,2,1,1,1]=>64
[2,5,8,1,7,6,4,3]=>[3,2,1,1,1]=>64
[2,5,8,7,1,6,3,4]=>[3,3,1,1]=>56
[2,4,8,7,1,6,3,5]=>[3,3,1,1]=>56
[2,8,4,7,1,5,3,6]=>[4,2,1,1]=>90
[8,2,4,6,1,5,3,7]=>[4,2,1,1]=>90
[8,1,4,6,2,5,3,7]=>[4,2,1,1]=>90
[1,8,4,7,2,5,3,6]=>[4,2,1,1]=>90
[1,4,8,7,2,6,3,5]=>[4,2,1,1]=>90
[1,5,8,7,2,6,3,4]=>[4,2,1,1]=>90
[1,5,8,2,7,6,4,3]=>[3,2,1,1,1]=>64
[2,5,8,3,7,6,4,1]=>[3,2,1,1,1]=>64
[1,4,2,8,7,6,5,3]=>[3,2,1,1,1]=>64
[1,3,8,2,7,6,4,5]=>[4,2,1,1]=>90
[1,8,3,2,7,5,4,6]=>[4,2,1,1]=>90
[8,1,3,2,6,5,4,7]=>[4,2,1,1]=>90
[8,2,3,1,6,5,4,7]=>[4,2,1,1]=>90
[2,8,3,1,7,5,4,6]=>[4,2,1,1]=>90
[2,3,8,1,7,6,4,5]=>[4,2,1,1]=>90
[3,4,1,8,7,6,5,2]=>[3,2,1,1,1]=>64
[4,3,1,8,7,6,5,2]=>[2,2,2,1,1]=>28
[4,2,1,8,7,6,5,3]=>[2,2,2,1,1]=>28
[3,8,2,1,7,5,4,6]=>[3,2,2,1]=>70
[8,3,2,1,6,5,4,7]=>[3,2,2,1]=>70
[8,4,2,6,1,5,3,7]=>[3,2,2,1]=>70
[4,2,8,7,1,6,3,5]=>[3,2,2,1]=>70
[5,2,8,7,1,6,3,4]=>[3,2,2,1]=>70
[5,2,8,1,7,6,4,3]=>[2,2,2,1,1]=>28
[5,3,8,1,7,6,4,2]=>[2,2,2,1,1]=>28
[5,3,8,2,7,6,4,1]=>[2,2,2,1,1]=>28
[6,8,3,2,7,5,4,1]=>[2,2,2,1,1]=>28
[6,8,3,1,7,5,4,2]=>[2,2,2,1,1]=>28
[6,8,2,1,7,5,4,3]=>[2,2,2,1,1]=>28
[6,8,2,7,1,5,3,4]=>[3,2,2,1]=>70
[6,8,7,2,1,4,3,5]=>[3,2,2,1]=>70
[8,5,6,1,2,4,3,7]=>[4,2,1,1]=>90
[5,8,7,1,2,4,3,6]=>[4,2,1,1]=>90
[6,8,1,2,7,5,4,3]=>[3,2,1,1,1]=>64
[6,8,2,3,7,5,4,1]=>[3,2,1,1,1]=>64
[5,2,8,3,7,6,4,1]=>[3,2,1,1,1]=>64
[5,1,8,3,7,6,4,2]=>[3,2,1,1,1]=>64
[5,1,8,7,2,6,3,4]=>[4,2,1,1]=>90
[4,1,8,7,2,6,3,5]=>[4,2,1,1]=>90
[4,8,1,7,2,5,3,6]=>[4,2,1,1]=>90
[8,4,1,6,2,5,3,7]=>[4,2,1,1]=>90
[8,3,1,2,6,5,4,7]=>[4,2,1,1]=>90
[3,8,1,2,7,5,4,6]=>[4,2,1,1]=>90
[3,1,8,2,7,6,4,5]=>[4,2,1,1]=>90
[3,1,2,8,7,6,5,4]=>[3,2,1,1,1]=>64
[4,1,3,8,7,6,5,2]=>[3,2,1,1,1]=>64
[3,1,4,8,7,6,5,2]=>[3,2,1,1,1]=>64
[2,1,8,3,7,6,4,5]=>[4,2,1,1]=>90
[2,8,1,3,7,5,4,6]=>[4,2,1,1]=>90
[8,2,1,3,6,5,4,7]=>[4,2,1,1]=>90
[8,1,2,3,6,5,4,7]=>[5,1,1,1]=>35
[1,8,2,3,7,5,4,6]=>[5,1,1,1]=>35
[1,2,8,3,7,6,4,5]=>[5,1,1,1]=>35
[1,4,3,6,8,2,5,7]=>[4,3,1]=>70
[3,1,6,2,5,8,4,7]=>[4,3,1]=>70
[3,5,1,8,2,4,7,6]=>[4,3,1]=>70
[1,4,5,2,8,3,7,6]=>[4,3,1]=>70
[1,4,2,6,5,8,3,7]=>[4,3,1]=>70
[1,5,4,2,6,8,3,7]=>[4,3,1]=>70
[3,1,6,5,8,2,4,7]=>[4,3,1]=>70
[1,6,4,2,5,8,3,7]=>[4,3,1]=>70
[1,5,2,6,4,8,3,7]=>[4,3,1]=>70
[1,2,6,5,4,8,3,7]=>[4,2,1,1]=>90
[1,2,5,4,7,3,8,6]=>[5,2,1]=>64
[4,1,2,6,3,8,7,5]=>[4,3,1]=>70
[7,1,5,4,2,8,3,6]=>[4,2,1,1]=>90
[1,4,7,5,2,8,3,6]=>[4,3,1]=>70
[7,1,3,5,2,8,4,6]=>[4,3,1]=>70
[7,2,5,1,8,3,4,6]=>[4,3,1]=>70
[1,4,5,2,8,7,3,6]=>[4,3,1]=>70
[1,6,4,2,8,3,7,5]=>[4,2,2]=>56
[1,4,2,8,3,7,6,5]=>[4,2,1,1]=>90
[1,2,5,3,8,7,6,4]=>[4,2,1,1]=>90
[1,2,8,6,5,3,7,4]=>[4,2,1,1]=>90
[1,5,2,8,6,3,7,4]=>[4,3,1]=>70
[1,6,4,2,8,7,3,5]=>[4,2,2]=>56
[6,2,1,8,7,3,4,5]=>[4,2,2]=>56
[7,6,2,1,8,3,4,5]=>[4,2,1,1]=>90
[7,3,1,6,2,8,4,5]=>[4,3,1]=>70
[1,7,6,4,2,8,3,5]=>[4,2,1,1]=>90
[1,7,5,2,6,3,8,4]=>[4,3,1]=>70
[1,6,2,7,5,3,8,4]=>[4,3,1]=>70
[1,2,7,6,5,3,8,4]=>[4,2,1,1]=>90
[1,2,6,5,3,8,7,4]=>[4,2,2]=>56
[1,5,2,6,3,8,7,4]=>[4,3,1]=>70
[1,5,2,7,6,3,8,4]=>[4,3,1]=>70
[1,6,5,2,7,3,8,4]=>[4,3,1]=>70
[1,5,7,4,2,8,3,6]=>[4,3,1]=>70
[4,1,2,8,6,3,7,5]=>[4,3,1]=>70
[3,1,8,6,2,4,7,5]=>[4,3,1]=>70
[4,3,7,1,8,2,5,6]=>[4,3,1]=>70
[8,3,1,6,2,4,7,5]=>[4,3,1]=>70
[7,1,8,3,2,4,6,5]=>[4,2,2]=>56
[1,8,7,3,2,4,6,5]=>[4,2,1,1]=>90
[1,4,2,8,7,3,6,5]=>[4,2,1,1]=>90
[1,7,4,2,8,3,6,5]=>[4,2,2]=>56
[8,1,5,4,2,7,3,6]=>[4,2,1,1]=>90
[1,4,8,5,2,7,3,6]=>[4,3,1]=>70
[8,5,3,1,7,2,4,6]=>[4,2,1,1]=>90
[8,6,2,1,7,3,4,5]=>[4,2,1,1]=>90
[1,8,6,4,2,7,3,5]=>[4,2,1,1]=>90
[1,8,5,2,6,3,7,4]=>[4,3,1]=>70
[1,5,2,7,3,8,6,4]=>[4,3,1]=>70
[1,2,8,5,3,7,6,4]=>[4,2,1,1]=>90
[1,2,6,3,8,7,5,4]=>[4,2,1,1]=>90
[1,2,7,6,3,8,5,4]=>[4,2,1,1]=>90
[1,6,2,7,3,8,5,4]=>[4,3,1]=>70
[1,7,2,8,5,3,6,4]=>[4,2,2]=>56
[1,7,4,2,8,6,3,5]=>[4,2,2]=>56
[7,1,8,3,2,6,4,5]=>[4,2,2]=>56
[7,2,1,8,6,3,4,5]=>[4,2,2]=>56
[1,8,7,3,2,6,4,5]=>[4,2,1,1]=>90
[1,4,2,8,7,6,3,5]=>[4,2,1,1]=>90
[1,2,8,7,5,3,6,4]=>[4,2,1,1]=>90
[1,2,8,6,3,7,5,4]=>[4,2,1,1]=>90
[1,2,7,3,8,6,5,4]=>[4,2,1,1]=>90
[4,1,7,3,6,5,8,2]=>[4,2,1,1]=>90
[5,1,8,7,6,2,4,3]=>[3,2,1,1,1]=>64
[8,1,7,6,3,4,5,2]=>[4,1,1,1,1]=>35
[5,7,8,6,2,4,1,3]=>[3,2,2,1]=>70
[5,7,1,6,2,4,3,8]=>[4,2,1,1]=>90
[6,4,1,5,2,7,3,8]=>[4,3,1]=>70
[8,1,4,5,3,7,6,2]=>[4,2,1,1]=>90
[6,1,4,5,3,8,7,2]=>[4,2,1,1]=>90
[6,1,4,5,3,7,8,2]=>[5,1,1,1]=>35
[5,1,7,8,6,2,4,3]=>[3,3,1,1]=>56
[6,1,4,8,3,5,7,2]=>[4,2,1,1]=>90
[7,1,8,6,3,4,5,2]=>[4,2,1,1]=>90
[7,1,4,5,3,8,6,2]=>[4,2,1,1]=>90
[7,1,4,5,3,6,8,2]=>[5,1,1,1]=>35
[8,1,4,5,3,6,7,2]=>[5,1,1,1]=>35
[7,4,1,5,2,6,3,8]=>[4,3,1]=>70
[6,3,5,7,2,1,4,8]=>[4,2,1,1]=>90
[6,3,5,8,2,1,7,4]=>[3,2,2,1]=>70
[6,3,5,7,2,1,8,4]=>[4,2,1,1]=>90
[8,4,5,7,3,6,1,2]=>[3,2,2,1]=>70
[6,4,5,8,3,7,2,1]=>[3,2,1,1,1]=>64
[5,8,7,6,2,4,1,3]=>[2,2,2,1,1]=>28
[5,4,8,6,3,1,7,2]=>[3,2,2,1]=>70
[5,4,1,8,2,3,7,6]=>[4,2,2]=>56
[5,8,1,6,2,4,3,7]=>[4,2,1,1]=>90
[8,4,1,5,2,6,3,7]=>[4,3,1]=>70
[6,3,5,8,2,1,4,7]=>[3,3,1,1]=>56
[2,3,4,1,8,6,5,7]=>[5,2,1]=>64
[8,3,5,6,2,1,4,7]=>[4,2,1,1]=>90
[2,3,8,5,1,4,7,6]=>[4,3,1]=>70
[2,3,8,6,1,5,7,4]=>[4,2,1,1]=>90
[2,8,6,7,1,3,5,4]=>[3,3,1,1]=>56
[8,3,5,7,2,1,6,4]=>[3,2,2,1]=>70
[2,3,8,5,6,1,7,4]=>[5,2,1]=>64
[7,4,5,6,3,1,8,2]=>[4,2,1,1]=>90
[8,4,5,6,3,1,7,2]=>[4,2,1,1]=>90
[7,3,5,6,2,8,1,4]=>[4,2,1,1]=>90
[7,3,5,8,2,1,6,4]=>[3,2,2,1]=>70
[7,3,5,6,2,1,4,8]=>[4,2,1,1]=>90
[2,7,6,5,1,3,4,8]=>[4,2,1,1]=>90
[2,7,6,8,1,3,5,4]=>[3,3,1,1]=>56
[2,7,6,5,8,3,1,4]=>[3,2,1,1,1]=>64
[8,7,5,6,1,4,2,3]=>[3,2,1,1,1]=>64
[2,6,4,1,8,5,7,3]=>[4,2,2]=>56
[2,6,1,3,8,5,7,4]=>[4,3,1]=>70
[2,7,1,3,6,5,8,4]=>[4,2,1,1]=>90
[2,7,6,8,4,3,1,5]=>[3,2,1,1,1]=>64
[2,7,6,1,8,3,4,5]=>[4,3,1]=>70
[2,7,6,1,4,3,5,8]=>[4,2,1,1]=>90
[7,3,5,1,2,8,4,6]=>[4,3,1]=>70
[8,4,1,5,2,3,7,6]=>[4,3,1]=>70
[7,8,1,6,3,4,2,5]=>[4,2,1,1]=>90
[6,4,1,8,3,2,7,5]=>[3,2,2,1]=>70
[2,3,8,6,4,1,7,5]=>[4,2,1,1]=>90
[2,8,6,7,4,3,1,5]=>[3,2,1,1,1]=>64
[8,3,5,7,2,4,1,6]=>[3,3,1,1]=>56
[2,3,4,1,8,7,5,6]=>[5,2,1]=>64
[2,8,6,1,7,3,4,5]=>[4,3,1]=>70
[2,3,8,1,6,4,7,5]=>[4,3,1]=>70
[2,3,8,1,4,5,7,6]=>[5,2,1]=>64
[2,8,6,1,4,3,5,7]=>[4,2,1,1]=>90
[1,2,3,4,5,6,7,9,8]=>[8,1]=>8
[2,1,3,4,5,6,7,8,9]=>[8,1]=>8
[1,2,3,4,5,6,7,8,10,9]=>[9,1]=>9
[2,1,3,4,5,6,7,8,9,10]=>[9,1]=>9
[1,2,3,4,5,6,7,8,9,11,10]=>[10,1]=>10
[9,1,2,3,4,5,6,7,10,8]=>[8,2]=>35
[1,8,2,3,4,5,6,9,7]=>[7,2]=>27
[7,1,2,3,4,5,6,9,8]=>[7,2]=>27
[2,1,9,3,4,5,6,7,8]=>[7,2]=>27
[2,8,1,3,4,5,6,7,9]=>[7,2]=>27
[2,10,1,3,4,5,6,7,8,9]=>[8,2]=>35
[2,1,3,4,5,6,7,8,9,10,11]=>[10,1]=>10
[8,4,3,6,5,1,7,2]=>[3,2,2,1]=>70
[8,5,6,3,4,1,7,2]=>[3,2,2,1]=>70
[8,6,5,4,3,1,7,2]=>[2,2,1,1,1,1]=>20
[1,7,6,5,4,2,3,8]=>[4,1,1,1,1]=>35
[1,8,6,5,2,7,3,4]=>[4,2,1,1]=>90
[8,7,5,4,1,6,3,2]=>[2,2,1,1,1,1]=>20
[7,8,5,4,1,3,6,2]=>[3,2,1,1,1]=>64
[6,8,5,4,2,1,7,3]=>[2,2,2,1,1]=>28
[5,8,6,2,4,1,7,3]=>[3,2,2,1]=>70
[4,8,2,6,5,1,7,3]=>[3,2,2,1]=>70
[3,2,8,6,5,1,7,4]=>[3,2,2,1]=>70
[3,2,1,7,6,4,5,8]=>[4,2,2]=>56
[4,1,3,7,6,2,5,8]=>[4,2,2]=>56
[5,1,7,3,6,2,4,8]=>[4,2,2]=>56
[6,1,7,5,3,2,4,8]=>[4,2,1,1]=>90
[7,1,6,5,2,4,3,8]=>[4,1,1,1,1]=>35
[8,1,6,5,2,3,7,4]=>[4,2,1,1]=>90
[1,2,7,6,3,4,5,8]=>[6,1,1]=>21
[1,2,8,3,7,4,5,6]=>[6,1,1]=>21
[8,1,7,2,6,3,5,4]=>[4,1,1,1,1]=>35
[7,1,8,2,6,4,3,5]=>[4,2,1,1]=>90
[6,1,8,2,4,7,3,5]=>[4,2,2]=>56
[5,1,8,3,2,7,4,6]=>[4,2,2]=>56
[4,1,3,8,2,7,5,6]=>[4,2,2]=>56
[3,2,1,8,4,7,5,6]=>[4,2,2]=>56
[3,2,8,7,1,6,5,4]=>[2,2,2,1,1]=>28
[4,8,2,7,1,6,5,3]=>[2,2,2,1,1]=>28
[5,8,7,2,1,6,4,3]=>[2,2,2,1,1]=>28
[6,8,7,1,3,5,4,2]=>[3,2,1,1,1]=>64
[7,8,6,1,5,3,4,2]=>[3,2,1,1,1]=>64
[8,7,6,1,5,4,3,2]=>[2,1,1,1,1,1,1]=>7
[1,8,7,2,6,5,3,4]=>[4,1,1,1,1]=>35
[1,7,8,2,5,6,3,4]=>[4,2,2]=>56
[8,6,7,1,4,5,3,2]=>[3,2,1,1,1]=>64
[7,6,8,1,4,3,5,2]=>[3,2,1,1,1]=>64
[6,5,8,3,2,1,7,4]=>[2,2,2,1,1]=>28
[7,5,8,3,1,4,6,2]=>[3,2,2,1]=>70
[8,5,7,3,1,6,4,2]=>[2,2,2,1,1]=>28
[1,6,8,4,2,7,3,5]=>[4,2,2]=>56
[1,5,4,8,2,7,3,6]=>[4,2,2]=>56
[8,4,3,7,1,6,5,2]=>[2,2,2,1,1]=>28
[7,4,3,8,1,5,6,2]=>[3,2,2,1]=>70
[6,4,3,1,5,2,7,8]=>[4,2,1,1]=>90
[7,4,3,1,2,6,5,8]=>[4,2,1,1]=>90
[8,4,3,1,2,5,7,6]=>[4,2,1,1]=>90
[1,5,4,2,3,6,7,8]=>[6,1,1]=>21
[8,5,1,4,2,3,7,6]=>[4,2,1,1]=>90
[7,5,1,4,2,6,3,8]=>[4,2,1,1]=>90
[6,5,1,4,3,2,7,8]=>[4,1,1,1,1]=>35
[5,6,1,3,4,2,7,8]=>[5,2,1]=>64
[4,6,2,1,5,3,7,8]=>[4,2,2]=>56
[3,2,6,1,5,4,7,8]=>[4,2,2]=>56
[3,2,7,1,4,6,5,8]=>[4,2,2]=>56
[4,7,2,1,3,6,5,8]=>[4,2,2]=>56
[5,7,1,3,2,6,4,8]=>[4,2,2]=>56
[6,7,1,2,4,5,3,8]=>[5,2,1]=>64
[7,6,1,2,5,4,3,8]=>[4,1,1,1,1]=>35
[8,6,1,2,5,3,7,4]=>[4,2,1,1]=>90
[1,7,2,3,6,4,5,8]=>[6,1,1]=>21
[8,7,1,2,3,6,5,4]=>[4,1,1,1,1]=>35
[7,8,1,2,3,5,6,4]=>[5,2,1]=>64
[6,8,1,2,4,3,7,5]=>[4,2,2]=>56
[5,8,1,3,2,4,7,6]=>[4,2,2]=>56
[4,8,2,1,3,5,7,6]=>[4,2,2]=>56
[3,2,8,1,4,5,7,6]=>[4,2,2]=>56
[4,1,3,2,5,6,7,8]=>[6,1,1]=>21
[5,1,2,4,3,6,7,8]=>[6,1,1]=>21
[6,1,2,3,5,4,7,8]=>[6,1,1]=>21
[7,1,2,3,4,6,5,8]=>[6,1,1]=>21
[8,1,2,3,4,5,7,6]=>[6,1,1]=>21
[6,7,3,8,5,1,2,4]=>[3,3,2]=>42
[6,7,4,5,1,8,3,2]=>[3,2,2,1]=>70
[5,4,7,6,8,1,2,3]=>[3,3,2]=>42
[5,3,7,8,6,1,2,4]=>[3,3,2]=>42
[3,8,4,5,7,1,2,6]=>[4,3,1]=>70
[3,4,8,6,7,1,2,5]=>[4,3,1]=>70
[4,5,6,7,1,8,3,2]=>[5,2,1]=>64
[3,5,6,2,7,4,8,1]=>[5,2,1]=>64
[3,5,6,1,7,8,4,2]=>[5,2,1]=>64
[2,5,6,1,8,7,4,3]=>[4,2,1,1]=>90
[2,5,6,8,1,7,3,4]=>[4,3,1]=>70
[8,2,4,5,1,6,3,7]=>[5,2,1]=>64
[1,4,8,6,2,3,7,5]=>[4,3,1]=>70
[1,5,6,8,2,3,7,4]=>[4,3,1]=>70
[1,5,6,2,8,4,7,3]=>[4,3,1]=>70
[2,5,6,3,4,7,8,1]=>[5,2,1]=>64
[1,4,2,6,8,5,7,3]=>[4,3,1]=>70
[8,1,3,2,5,4,6,7]=>[5,2,1]=>64
[8,2,3,1,5,6,4,7]=>[5,2,1]=>64
[2,8,3,1,5,7,4,6]=>[4,3,1]=>70
[2,4,1,6,8,7,5,3]=>[4,2,1,1]=>90
[3,4,1,6,7,8,5,2]=>[5,2,1]=>64
[4,3,1,7,6,8,5,2]=>[3,2,2,1]=>70
[5,2,7,8,1,6,3,4]=>[3,3,2]=>42
[5,3,7,2,6,4,8,1]=>[3,2,2,1]=>70
[6,7,3,1,5,8,4,2]=>[3,2,2,1]=>70
[6,7,2,1,8,5,4,3]=>[3,2,2,1]=>70
[6,7,2,8,1,5,3,4]=>[3,3,2]=>42
[6,7,8,2,1,4,3,5]=>[3,3,2]=>42
[6,7,1,2,8,4,5,3]=>[4,3,1]=>70
[6,7,1,3,4,8,5,2]=>[4,3,1]=>70
[5,2,7,3,4,6,8,1]=>[5,2,1]=>64
[5,1,7,3,4,8,6,2]=>[4,3,1]=>70
[5,1,7,8,2,3,6,4]=>[4,3,1]=>70
[4,1,8,7,2,3,6,5]=>[4,2,1,1]=>90
[3,8,1,2,7,4,5,6]=>[5,2,1]=>64
[4,1,3,7,5,8,6,2]=>[4,3,1]=>70
[3,1,4,5,7,8,6,2]=>[5,2,1]=>64
[2,1,8,3,4,7,6,5]=>[4,2,1,1]=>90
[8,2,1,3,4,6,5,7]=>[5,2,1]=>64
[1,8,2,3,4,5,7,6]=>[6,1,1]=>21
[1,2,8,3,4,6,7,5]=>[6,1,1]=>21
[4,2,1,6,5,8,7,3]=>[3,3,2]=>42
[5,2,6,1,4,8,7,3]=>[3,3,2]=>42
[5,2,6,4,1,8,7,3]=>[3,3,2]=>42
[5,2,7,4,8,1,6,3]=>[3,3,2]=>42
[5,2,7,4,8,6,1,3]=>[3,3,2]=>42
[5,7,2,3,8,6,1,4]=>[3,3,2]=>42
[5,7,2,3,8,1,6,4]=>[3,3,2]=>42
[5,6,2,3,1,8,7,4]=>[3,3,2]=>42
[5,6,2,1,3,8,7,4]=>[3,3,2]=>42
[5,1,6,4,2,8,7,3]=>[3,3,2]=>42
[5,6,1,3,2,8,7,4]=>[3,3,2]=>42
[5,6,3,1,2,8,7,4]=>[3,3,2]=>42
[5,6,3,2,1,8,7,4]=>[3,2,2,1]=>70
[5,7,3,2,8,1,6,4]=>[3,2,2,1]=>70
[5,7,3,2,8,6,1,4]=>[3,2,2,1]=>70
[6,7,3,8,2,1,5,4]=>[3,2,2,1]=>70
[6,7,3,8,1,2,5,4]=>[3,3,2]=>42
[5,7,3,1,8,2,6,4]=>[3,3,2]=>42
[5,7,1,3,8,2,6,4]=>[3,3,2]=>42
[5,1,7,4,8,2,6,3]=>[3,3,2]=>42
[1,5,7,4,8,3,6,2]=>[4,2,1,1]=>90
[1,5,7,4,8,6,3,2]=>[4,2,1,1]=>90
[5,1,7,4,8,6,2,3]=>[3,3,2]=>42
[5,7,1,3,8,6,2,4]=>[3,3,2]=>42
[5,7,3,1,8,6,2,4]=>[3,3,2]=>42
[6,7,3,8,1,5,2,4]=>[3,3,2]=>42
[6,7,3,8,5,2,1,4]=>[3,2,2,1]=>70
[6,7,8,3,1,4,2,5]=>[3,3,2]=>42
[6,7,1,8,3,5,2,4]=>[3,3,2]=>42
[6,1,7,8,4,5,2,3]=>[3,3,2]=>42
[1,6,7,8,4,5,3,2]=>[4,2,1,1]=>90
[1,6,7,8,4,3,5,2]=>[4,2,1,1]=>90
[6,1,7,8,4,2,5,3]=>[3,3,2]=>42
[6,7,1,8,3,2,5,4]=>[3,3,2]=>42
[5,7,2,1,8,3,6,4]=>[3,3,2]=>42
[6,7,2,8,1,3,5,4]=>[3,3,2]=>42
[6,7,2,8,3,1,5,4]=>[3,3,2]=>42
[6,7,2,8,3,5,1,4]=>[3,3,2]=>42
[6,2,7,8,4,5,1,3]=>[3,3,2]=>42
[6,2,7,8,4,1,5,3]=>[3,3,2]=>42
[6,2,7,8,1,4,5,3]=>[3,3,2]=>42
[5,2,7,1,8,4,6,3]=>[3,3,2]=>42
[4,2,1,7,8,5,6,3]=>[3,3,2]=>42
[4,1,2,7,8,6,5,3]=>[4,2,1,1]=>90
[6,2,7,8,1,5,4,3]=>[3,2,2,1]=>70
[6,2,7,8,5,1,4,3]=>[3,2,2,1]=>70
[6,2,7,8,5,4,1,3]=>[3,2,2,1]=>70
[6,7,2,8,5,3,1,4]=>[3,3,1,1]=>56
[5,7,2,1,8,6,3,4]=>[3,3,2]=>42
[5,7,1,2,8,6,3,4]=>[4,3,1]=>70
[5,1,7,2,8,6,4,3]=>[3,3,1,1]=>56
[1,5,7,3,8,6,4,2]=>[4,2,1,1]=>90
[1,6,7,8,3,5,4,2]=>[4,2,1,1]=>90
[6,1,7,8,2,5,4,3]=>[3,3,1,1]=>56
[6,7,1,8,2,5,3,4]=>[4,3,1]=>70
[6,7,8,2,4,1,3,5]=>[3,3,2]=>42
[6,7,8,2,4,3,1,5]=>[3,3,1,1]=>56
[6,7,1,8,5,2,3,4]=>[4,3,1]=>70
[6,1,7,8,5,2,4,3]=>[3,3,1,1]=>56
[1,6,7,8,5,3,4,2]=>[4,2,1,1]=>90
[6,1,7,8,5,4,2,3]=>[3,3,1,1]=>56
[6,7,1,8,5,3,2,4]=>[3,3,1,1]=>56
[6,7,8,4,1,3,2,5]=>[3,3,1,1]=>56
[6,3,8,5,2,7,4,1]=>[3,2,2,1]=>70
[6,3,4,5,8,7,2,1]=>[4,2,1,1]=>90
[5,6,1,4,8,7,3,2]=>[3,3,1,1]=>56
[5,1,4,8,6,3,7,2]=>[4,2,1,1]=>90
[3,4,7,1,8,6,5,2]=>[4,2,1,1]=>90
[6,3,8,4,2,7,1,5]=>[3,2,2,1]=>70
[4,3,8,5,6,7,2,1]=>[4,2,1,1]=>90
[4,6,1,2,7,8,5,3]=>[4,3,1]=>70
[3,6,4,2,8,7,5,1]=>[3,2,2,1]=>70
[6,3,7,5,2,8,1,4]=>[3,2,2,1]=>70
[6,5,2,7,4,8,1,3]=>[3,2,2,1]=>70
[5,7,1,4,8,3,2,6]=>[3,3,1,1]=>56
[7,8,3,5,1,4,6,2]=>[3,2,2,1]=>70
[5,8,1,4,6,7,2,3]=>[4,2,2]=>56
[6,5,8,4,3,7,2,1]=>[2,2,1,1,1,1]=>20
[6,3,7,4,2,8,5,1]=>[3,3,1,1]=>56
[8,7,1,6,2,4,5,3]=>[4,1,1,1,1]=>35
[3,8,6,7,1,4,5,2]=>[3,3,1,1]=>56
[5,3,8,7,4,1,2,6]=>[3,2,2,1]=>70
[4,3,8,7,1,5,6,2]=>[3,2,2,1]=>70
[8,3,6,1,2,5,7,4]=>[4,2,1,1]=>90
[5,6,1,8,7,3,2,4]=>[3,3,1,1]=>56
[7,5,3,6,4,2,8,1]=>[3,2,1,1,1]=>64
[6,4,1,5,3,8,2,7]=>[3,3,1,1]=>56
[8,2,6,3,4,7,5,1]=>[4,2,1,1]=>90
[7,2,6,3,5,4,8,1]=>[4,1,1,1,1]=>35
[6,2,7,4,3,5,8,1]=>[4,2,1,1]=>90
[3,7,6,4,5,2,8,1]=>[4,1,1,1,1]=>35
[2,7,6,5,3,4,8,1]=>[4,1,1,1,1]=>35
[8,6,5,4,2,7,3,1]=>[2,2,1,1,1,1]=>20
[1,6,5,3,4,8,2,7]=>[4,2,1,1]=>90
[6,5,8,4,2,7,3,1]=>[2,2,2,1,1]=>28
[5,8,2,6,4,7,3,1]=>[3,2,1,1,1]=>64
[7,8,5,3,2,6,4,1]=>[2,2,2,1,1]=>28
[6,8,3,1,7,2,5,4]=>[3,2,2,1]=>70
[1,8,6,3,7,5,2,4]=>[3,2,2,1]=>70
[8,7,5,2,6,4,3,1]=>[2,2,1,1,1,1]=>20
[8,7,1,6,2,5,4,3]=>[3,1,1,1,1,1]=>21
[2,8,1,7,3,5,6,4]=>[4,2,1,1]=>90
[4,2,8,5,7,3,6,1]=>[3,3,1,1]=>56
[5,1,7,6,8,3,2,4]=>[3,3,1,1]=>56
[6,7,3,1,8,4,2,5]=>[3,3,2]=>42
[1,7,3,8,4,5,2,6]=>[5,2,1]=>64
[1,7,2,8,5,3,4,6]=>[5,2,1]=>64
[7,6,1,8,4,3,2,5]=>[3,2,1,1,1]=>64
[8,6,1,7,4,2,5,3]=>[3,2,2,1]=>70
[8,1,2,7,3,4,6,5]=>[5,1,1,1]=>35
[7,1,2,8,3,5,4,6]=>[5,2,1]=>64
[8,2,6,1,7,3,5,4]=>[3,3,1,1]=>56
[5,4,3,1,6,8,2,7]=>[3,3,1,1]=>56
[4,7,5,6,8,3,2,1]=>[4,1,1,1,1]=>35
[6,5,4,8,2,7,3,1]=>[2,2,2,1,1]=>28
[6,5,1,8,7,4,2,3]=>[3,2,2,1]=>70
[8,6,4,7,5,3,2,1]=>[2,2,1,1,1,1]=>20
[5,1,8,3,7,6,2,4]=>[3,2,2,1]=>70
[5,4,8,1,7,2,6,3]=>[3,2,2,1]=>70
[3,6,8,2,4,7,5,1]=>[3,3,1,1]=>56
[4,7,2,8,6,3,5,1]=>[3,3,1,1]=>56
[2,3,8,7,4,5,6,1]=>[5,1,1,1]=>35
[7,2,8,6,4,3,5,1]=>[3,2,1,1,1]=>64
[2,1,8,7,5,6,3,4]=>[3,3,1,1]=>56
[8,2,7,6,3,5,4,1]=>[3,1,1,1,1,1]=>21
[8,1,7,6,5,2,4,3]=>[3,1,1,1,1,1]=>21
[7,1,8,6,5,3,2,4]=>[3,2,1,1,1]=>64
[1,2,8,7,6,3,4,5]=>[5,1,1,1]=>35
[1,3,8,7,4,6,2,5]=>[4,2,1,1]=>90
[6,8,7,2,5,4,3,1]=>[2,2,1,1,1,1]=>20
[3,8,7,6,4,5,2,1]=>[3,1,1,1,1,1]=>21
[2,8,7,6,5,3,4,1]=>[3,1,1,1,1,1]=>21
[1,8,7,6,5,4,2,3]=>[3,1,1,1,1,1]=>21
[5,8,6,7,3,4,1,2]=>[3,2,2,1]=>70
[4,8,6,7,3,5,1,2]=>[3,2,2,1]=>70
[1,8,6,7,4,5,2,3]=>[3,2,2,1]=>70
[1,8,5,7,4,6,2,3]=>[3,2,2,1]=>70
[4,8,5,7,3,6,1,2]=>[3,2,2,1]=>70
[4,7,3,8,5,6,1,2]=>[3,3,2]=>42
[4,7,2,8,5,6,1,3]=>[3,3,2]=>42
[3,7,1,8,5,6,2,4]=>[3,3,2]=>42
[3,7,2,8,5,6,1,4]=>[3,3,2]=>42
[2,7,3,8,5,6,1,4]=>[4,2,2]=>56
[2,7,4,8,5,6,1,3]=>[4,2,2]=>56
[5,8,2,7,4,6,1,3]=>[3,2,2,1]=>70
[6,8,2,7,4,5,1,3]=>[3,2,2,1]=>70
[7,8,2,6,4,5,1,3]=>[3,2,2,1]=>70
[6,8,1,7,4,5,2,3]=>[3,2,2,1]=>70
[1,7,4,8,5,6,2,3]=>[4,2,2]=>56
[1,7,3,8,5,6,2,4]=>[4,2,2]=>56
[1,8,5,6,2,7,3,4]=>[4,3,1]=>70
[1,7,3,8,4,6,2,5]=>[4,2,2]=>56
[4,8,1,7,3,6,2,5]=>[3,2,2,1]=>70
[7,8,2,6,3,5,1,4]=>[3,2,2,1]=>70
[6,8,2,7,3,5,1,4]=>[3,2,2,1]=>70
[5,8,2,7,3,6,1,4]=>[3,2,2,1]=>70
[4,8,2,7,3,6,1,5]=>[3,2,2,1]=>70
[2,7,3,8,4,6,1,5]=>[4,2,2]=>56
[1,8,4,7,3,6,2,5]=>[3,2,2,1]=>70
[3,8,4,7,2,6,1,5]=>[3,2,2,1]=>70
[3,8,5,7,2,6,1,4]=>[3,2,2,1]=>70
[2,8,5,7,3,6,1,4]=>[3,2,2,1]=>70
[1,8,5,7,3,6,2,4]=>[3,2,2,1]=>70
[1,8,6,7,3,5,2,4]=>[3,2,2,1]=>70
[2,8,6,7,3,5,1,4]=>[3,2,2,1]=>70
[3,8,6,7,2,5,1,4]=>[3,2,2,1]=>70
[6,8,5,7,1,4,2,3]=>[3,2,2,1]=>70
[5,8,6,7,1,4,2,3]=>[3,3,1,1]=>56
[3,8,6,7,1,5,2,4]=>[3,3,1,1]=>56
[1,5,2,8,6,7,3,4]=>[4,3,1]=>70
[2,6,1,8,5,7,3,4]=>[3,3,2]=>42
[1,6,2,8,5,7,3,4]=>[4,2,2]=>56
[6,8,4,7,1,5,2,3]=>[3,2,2,1]=>70
[6,8,3,7,1,5,2,4]=>[3,2,2,1]=>70
[4,8,3,7,1,6,2,5]=>[3,2,2,1]=>70
[3,8,4,7,1,6,2,5]=>[3,3,1,1]=>56
[1,6,2,8,4,7,3,5]=>[4,2,2]=>56
[2,6,1,8,4,7,3,5]=>[3,3,2]=>42
[4,8,1,6,2,7,3,5]=>[4,3,1]=>70
[5,8,1,6,2,7,3,4]=>[4,3,1]=>70
[7,8,1,5,2,6,3,4]=>[4,2,2]=>56
[6,8,2,5,1,7,3,4]=>[3,3,2]=>42
[5,8,2,6,1,7,3,4]=>[3,3,2]=>42
[4,8,2,6,1,7,3,5]=>[3,3,2]=>42
[1,7,3,6,2,8,4,5]=>[4,3,1]=>70
[1,2,3,4,5,6,7,8,9]=>[9]=>1
[1,2,3,4,5,6,8,9,7]=>[8,1]=>8
[1,2,3,4,5,7,8,9,6]=>[8,1]=>8
[1,2,3,4,6,7,8,9,5]=>[8,1]=>8
[1,2,3,5,6,7,8,9,4]=>[8,1]=>8
[1,2,4,5,6,7,8,9,3]=>[8,1]=>8
[1,3,4,5,6,7,8,9,2]=>[8,1]=>8
[1,2,3,4,5,6,7,8,9,10]=>[10]=>1
[1,2,3,4,5,6,9,8,7]=>[7,1,1]=>28
[1,2,3,4,5,6,7,9,10,8]=>[9,1]=>9
[1,2,3,4,5,8,7,9,6]=>[7,1,1]=>28
[1,2,3,4,5,6,8,9,10,7]=>[9,1]=>9
[1,2,3,4,7,6,8,9,5]=>[7,1,1]=>28
[1,2,3,4,5,7,8,9,10,6]=>[9,1]=>9
[1,2,3,6,5,7,8,9,4]=>[7,1,1]=>28
[1,2,3,4,6,7,8,9,10,5]=>[9,1]=>9
[1,2,5,4,6,7,8,9,3]=>[7,1,1]=>28
[1,2,3,5,6,7,8,9,10,4]=>[9,1]=>9
[1,4,3,5,6,7,8,9,2]=>[7,1,1]=>28
[1,2,4,5,6,7,8,9,10,3]=>[9,1]=>9
[3,2,4,5,6,7,8,9,1]=>[7,1,1]=>28
[1,3,4,5,6,7,8,9,10,2]=>[9,1]=>9
[5,7,4,6,2,3,1,8]=>[3,2,2,1]=>70
[5,7,4,6,3,8,1,2]=>[3,2,2,1]=>70
[5,7,4,8,3,6,1,2]=>[3,2,2,1]=>70
[5,6,4,8,3,7,1,2]=>[3,2,2,1]=>70
[5,6,3,7,2,8,1,4]=>[4,2,1,1]=>90
[7,8,4,5,2,6,1,3]=>[3,2,2,1]=>70
[5,6,4,8,2,3,1,7]=>[3,3,1,1]=>56
[5,6,3,8,2,4,1,7]=>[3,3,1,1]=>56
[4,6,3,5,2,8,1,7]=>[3,3,1,1]=>56
[7,8,3,5,2,4,1,6]=>[3,2,2,1]=>70
[4,6,3,8,2,7,1,5]=>[3,2,2,1]=>70
[4,6,3,7,2,8,1,5]=>[4,2,1,1]=>90
[5,7,4,8,2,6,1,3]=>[3,2,2,1]=>70
[5,7,3,6,2,8,1,4]=>[3,2,2,1]=>70
[6,7,3,5,2,4,1,8]=>[3,2,2,1]=>70
[6,7,3,5,2,8,1,4]=>[3,2,2,1]=>70
[6,7,5,8,2,4,1,3]=>[3,2,2,1]=>70
[6,8,5,7,2,3,1,4]=>[3,2,2,1]=>70
[6,7,3,8,2,4,1,5]=>[3,3,1,1]=>56
[6,7,3,4,2,8,1,5]=>[3,3,1,1]=>56
[5,7,3,4,2,8,1,6]=>[3,3,1,1]=>56
[4,7,3,8,2,5,1,6]=>[3,3,1,1]=>56
[4,7,3,5,2,8,1,6]=>[3,3,1,1]=>56
[4,7,3,5,2,6,1,8]=>[4,2,1,1]=>90
[4,5,3,7,2,6,1,8]=>[4,2,1,1]=>90
[4,5,3,7,2,8,1,6]=>[4,2,1,1]=>90
[4,8,3,5,2,7,1,6]=>[3,2,2,1]=>70
[7,8,3,4,2,6,1,5]=>[3,2,2,1]=>70
[5,8,3,4,2,6,1,7]=>[4,2,1,1]=>90
[4,5,3,6,2,8,1,7]=>[4,2,1,1]=>90
[4,7,5,2,1,8,3,6]=>[3,3,1,1]=>56
[4,8,5,2,1,7,6,3]=>[3,2,2,1]=>70
[4,6,5,2,1,3,8,7]=>[3,3,1,1]=>56
[5,6,4,2,3,1,8,7]=>[3,3,1,1]=>56
[6,4,5,3,1,2,8,7]=>[3,3,1,1]=>56
[5,4,6,1,3,2,8,7]=>[3,3,1,1]=>56
[4,6,8,1,7,3,2,5]=>[3,3,1,1]=>56
[4,7,8,1,6,3,5,2]=>[3,3,1,1]=>56
[7,4,8,1,6,5,3,2]=>[2,2,2,1,1]=>28
[5,4,8,1,3,7,6,2]=>[3,2,2,1]=>70
[8,4,5,3,1,7,6,2]=>[3,2,2,1]=>70
[5,4,7,1,3,8,2,6]=>[3,3,1,1]=>56
[6,4,8,1,7,5,2,3]=>[3,2,2,1]=>70
[5,6,8,7,2,1,3,4]=>[3,3,1,1]=>56
[8,5,7,6,4,2,1,3]=>[2,2,1,1,1,1]=>20
[8,4,6,3,7,2,1,5]=>[3,2,1,1,1]=>64
[6,3,2,8,7,4,1,5]=>[3,2,2,1]=>70
[2,1,6,8,7,4,3,5]=>[3,3,1,1]=>56
[2,1,7,8,6,4,5,3]=>[3,3,1,1]=>56
[7,3,2,8,6,4,5,1]=>[3,2,2,1]=>70
[7,6,8,5,2,4,3,1]=>[2,2,1,1,1,1]=>20
[5,7,8,6,2,3,1,4]=>[3,3,1,1]=>56
[5,8,7,6,3,2,1,4]=>[2,2,1,1,1,1]=>20
[6,8,7,5,3,2,4,1]=>[2,2,1,1,1,1]=>20
[5,8,4,2,3,7,6,1]=>[3,2,2,1]=>70
[7,8,4,2,6,5,3,1]=>[2,2,2,1,1]=>28
[4,8,7,2,6,3,5,1]=>[3,2,1,1,1]=>64
[4,8,6,2,7,3,1,5]=>[3,3,1,1]=>56
[3,6,1,8,7,4,2,5]=>[3,3,1,1]=>56
[3,7,1,8,6,4,5,2]=>[3,3,1,1]=>56
[3,8,1,6,7,5,2,4]=>[3,3,1,1]=>56
[3,7,1,6,8,2,5,4]=>[3,3,1,1]=>56
[4,7,6,2,8,1,3,5]=>[3,3,1,1]=>56
[6,7,4,2,8,1,5,3]=>[3,2,2,1]=>70
[6,8,4,2,7,5,1,3]=>[2,2,2,2]=>14
[2,1,8,6,7,5,3,4]=>[3,3,1,1]=>56
[8,3,2,6,7,5,1,4]=>[3,2,2,1]=>70
[8,6,4,3,7,5,1,2]=>[2,2,2,1,1]=>28
[5,8,6,7,3,1,2,4]=>[3,3,1,1]=>56
[6,7,5,8,1,3,4,2]=>[3,3,1,1]=>56
[7,6,5,8,1,4,3,2]=>[2,2,1,1,1,1]=>20
[8,6,5,7,4,1,3,2]=>[2,2,1,1,1,1]=>20
[7,6,4,3,8,1,5,2]=>[2,2,2,1,1]=>28
[7,3,2,6,8,1,5,4]=>[3,2,2,1]=>70
[2,1,7,6,8,3,5,4]=>[3,3,1,1]=>56
[7,5,6,8,1,4,2,3]=>[3,3,1,1]=>56
[6,5,7,8,1,2,4,3]=>[3,3,1,1]=>56
[8,1,3,7,4,6,5,2]=>[4,1,1,1,1]=>35
[5,2,8,7,4,6,1,3]=>[3,2,2,1]=>70
[1,6,2,5,4,7,3,8]=>[5,1,1,1]=>35
[6,2,7,5,4,8,3,1]=>[3,2,1,1,1]=>64
[8,1,3,5,4,7,6,2]=>[4,2,1,1]=>90
[6,1,5,4,3,8,7,2]=>[3,2,1,1,1]=>64
[6,1,8,3,4,5,7,2]=>[5,2,1]=>64
[7,1,5,3,4,8,6,2]=>[4,2,1,1]=>90
[7,1,4,3,5,6,8,2]=>[5,1,1,1]=>35
[8,1,3,4,5,6,7,2]=>[6,1,1]=>21
[1,7,2,4,5,6,3,8]=>[6,1,1]=>21
[6,3,2,7,5,1,8,4]=>[3,2,2,1]=>70
[8,4,7,2,5,6,1,3]=>[3,2,2,1]=>70
[6,5,8,2,4,7,3,1]=>[3,2,1,1,1]=>64
[8,5,2,1,4,3,7,6]=>[3,3,1,1]=>56
[6,5,2,8,4,1,3,7]=>[3,2,2,1]=>70
[5,6,2,1,4,8,3,7]=>[3,3,2]=>42
[3,6,1,8,5,2,4,7]=>[4,3,1]=>70
[1,2,6,3,5,4,7,8]=>[6,1,1]=>21
[3,4,1,2,8,6,5,7]=>[4,3,1]=>70
[4,3,1,2,6,8,5,7]=>[4,3,1]=>70
[5,8,1,6,3,2,4,7]=>[4,2,1,1]=>90
[6,3,8,5,2,1,4,7]=>[3,2,2,1]=>70
[8,3,1,5,2,4,7,6]=>[4,3,1]=>70
[3,8,2,6,1,5,7,4]=>[3,2,2,1]=>70
[3,8,6,7,2,1,5,4]=>[3,2,2,1]=>70
[8,5,6,4,2,1,7,3]=>[3,2,1,1,1]=>64
[7,2,5,8,3,1,6,4]=>[3,2,2,1]=>70
[1,7,5,6,3,2,4,8]=>[4,2,1,1]=>90
[6,1,2,3,8,5,7,4]=>[5,2,1]=>64
[7,1,2,3,6,5,8,4]=>[5,1,1,1]=>35
[7,2,1,3,8,6,4,5]=>[4,2,2]=>56
[1,5,7,3,2,4,6,8]=>[5,2,1]=>64
[5,2,7,3,1,8,4,6]=>[4,3,1]=>70
[5,8,2,4,1,3,7,6]=>[3,3,2]=>42
[8,7,2,6,3,4,1,5]=>[4,1,1,1,1]=>35
[4,8,1,6,3,2,7,5]=>[3,3,1,1]=>56
[3,1,8,6,4,2,7,5]=>[3,3,1,1]=>56
[8,1,6,7,4,3,2,5]=>[3,2,1,1,1]=>64
[3,5,8,7,2,4,1,6]=>[3,3,1,1]=>56
[4,2,1,3,7,8,5,6]=>[4,3,1]=>70
[2,4,1,3,8,7,5,6]=>[4,3,1]=>70
[2,5,8,3,1,7,4,6]=>[4,2,2]=>56
[8,6,1,3,7,2,4,5]=>[4,2,1,1]=>90
[2,8,1,3,6,4,7,5]=>[4,3,1]=>70
[6,8,2,3,4,1,5,7]=>[5,2,1]=>64
[5,1,8,3,2,4,6,7]=>[5,2,1]=>64
[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]=>1
[8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,9,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,9,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,5,9,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,5,4,9,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,5,4,3,9,2,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,5,4,3,2,9,1]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,1]=>8
[9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[7,8,9,6,5,4,3,2,1]=>[3,1,1,1,1,1,1]=>28
[9,8,10,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,10,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,6,10,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,6,5,10,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,6,5,4,10,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,6,5,4,3,10,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[8,7,6,5,4,3,1,2,9]=>[3,1,1,1,1,1,1]=>28
[9,8,7,6,5,4,3,2,10,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,6,5,4,3,2,1,10]=>[2,1,1,1,1,1,1,1,1]=>9
[1,4,2,7,8,6,3,5]=>[4,3,1]=>70
[1,6,2,4,8,5,3,7]=>[5,2,1]=>64
[1,6,2,4,7,5,3,8]=>[5,2,1]=>64
[1,7,3,8,5,2,4,6]=>[4,2,2]=>56
[1,7,3,2,8,6,4,5]=>[4,2,2]=>56
[4,2,5,7,8,6,1,3]=>[4,2,2]=>56
[7,2,3,1,8,5,6,4]=>[4,2,2]=>56
[8,2,5,1,7,3,4,6]=>[4,3,1]=>70
[6,2,1,8,3,4,7,5]=>[4,2,2]=>56
[6,2,8,3,5,1,7,4]=>[4,2,2]=>56
[6,2,4,8,5,7,1,3]=>[4,2,2]=>56
[1,3,6,4,8,5,7,2]=>[5,2,1]=>64
[1,3,6,4,7,5,8,2]=>[5,2,1]=>64
[6,2,4,7,5,8,1,3]=>[4,2,2]=>56
[6,2,1,3,7,8,4,5]=>[4,3,1]=>70
[7,8,2,1,4,3,5,6]=>[4,2,2]=>56
[7,6,4,2,3,1,8,5]=>[3,2,1,1,1]=>64
[5,7,2,3,1,6,8,4]=>[4,2,2]=>56
[7,5,4,2,6,8,1,3]=>[3,2,1,1,1]=>64
[1,7,5,3,4,6,8,2]=>[5,1,1,1]=>35
[8,2,5,4,6,7,1,3]=>[4,2,1,1]=>90
[5,2,6,3,1,8,7,4]=>[3,3,2]=>42
[8,2,6,4,3,1,7,5]=>[3,2,1,1,1]=>64
[8,2,7,4,1,3,5,6]=>[4,2,1,1]=>90
[1,2,8,4,3,5,6,7]=>[6,1,1]=>21
[1,7,4,2,3,5,6,8]=>[6,1,1]=>21
[6,8,4,1,3,2,5,7]=>[4,2,1,1]=>90
[1,8,7,4,3,2,5,6]=>[4,1,1,1,1]=>35
[1,6,3,8,2,4,7,5]=>[4,2,2]=>56
[5,3,8,1,2,7,4,6]=>[4,2,2]=>56
[5,1,8,3,2,6,4,7]=>[4,2,2]=>56
[5,7,3,1,2,6,4,8]=>[4,2,2]=>56
[1,7,5,4,2,6,3,8]=>[4,2,1,1]=>90
[1,5,8,2,4,6,3,7]=>[5,2,1]=>64
[1,5,8,4,2,7,3,6]=>[4,2,2]=>56
[1,4,6,2,8,3,7,5]=>[4,3,1]=>70
[5,3,1,6,7,2,4,8]=>[4,3,1]=>70
[5,3,6,1,2,8,4,7]=>[4,3,1]=>70
[1,6,3,2,7,8,4,5]=>[4,3,1]=>70
[1,7,4,5,3,8,6,2]=>[4,2,1,1]=>90
[6,3,4,1,2,5,8,7]=>[4,3,1]=>70
[6,3,1,4,2,7,5,8]=>[4,3,1]=>70
[1,8,3,2,4,5,6,7]=>[6,1,1]=>21
[8,6,3,2,4,1,7,5]=>[3,2,1,1,1]=>64
[8,5,3,2,6,7,1,4]=>[3,2,1,1,1]=>64
[4,5,2,6,8,1,7,3]=>[4,2,2]=>56
[4,2,5,6,7,8,1,3]=>[5,2,1]=>64
[5,2,3,6,7,1,8,4]=>[5,2,1]=>64
[6,2,3,4,1,7,8,5]=>[5,2,1]=>64
[7,2,3,1,4,5,8,6]=>[5,2,1]=>64
[8,6,1,4,3,2,5,7]=>[4,1,1,1,1]=>35
[8,3,1,6,5,2,4,7]=>[4,2,1,1]=>90
[3,7,5,1,8,2,4,6]=>[4,3,1]=>70
[4,1,5,2,8,7,3,6]=>[4,3,1]=>70
[8,1,2,4,6,5,3,7]=>[5,1,1,1]=>35
[8,1,2,5,4,6,3,7]=>[5,1,1,1]=>35
[8,2,6,5,1,3,4,7]=>[4,2,1,1]=>90
[8,3,1,6,2,5,4,7]=>[4,2,1,1]=>90
[8,1,2,6,4,5,3,7]=>[5,1,1,1]=>35
[8,1,2,5,6,4,3,7]=>[5,1,1,1]=>35
[8,1,2,6,5,4,3,7]=>[4,1,1,1,1]=>35
[1,7,5,4,2,8,3,6]=>[4,2,1,1]=>90
[5,1,4,8,2,7,3,6]=>[4,2,2]=>56
[1,4,6,8,2,7,3,5]=>[4,3,1]=>70
[1,4,7,6,2,8,3,5]=>[4,3,1]=>70
[5,1,4,7,2,8,3,6]=>[4,3,1]=>70
[1,7,4,5,2,8,3,6]=>[4,3,1]=>70
[3,7,5,1,2,8,4,6]=>[4,3,1]=>70
[5,7,2,8,1,3,4,6]=>[4,3,1]=>70
[5,2,8,7,1,3,4,6]=>[4,2,2]=>56
[4,1,5,8,2,7,3,6]=>[4,3,1]=>70
[1,4,6,2,8,7,3,5]=>[4,3,1]=>70
[1,4,2,8,6,7,3,5]=>[4,3,1]=>70
[3,1,2,6,4,8,7,5]=>[4,3,1]=>70
[2,1,7,6,3,4,8,5]=>[4,3,1]=>70
[3,1,2,7,4,6,8,5]=>[5,2,1]=>64
[1,4,7,2,6,8,3,5]=>[4,3,1]=>70
[1,2,3,6,8,5,7,4]=>[5,2,1]=>64
[5,1,4,2,7,8,3,6]=>[4,3,1]=>70
[1,4,2,7,6,8,3,5]=>[4,3,1]=>70
[1,4,2,6,8,7,3,5]=>[4,3,1]=>70
[3,1,2,8,4,6,7,5]=>[5,2,1]=>64
[3,1,2,7,6,4,8,5]=>[4,3,1]=>70
[5,3,7,1,8,2,4,6]=>[4,3,1]=>70
[1,7,4,3,2,5,8,6]=>[4,2,1,1]=>90
[4,8,7,2,1,3,5,6]=>[4,2,1,1]=>90
[1,8,7,3,4,2,5,6]=>[5,1,1,1]=>35
[3,1,7,8,2,6,4,5]=>[4,3,1]=>70
[1,4,2,7,8,3,6,5]=>[4,3,1]=>70
[5,2,8,1,3,4,7,6]=>[4,2,2]=>56
[2,1,8,6,3,4,7,5]=>[4,3,1]=>70
[1,4,2,6,8,3,7,5]=>[4,3,1]=>70
[1,2,3,7,8,5,6,4]=>[5,2,1]=>64
[1,2,3,7,5,8,6,4]=>[5,2,1]=>64
[1,4,2,7,3,8,6,5]=>[4,3,1]=>70
[3,1,7,2,8,6,4,5]=>[4,3,1]=>70
[2,1,7,8,3,4,6,5]=>[4,3,1]=>70
[1,2,3,8,7,5,6,4]=>[5,1,1,1]=>35
[10,1,2,3,4,5,6,7,8,9]=>[9,1]=>9
[10,1,2,3,4,5,6,9,7,8]=>[8,1,1]=>36
[10,1,2,3,4,5,9,6,7,8]=>[8,1,1]=>36
[9,1,2,3,4,10,5,6,7,8]=>[8,2]=>35
[10,1,2,3,9,4,5,6,7,8]=>[8,1,1]=>36
[10,1,2,9,3,4,5,6,7,8]=>[8,1,1]=>36
[9,1,10,2,3,4,5,6,7,8]=>[8,2]=>35
[10,9,1,2,3,4,5,6,7,8]=>[8,1,1]=>36
[11,1,2,3,4,5,6,7,8,9,10]=>[10,1]=>10
[10,1,2,3,4,5,6,7,8,11,9]=>[9,2]=>44
[8,1,2,3,4,5,6,9,10,7]=>[8,2]=>35
[11,1,2,3,4,5,6,7,10,8,9]=>[9,1,1]=>45
[7,1,2,3,4,5,10,9,6,8]=>[7,2,1]=>160
[11,1,2,3,4,5,6,10,7,8,9]=>[9,1,1]=>45
[6,1,2,3,4,10,9,5,7,8]=>[7,2,1]=>160
[10,1,2,3,4,5,11,6,7,8,9]=>[9,2]=>44
[5,1,2,3,9,10,4,6,7,8]=>[7,3]=>75
[11,1,2,3,4,10,5,6,7,8,9]=>[9,1,1]=>45
[4,1,2,10,9,3,5,6,7,8]=>[7,2,1]=>160
[11,1,2,3,10,4,5,6,7,8,9]=>[9,1,1]=>45
[3,1,10,9,2,4,5,6,7,8]=>[7,2,1]=>160
[10,1,2,11,3,4,5,6,7,8,9]=>[9,2]=>44
[2,9,10,1,3,4,5,6,7,8]=>[7,3]=>75
[11,1,10,2,3,4,5,6,7,8,9]=>[9,1,1]=>45
[11,10,1,2,3,4,5,6,7,8,9]=>[9,1,1]=>45
[4,7,8,5,6,2,1,3]=>[3,2,2,1]=>70
[5,7,8,4,2,6,1,3]=>[3,2,2,1]=>70
[8,6,3,7,2,1,5,4]=>[2,2,2,1,1]=>28
[7,6,3,8,2,1,5,4]=>[2,2,2,1,1]=>28
[4,7,8,3,2,1,5,6]=>[3,3,1,1]=>56
[5,7,8,3,2,1,4,6]=>[3,3,1,1]=>56
[8,6,3,7,2,1,4,5]=>[3,2,1,1,1]=>64
[2,6,4,7,3,5,8,1]=>[4,2,1,1]=>90
[8,4,3,2,1,6,5,7]=>[3,2,1,1,1]=>64
[7,4,3,2,1,8,6,5]=>[2,2,2,1,1]=>28
[6,4,3,2,1,8,7,5]=>[2,2,2,1,1]=>28
[8,5,4,2,6,7,1,3]=>[3,2,1,1,1]=>64
[8,5,3,2,6,1,7,4]=>[3,2,1,1,1]=>64
[7,5,3,2,6,1,8,4]=>[3,2,1,1,1]=>64
[2,6,4,7,3,8,5,1]=>[4,2,1,1]=>90
[3,5,4,2,7,8,1,6]=>[4,2,1,1]=>90
[5,6,3,4,1,2,8,7]=>[3,3,2]=>42
[8,5,3,7,2,6,4,1]=>[2,2,2,1,1]=>28
[8,5,7,4,2,6,3,1]=>[2,2,2,1,1]=>28
[7,5,8,4,2,6,1,3]=>[2,2,2,1,1]=>28
[2,1,7,8,5,6,3,4]=>[3,3,2]=>42
[6,8,3,7,5,1,4,2]=>[2,2,2,1,1]=>28
[5,7,3,8,1,6,2,4]=>[3,3,2]=>42
[3,2,6,4,8,5,1,7]=>[4,3,1]=>70
[3,5,2,4,1,7,6,8]=>[4,3,1]=>70
[4,2,5,8,3,1,6,7]=>[4,3,1]=>70
[3,1,5,4,2,8,6,7]=>[4,3,1]=>70
[4,1,5,8,3,2,6,7]=>[4,3,1]=>70
[4,3,8,5,2,1,6,7]=>[4,2,1,1]=>90
[4,3,6,2,5,1,7,8]=>[4,2,1,1]=>90
[4,6,3,2,5,1,7,8]=>[4,2,1,1]=>90
[4,3,6,1,5,2,7,8]=>[4,2,2]=>56
[4,6,3,1,5,2,7,8]=>[4,2,2]=>56
[5,3,6,4,1,2,7,8]=>[4,2,2]=>56
[4,3,6,1,7,2,5,8]=>[4,3,1]=>70
[6,2,4,1,3,7,8,5]=>[4,3,1]=>70
[4,6,3,1,7,2,5,8]=>[4,3,1]=>70
[5,6,2,7,1,3,4,8]=>[4,3,1]=>70
[4,5,2,7,3,1,6,8]=>[4,3,1]=>70
[3,2,6,1,4,7,5,8]=>[4,3,1]=>70
[3,5,2,7,4,6,1,8]=>[4,3,1]=>70
[3,7,2,4,8,5,1,6]=>[4,3,1]=>70
[7,3,1,4,6,8,2,5]=>[4,3,1]=>70
[3,2,6,1,5,7,4,8]=>[4,2,2]=>56
[6,3,2,1,5,7,4,8]=>[4,2,1,1]=>90
[6,4,2,1,5,3,7,8]=>[4,2,1,1]=>90
[4,2,6,1,5,3,7,8]=>[4,2,2]=>56
[4,2,1,7,5,3,6,8]=>[4,2,2]=>56
[7,4,1,5,6,2,3,8]=>[4,3,1]=>70
[7,3,1,5,2,6,4,8]=>[4,3,1]=>70
[6,3,5,1,2,7,4,8]=>[4,3,1]=>70
[5,2,6,4,1,3,7,8]=>[4,2,2]=>56
[3,6,5,1,2,7,4,8]=>[4,3,1]=>70
[2,3,1,8,5,4,7,6]=>[4,3,1]=>70
[2,4,1,5,8,3,7,6]=>[4,3,1]=>70
[3,4,5,1,2,8,7,6]=>[4,3,1]=>70
[3,4,5,1,8,2,7,6]=>[4,3,1]=>70
[3,4,5,8,2,1,7,6]=>[4,2,2]=>56
[3,4,5,2,8,1,7,6]=>[4,2,2]=>56
[3,5,6,2,7,1,4,8]=>[5,2,1]=>64
[3,5,6,2,7,1,8,4]=>[5,2,1]=>64
[1,8,4,6,3,7,2,5]=>[4,2,1,1]=>90
[3,4,6,8,2,7,5,1]=>[4,2,1,1]=>90
[3,4,6,2,8,7,5,1]=>[4,2,1,1]=>90
[3,5,6,2,7,8,4,1]=>[5,2,1]=>64
[3,5,6,2,7,4,1,8]=>[5,2,1]=>64
[4,5,6,7,2,8,3,1]=>[5,2,1]=>64
[3,5,6,8,7,2,4,1]=>[4,2,1,1]=>90
[2,5,8,6,7,3,4,1]=>[4,2,1,1]=>90
[2,5,8,6,7,3,1,4]=>[4,2,1,1]=>90
[3,5,6,8,7,2,1,4]=>[4,2,1,1]=>90
[4,5,6,7,2,1,8,3]=>[5,2,1]=>64
[2,5,1,6,7,8,4,3]=>[5,2,1]=>64
[3,5,6,1,7,4,2,8]=>[5,2,1]=>64
[3,5,6,1,7,4,8,2]=>[5,2,1]=>64
[3,5,6,8,7,1,4,2]=>[4,2,1,1]=>90
[4,5,6,7,8,1,3,2]=>[5,2,1]=>64
[4,5,6,7,1,3,8,2]=>[5,2,1]=>64
[4,5,6,7,1,3,2,8]=>[5,2,1]=>64
[4,5,6,7,3,1,8,2]=>[5,2,1]=>64
[3,5,6,8,7,4,1,2]=>[4,2,1,1]=>90
[2,5,8,6,7,4,1,3]=>[4,2,1,1]=>90
[1,8,5,6,7,4,3,2]=>[4,1,1,1,1]=>35
[2,5,8,6,7,4,3,1]=>[4,1,1,1,1]=>35
[8,2,5,3,7,1,6,4]=>[3,2,2,1]=>70
[8,2,4,3,7,1,6,5]=>[3,2,2,1]=>70
[5,8,2,4,3,7,1,6]=>[3,2,2,1]=>70
[4,2,5,6,1,8,3,7]=>[4,3,1]=>70
[4,2,5,6,1,7,3,8]=>[5,2,1]=>64
[6,1,5,7,3,2,4,8]=>[4,2,1,1]=>90
[6,1,5,8,3,2,4,7]=>[4,2,1,1]=>90
[3,8,2,4,7,1,5,6]=>[4,2,2]=>56
[3,6,8,2,4,7,1,5]=>[3,3,2]=>42
[4,3,5,6,7,1,8,2]=>[5,2,1]=>64
[3,7,1,5,6,8,2,4]=>[4,3,1]=>70
[3,7,1,5,8,2,4,6]=>[4,3,1]=>70
[8,3,2,4,6,1,5,7]=>[4,2,1,1]=>90
[7,3,2,4,6,1,5,8]=>[4,2,1,1]=>90
[3,2,5,1,7,4,6,8]=>[4,3,1]=>70
[3,2,5,1,8,4,6,7]=>[4,3,1]=>70
[3,2,5,1,7,8,4,6]=>[4,3,1]=>70
[7,8,3,2,4,6,1,5]=>[3,2,2,1]=>70
[6,1,5,7,8,3,2,4]=>[4,2,1,1]=>90
[4,2,5,6,1,7,8,3]=>[5,2,1]=>64
[5,7,6,1,8,3,4,2]=>[3,3,1,1]=>56
[5,8,6,1,7,3,4,2]=>[3,3,1,1]=>56
[6,1,5,8,7,3,2,4]=>[3,2,2,1]=>70
[8,7,3,2,4,6,1,5]=>[3,2,1,1,1]=>64
[3,2,5,1,8,7,4,6]=>[3,3,2]=>42
[3,2,5,1,6,4,7,8]=>[5,2,1]=>64
[3,2,4,1,8,7,5,6]=>[4,2,2]=>56
[3,2,5,1,6,8,7,4]=>[4,2,2]=>56
[3,8,6,5,1,7,4,2]=>[3,2,1,1,1]=>64
[3,7,6,5,1,8,4,2]=>[3,2,1,1,1]=>64
[6,5,1,7,8,4,2,3]=>[3,3,1,1]=>56
[3,2,5,1,6,7,8,4]=>[5,2,1]=>64
[3,2,4,1,8,5,6,7]=>[5,2,1]=>64
[3,2,4,1,7,5,6,8]=>[5,2,1]=>64
[3,2,4,1,6,8,5,7]=>[4,3,1]=>70
[3,2,4,1,8,5,7,6]=>[4,2,2]=>56
[8,3,2,4,7,6,1,5]=>[3,2,2,1]=>70
[3,2,5,1,8,4,7,6]=>[3,3,2]=>42
[3,2,5,1,6,7,4,8]=>[5,2,1]=>64
[6,5,1,7,4,2,3,8]=>[4,2,1,1]=>90
[6,5,1,8,4,2,3,7]=>[4,2,1,1]=>90
[8,4,2,3,7,5,1,6]=>[4,2,1,1]=>90
[4,2,6,1,8,3,7,5]=>[3,3,2]=>42
[5,2,6,1,8,3,7,4]=>[3,3,2]=>42
[8,4,6,1,7,3,5,2]=>[3,3,1,1]=>56
[5,2,6,1,8,4,7,3]=>[3,3,2]=>42
[7,4,2,3,8,5,1,6]=>[4,2,1,1]=>90
[8,5,1,6,4,2,3,7]=>[4,2,1,1]=>90
[7,5,1,6,4,2,3,8]=>[4,2,1,1]=>90
[3,2,5,1,7,6,4,8]=>[4,2,2]=>56
[3,2,5,1,8,6,4,7]=>[4,2,2]=>56
[7,3,2,4,8,6,1,5]=>[3,2,2,1]=>70
[8,6,1,5,7,3,2,4]=>[3,2,1,1,1]=>64
[4,2,6,1,8,5,7,3]=>[3,3,2]=>42
[8,5,6,1,7,3,4,2]=>[3,3,1,1]=>56
[3,6,8,5,1,7,4,2]=>[3,2,2,1]=>70
[8,5,1,6,7,4,2,3]=>[3,3,1,1]=>56
[3,2,5,1,8,6,7,4]=>[4,2,2]=>56
[3,2,4,1,8,6,5,7]=>[4,2,2]=>56
[3,2,4,1,5,8,6,7]=>[5,2,1]=>64
[3,2,5,1,7,8,6,4]=>[4,2,2]=>56
[7,8,5,1,6,4,2,3]=>[3,2,2,1]=>70
[3,8,5,1,7,6,4,2]=>[3,2,1,1,1]=>64
[3,7,5,1,8,6,4,2]=>[3,2,2,1]=>70
[8,7,5,1,6,4,2,3]=>[3,2,1,1,1]=>64
[3,2,5,1,8,7,6,4]=>[3,2,2,1]=>70
[6,5,7,3,1,8,4,2]=>[3,2,2,1]=>70
[4,6,3,7,1,8,5,2]=>[4,2,2]=>56
[4,6,3,7,5,1,8,2]=>[4,2,2]=>56
[4,2,6,1,7,5,3,8]=>[4,2,2]=>56
[2,5,7,4,1,6,3,8]=>[4,2,2]=>56
[2,5,7,4,1,6,8,3]=>[4,2,2]=>56
[5,4,7,3,6,1,8,2]=>[3,2,2,1]=>70
[5,4,7,8,3,1,6,2]=>[3,2,2,1]=>70
[4,3,7,5,1,8,6,2]=>[3,3,2]=>42
[6,4,3,8,5,1,7,2]=>[3,2,2,1]=>70
[5,8,4,3,6,1,7,2]=>[3,2,2,1]=>70
[5,4,8,3,6,1,7,2]=>[3,2,2,1]=>70
[5,4,3,6,7,1,8,2]=>[4,2,1,1]=>90
[2,5,4,6,1,7,3,8]=>[5,2,1]=>64
[3,2,5,8,1,6,7,4]=>[4,2,2]=>56
[2,5,4,6,8,1,7,3]=>[4,2,2]=>56
[5,2,8,4,1,6,7,3]=>[4,2,2]=>56
[4,6,2,1,8,5,7,3]=>[3,3,2]=>42
[2,4,1,7,5,8,6,3]=>[4,3,1]=>70
[2,4,1,7,5,3,8,6]=>[4,3,1]=>70
[2,6,4,1,8,5,3,7]=>[4,2,2]=>56
[5,4,8,2,1,6,3,7]=>[3,2,2,1]=>70
[2,5,8,4,1,6,3,7]=>[4,2,2]=>56
[3,2,5,6,1,8,4,7]=>[4,3,1]=>70
[4,8,3,2,6,1,5,7]=>[3,2,2,1]=>70
[3,5,2,8,1,6,4,7]=>[4,2,2]=>56
[3,2,1,6,8,5,4,7]=>[3,3,2]=>42
[3,2,7,1,5,4,8,6]=>[3,3,2]=>42
[3,2,7,1,5,8,6,4]=>[3,3,2]=>42
[3,8,2,5,1,6,7,4]=>[4,2,2]=>56
[4,8,3,2,6,7,1,5]=>[3,2,2,1]=>70
[4,3,8,2,6,7,1,5]=>[3,2,2,1]=>70
[4,3,2,6,7,8,1,5]=>[4,2,1,1]=>90
[4,3,2,6,7,1,5,8]=>[4,2,1,1]=>90
[4,3,7,2,6,8,1,5]=>[3,2,2,1]=>70
[4,3,7,8,2,6,1,5]=>[3,2,2,1]=>70
[2,5,7,4,8,1,6,3]=>[4,2,2]=>56
[3,2,5,7,8,1,6,4]=>[4,2,2]=>56
[3,2,5,7,1,6,8,4]=>[4,2,2]=>56
[3,2,5,7,1,6,4,8]=>[4,2,2]=>56
[6,3,2,7,1,5,4,8]=>[3,2,2,1]=>70
[6,3,2,7,1,5,8,4]=>[3,2,2,1]=>70
[6,3,2,7,8,1,5,4]=>[3,2,2,1]=>70
[4,2,6,1,7,8,5,3]=>[4,2,2]=>56
[6,5,2,1,7,8,4,3]=>[3,2,2,1]=>70
[2,1,7,5,3,8,6,4]=>[3,3,2]=>42
[6,2,1,8,5,3,7,4]=>[3,3,2]=>42
[6,3,2,7,1,4,8,5]=>[3,3,1,1]=>56
[6,3,2,1,4,7,8,5]=>[4,2,1,1]=>90
[6,3,2,1,4,7,5,8]=>[4,2,1,1]=>90
[3,5,2,1,7,4,6,8]=>[4,3,1]=>70
[3,5,2,1,7,8,4,6]=>[4,3,1]=>70
[5,8,4,2,1,7,3,6]=>[3,2,2,1]=>70
[4,6,2,1,8,3,7,5]=>[3,3,2]=>42
[2,4,1,7,3,8,6,5]=>[4,3,1]=>70
[3,2,7,1,4,8,6,5]=>[3,3,2]=>42
[3,5,8,2,1,7,4,6]=>[3,3,2]=>42
[4,8,3,7,2,1,5,6]=>[3,2,2,1]=>70
[4,3,7,2,8,1,5,6]=>[3,3,1,1]=>56
[4,3,7,2,1,5,6,8]=>[4,2,1,1]=>90
[4,8,3,2,7,1,5,6]=>[3,2,2,1]=>70
[3,5,2,8,1,7,4,6]=>[3,3,2]=>42
[6,3,2,8,1,4,7,5]=>[3,2,2,1]=>70
[3,2,1,4,7,5,8,6]=>[4,3,1]=>70
[5,3,2,1,8,4,6,7]=>[4,2,1,1]=>90
[4,8,3,2,1,5,6,7]=>[4,2,1,1]=>90
[4,3,8,2,1,5,6,7]=>[4,2,1,1]=>90
[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]=>8
[8,7,6,4,5,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[1,9,8,7,5,6,4,3,2]=>[3,1,1,1,1,1,1]=>28
[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]=>9
[10,9,8,7,6,5,4,3,2,1,11]=>[2,1,1,1,1,1,1,1,1,1]=>10
[9,8,7,5,6,4,3,2,1,10]=>[3,1,1,1,1,1,1,1]=>36
[8,7,5,4,6,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[8,7,4,6,5,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[1,9,8,6,5,7,4,3,2]=>[3,1,1,1,1,1,1]=>28
[1,9,8,5,7,6,4,3,2]=>[3,1,1,1,1,1,1]=>28
[1,10,9,8,6,7,5,4,3,2]=>[3,1,1,1,1,1,1,1]=>36
[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1]=>10
[6,2,3,1,5,4,8,7]=>[4,3,1]=>70
[8,4,5,2,3,1,7,6]=>[3,3,1,1]=>56
[8,6,7,2,5,3,4,1]=>[3,2,1,1,1]=>64
[8,2,5,3,4,1,7,6]=>[4,2,1,1]=>90
[6,2,5,3,4,1,8,7]=>[4,2,1,1]=>90
[6,1,5,2,4,3,8,7]=>[4,2,1,1]=>90
[6,4,5,1,3,2,8,7]=>[3,3,1,1]=>56
[6,1,5,3,4,2,8,7]=>[4,2,1,1]=>90
[6,3,5,1,4,2,8,7]=>[3,3,1,1]=>56
[8,3,5,2,4,1,7,6]=>[3,3,1,1]=>56
[8,3,7,5,6,2,4,1]=>[3,2,1,1,1]=>64
[8,3,7,2,4,1,6,5]=>[3,2,2,1]=>70
[8,3,5,1,4,2,7,6]=>[3,3,1,1]=>56
[8,1,5,3,4,2,7,6]=>[4,2,1,1]=>90
[8,4,5,1,3,2,7,6]=>[3,3,1,1]=>56
[2,1,8,4,5,3,7,6]=>[4,3,1]=>70
[8,6,7,4,5,1,3,2]=>[2,2,2,1,1]=>28
[8,6,7,1,5,3,4,2]=>[3,2,1,1,1]=>64
[8,6,7,3,5,1,4,2]=>[2,2,2,1,1]=>28
[8,3,7,5,6,1,4,2]=>[3,2,1,1,1]=>64
[8,5,7,3,6,1,4,2]=>[2,2,2,1,1]=>28
[8,3,7,4,6,2,5,1]=>[3,2,1,1,1]=>64
[8,3,7,4,6,1,5,2]=>[3,2,1,1,1]=>64
[8,3,7,1,6,4,5,2]=>[3,2,1,1,1]=>64
[8,1,7,3,6,4,5,2]=>[4,1,1,1,1]=>35
[8,1,7,5,6,3,4,2]=>[3,2,1,1,1]=>64
[8,4,7,5,6,1,3,2]=>[3,2,1,1,1]=>64
[2,1,8,4,7,5,6,3]=>[4,2,1,1]=>90
[8,1,7,3,4,2,6,5]=>[4,2,1,1]=>90
[8,1,7,3,6,2,5,4]=>[3,2,1,1,1]=>64
[8,3,7,1,6,2,5,4]=>[3,2,1,1,1]=>64
[8,3,7,2,6,4,5,1]=>[3,2,1,1,1]=>64
[8,2,7,3,6,4,5,1]=>[4,1,1,1,1]=>35
[8,2,7,3,6,1,5,4]=>[3,2,1,1,1]=>64
[8,2,7,1,6,3,5,4]=>[3,2,1,1,1]=>64
[8,1,7,2,4,3,6,5]=>[4,2,1,1]=>90
[8,1,3,2,7,4,6,5]=>[4,2,1,1]=>90
[2,1,8,3,7,4,6,5]=>[4,2,1,1]=>90
[8,1,5,2,4,3,7,6]=>[4,2,1,1]=>90
[8,2,7,1,4,3,6,5]=>[3,3,1,1]=>56
[8,2,7,3,4,1,6,5]=>[4,2,1,1]=>90
[8,2,7,5,6,3,4,1]=>[3,2,1,1,1]=>64
[8,4,7,5,6,2,3,1]=>[3,2,1,1,1]=>64
[8,4,7,2,3,1,6,5]=>[3,2,2,1]=>70
[8,2,3,1,7,4,6,5]=>[4,2,1,1]=>90
[8,2,3,1,5,4,7,6]=>[4,3,1]=>70
[4,2,3,1,8,5,7,6]=>[4,2,2]=>56
[4,1,3,2,8,6,7,5]=>[4,2,2]=>56
[8,6,7,2,3,1,5,4]=>[3,2,2,1]=>70
[8,2,3,1,7,5,6,4]=>[4,2,1,1]=>90
[8,5,7,2,6,3,4,1]=>[3,2,1,1,1]=>64
[8,5,7,2,6,1,4,3]=>[2,2,2,1,1]=>28
[8,2,7,5,6,1,4,3]=>[3,2,1,1,1]=>64
[8,6,7,2,5,1,4,3]=>[2,2,2,1,1]=>28
[8,6,7,1,5,2,4,3]=>[3,2,1,1,1]=>64
[8,6,7,1,3,2,5,4]=>[3,2,2,1]=>70
[2,1,8,6,7,3,5,4]=>[3,3,1,1]=>56
[2,1,8,3,7,5,6,4]=>[4,2,1,1]=>90
[8,1,3,2,7,5,6,4]=>[4,2,1,1]=>90
[8,1,7,5,6,2,4,3]=>[3,2,1,1,1]=>64
[8,1,7,2,6,4,5,3]=>[4,1,1,1,1]=>35
[8,2,7,1,6,4,5,3]=>[3,2,1,1,1]=>64
[8,2,7,4,6,1,5,3]=>[3,2,1,1,1]=>64
[8,2,7,4,6,3,5,1]=>[3,2,1,1,1]=>64
[8,4,7,2,6,3,5,1]=>[3,2,1,1,1]=>64
[8,4,7,2,6,1,5,3]=>[2,2,2,1,1]=>28
[8,4,7,1,6,2,5,3]=>[3,2,1,1,1]=>64
[8,1,7,4,6,2,5,3]=>[3,2,1,1,1]=>64
[8,5,7,1,6,2,4,3]=>[3,2,1,1,1]=>64
[2,1,8,5,7,3,6,4]=>[3,3,1,1]=>56
[8,5,7,4,6,1,3,2]=>[2,2,2,1,1]=>28
[8,5,7,1,6,3,4,2]=>[3,2,1,1,1]=>64
[8,1,7,4,6,3,5,2]=>[3,2,1,1,1]=>64
[8,4,7,1,6,3,5,2]=>[3,2,1,1,1]=>64
[8,4,7,3,6,1,5,2]=>[2,2,2,1,1]=>28
[2,4,8,3,6,1,7,5]=>[4,2,2]=>56
[6,5,8,1,3,2,7,4]=>[3,2,2,1]=>70
[4,5,8,6,3,2,7,1]=>[4,1,1,1,1]=>35
[6,5,8,7,3,1,2,4]=>[3,2,2,1]=>70
[1,5,8,7,3,6,2,4]=>[3,2,2,1]=>70
[1,7,2,8,4,6,5,3]=>[4,2,1,1]=>90
[6,7,2,8,4,1,5,3]=>[3,3,2]=>42
[3,6,2,8,4,5,7,1]=>[4,3,1]=>70
[2,6,1,8,4,5,7,3]=>[4,3,1]=>70
[2,8,4,6,1,5,7,3]=>[4,2,1,1]=>90
[6,3,1,8,4,5,7,2]=>[4,2,2]=>56
[3,1,6,8,4,5,7,2]=>[4,3,1]=>70
[2,3,6,8,4,5,7,1]=>[5,2,1]=>64
[6,3,7,8,4,1,5,2]=>[3,3,2]=>42
[1,3,7,8,4,6,5,2]=>[4,2,1,1]=>90
[1,5,7,8,2,4,6,3]=>[4,3,1]=>70
[5,1,7,8,2,4,6,3]=>[4,3,1]=>70
[3,6,7,8,4,2,5,1]=>[4,2,1,1]=>90
[7,6,1,8,4,2,5,3]=>[3,2,2,1]=>70
[5,6,8,7,3,2,1,4]=>[3,2,1,1,1]=>64
[2,8,3,7,1,6,5,4]=>[3,2,1,1,1]=>64
[5,2,8,7,3,6,1,4]=>[3,2,2,1]=>70
[7,2,1,8,4,6,5,3]=>[3,2,2,1]=>70
[3,2,7,8,4,6,5,1]=>[3,3,1,1]=>56
[5,2,7,8,1,4,6,3]=>[3,3,2]=>42
[1,2,7,8,5,4,6,3]=>[4,2,1,1]=>90
[4,2,1,3,8,5,6,7]=>[5,2,1]=>64
[7,2,5,8,3,4,6,1]=>[4,2,1,1]=>90
[6,2,8,5,4,3,1,7]=>[3,2,1,1,1]=>64
[2,8,3,5,4,1,6,7]=>[5,1,1,1]=>35
[2,8,4,5,3,1,6,7]=>[5,1,1,1]=>35
[6,4,8,5,2,3,1,7]=>[3,2,2,1]=>70
[7,3,5,8,2,4,6,1]=>[3,3,1,1]=>56
[4,3,1,2,8,5,6,7]=>[5,2,1]=>64
[3,4,2,1,8,5,6,7]=>[5,2,1]=>64
[2,7,6,8,4,3,5,1]=>[3,2,1,1,1]=>64
[5,7,1,8,3,4,6,2]=>[4,3,1]=>70
[3,7,5,8,1,4,6,2]=>[3,3,1,1]=>56
[1,7,5,8,3,4,6,2]=>[4,2,1,1]=>90
[1,6,8,5,4,3,2,7]=>[3,2,1,1,1]=>64
[4,6,8,5,1,3,2,7]=>[3,3,1,1]=>56
[5,6,8,1,4,3,2,7]=>[3,3,1,1]=>56
[7,5,8,6,3,4,2,1]=>[2,2,2,1,1]=>28
[2,4,8,3,6,5,1,7]=>[4,2,1,1]=>90
[2,8,4,1,5,6,3,7]=>[5,2,1]=>64
[4,1,8,3,5,6,2,7]=>[5,2,1]=>64
[5,6,8,4,1,3,2,7]=>[3,3,1,1]=>56
[4,6,8,1,5,3,2,7]=>[3,3,1,1]=>56
[1,6,8,4,5,3,2,7]=>[4,2,1,1]=>90
[1,7,3,8,5,4,6,2]=>[4,2,1,1]=>90
[3,7,1,8,5,4,6,2]=>[3,3,1,1]=>56
[2,7,3,8,4,6,5,1]=>[4,2,1,1]=>90
[7,1,3,8,4,6,5,2]=>[4,2,1,1]=>90
[5,7,8,4,3,6,1,2]=>[3,2,2,1]=>70
[2,8,7,4,1,6,5,3]=>[3,2,1,1,1]=>64
[2,8,5,4,3,1,6,7]=>[4,1,1,1,1]=>35
[6,5,8,4,2,3,1,7]=>[3,2,1,1,1]=>64
[4,1,3,2,8,5,6,7]=>[5,2,1]=>64
[1,4,3,2,8,5,6,7]=>[5,2,1]=>64
[7,3,2,8,5,4,6,1]=>[3,2,2,1]=>70
[6,4,8,2,5,3,1,7]=>[3,2,2,1]=>70
[2,8,4,3,5,1,6,7]=>[5,1,1,1]=>35
[2,8,3,4,5,1,6,7]=>[6,1,1]=>21
[6,2,8,4,5,3,1,7]=>[4,2,1,1]=>90
[7,2,3,8,5,4,6,1]=>[4,2,1,1]=>90
[4,2,3,1,8,5,6,7]=>[5,2,1]=>64
[3,2,1,4,8,5,6,7]=>[5,2,1]=>64
[5,1,3,2,4,8,6,7]=>[5,2,1]=>64
[2,8,1,5,3,4,7,6]=>[4,3,1]=>70
[1,2,8,4,5,3,7,6]=>[5,2,1]=>64
[1,4,2,8,5,3,6,7]=>[5,2,1]=>64
[1,8,4,2,5,3,6,7]=>[5,2,1]=>64
[8,1,5,3,2,4,6,7]=>[5,1,1,1]=>35
[3,8,1,5,2,4,6,7]=>[5,2,1]=>64
[3,5,1,4,8,2,6,7]=>[4,3,1]=>70
[1,5,2,8,4,3,6,7]=>[5,2,1]=>64
[1,2,8,5,4,3,6,7]=>[5,1,1,1]=>35
[1,2,5,4,3,8,6,7]=>[5,2,1]=>64
[1,2,4,8,5,3,7,6]=>[5,2,1]=>64
[1,2,7,4,8,5,3,6]=>[5,2,1]=>64
[1,5,2,7,8,4,3,6]=>[4,3,1]=>70
[5,1,2,7,4,8,3,6]=>[4,3,1]=>70
[8,3,5,1,4,7,2,6]=>[3,3,1,1]=>56
[2,8,1,5,4,7,3,6]=>[3,3,1,1]=>56
[1,2,8,5,7,4,3,6]=>[4,2,1,1]=>90
[1,2,4,8,7,5,3,6]=>[5,1,1,1]=>35
[2,8,1,4,3,7,6,5]=>[3,3,1,1]=>56
[6,1,2,8,7,4,3,5]=>[4,2,1,1]=>90
[6,4,1,2,8,7,3,5]=>[4,2,2]=>56
[3,6,4,8,1,7,2,5]=>[3,3,2]=>42
[7,6,1,4,2,8,3,5]=>[4,2,1,1]=>90
[7,1,6,2,8,4,3,5]=>[4,2,1,1]=>90
[1,6,7,2,8,4,3,5]=>[4,3,1]=>70
[6,7,1,4,2,8,3,5]=>[4,3,1]=>70
[6,3,7,1,4,8,2,5]=>[3,3,2]=>42
[3,7,8,1,5,2,4,6]=>[4,3,1]=>70
[7,1,2,8,5,3,4,6]=>[5,2,1]=>64
[1,7,2,8,4,5,3,6]=>[5,2,1]=>64
[1,4,2,7,8,5,3,6]=>[4,3,1]=>70
[6,1,2,8,4,3,7,5]=>[4,2,2]=>56
[6,4,1,2,8,3,7,5]=>[4,2,2]=>56
[7,6,1,3,2,4,8,5]=>[4,2,1,1]=>90
[6,7,1,3,2,4,8,5]=>[4,3,1]=>70
[1,2,7,3,5,8,4,6]=>[5,2,1]=>64
[1,2,7,5,8,3,4,6]=>[5,2,1]=>64
[5,8,1,3,7,2,4,6]=>[4,2,2]=>56
[1,2,5,8,7,3,4,6]=>[5,2,1]=>64
[1,2,5,8,3,7,4,6]=>[5,2,1]=>64
[2,8,1,7,3,5,4,6]=>[4,2,1,1]=>90
[8,6,1,3,2,4,7,5]=>[4,2,1,1]=>90
[4,2,8,1,7,3,6,5]=>[3,2,2,1]=>70
[2,8,1,7,4,3,6,5]=>[3,3,1,1]=>56
[7,1,2,8,4,3,6,5]=>[4,2,2]=>56
[1,2,8,4,7,5,3,6]=>[5,1,1,1]=>35
[1,2,8,7,4,5,3,6]=>[5,1,1,1]=>35
[2,8,1,7,5,3,4,6]=>[4,2,1,1]=>90
[8,3,7,1,5,2,4,6]=>[4,2,1,1]=>90
[3,8,6,1,4,7,2,5]=>[3,3,1,1]=>56
[8,6,1,4,2,7,3,5]=>[4,2,1,1]=>90
[8,1,6,2,7,4,3,5]=>[4,2,1,1]=>90
[7,1,2,8,6,4,3,5]=>[4,2,1,1]=>90
[7,4,1,2,8,6,3,5]=>[4,2,2]=>56
[3,7,4,8,1,6,2,5]=>[3,3,2]=>42
[3,4,8,7,1,6,2,5]=>[3,3,1,1]=>56
[4,2,8,1,7,6,3,5]=>[3,2,2,1]=>70
[2,8,1,7,6,4,3,5]=>[3,2,1,1,1]=>64
[7,8,3,4,1,6,2,5]=>[3,3,2]=>42
[6,7,3,4,1,8,2,5]=>[3,3,2]=>42
[5,8,3,4,1,7,2,6]=>[3,3,2]=>42
[6,7,3,4,1,5,2,8]=>[4,2,2]=>56
[5,7,3,4,1,6,2,8]=>[4,2,2]=>56
[5,6,2,7,3,4,1,8]=>[4,3,1]=>70
[4,6,2,8,3,5,1,7]=>[4,3,1]=>70
[4,8,3,5,1,6,2,7]=>[4,2,2]=>56
[5,6,2,4,1,7,3,8]=>[4,2,2]=>56
[4,5,1,7,3,8,2,6]=>[4,3,1]=>70
[4,6,2,7,3,8,1,5]=>[4,3,1]=>70
[5,6,2,7,3,8,1,4]=>[4,3,1]=>70
[5,6,2,7,4,8,1,3]=>[4,2,2]=>56
[4,6,2,8,3,7,1,5]=>[3,3,2]=>42
[9,2,1,3,4,5,6,7,8]=>[7,1,1]=>28
[10,2,1,3,4,5,6,7,8,9]=>[8,1,1]=>36
[9,2,3,1,4,5,6,7,8]=>[7,1,1]=>28
[4,2,3,5,6,7,8,9,1]=>[7,1,1]=>28
[3,4,2,5,6,7,8,9,1]=>[7,1,1]=>28
[3,2,4,5,6,7,8,9,10,1]=>[8,1,1]=>36
[2,3,4,5,6,7,8,9,10,11,1]=>[10,1]=>10
[6,5,3,2,1,4,8,7]=>[3,2,1,1,1]=>64
[4,6,3,5,2,1,8,7]=>[3,3,1,1]=>56
[8,7,3,5,2,4,1,6]=>[3,2,1,1,1]=>64
[6,8,2,4,5,7,3,1]=>[4,2,1,1]=>90
[8,7,2,4,5,3,1,6]=>[4,1,1,1,1]=>35
[3,6,1,4,5,2,8,7]=>[4,3,1]=>70
[8,3,7,4,5,2,1,6]=>[4,1,1,1,1]=>35
[6,3,8,4,5,7,2,1]=>[4,2,1,1]=>90
[5,8,7,4,3,6,2,1]=>[2,2,1,1,1,1]=>20
[2,8,7,4,3,6,1,5]=>[3,2,1,1,1]=>64
[8,1,7,4,3,6,2,5]=>[3,2,1,1,1]=>64
[8,7,3,5,1,4,2,6]=>[3,2,1,1,1]=>64
[2,1,6,8,5,7,4,3]=>[3,3,1,1]=>56
[6,8,3,5,1,7,4,2]=>[3,2,2,1]=>70
[5,1,8,4,7,6,3,2]=>[3,2,1,1,1]=>64
[2,5,8,4,7,6,3,1]=>[3,2,1,1,1]=>64
[4,3,8,1,5,6,7,2]=>[4,2,2]=>56
[4,8,1,3,5,6,7,2]=>[5,2,1]=>64
[5,8,7,4,1,6,3,2]=>[2,2,2,1,1]=>28
[5,8,3,6,1,4,7,2]=>[3,2,2,1]=>70
[4,8,3,6,1,2,7,5]=>[3,3,2]=>42
[3,8,7,4,1,6,2,5]=>[3,3,1,1]=>56
[3,8,1,2,5,6,7,4]=>[5,2,1]=>64
[8,7,1,4,2,6,3,5]=>[4,2,1,1]=>90
[8,6,3,1,2,4,7,5]=>[4,2,1,1]=>90
[8,1,7,4,5,2,3,6]=>[4,2,1,1]=>90
[2,8,7,4,5,1,3,6]=>[4,2,1,1]=>90
[8,7,2,4,1,6,3,5]=>[3,3,1,1]=>56
[5,8,3,6,2,4,7,1]=>[3,2,2,1]=>70
[8,6,3,2,1,4,7,5]=>[3,2,1,1,1]=>64
[8,7,3,5,2,1,4,6]=>[3,2,1,1,1]=>64
[5,8,3,6,2,1,7,4]=>[3,2,2,1]=>70
[5,8,7,4,2,6,1,3]=>[2,2,2,1,1]=>28
[2,6,8,4,5,7,1,3]=>[4,2,2]=>56
[6,1,8,4,5,7,2,3]=>[4,2,2]=>56
[6,8,3,5,1,7,2,4]=>[3,3,2]=>42
[2,1,5,8,3,6,7,4]=>[4,3,1]=>70
[5,8,3,6,1,2,7,4]=>[3,3,2]=>42
[4,1,8,2,5,6,7,3]=>[5,2,1]=>64
[2,4,8,1,5,6,7,3]=>[5,2,1]=>64
[4,8,2,1,5,6,7,3]=>[4,2,2]=>56
[3,4,8,2,5,6,7,1]=>[5,2,1]=>64
[5,8,1,4,7,6,2,3]=>[3,2,2,1]=>70
[5,8,3,1,6,2,7,4]=>[3,3,2]=>42
[4,5,3,8,6,1,7,2]=>[4,2,2]=>56
[3,4,1,8,5,6,7,2]=>[5,2,1]=>64
[2,4,6,8,10,1,3,5,7,9]=>[5,5]=>42
[2,7,8,9,10,1,3,4,5,6]=>[5,5]=>42
[5,6,7,8,10,1,2,3,4,9]=>[5,5]=>42
[2,4,6,8,10,12,1,3,5,7,9,11]=>[6,6]=>132
[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,6]=>132
[4,5,7,6,2,3,8,1]=>[4,2,1,1]=>90
[3,5,7,2,6,4,8,1]=>[4,2,1,1]=>90
[8,4,3,7,6,1,5,2]=>[2,2,2,1,1]=>28
[8,2,4,7,1,6,5,3]=>[3,2,1,1,1]=>64
[6,7,1,3,5,8,4,2]=>[4,2,1,1]=>90
[4,8,3,7,6,1,5,2]=>[2,2,2,1,1]=>28
[3,8,4,7,6,1,5,2]=>[3,2,1,1,1]=>64
[2,8,4,7,1,6,5,3]=>[3,2,1,1,1]=>64
[8,1,4,7,2,6,5,3]=>[3,2,1,1,1]=>64
[8,1,3,2,7,6,5,4]=>[3,2,1,1,1]=>64
[3,8,2,1,7,6,5,4]=>[2,2,2,1,1]=>28
[6,7,1,2,8,5,4,3]=>[3,3,1,1]=>56
[8,3,2,1,7,6,5,4]=>[2,2,2,1,1]=>28
[1,4,2,7,8,6,5,3]=>[4,2,1,1]=>90
[8,4,2,7,1,6,5,3]=>[2,2,2,1,1]=>28
[8,5,7,2,1,6,4,3]=>[2,2,2,1,1]=>28
[1,5,7,2,8,6,4,3]=>[4,2,1,1]=>90
[5,4,7,6,8,1,3,2]=>[3,2,2,1]=>70
[1,4,8,7,2,6,5,3]=>[3,2,1,1,1]=>64
[4,3,8,7,6,1,5,2]=>[2,2,2,1,1]=>28
[6,7,2,8,1,5,4,3]=>[3,2,2,1]=>70
[5,2,7,8,1,6,4,3]=>[3,2,2,1]=>70
[4,2,8,7,1,6,5,3]=>[2,2,2,1,1]=>28
[3,2,8,1,7,6,5,4]=>[2,2,2,1,1]=>28
[1,3,8,2,7,6,5,4]=>[3,2,1,1,1]=>64
[2,1,8,3,7,6,5,4]=>[3,2,1,1,1]=>64
[5,1,7,8,2,6,4,3]=>[3,3,1,1]=>56
[4,8,1,7,2,6,5,3]=>[3,2,1,1,1]=>64
[3,8,1,2,7,6,5,4]=>[3,2,1,1,1]=>64
[8,1,2,3,7,6,5,4]=>[4,1,1,1,1]=>35
[3,1,4,5,6,7,8,9,10,2]=>[8,2]=>35
[2,3,4,5,6,7,8,9,11,1,10]=>[9,2]=>44
[10,3,4,5,6,7,8,1,2,9]=>[7,2,1]=>160
[10,1,4,5,6,7,8,9,2,3]=>[7,2,1]=>160
[3,1,4,5,6,7,8,9,10,11,2]=>[9,2]=>44
[2,3,4,5,6,7,8,9,10,12,1,11]=>[10,2]=>54
[11,3,4,5,6,7,8,9,1,2,10]=>[8,2,1]=>231
[2,10,4,5,6,7,8,1,3,9]=>[7,2,1]=>160
[8,3,4,5,6,7,1,10,2,9]=>[6,3,1]=>315
[3,1,10,5,6,7,8,9,2,4]=>[6,3,1]=>315
[9,1,4,5,6,7,8,2,10,3]=>[7,2,1]=>160
[11,1,4,5,6,7,8,9,10,2,3]=>[8,2,1]=>231
[3,1,4,5,6,7,8,9,10,11,12,2]=>[10,2]=>54
[6,7,1,8,4,5,2,3]=>[3,3,2]=>42
[3,7,1,5,8,2,6,4]=>[3,3,2]=>42
[2,7,1,5,8,3,6,4]=>[3,3,2]=>42
[2,6,5,1,8,3,7,4]=>[3,3,2]=>42
[3,6,5,1,8,2,7,4]=>[3,3,2]=>42
[4,6,5,1,8,7,2,3]=>[3,3,2]=>42
[5,6,4,1,8,7,2,3]=>[3,3,2]=>42
[8,1,4,5,7,6,2,3]=>[4,2,1,1]=>90
[6,4,5,1,8,7,2,3]=>[3,3,2]=>42
[5,4,6,1,8,7,2,3]=>[3,3,2]=>42
[4,5,6,1,8,7,2,3]=>[4,3,1]=>70
[3,5,6,1,8,2,7,4]=>[4,3,1]=>70
[2,5,6,1,8,3,7,4]=>[4,3,1]=>70
[2,4,6,1,3,8,7,5]=>[4,3,1]=>70
[3,4,6,1,2,8,7,5]=>[4,3,1]=>70
[4,3,6,1,2,8,7,5]=>[3,3,2]=>42
[5,3,6,1,8,2,7,4]=>[3,3,2]=>42
[7,3,1,5,8,2,6,4]=>[3,3,2]=>42
[8,1,3,5,7,2,6,4]=>[4,2,1,1]=>90
[8,1,2,5,7,3,6,4]=>[4,2,1,1]=>90
[7,2,1,5,8,3,6,4]=>[3,3,2]=>42
[6,2,5,1,8,3,7,4]=>[3,3,2]=>42
[4,2,6,1,3,8,7,5]=>[3,3,2]=>42
[2,3,6,1,4,8,7,5]=>[4,3,1]=>70
[4,2,5,3,1,8,7,6]=>[3,3,2]=>42
[6,2,4,1,3,8,7,5]=>[3,3,2]=>42
[7,2,1,4,3,8,6,5]=>[3,3,2]=>42
[8,1,2,4,3,7,6,5]=>[4,2,1,1]=>90
[8,1,3,4,2,7,6,5]=>[4,2,1,1]=>90
[7,3,1,4,2,8,6,5]=>[3,3,2]=>42
[6,3,4,1,2,8,7,5]=>[3,3,2]=>42
[4,6,3,1,2,8,7,5]=>[3,3,2]=>42
[3,6,4,1,2,8,7,5]=>[3,3,2]=>42
[2,6,4,1,3,8,7,5]=>[3,3,2]=>42
[2,7,1,4,3,8,6,5]=>[3,3,2]=>42
[3,7,1,4,2,8,6,5]=>[3,3,2]=>42
[4,7,1,3,2,8,6,5]=>[3,3,2]=>42
[8,1,6,7,2,3,5,4]=>[4,2,1,1]=>90
[4,7,1,2,3,8,6,5]=>[4,3,1]=>70
[3,7,1,2,4,8,6,5]=>[4,3,1]=>70
[2,7,1,3,4,8,6,5]=>[4,3,1]=>70
[2,6,3,1,4,8,7,5]=>[4,2,2]=>56
[3,6,2,1,4,8,7,5]=>[3,3,2]=>42
[5,6,2,1,8,3,7,4]=>[3,3,2]=>42
[6,5,2,1,8,3,7,4]=>[3,2,2,1]=>70
[8,1,5,2,7,3,6,4]=>[4,2,1,1]=>90
[8,1,4,2,3,7,6,5]=>[4,2,1,1]=>90
[7,4,1,2,3,8,6,5]=>[4,2,2]=>56
[6,4,2,1,3,8,7,5]=>[3,2,2,1]=>70
[5,4,2,3,1,8,7,6]=>[3,2,2,1]=>70
[3,5,2,4,1,8,7,6]=>[3,3,2]=>42
[6,3,2,1,4,8,7,5]=>[3,2,2,1]=>70
[7,3,1,2,4,8,6,5]=>[4,2,2]=>56
[8,1,3,2,4,7,6,5]=>[4,2,1,1]=>90
[8,1,2,3,4,7,6,5]=>[5,1,1,1]=>35
[7,2,1,3,4,8,6,5]=>[4,2,2]=>56
[6,2,3,1,4,8,7,5]=>[4,2,2]=>56
[2,4,3,6,1,5,8,7]=>[4,3,1]=>70
[2,4,3,6,5,8,1,7]=>[4,3,1]=>70
[2,4,6,3,5,8,7,1]=>[4,3,1]=>70
[2,4,6,3,5,8,1,7]=>[4,3,1]=>70
[2,4,6,1,5,3,8,7]=>[4,3,1]=>70
[4,2,6,5,3,1,8,7]=>[3,3,1,1]=>56
[4,2,6,5,1,8,7,3]=>[3,3,2]=>42
[4,2,6,5,8,1,7,3]=>[3,3,2]=>42
[4,2,6,5,8,3,1,7]=>[3,3,1,1]=>56
[2,4,6,1,5,8,3,7]=>[4,3,1]=>70
[2,1,4,6,5,8,3,7]=>[4,3,1]=>70
[2,4,1,6,5,8,7,3]=>[4,3,1]=>70
[2,4,6,1,5,8,7,3]=>[4,3,1]=>70
[2,6,4,3,8,7,5,1]=>[3,2,2,1]=>70
[2,4,6,8,1,5,7,3]=>[4,3,1]=>70
[2,4,6,1,8,5,7,3]=>[4,3,1]=>70
[2,4,1,6,8,5,7,3]=>[4,3,1]=>70
[2,1,4,6,8,5,7,3]=>[4,3,1]=>70
[2,1,4,6,8,5,3,7]=>[4,3,1]=>70
[2,4,6,1,8,5,3,7]=>[4,3,1]=>70
[2,4,6,8,1,5,3,7]=>[4,3,1]=>70
[2,4,6,8,3,5,7,1]=>[4,3,1]=>70
[2,4,6,8,3,5,1,7]=>[4,3,1]=>70
[2,4,6,8,3,1,5,7]=>[4,3,1]=>70
[2,4,6,3,1,8,5,7]=>[4,3,1]=>70
[2,4,6,3,8,1,5,7]=>[4,3,1]=>70
[2,4,6,3,8,5,1,7]=>[4,3,1]=>70
[2,4,6,3,8,5,7,1]=>[4,3,1]=>70
[2,4,3,6,8,5,7,1]=>[4,3,1]=>70
[2,4,3,6,8,5,1,7]=>[4,3,1]=>70
[2,4,3,6,8,1,5,7]=>[4,3,1]=>70
[2,4,3,1,6,8,5,7]=>[4,3,1]=>70
[2,4,1,3,6,8,7,5]=>[4,3,1]=>70
[2,4,3,6,1,8,7,5]=>[4,2,2]=>56
[2,4,3,6,8,1,7,5]=>[4,2,2]=>56
[2,4,6,3,8,1,7,5]=>[4,2,2]=>56
[2,1,4,6,8,3,7,5]=>[4,3,1]=>70
[2,4,1,6,8,3,7,5]=>[4,3,1]=>70
[2,4,6,1,8,3,7,5]=>[4,3,1]=>70
[2,4,6,8,1,3,7,5]=>[4,3,1]=>70
[2,4,6,8,3,1,7,5]=>[4,2,2]=>56
[4,6,2,8,5,7,1,3]=>[3,3,2]=>42
[6,2,4,8,7,1,3,5]=>[3,3,2]=>42
[6,4,2,8,7,5,3,1]=>[2,2,2,1,1]=>28
[2,6,4,8,1,7,5,3]=>[3,2,2,1]=>70
[2,1,6,4,8,7,5,3]=>[3,3,1,1]=>56
[2,6,1,4,8,7,3,5]=>[3,3,2]=>42
[6,4,2,8,7,5,1,3]=>[2,2,2,2]=>14
[1,6,4,7,3,8,2,5]=>[4,2,1,1]=>90
[1,3,7,4,5,8,2,6]=>[5,2,1]=>64
[5,2,4,7,3,6,8,1]=>[4,2,1,1]=>90
[1,7,6,3,4,8,2,5]=>[4,2,1,1]=>90
[8,1,6,3,7,2,4,5]=>[4,2,1,1]=>90
[7,1,6,3,8,2,4,5]=>[4,2,1,1]=>90
[1,2,7,4,8,3,5,6]=>[5,2,1]=>64
[6,1,7,3,4,8,2,5]=>[4,3,1]=>70
[2,1,7,4,5,8,3,6]=>[4,3,1]=>70
[5,1,4,7,3,8,2,6]=>[4,2,1,1]=>90
[4,3,1,7,5,8,2,6]=>[3,3,2]=>42
[2,8,6,3,7,1,4,5]=>[4,2,1,1]=>90
[6,8,1,3,7,2,4,5]=>[4,2,2]=>56
[5,8,2,1,7,3,4,6]=>[4,2,2]=>56
[5,7,2,1,8,3,4,6]=>[4,3,1]=>70
[6,7,1,3,8,2,4,5]=>[4,3,1]=>70
[5,1,2,4,8,3,6,7]=>[5,2,1]=>64
[4,3,6,1,5,8,2,7]=>[3,3,2]=>42
[2,6,1,4,5,8,3,7]=>[4,3,1]=>70
[6,5,1,3,4,8,2,7]=>[4,2,1,1]=>90
[1,6,2,4,8,3,5,7]=>[5,2,1]=>64
[8,5,1,3,7,2,4,6]=>[4,2,1,1]=>90
[1,5,3,2,8,4,6,7]=>[5,2,1]=>64
[6,4,2,1,5,8,3,7]=>[3,3,1,1]=>56
[2,5,3,4,1,8,6,7]=>[5,2,1]=>64
[4,3,5,2,1,8,6,7]=>[4,2,1,1]=>90
[2,6,4,8,7,1,3,5]=>[3,3,2]=>42
[1,6,4,8,7,2,3,5]=>[4,2,2]=>56
[2,7,8,3,6,1,4,5]=>[4,2,2]=>56
[4,3,2,8,7,1,5,6]=>[3,2,2,1]=>70
[5,2,4,8,7,1,3,6]=>[3,3,2]=>42
[6,2,8,3,7,1,4,5]=>[4,2,2]=>56
[5,1,4,8,7,2,3,6]=>[4,2,2]=>56
[4,8,2,5,1,3,7,6]=>[3,3,2]=>42
[4,7,2,5,1,3,8,6]=>[3,3,2]=>42
[3,7,2,1,5,4,8,6]=>[3,3,2]=>42
[3,8,2,1,5,4,7,6]=>[3,3,2]=>42
[8,3,2,1,5,4,6,7]=>[4,2,1,1]=>90
[8,3,2,1,6,4,5,7]=>[4,2,1,1]=>90
[8,4,2,5,1,6,3,7]=>[4,2,1,1]=>90
[8,3,2,1,5,6,4,7]=>[4,2,1,1]=>90
[8,3,2,1,4,6,5,7]=>[4,2,1,1]=>90
[3,8,2,1,4,5,7,6]=>[4,2,2]=>56
[3,7,2,1,4,5,8,6]=>[4,3,1]=>70
[3,2,7,1,4,6,8,5]=>[4,2,2]=>56
[3,2,8,1,4,6,7,5]=>[4,2,2]=>56
[3,2,8,1,4,7,6,5]=>[3,2,2,1]=>70
[3,8,2,1,4,7,5,6]=>[4,2,2]=>56
[3,8,2,1,5,7,4,6]=>[3,3,2]=>42
[4,8,2,5,1,7,3,6]=>[3,3,2]=>42
[4,7,2,5,1,8,3,6]=>[3,3,2]=>42
[3,7,2,1,5,8,4,6]=>[3,3,2]=>42
[3,7,2,1,4,8,5,6]=>[4,3,1]=>70
[3,2,1,7,5,8,6,4]=>[3,3,2]=>42
[3,2,7,1,6,8,4,5]=>[3,3,2]=>42
[4,2,7,6,1,8,3,5]=>[3,3,2]=>42
[4,3,7,6,8,1,2,5]=>[3,3,2]=>42
[4,3,8,6,7,1,2,5]=>[3,3,2]=>42
[4,2,8,6,1,7,3,5]=>[3,3,2]=>42
[3,2,8,1,6,7,4,5]=>[3,3,2]=>42
[3,2,1,8,7,5,6,4]=>[3,2,2,1]=>70
[3,8,2,1,7,4,5,6]=>[4,2,2]=>56
[3,2,8,1,7,4,6,5]=>[3,2,2,1]=>70
[3,2,8,1,6,4,7,5]=>[3,3,2]=>42
[3,2,7,1,6,4,8,5]=>[3,3,2]=>42
[4,2,7,6,1,3,8,5]=>[3,3,2]=>42
[4,2,8,6,1,3,7,5]=>[3,3,2]=>42
[4,2,8,7,1,3,6,5]=>[3,2,2,1]=>70
[5,7,8,3,4,1,2,6]=>[3,3,2]=>42
[4,2,7,8,1,3,6,5]=>[3,3,2]=>42
[4,2,6,8,1,3,7,5]=>[3,3,2]=>42
[4,2,6,7,1,3,8,5]=>[4,3,1]=>70
[3,2,6,1,8,4,7,5]=>[3,3,2]=>42
[3,7,2,1,8,4,5,6]=>[4,3,1]=>70
[3,7,2,1,8,5,4,6]=>[3,3,2]=>42
[4,7,3,8,5,1,2,6]=>[3,3,2]=>42
[4,3,7,8,6,1,2,5]=>[3,3,2]=>42
[3,2,7,1,8,6,4,5]=>[3,3,2]=>42
[3,2,1,6,8,5,7,4]=>[3,3,2]=>42
[3,2,6,1,8,7,4,5]=>[3,3,2]=>42
[4,2,6,8,1,7,3,5]=>[3,3,2]=>42
[4,3,6,8,7,1,2,5]=>[3,3,2]=>42
[4,2,6,7,1,8,3,5]=>[4,3,1]=>70
[3,2,6,1,7,8,4,5]=>[4,3,1]=>70
[5,3,6,4,8,7,1,2]=>[3,3,2]=>42
[1,4,6,2,7,8,5,3]=>[5,2,1]=>64
[7,3,8,5,4,6,1,2]=>[3,2,2,1]=>70
[3,8,7,5,4,6,1,2]=>[3,2,1,1,1]=>64
[6,8,3,5,4,7,1,2]=>[3,2,2,1]=>70
[1,6,2,5,4,8,7,3]=>[4,2,1,1]=>90
[4,1,6,2,8,7,5,3]=>[3,3,1,1]=>56
[7,8,1,2,4,6,5,3]=>[4,2,1,1]=>90
[4,3,6,1,8,2,7,5]=>[3,3,2]=>42
[2,3,8,5,4,1,6,7]=>[5,1,1,1]=>35
[4,8,1,5,2,3,7,6]=>[4,3,1]=>70
[7,8,4,1,5,3,2,6]=>[3,2,2,1]=>70
[7,8,5,1,6,3,2,4]=>[3,2,2,1]=>70
[5,1,7,6,4,3,2,8]=>[3,2,1,1,1]=>64
[6,1,7,8,4,3,2,5]=>[3,3,1,1]=>56
[7,1,8,6,4,3,2,5]=>[3,2,1,1,1]=>64
[1,8,7,6,4,3,2,5]=>[3,1,1,1,1,1]=>21
[3,1,6,7,5,8,2,4]=>[4,3,1]=>70
[7,8,2,1,4,5,6,3]=>[4,2,2]=>56
[6,1,2,5,7,3,8,4]=>[5,2,1]=>64
[4,2,1,5,6,3,7,8]=>[5,2,1]=>64
[4,3,6,1,5,7,2,8]=>[4,2,2]=>56
[1,3,6,8,5,7,2,4]=>[4,2,2]=>56
[6,4,1,5,2,3,7,8]=>[5,2,1]=>64
[4,1,7,5,2,3,8,6]=>[4,3,1]=>70
[4,2,6,3,8,1,7,5]=>[3,3,2]=>42
[7,8,2,3,4,1,6,5]=>[4,2,2]=>56
[3,1,6,4,7,8,2,5]=>[4,3,1]=>70
[1,8,5,7,4,3,2,6]=>[3,2,1,1,1]=>64
[7,1,5,8,4,3,2,6]=>[3,2,1,1,1]=>64
[5,1,8,7,4,3,2,6]=>[3,2,1,1,1]=>64
[6,5,7,1,4,3,2,8]=>[3,2,1,1,1]=>64
[7,5,8,1,4,3,2,6]=>[3,2,1,1,1]=>64
[5,8,7,1,4,3,2,6]=>[3,2,1,1,1]=>64
[7,8,5,4,1,3,2,6]=>[3,2,1,1,1]=>64
[3,5,6,4,1,8,2,7]=>[4,3,1]=>70
[6,8,5,1,4,3,2,7]=>[3,2,1,1,1]=>64
[7,6,5,1,4,3,2,8]=>[3,1,1,1,1,1]=>21
[1,2,3,4,5,6,9,7,8]=>[8,1]=>8
[1,2,3,4,5,8,6,9,7]=>[7,2]=>27
[1,2,3,4,7,5,8,9,6]=>[7,2]=>27
[1,2,3,6,4,7,8,9,5]=>[7,2]=>27
[1,2,5,3,6,7,8,9,4]=>[7,2]=>27
[1,4,2,5,6,7,8,9,3]=>[7,2]=>27
[9,8,1,2,3,4,5,6,7]=>[7,1,1]=>28
[7,8,9,1,2,3,4,5,6]=>[6,3]=>48
[6,7,8,9,1,2,3,4,5]=>[5,4]=>42
[9,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,1]=>8
[9,10,1,2,3,4,5,6,7,8]=>[8,2]=>35
[8,9,10,1,2,3,4,5,6,7]=>[7,3]=>75
[10,9,8,1,2,3,4,5,6,7]=>[7,1,1,1]=>84
[7,8,9,10,1,2,3,4,5,6]=>[6,4]=>90
[10,9,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,1,1]=>9
[3,4,6,2,7,1,5,8]=>[5,2,1]=>64
[3,2,7,5,4,1,6,8]=>[4,2,1,1]=>90
[4,3,6,2,8,1,5,7]=>[3,3,1,1]=>56
[6,1,2,5,4,7,8,3]=>[5,1,1,1]=>35
[1,4,6,3,7,5,8,2]=>[5,2,1]=>64
[4,6,7,2,5,8,1,3]=>[4,2,2]=>56
[2,4,6,1,7,5,3,8]=>[5,2,1]=>64
[7,5,4,6,2,8,1,3]=>[3,2,1,1,1]=>64
[1,4,6,3,5,8,7,2]=>[4,3,1]=>70
[5,6,3,2,7,1,4,8]=>[4,2,1,1]=>90
[5,6,3,2,7,1,8,4]=>[4,2,1,1]=>90
[2,4,1,7,8,5,3,6]=>[4,3,1]=>70
[2,5,4,1,6,3,8,7]=>[4,3,1]=>70
[3,5,2,1,6,4,7,8]=>[5,2,1]=>64
[6,8,4,3,2,1,5,7]=>[3,2,1,1,1]=>64
[5,3,8,2,1,6,4,7]=>[3,2,2,1]=>70
[3,7,5,8,2,1,4,6]=>[3,3,1,1]=>56
[8,6,4,3,2,1,7,5]=>[2,2,1,1,1,1]=>20
[6,3,7,2,5,1,8,4]=>[3,2,2,1]=>70
[3,6,7,2,8,1,4,5]=>[4,3,1]=>70
[6,3,7,2,8,1,4,5]=>[3,3,1,1]=>56
[3,5,2,1,4,7,6,8]=>[4,3,1]=>70
[7,3,5,2,1,8,4,6]=>[3,3,1,1]=>56
[2,5,4,1,3,7,8,6]=>[4,3,1]=>70
[3,7,2,8,6,1,4,5]=>[3,3,2]=>42
[5,3,8,2,1,4,7,6]=>[3,2,2,1]=>70
[4,8,7,3,2,1,5,6]=>[3,2,1,1,1]=>64
[8,4,7,3,2,1,5,6]=>[3,2,1,1,1]=>64
[8,3,5,2,1,4,7,6]=>[3,3,1,1]=>56
[7,3,2,8,6,1,4,5]=>[3,2,2,1]=>70
[7,8,6,5,4,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[8,9,7,6,5,4,3,2,1,10]=>[3,1,1,1,1,1,1,1]=>36
[7,6,8,5,4,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[7,8,3,5,4,6,1,2]=>[3,2,2,1]=>70
[8,6,3,7,5,2,4,1]=>[2,2,2,1,1]=>28
[5,4,1,6,3,2,8,7]=>[3,3,1,1]=>56
[5,4,1,6,2,3,8,7]=>[4,3,1]=>70
[5,7,1,6,2,8,3,4]=>[4,3,1]=>70
[5,7,1,6,2,8,4,3]=>[3,3,1,1]=>56
[2,7,6,5,1,8,3,4]=>[3,3,1,1]=>56
[2,7,6,5,1,8,4,3]=>[3,2,1,1,1]=>64
[2,3,6,5,1,4,8,7]=>[4,3,1]=>70
[2,3,6,4,1,5,8,7]=>[5,2,1]=>64
[2,3,6,1,5,4,8,7]=>[4,3,1]=>70
[2,7,6,1,4,8,5,3]=>[3,3,1,1]=>56
[2,7,6,1,4,8,3,5]=>[3,3,1,1]=>56
[7,3,5,1,8,4,2,6]=>[3,3,1,1]=>56
[7,3,5,1,8,6,4,2]=>[3,2,2,1]=>70
[2,7,6,1,5,8,4,3]=>[3,2,1,1,1]=>64
[2,7,6,4,1,8,5,3]=>[3,2,2,1]=>70
[2,1,7,6,3,8,5,4]=>[3,3,1,1]=>56
[2,1,7,6,3,8,4,5]=>[4,3,1]=>70
[5,7,3,6,2,8,4,1]=>[3,2,2,1]=>70
[2,7,6,4,1,8,3,5]=>[3,3,1,1]=>56
[7,3,5,1,8,6,2,4]=>[3,3,2]=>42
[6,3,5,1,8,2,4,7]=>[4,3,1]=>70
[2,3,4,8,7,6,1,5]=>[4,2,1,1]=>90
[2,3,4,8,5,7,1,6]=>[5,2,1]=>64
[7,3,5,4,8,1,2,6]=>[3,3,1,1]=>56
[6,4,3,5,8,7,2,1]=>[3,2,1,1,1]=>64
[2,1,4,5,8,7,3,6]=>[4,3,1]=>70
[6,4,3,5,8,7,1,2]=>[3,2,2,1]=>70
[7,3,5,4,8,1,6,2]=>[3,2,2,1]=>70
[2,3,4,8,7,5,6,1]=>[5,1,1,1]=>35
[2,3,4,8,7,5,1,6]=>[5,1,1,1]=>35
[2,7,6,5,4,8,1,3]=>[3,2,1,1,1]=>64
[7,3,5,6,8,4,1,2]=>[4,2,1,1]=>90
[7,3,5,6,8,1,4,2]=>[4,2,1,1]=>90
[7,3,5,6,8,1,2,4]=>[4,3,1]=>70
[6,4,1,5,8,7,2,3]=>[3,3,2]=>42
[6,4,1,5,8,7,3,2]=>[3,2,2,1]=>70
[6,4,1,5,8,3,7,2]=>[3,3,1,1]=>56
[5,7,1,6,3,8,2,4]=>[3,3,1,1]=>56
[6,4,1,5,8,3,2,7]=>[3,3,1,1]=>56
[7,4,1,5,8,2,3,6]=>[4,3,1]=>70
[7,4,1,5,8,2,6,3]=>[3,3,2]=>42
[6,3,5,7,8,2,1,4]=>[4,2,1,1]=>90
[6,3,5,7,8,2,4,1]=>[4,2,1,1]=>90
[2,7,6,4,5,8,3,1]=>[4,1,1,1,1]=>35
[5,7,3,6,1,8,4,2]=>[3,2,2,1]=>70
[2,1,4,5,8,6,3,7]=>[5,2,1]=>64
[7,3,5,4,8,6,2,1]=>[3,2,1,1,1]=>64
[2,3,4,8,5,6,1,7]=>[6,1,1]=>21
[2,3,4,8,7,1,6,5]=>[4,2,1,1]=>90
[2,3,4,8,1,7,6,5]=>[4,2,1,1]=>90
[2,3,4,8,1,6,7,5]=>[5,2,1]=>64
[2,3,4,8,5,1,7,6]=>[5,2,1]=>64
[6,3,5,4,8,2,7,1]=>[3,2,1,1,1]=>64
[7,4,3,5,8,2,1,6]=>[3,2,1,1,1]=>64
[2,1,4,5,8,3,7,6]=>[4,3,1]=>70
[7,4,3,5,8,2,6,1]=>[3,2,1,1,1]=>64
[6,3,5,4,8,2,1,7]=>[3,2,1,1,1]=>64
[2,3,4,8,5,1,6,7]=>[6,1,1]=>21
[2,3,4,8,1,6,5,7]=>[5,2,1]=>64
[2,3,4,8,1,5,7,6]=>[5,2,1]=>64
[7,8,2,6,1,5,3,4]=>[3,2,2,1]=>70
[1,8,6,7,2,5,3,4]=>[4,2,1,1]=>90
[5,8,1,7,2,6,3,4]=>[4,2,1,1]=>90
[2,8,1,7,5,6,3,4]=>[3,3,1,1]=>56
[1,8,2,7,5,6,3,4]=>[4,2,1,1]=>90
[1,8,2,7,4,6,3,5]=>[4,2,1,1]=>90
[2,8,4,7,1,6,3,5]=>[3,3,1,1]=>56
[4,8,2,7,1,6,3,5]=>[3,2,2,1]=>70
[4,8,1,7,2,6,3,5]=>[4,2,1,1]=>90
[1,8,4,7,2,6,3,5]=>[4,2,1,1]=>90
[1,8,3,7,5,6,2,4]=>[4,2,1,1]=>90
[3,8,1,7,4,6,2,5]=>[3,3,1,1]=>56
[3,8,2,7,5,6,1,4]=>[3,2,2,1]=>70
[3,8,4,7,5,6,1,2]=>[4,2,1,1]=>90
[2,8,4,7,5,6,1,3]=>[4,2,1,1]=>90
[2,8,3,7,5,6,1,4]=>[4,2,1,1]=>90
[2,8,3,7,1,6,4,5]=>[4,2,1,1]=>90
[2,8,1,7,3,6,4,5]=>[4,2,1,1]=>90
[7,5,2,8,6,4,1,3]=>[2,2,2,2]=>14
[7,5,1,8,6,2,3,4]=>[4,2,2]=>56
[1,6,7,4,2,8,5,3]=>[4,2,2]=>56
[1,6,7,3,8,5,2,4]=>[4,2,2]=>56
[7,1,8,3,5,6,2,4]=>[4,2,2]=>56
[7,3,8,6,2,5,1,4]=>[2,2,2,2]=>14
[7,4,2,8,6,1,3,5]=>[3,2,2,1]=>70
[7,3,1,8,4,2,5,6]=>[4,2,2]=>56
[1,5,7,8,2,6,3,4]=>[4,3,1]=>70
[2,6,3,7,8,5,4,1]=>[4,2,1,1]=>90
[2,6,3,7,8,4,5,1]=>[4,3,1]=>70
[2,5,3,7,8,1,6,4]=>[4,2,2]=>56
[3,1,5,4,7,8,2,6]=>[4,3,1]=>70
[5,3,1,4,8,2,6,7]=>[4,3,1]=>70
[5,2,4,8,6,1,3,7]=>[4,2,2]=>56
[5,2,3,8,4,6,7,1]=>[5,2,1]=>64
[4,8,1,3,6,7,2,5]=>[4,2,2]=>56
[6,4,2,8,1,3,7,5]=>[3,2,2,1]=>70
[6,3,8,1,4,7,2,5]=>[3,3,2]=>42
[5,8,1,3,6,2,7,4]=>[4,2,2]=>56
[1,5,7,4,2,6,8,3]=>[4,2,2]=>56
[6,5,1,2,8,7,3,4]=>[4,2,2]=>56
[6,5,3,1,4,2,8,7]=>[3,3,1,1]=>56
[5,3,1,6,4,2,7,8]=>[4,2,2]=>56
[3,4,5,8,2,7,1,6]=>[4,2,2]=>56
[3,4,6,2,8,1,5,7]=>[4,3,1]=>70
[3,5,2,6,8,1,7,4]=>[4,2,2]=>56
[4,2,5,6,1,3,8,7]=>[4,3,1]=>70
[5,3,6,8,4,7,2,1]=>[3,3,1,1]=>56
[3,7,2,5,4,8,6,1]=>[3,3,1,1]=>56
[3,1,6,5,4,8,2,7]=>[3,3,1,1]=>56
[4,1,6,5,8,3,2,7]=>[3,3,1,1]=>56
[5,1,6,8,4,3,2,7]=>[3,3,1,1]=>56
[8,5,4,7,6,3,2,1]=>[2,2,1,1,1,1]=>20
[2,7,1,5,4,3,8,6]=>[3,3,1,1]=>56
[8,2,1,5,4,3,7,6]=>[3,3,1,1]=>56
[8,4,1,5,7,3,2,6]=>[3,3,1,1]=>56
[8,3,6,1,4,7,2,5]=>[3,3,1,1]=>56
[2,7,6,1,4,3,8,5]=>[3,3,1,1]=>56
[6,7,8,5,1,3,2,4]=>[3,3,1,1]=>56
[6,7,8,2,4,3,5,1]=>[3,3,1,1]=>56
[3,7,6,2,4,8,5,1]=>[3,3,1,1]=>56
[5,7,3,8,4,6,2,1]=>[3,3,1,1]=>56
[4,7,3,5,8,6,2,1]=>[3,3,1,1]=>56
[8,7,2,1,4,3,6,5]=>[3,3,1,1]=>56
[8,7,3,1,4,6,2,5]=>[3,3,1,1]=>56
[8,7,6,3,2,5,4,1]=>[2,2,1,1,1,1]=>20
[8,7,3,5,1,6,2,4]=>[3,3,1,1]=>56
[8,4,6,5,7,1,2,3]=>[3,3,1,1]=>56
[3,7,6,5,1,8,2,4]=>[3,3,1,1]=>56
[8,1,2,3,4,5,6,7,9]=>[8,1]=>8
[1,9,2,3,4,5,6,7,8]=>[8,1]=>8
[9,1,2,3,4,5,6,7,8,10]=>[9,1]=>9
[7,8,1,2,3,4,5,6,9]=>[7,2]=>27
[1,8,9,2,3,4,5,6,7]=>[7,2]=>27
[1,10,2,3,4,5,6,7,8,9]=>[9,1]=>9
[10,1,2,3,4,5,6,7,8,9,11]=>[10,1]=>10
[8,9,1,2,3,4,5,6,7,10]=>[8,2]=>35
[7,1,8,2,3,4,5,6,9]=>[7,2]=>27
[6,8,1,2,3,4,5,7,9]=>[7,2]=>27
[1,8,2,9,3,4,5,6,7]=>[7,2]=>27
[1,7,9,2,3,4,5,6,8]=>[7,2]=>27
[1,9,10,2,3,4,5,6,7,8]=>[8,2]=>35
[1,11,2,3,4,5,6,7,8,9,10]=>[10,1]=>10
[3,6,4,8,7,5,1,2]=>[3,2,2,1]=>70
[5,6,4,3,8,7,1,2]=>[3,2,2,1]=>70
[1,6,2,4,7,8,5,3]=>[5,2,1]=>64
[3,6,2,4,8,1,5,7]=>[4,3,1]=>70
[3,4,7,2,8,1,6,5]=>[4,2,2]=>56
[7,3,8,4,5,6,1,2]=>[4,2,2]=>56
[3,5,6,4,8,7,1,2]=>[4,2,2]=>56
[4,6,8,5,3,7,1,2]=>[3,2,2,1]=>70
[1,6,5,4,2,8,7,3]=>[3,2,2,1]=>70
[1,8,5,2,7,3,6,4]=>[4,2,1,1]=>90
[6,5,1,3,4,2,8,7]=>[4,2,1,1]=>90
[7,4,5,3,2,8,1,6]=>[3,2,1,1,1]=>64
[1,6,8,7,4,2,3,5]=>[4,2,1,1]=>90
[7,1,8,6,3,4,2,5]=>[4,2,1,1]=>90
[7,2,1,4,5,6,8,3]=>[5,2,1]=>64
[1,2,8,3,6,5,7,4]=>[5,1,1,1]=>35
[6,1,3,2,7,5,8,4]=>[4,2,2]=>56
[1,6,3,8,5,7,2,4]=>[4,2,2]=>56
[7,6,5,8,1,4,2,3]=>[3,2,1,1,1]=>64
[5,8,6,7,3,2,1,4]=>[3,2,1,1,1]=>64
[1,6,4,3,7,2,8,5]=>[4,2,1,1]=>90
[1,8,3,5,4,2,7,6]=>[4,2,1,1]=>90
[2,8,5,7,4,3,1,6]=>[3,2,1,1,1]=>64
[5,3,8,7,1,2,6,4]=>[3,2,2,1]=>70
[6,5,3,8,2,1,7,4]=>[2,2,2,1,1]=>28
[3,5,7,8,4,1,2,6]=>[4,3,1]=>70
[7,8,4,6,3,1,2,5]=>[3,2,2,1]=>70
[6,8,5,4,3,1,2,7]=>[3,2,1,1,1]=>64
[6,1,4,2,8,5,7,3]=>[4,2,2]=>56
[4,8,6,5,3,2,7,1]=>[3,1,1,1,1,1]=>21
[8,6,5,1,2,4,7,3]=>[4,1,1,1,1]=>35
[6,7,5,8,2,1,4,3]=>[3,2,2,1]=>70
[1,7,5,8,2,6,4,3]=>[3,2,2,1]=>70
[1,3,8,5,7,6,2,4]=>[4,2,1,1]=>90
[6,3,8,5,7,1,2,4]=>[3,3,2]=>42
[8,3,1,5,6,2,7,4]=>[4,3,1]=>70
[6,8,5,2,1,4,7,3]=>[3,2,2,1]=>70
[3,8,2,5,6,1,7,4]=>[4,2,2]=>56
[2,8,1,5,6,3,7,4]=>[4,3,1]=>70
[8,1,2,5,6,3,7,4]=>[5,2,1]=>64
[1,8,2,5,7,6,3,4]=>[4,2,1,1]=>90
[5,1,8,6,2,7,3,4]=>[4,3,1]=>70
[2,5,8,6,1,7,3,4]=>[4,3,1]=>70
[8,6,1,5,7,2,3,4]=>[4,2,1,1]=>90
[3,8,6,5,7,1,2,4]=>[3,3,1,1]=>56
[7,6,5,8,1,2,4,3]=>[3,2,1,1,1]=>64
[5,1,7,6,8,4,2,3]=>[3,3,1,1]=>56
[5,1,3,7,8,6,2,4]=>[4,2,2]=>56
[7,2,5,8,1,6,4,3]=>[3,2,2,1]=>70
[3,2,8,5,7,6,1,4]=>[3,2,2,1]=>70
[8,2,1,5,7,6,3,4]=>[3,3,1,1]=>56
[5,2,8,6,1,7,3,4]=>[3,3,2]=>42
[1,2,8,6,5,7,3,4]=>[4,2,1,1]=>90
[4,2,1,3,6,7,8,5]=>[5,2,1]=>64
[8,2,5,6,3,7,1,4]=>[4,2,1,1]=>90
[7,2,6,5,4,1,8,3]=>[3,2,1,1,1]=>64
[6,1,3,5,4,7,8,2]=>[5,1,1,1]=>35
[6,1,5,3,4,7,8,2]=>[5,1,1,1]=>35
[7,5,6,2,4,1,8,3]=>[3,2,2,1]=>70
[8,5,2,6,3,7,1,4]=>[3,3,1,1]=>56
[4,3,1,2,6,7,8,5]=>[5,2,1]=>64
[8,1,6,5,7,3,2,4]=>[3,2,1,1,1]=>64
[3,5,8,6,2,7,1,4]=>[4,2,1,1]=>90
[5,8,1,6,3,7,2,4]=>[3,3,1,1]=>56
[1,8,5,6,3,7,2,4]=>[4,2,1,1]=>90
[1,7,6,5,4,2,8,3]=>[3,2,1,1,1]=>64
[5,7,6,1,4,2,8,3]=>[3,3,1,1]=>56
[7,1,4,2,6,5,8,3]=>[4,2,1,1]=>90
[4,1,7,3,5,6,8,2]=>[5,2,1]=>64
[2,7,4,1,5,6,8,3]=>[5,2,1]=>64
[5,7,6,4,1,2,8,3]=>[3,3,1,1]=>56
[4,7,6,1,5,2,8,3]=>[3,3,1,1]=>56
[1,7,6,4,5,2,8,3]=>[4,2,1,1]=>90
[1,8,3,6,5,7,2,4]=>[4,2,1,1]=>90
[3,8,1,6,5,7,2,4]=>[3,3,1,1]=>56
[8,1,3,5,7,6,2,4]=>[4,2,1,1]=>90
[7,8,5,4,1,6,2,3]=>[3,2,2,1]=>70
[6,1,5,4,3,7,8,2]=>[4,1,1,1,1]=>35
[7,5,6,4,2,1,8,3]=>[3,2,1,1,1]=>64
[8,3,2,6,5,7,1,4]=>[3,2,2,1]=>70
[7,4,6,2,5,1,8,3]=>[3,2,2,1]=>70
[6,1,4,3,5,7,8,2]=>[5,1,1,1]=>35
[6,1,3,4,5,7,8,2]=>[6,1,1]=>21
[7,2,6,4,5,1,8,3]=>[4,2,1,1]=>90
[8,2,3,6,5,7,1,4]=>[4,2,1,1]=>90
[3,4,7,8,5,6,1,2]=>[4,2,2]=>56
[3,4,7,2,5,1,6,8]=>[5,2,1]=>64
[1,4,7,2,5,8,3,6]=>[4,3,1]=>70
[3,6,2,4,7,1,5,8]=>[4,3,1]=>70
[4,3,6,7,5,8,1,2]=>[4,2,2]=>56
[6,3,7,5,8,4,1,2]=>[3,2,2,1]=>70
[4,8,2,6,1,5,3,7]=>[3,2,2,1]=>70
[4,3,6,2,5,1,8,7]=>[3,3,1,1]=>56
[7,8,1,2,5,6,3,4]=>[4,2,2]=>56
[4,1,6,2,5,7,3,8]=>[5,2,1]=>64
[2,1,8,6,4,7,3,5]=>[3,3,1,1]=>56
[1,8,3,6,7,4,5,2]=>[4,2,1,1]=>90
[7,1,5,8,3,6,2,4]=>[3,2,2,1]=>70
[3,1,6,4,7,2,5,8]=>[4,3,1]=>70
[6,8,5,1,3,4,2,7]=>[4,2,1,1]=>90
[2,8,3,4,5,1,7,6]=>[5,2,1]=>64
[6,2,4,3,1,5,7,8]=>[5,1,1,1]=>35
[1,3,7,4,8,2,5,6]=>[5,2,1]=>64
[5,3,7,4,1,6,2,8]=>[4,2,2]=>56
[5,8,7,6,3,1,2,4]=>[3,2,1,1,1]=>64
[1,2,7,8,5,4,3,6]=>[4,2,1,1]=>90
[6,3,1,2,8,4,5,7]=>[5,2,1]=>64
[4,2,1,3,6,5,8,7]=>[4,3,1]=>70
[7,8,2,1,4,5,3,6]=>[4,2,2]=>56
[7,8,4,1,5,3,6,2]=>[3,2,2,1]=>70
[7,5,1,6,4,3,8,2]=>[3,2,1,1,1]=>64
[6,5,1,8,2,7,4,3]=>[3,2,2,1]=>70
[6,8,1,7,5,2,3,4]=>[4,2,1,1]=>90
[5,6,1,7,4,8,2,3]=>[4,3,1]=>70
[3,1,7,5,6,4,8,2]=>[4,2,1,1]=>90
[7,1,8,6,5,4,2,3]=>[3,2,1,1,1]=>64
[2,6,5,7,3,4,8,1]=>[4,2,1,1]=>90
[1,6,4,7,5,8,2,3]=>[4,2,2]=>56
[8,5,3,6,2,7,4,1]=>[3,2,1,1,1]=>64
[1,3,7,4,6,8,2,5]=>[5,2,1]=>64
[4,7,5,6,3,2,8,1]=>[4,1,1,1,1]=>35
[1,7,6,5,4,8,2,3]=>[3,2,1,1,1]=>64
[8,1,6,5,7,2,4,3]=>[3,2,1,1,1]=>64
[1,2,7,6,8,3,4,5]=>[5,2,1]=>64
[6,1,7,5,3,8,2,4]=>[3,3,1,1]=>56
[2,1,7,5,6,8,3,4]=>[4,3,1]=>70
[5,4,1,7,6,8,2,3]=>[3,3,2]=>42
[4,8,5,6,2,7,3,1]=>[4,2,1,1]=>90
[3,8,6,4,2,7,5,1]=>[3,2,1,1,1]=>64
[7,8,5,2,4,6,3,1]=>[3,2,1,1,1]=>64
[2,8,6,3,7,4,5,1]=>[4,2,1,1]=>90
[7,8,1,6,2,4,5,3]=>[4,2,1,1]=>90
[6,8,1,4,7,2,5,3]=>[3,2,2,1]=>70
[3,8,4,1,7,2,6,5]=>[3,3,1,1]=>56
[5,4,7,1,8,3,2,6]=>[3,3,1,1]=>56
[3,7,4,1,8,5,2,6]=>[4,2,2]=>56
[6,7,1,4,8,3,2,5]=>[3,3,1,1]=>56
[2,7,1,8,4,5,3,6]=>[4,3,1]=>70
[6,1,2,8,4,3,5,7]=>[5,2,1]=>64
[6,5,1,4,3,8,2,7]=>[3,2,1,1,1]=>64
[1,6,2,5,8,3,4,7]=>[5,2,1]=>64
[8,5,1,3,7,2,6,4]=>[3,2,2,1]=>70
[8,4,2,1,7,3,6,5]=>[3,2,2,1]=>70
[7,4,2,1,8,5,3,6]=>[3,2,2,1]=>70
[1,5,4,2,8,3,6,7]=>[5,2,1]=>64
[6,4,3,1,5,8,2,7]=>[3,3,1,1]=>56
[3,7,6,8,4,5,2,1]=>[3,2,1,1,1]=>64
[2,7,6,8,5,3,4,1]=>[3,2,1,1,1]=>64
[1,7,6,8,5,4,2,3]=>[3,2,1,1,1]=>64
[1,4,8,6,7,5,2,3]=>[4,2,1,1]=>90
[2,4,8,6,7,3,5,1]=>[4,2,1,1]=>90
[7,3,8,5,4,6,2,1]=>[3,2,1,1,1]=>64
[3,4,8,5,6,7,2,1]=>[5,1,1,1]=>35
[6,3,5,8,4,7,2,1]=>[3,2,1,1,1]=>64
[5,4,3,8,6,7,2,1]=>[3,2,1,1,1]=>64
[5,4,2,8,7,3,6,1]=>[3,2,2,1]=>70
[6,2,5,8,7,3,4,1]=>[3,2,2,1]=>70
[3,2,8,5,7,4,6,1]=>[3,3,1,1]=>56
[1,3,8,7,5,6,2,4]=>[4,2,1,1]=>90
[2,1,8,7,4,6,3,5]=>[3,3,1,1]=>56
[3,1,8,5,7,6,2,4]=>[3,3,1,1]=>56
[6,1,5,8,7,4,2,3]=>[3,2,2,1]=>70
[5,4,1,8,7,6,2,3]=>[3,2,2,1]=>70
[5,8,6,7,4,3,2,1]=>[3,1,1,1,1,1]=>21
[4,8,7,5,6,3,2,1]=>[3,1,1,1,1,1]=>21
[4,2,1,6,3,5,8,7]=>[4,3,1]=>70
[6,2,1,4,3,5,8,7]=>[4,3,1]=>70
[6,2,1,4,3,8,5,7]=>[4,3,1]=>70
[8,2,1,4,3,6,5,7]=>[4,3,1]=>70
[6,2,4,1,3,5,8,7]=>[4,3,1]=>70
[2,1,6,4,3,5,8,7]=>[4,3,1]=>70
[2,6,1,4,3,5,8,7]=>[4,3,1]=>70
[2,6,4,1,3,5,8,7]=>[4,3,1]=>70
[4,6,2,1,3,5,8,7]=>[4,3,1]=>70
[6,4,2,1,3,5,8,7]=>[4,2,1,1]=>90
[8,4,2,1,3,6,5,7]=>[4,2,1,1]=>90
[8,4,2,1,6,3,5,7]=>[4,2,1,1]=>90
[6,4,2,1,8,3,5,7]=>[4,2,1,1]=>90
[2,6,1,4,3,8,5,7]=>[4,3,1]=>70
[2,1,6,4,3,8,5,7]=>[4,3,1]=>70
[2,1,8,4,3,6,5,7]=>[4,3,1]=>70
[2,8,1,4,3,6,5,7]=>[4,3,1]=>70
[2,8,4,1,3,6,5,7]=>[4,3,1]=>70
[4,8,2,1,3,6,5,7]=>[4,2,2]=>56
[6,8,2,1,4,3,5,7]=>[4,2,2]=>56
[8,6,2,1,4,3,5,7]=>[4,2,1,1]=>90
[2,8,1,4,6,3,5,7]=>[4,3,1]=>70
[2,6,1,4,8,3,5,7]=>[4,3,1]=>70
[2,6,4,1,8,3,5,7]=>[4,3,1]=>70
[4,6,2,8,1,3,5,7]=>[4,3,1]=>70
[4,2,6,1,8,3,5,7]=>[4,3,1]=>70
[6,2,4,1,8,3,5,7]=>[4,3,1]=>70
[4,2,1,6,8,3,5,7]=>[4,3,1]=>70
[4,2,1,6,3,8,5,7]=>[4,3,1]=>70
[4,2,1,3,6,8,5,7]=>[4,3,1]=>70
[2,1,4,3,8,6,5,7]=>[4,3,1]=>70
[2,4,1,3,8,6,5,7]=>[4,3,1]=>70
[4,2,1,3,8,6,5,7]=>[4,2,2]=>56
[4,2,1,8,3,6,5,7]=>[4,2,2]=>56
[4,2,1,8,6,3,5,7]=>[4,2,2]=>56
[8,2,1,6,4,3,5,7]=>[4,2,1,1]=>90
[8,2,6,1,4,3,5,7]=>[4,2,1,1]=>90
[4,2,8,1,3,6,5,7]=>[4,2,2]=>56
[2,4,8,1,3,6,5,7]=>[4,3,1]=>70
[2,4,1,8,3,6,5,7]=>[4,3,1]=>70
[2,1,4,8,3,6,5,7]=>[4,3,1]=>70
[2,1,4,8,6,3,5,7]=>[4,3,1]=>70
[2,4,8,1,6,3,5,7]=>[4,3,1]=>70
[2,4,8,6,1,3,5,7]=>[4,3,1]=>70
[4,2,8,6,1,3,5,7]=>[4,2,2]=>56
[8,4,6,2,1,3,5,7]=>[4,2,1,1]=>90
[4,6,8,2,1,3,5,7]=>[4,3,1]=>70
[2,6,8,4,1,3,5,7]=>[4,3,1]=>70
[2,6,8,1,4,3,5,7]=>[4,3,1]=>70
[2,6,1,8,4,3,5,7]=>[4,3,1]=>70
[2,1,6,8,4,3,5,7]=>[4,3,1]=>70
[2,1,8,6,4,3,5,7]=>[4,2,1,1]=>90
[2,8,6,4,1,3,5,7]=>[4,2,1,1]=>90
[4,8,6,2,1,3,5,7]=>[4,2,1,1]=>90
[6,8,4,2,1,3,5,7]=>[4,2,1,1]=>90
[3,2,6,1,5,4,8,7]=>[3,3,2]=>42
[5,2,4,3,8,1,7,6]=>[3,2,2,1]=>70
[6,2,4,1,5,3,8,7]=>[4,3,1]=>70
[4,3,6,1,5,2,8,7]=>[3,3,2]=>42
[4,3,5,2,8,1,7,6]=>[3,2,2,1]=>70
[4,3,7,2,6,5,8,1]=>[3,2,2,1]=>70
[4,3,8,2,6,1,7,5]=>[3,2,2,1]=>70
[4,3,8,1,7,2,6,5]=>[3,2,2,1]=>70
[4,3,8,1,5,2,7,6]=>[3,3,2]=>42
[5,1,8,3,4,2,7,6]=>[4,2,2]=>56
[5,4,8,1,3,2,7,6]=>[3,2,2,1]=>70
[2,1,5,4,8,3,7,6]=>[3,3,2]=>42
[5,1,7,6,8,3,4,2]=>[3,3,1,1]=>56
[4,3,7,6,8,1,5,2]=>[3,2,2,1]=>70
[4,3,7,1,8,5,6,2]=>[3,3,2]=>42
[4,3,6,5,8,1,7,2]=>[3,3,2]=>42
[6,3,5,4,7,2,8,1]=>[4,1,1,1,1]=>35
[6,3,5,4,8,1,7,2]=>[3,2,2,1]=>70
[7,1,6,3,8,4,5,2]=>[4,2,1,1]=>90
[7,4,6,5,8,1,3,2]=>[3,2,1,1,1]=>64
[2,1,8,4,6,3,7,5]=>[4,3,1]=>70
[8,4,6,1,3,2,7,5]=>[3,3,1,1]=>56
[8,1,6,3,4,2,7,5]=>[4,2,1,1]=>90
[8,1,6,3,7,2,5,4]=>[3,2,2,1]=>70
[8,3,5,1,7,2,6,4]=>[3,3,1,1]=>56
[8,3,5,2,6,1,7,4]=>[4,2,1,1]=>90
[7,3,5,2,6,4,8,1]=>[4,2,1,1]=>90
[8,2,6,3,5,1,7,4]=>[4,2,1,1]=>90
[8,2,7,1,5,3,6,4]=>[3,3,1,1]=>56
[8,2,4,1,5,3,7,6]=>[4,3,1]=>70
[8,2,4,1,7,3,6,5]=>[3,3,1,1]=>56
[8,2,4,3,6,1,7,5]=>[4,2,1,1]=>90
[3,2,8,4,6,1,7,5]=>[4,2,2]=>56
[3,2,8,1,5,4,7,6]=>[3,3,2]=>42
[3,2,7,6,8,1,5,4]=>[3,2,2,1]=>70
[3,2,7,1,8,5,6,4]=>[3,3,2]=>42
[3,2,6,5,8,1,7,4]=>[3,3,2]=>42
[6,5,7,2,4,3,8,1]=>[3,2,1,1,1]=>64
[6,5,8,2,4,1,7,3]=>[3,2,2,1]=>70
[7,2,4,1,8,5,6,3]=>[4,2,2]=>56
[7,6,8,2,4,1,5,3]=>[3,2,2,1]=>70
[7,6,8,1,5,2,4,3]=>[3,2,1,1,1]=>64
[2,1,7,3,8,5,6,4]=>[4,3,1]=>70
[7,1,3,2,8,5,6,4]=>[4,2,2]=>56
[7,1,8,5,6,2,4,3]=>[3,2,2,1]=>70
[7,1,8,2,6,4,5,3]=>[4,2,1,1]=>90
[7,2,8,1,5,4,6,3]=>[3,2,2,1]=>70
[6,2,7,4,5,3,8,1]=>[4,2,1,1]=>90
[5,4,7,2,6,3,8,1]=>[3,2,2,1]=>70
[5,4,8,2,6,1,7,3]=>[3,2,2,1]=>70
[6,5,8,1,7,2,4,3]=>[3,2,2,1]=>70
[2,1,6,5,8,3,7,4]=>[3,3,2]=>42
[6,5,7,4,8,1,3,2]=>[3,2,1,1,1]=>64
[6,5,7,1,8,3,4,2]=>[3,3,1,1]=>56
[6,1,7,4,8,3,5,2]=>[3,3,1,1]=>56
[5,4,7,1,8,3,6,2]=>[3,3,1,1]=>56
[5,4,6,3,8,1,7,2]=>[3,2,2,1]=>70
[2,1,4,3,6,5,8,7,11,12,10,9]=>[6,5,1]=>1155
[2,1,4,3,6,5,9,10,8,7,12,11]=>[6,5,1]=>1155
[2,1,4,3,6,5,9,11,8,12,10,7]=>[6,5,1]=>1155
[2,1,4,3,6,5,10,11,12,9,8,7]=>[6,4,1,1]=>3080
[2,1,4,3,7,8,6,5,10,9,12,11]=>[6,5,1]=>1155
[2,1,4,3,7,8,6,5,11,12,10,9]=>[6,4,2]=>2673
[2,1,4,3,7,9,6,10,8,5,12,11]=>[6,5,1]=>1155
[2,1,4,3,7,9,6,11,8,12,10,5]=>[6,5,1]=>1155
[2,1,4,3,7,10,6,11,12,9,8,5]=>[6,4,1,1]=>3080
[2,1,4,3,8,9,10,7,6,5,12,11]=>[6,4,1,1]=>3080
[2,1,4,3,8,9,11,7,6,12,10,5]=>[6,4,1,1]=>3080
[2,1,4,3,8,10,11,7,12,9,6,5]=>[6,4,1,1]=>3080
[2,1,4,3,9,10,11,12,8,7,6,5]=>[6,3,1,1,1]=>3696
[2,1,5,6,4,3,8,7,10,9,12,11]=>[6,5,1]=>1155
[2,1,5,6,4,3,8,7,11,12,10,9]=>[6,4,2]=>2673
[2,1,5,6,4,3,9,10,8,7,12,11]=>[6,4,2]=>2673
[2,1,5,6,4,3,9,11,8,12,10,7]=>[6,4,2]=>2673
[2,1,5,6,4,3,10,11,12,9,8,7]=>[6,3,2,1]=>5632
[2,1,5,7,4,8,6,3,10,9,12,11]=>[6,5,1]=>1155
[2,1,5,7,4,8,6,3,11,12,10,9]=>[6,4,2]=>2673
[2,1,5,7,4,9,6,10,8,3,12,11]=>[6,5,1]=>1155
[2,1,5,7,4,9,6,11,8,12,10,3]=>[6,5,1]=>1155
[2,1,5,7,4,10,6,11,12,9,8,3]=>[6,4,1,1]=>3080
[2,1,5,8,4,9,10,7,6,3,12,11]=>[6,4,1,1]=>3080
[2,1,5,8,4,9,11,7,6,12,10,3]=>[6,4,1,1]=>3080
[2,1,5,8,4,10,11,7,12,9,6,3]=>[6,4,1,1]=>3080
[2,1,5,9,4,10,11,12,8,7,6,3]=>[6,3,1,1,1]=>3696
[2,1,6,7,8,5,4,3,10,9,12,11]=>[6,4,1,1]=>3080
[2,1,6,7,8,5,4,3,11,12,10,9]=>[6,3,2,1]=>5632
[2,1,6,7,9,5,4,10,8,3,12,11]=>[6,4,1,1]=>3080
[2,1,6,7,9,5,4,11,8,12,10,3]=>[6,4,1,1]=>3080
[2,1,6,7,10,5,4,11,12,9,8,3]=>[6,3,2,1]=>5632
[2,1,6,8,9,5,10,7,4,3,12,11]=>[6,4,1,1]=>3080
[2,1,6,8,9,5,11,7,4,12,10,3]=>[6,4,1,1]=>3080
[2,1,6,8,10,5,11,7,12,9,4,3]=>[6,4,1,1]=>3080
[2,1,6,9,10,5,11,12,8,7,4,3]=>[6,3,1,1,1]=>3696
[2,1,7,8,9,10,6,5,4,3,12,11]=>[6,3,1,1,1]=>3696
[2,1,7,8,9,11,6,5,4,12,10,3]=>[6,3,1,1,1]=>3696
[2,1,7,8,10,11,6,5,12,9,4,3]=>[6,3,1,1,1]=>3696
[2,1,7,9,10,11,6,12,8,5,4,3]=>[6,3,1,1,1]=>3696
[2,1,8,9,10,11,12,7,6,5,4,3]=>[6,2,1,1,1,1]=>2100
[3,4,2,1,6,5,8,7,10,9,12,11]=>[6,5,1]=>1155
[3,4,2,1,6,5,8,7,11,12,10,9]=>[6,4,2]=>2673
[3,4,2,1,6,5,9,10,8,7,12,11]=>[6,4,2]=>2673
[3,4,2,1,6,5,9,11,8,12,10,7]=>[6,4,2]=>2673
[3,4,2,1,6,5,10,11,12,9,8,7]=>[6,3,2,1]=>5632
[3,4,2,1,7,8,6,5,10,9,12,11]=>[6,4,2]=>2673
[3,4,2,1,7,8,6,5,11,12,10,9]=>[6,3,3]=>1650
[3,4,2,1,7,9,6,10,8,5,12,11]=>[6,4,2]=>2673
[3,4,2,1,7,9,6,11,8,12,10,5]=>[6,4,2]=>2673
[3,4,2,1,7,10,6,11,12,9,8,5]=>[6,3,2,1]=>5632
[3,4,2,1,8,9,10,7,6,5,12,11]=>[6,3,2,1]=>5632
[3,4,2,1,8,9,11,7,6,12,10,5]=>[6,3,2,1]=>5632
[3,4,2,1,8,10,11,7,12,9,6,5]=>[6,3,2,1]=>5632
[3,4,2,1,9,10,11,12,8,7,6,5]=>[6,2,2,1,1]=>3564
[3,5,2,6,4,1,8,7,10,9,12,11]=>[6,5,1]=>1155
[3,5,2,6,4,1,8,7,11,12,10,9]=>[6,4,2]=>2673
[3,5,2,6,4,1,9,10,8,7,12,11]=>[6,4,2]=>2673
[3,5,2,6,4,1,9,11,8,12,10,7]=>[6,4,2]=>2673
[3,5,2,6,4,1,10,11,12,9,8,7]=>[6,3,2,1]=>5632
[3,5,2,7,4,8,6,1,10,9,12,11]=>[6,5,1]=>1155
[3,5,2,7,4,8,6,1,11,12,10,9]=>[6,4,2]=>2673
[3,5,2,7,4,9,6,10,8,1,12,11]=>[6,5,1]=>1155
[3,5,2,7,4,9,6,11,8,12,10,1]=>[6,5,1]=>1155
[3,5,2,7,4,10,6,11,12,9,8,1]=>[6,4,1,1]=>3080
[3,5,2,8,4,9,10,7,6,1,12,11]=>[6,4,1,1]=>3080
[3,5,2,8,4,9,11,7,6,12,10,1]=>[6,4,1,1]=>3080
[3,5,2,8,4,10,11,7,12,9,6,1]=>[6,4,1,1]=>3080
[3,5,2,9,4,10,11,12,8,7,6,1]=>[6,3,1,1,1]=>3696
[3,6,2,7,8,5,4,1,10,9,12,11]=>[6,4,1,1]=>3080
[3,6,2,7,8,5,4,1,11,12,10,9]=>[6,3,2,1]=>5632
[3,6,2,7,9,5,4,10,8,1,12,11]=>[6,4,1,1]=>3080
[3,6,2,7,9,5,4,11,8,12,10,1]=>[6,4,1,1]=>3080
[3,6,2,7,10,5,4,11,12,9,8,1]=>[6,3,2,1]=>5632
[3,6,2,8,9,5,10,7,4,1,12,11]=>[6,4,1,1]=>3080
[3,6,2,8,9,5,11,7,4,12,10,1]=>[6,4,1,1]=>3080
[3,6,2,8,10,5,11,7,12,9,4,1]=>[6,4,1,1]=>3080
[3,6,2,9,10,5,11,12,8,7,4,1]=>[6,3,1,1,1]=>3696
[3,7,2,8,9,10,6,5,4,1,12,11]=>[6,3,1,1,1]=>3696
[3,7,2,8,9,11,6,5,4,12,10,1]=>[6,3,1,1,1]=>3696
[3,7,2,8,10,11,6,5,12,9,4,1]=>[6,3,1,1,1]=>3696
[3,7,2,9,10,11,6,12,8,5,4,1]=>[6,3,1,1,1]=>3696
[3,8,2,9,10,11,12,7,6,5,4,1]=>[6,2,1,1,1,1]=>2100
[4,5,6,3,2,1,8,7,10,9,12,11]=>[6,4,1,1]=>3080
[4,5,6,3,2,1,8,7,11,12,10,9]=>[6,3,2,1]=>5632
[4,5,6,3,2,1,9,10,8,7,12,11]=>[6,3,2,1]=>5632
[4,5,6,3,2,1,9,11,8,12,10,7]=>[6,3,2,1]=>5632
[4,5,6,3,2,1,10,11,12,9,8,7]=>[6,2,2,2]=>1925
[4,5,7,3,2,8,6,1,10,9,12,11]=>[6,4,1,1]=>3080
[4,5,7,3,2,8,6,1,11,12,10,9]=>[6,3,2,1]=>5632
[4,5,7,3,2,9,6,10,8,1,12,11]=>[6,4,1,1]=>3080
[4,5,7,3,2,9,6,11,8,12,10,1]=>[6,4,1,1]=>3080
[4,5,7,3,2,10,6,11,12,9,8,1]=>[6,3,2,1]=>5632
[4,5,8,3,2,9,10,7,6,1,12,11]=>[6,3,2,1]=>5632
[4,5,8,3,2,9,11,7,6,12,10,1]=>[6,3,2,1]=>5632
[4,5,8,3,2,10,11,7,12,9,6,1]=>[6,3,2,1]=>5632
[4,5,9,3,2,10,11,12,8,7,6,1]=>[6,2,2,1,1]=>3564
[4,6,7,3,8,5,2,1,10,9,12,11]=>[6,4,1,1]=>3080
[4,6,7,3,8,5,2,1,11,12,10,9]=>[6,3,2,1]=>5632
[4,6,7,3,9,5,2,10,8,1,12,11]=>[6,4,1,1]=>3080
[4,6,7,3,9,5,2,11,8,12,10,1]=>[6,4,1,1]=>3080
[4,6,7,3,10,5,2,11,12,9,8,1]=>[6,3,2,1]=>5632
[4,6,8,3,9,5,10,7,2,1,12,11]=>[6,4,1,1]=>3080
[4,6,8,3,9,5,11,7,2,12,10,1]=>[6,4,1,1]=>3080
[4,6,8,3,10,5,11,7,12,9,2,1]=>[6,4,1,1]=>3080
[4,6,9,3,10,5,11,12,8,7,2,1]=>[6,3,1,1,1]=>3696
[4,7,8,3,9,10,6,5,2,1,12,11]=>[6,3,1,1,1]=>3696
[4,7,8,3,9,11,6,5,2,12,10,1]=>[6,3,1,1,1]=>3696
[4,7,8,3,10,11,6,5,12,9,2,1]=>[6,3,1,1,1]=>3696
[4,7,9,3,10,11,6,12,8,5,2,1]=>[6,3,1,1,1]=>3696
[4,8,9,3,10,11,12,7,6,5,2,1]=>[6,2,1,1,1,1]=>2100
[5,6,7,8,4,3,2,1,10,9,12,11]=>[6,3,1,1,1]=>3696
[5,6,7,8,4,3,2,1,11,12,10,9]=>[6,2,2,1,1]=>3564
[5,6,7,9,4,3,2,10,8,1,12,11]=>[6,3,1,1,1]=>3696
[5,6,7,9,4,3,2,11,8,12,10,1]=>[6,3,1,1,1]=>3696
[5,6,7,10,4,3,2,11,12,9,8,1]=>[6,2,2,1,1]=>3564
[5,6,8,9,4,3,10,7,2,1,12,11]=>[6,3,1,1,1]=>3696
[5,6,8,9,4,3,11,7,2,12,10,1]=>[6,3,1,1,1]=>3696
[5,6,8,10,4,3,11,7,12,9,2,1]=>[6,3,1,1,1]=>3696
[5,6,9,10,4,3,11,12,8,7,2,1]=>[6,2,2,1,1]=>3564
[5,7,8,9,4,10,6,3,2,1,12,11]=>[6,3,1,1,1]=>3696
[5,7,8,9,4,11,6,3,2,12,10,1]=>[6,3,1,1,1]=>3696
[5,7,8,10,4,11,6,3,12,9,2,1]=>[6,3,1,1,1]=>3696
[5,7,9,10,4,11,6,12,8,3,2,1]=>[6,3,1,1,1]=>3696
[5,8,9,10,4,11,12,7,6,3,2,1]=>[6,2,1,1,1,1]=>2100
[6,7,8,9,10,5,4,3,2,1,12,11]=>[6,2,1,1,1,1]=>2100
[6,7,8,9,11,5,4,3,2,12,10,1]=>[6,2,1,1,1,1]=>2100
[6,7,8,10,11,5,4,3,12,9,2,1]=>[6,2,1,1,1,1]=>2100
[6,7,9,10,11,5,4,12,8,3,2,1]=>[6,2,1,1,1,1]=>2100
[6,8,9,10,11,5,12,7,4,3,2,1]=>[6,2,1,1,1,1]=>2100
[7,8,9,10,11,12,6,5,4,3,2,1]=>[6,1,1,1,1,1,1]=>462
[2,8,3,1,5,4,6,7]=>[5,2,1]=>64
[2,5,3,4,7,1,8,6]=>[5,2,1]=>64
[2,4,8,3,5,7,6,1]=>[4,2,1,1]=>90
[4,2,5,3,1,8,6,7]=>[4,3,1]=>70
[4,2,1,8,5,3,6,7]=>[4,2,2]=>56
[5,4,1,3,8,2,6,7]=>[4,2,1,1]=>90
[5,1,4,8,3,2,6,7]=>[4,2,1,1]=>90
[1,5,8,4,3,2,6,7]=>[4,2,1,1]=>90
[1,8,5,4,3,2,6,7]=>[4,1,1,1,1]=>35
[1,7,4,3,8,5,2,6]=>[4,2,1,1]=>90
[1,5,7,3,8,4,2,6]=>[4,3,1]=>70
[5,1,4,7,8,3,2,6]=>[4,2,1,1]=>90
[4,8,1,5,7,3,6,2]=>[3,3,1,1]=>56
[8,1,5,3,7,4,6,2]=>[4,2,1,1]=>90
[3,8,4,7,6,5,2,1]=>[3,1,1,1,1,1]=>21
[1,6,8,5,3,7,4,2]=>[3,2,2,1]=>70
[6,8,1,7,4,3,5,2]=>[3,2,1,1,1]=>64
[6,4,8,1,7,3,5,2]=>[3,2,2,1]=>70
[6,4,8,7,1,5,2,3]=>[3,2,2,1]=>70
[7,6,4,1,3,8,2,5]=>[3,2,1,1,1]=>64
[1,7,5,6,3,2,8,4]=>[4,2,1,1]=>90
[4,2,1,7,8,5,3,6]=>[3,3,2]=>42
[2,7,4,6,3,1,8,5]=>[4,2,1,1]=>90
[2,6,8,4,3,7,5,1]=>[3,2,2,1]=>70
[6,2,4,8,3,7,5,1]=>[3,2,2,1]=>70
[7,2,6,3,4,1,8,5]=>[4,2,1,1]=>90
[2,6,7,3,1,4,8,5]=>[4,3,1]=>70
[2,7,1,8,3,5,4,6]=>[4,3,1]=>70
[2,1,7,3,5,8,4,6]=>[4,3,1]=>70
[8,7,1,3,6,2,4,5]=>[4,2,1,1]=>90
[8,2,1,7,3,5,6,4]=>[4,2,1,1]=>90
[7,8,2,6,3,1,5,4]=>[3,2,2,1]=>70
[8,7,2,6,3,5,4,1]=>[3,1,1,1,1,1]=>21
[1,2,8,7,4,5,6,3]=>[5,1,1,1]=>35
[8,3,7,1,5,6,2,4]=>[3,3,1,1]=>56
[8,6,1,2,7,5,3,4]=>[4,2,1,1]=>90
[8,1,6,2,7,4,5,3]=>[4,2,1,1]=>90
[1,8,5,2,6,7,4,3]=>[4,2,1,1]=>90
[5,2,1,8,6,7,4,3]=>[3,2,2,1]=>70
[2,8,5,7,6,4,3,1]=>[3,1,1,1,1,1]=>21
[1,7,8,5,2,6,4,3]=>[3,2,2,1]=>70
[7,8,1,6,4,2,5,3]=>[3,2,2,1]=>70
[7,8,6,1,5,3,2,4]=>[3,2,1,1,1]=>64
[7,3,8,6,1,5,2,4]=>[3,2,2,1]=>70
[8,7,6,1,5,3,4,2]=>[3,1,1,1,1,1]=>21
[8,7,1,6,4,5,3,2]=>[3,1,1,1,1,1]=>21
[8,1,7,5,6,4,3,2]=>[3,1,1,1,1,1]=>21
[1,8,6,7,5,4,3,2]=>[3,1,1,1,1,1]=>21
[6,3,5,2,1,4,8,7]=>[3,3,1,1]=>56
[6,3,5,7,2,8,4,1]=>[4,2,1,1]=>90
[8,5,2,7,4,3,1,6]=>[3,2,1,1,1]=>64
[4,5,3,6,1,2,8,7]=>[4,3,1]=>70
[3,5,1,4,6,2,8,7]=>[4,3,1]=>70
[8,3,4,5,7,2,1,6]=>[4,2,1,1]=>90
[5,7,4,6,3,8,2,1]=>[3,2,1,1,1]=>64
[2,8,4,6,3,7,1,5]=>[4,2,1,1]=>90
[8,1,4,7,3,6,2,5]=>[3,2,2,1]=>70
[8,3,4,7,5,1,2,6]=>[4,2,1,1]=>90
[8,5,1,4,7,3,2,6]=>[3,2,1,1,1]=>64
[8,5,3,7,1,4,2,6]=>[3,2,2,1]=>70
[2,1,8,5,7,4,3,6]=>[3,3,1,1]=>56
[6,5,3,7,1,8,4,2]=>[3,2,2,1]=>70
[6,5,1,4,7,8,3,2]=>[4,1,1,1,1]=>35
[6,3,4,7,5,8,1,2]=>[4,2,2]=>56
[5,1,4,6,8,3,7,2]=>[4,2,1,1]=>90
[4,7,1,3,5,8,6,2]=>[4,3,1]=>70
[4,8,3,7,1,2,6,5]=>[3,2,2,1]=>70
[3,8,6,4,1,7,2,5]=>[3,3,1,1]=>56
[3,8,1,2,5,7,6,4]=>[4,2,1,1]=>90
[2,8,7,5,4,1,3,6]=>[3,2,1,1,1]=>64
[8,7,2,6,4,1,3,5]=>[3,2,1,1,1]=>64
[3,8,6,7,4,2,1,5]=>[3,2,1,1,1]=>64
[5,7,6,8,4,2,3,1]=>[3,2,1,1,1]=>64
[5,3,7,8,2,4,6,1]=>[3,3,1,1]=>56
[8,3,6,2,1,4,7,5]=>[3,3,1,1]=>56
[5,3,7,6,2,1,8,4]=>[3,2,2,1]=>70
[5,3,6,2,8,7,1,4]=>[3,2,2,1]=>70
[5,7,8,6,4,2,1,3]=>[3,2,1,1,1]=>64
[2,6,7,5,4,8,1,3]=>[4,2,1,1]=>90
[6,1,7,4,5,8,2,3]=>[4,2,2]=>56
[6,7,3,5,1,8,2,4]=>[3,3,2]=>42
[2,1,6,7,5,8,3,4]=>[4,3,1]=>70
[2,1,5,7,3,6,8,4]=>[4,3,1]=>70
[5,7,3,6,1,2,8,4]=>[3,3,2]=>42
[4,1,7,2,5,6,8,3]=>[5,2,1]=>64
[2,4,7,1,6,5,8,3]=>[4,2,1,1]=>90
[4,6,2,1,8,7,5,3]=>[3,2,2,1]=>70
[3,4,6,2,7,8,5,1]=>[5,2,1]=>64
[4,6,1,2,5,8,7,3]=>[4,3,1]=>70
[5,6,1,4,8,2,7,3]=>[3,3,2]=>42
[5,6,3,1,8,7,2,4]=>[3,3,2]=>42
[3,5,6,4,7,1,8,2]=>[5,2,1]=>64
[3,4,6,1,5,7,8,2]=>[5,2,1]=>64
[3,4,1,5,7,6,8,2]=>[5,2,1]=>64
[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]=>28
[3,8,2,7,6,1,5,4]=>[2,2,2,1,1]=>28
[3,8,2,7,6,5,1,4]=>[2,2,2,1,1]=>28
[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1]=>20
[4,8,7,2,6,5,3,1]=>[2,2,1,1,1,1]=>20
[4,8,7,2,6,5,1,3]=>[2,2,2,1,1]=>28
[4,8,7,2,6,1,5,3]=>[2,2,2,1,1]=>28
[4,8,7,2,1,6,5,3]=>[2,2,2,1,1]=>28
[4,8,7,3,1,6,5,2]=>[2,2,2,1,1]=>28
[4,8,7,3,2,1,6,5]=>[2,2,2,1,1]=>28
[4,8,7,3,2,6,1,5]=>[2,2,2,1,1]=>28
[4,8,7,3,2,6,5,1]=>[2,2,2,1,1]=>28
[4,8,7,3,6,2,5,1]=>[2,2,2,1,1]=>28
[4,8,7,3,6,2,1,5]=>[2,2,2,1,1]=>28
[4,8,7,3,6,1,5,2]=>[2,2,2,1,1]=>28
[4,8,7,3,6,5,1,2]=>[2,2,2,1,1]=>28
[4,8,7,3,6,5,2,1]=>[2,2,1,1,1,1]=>20
[5,8,7,6,3,4,2,1]=>[2,2,1,1,1,1]=>20
[5,8,7,6,3,1,4,2]=>[2,2,2,1,1]=>28
[5,8,7,6,3,2,4,1]=>[2,2,1,1,1,1]=>20
[5,8,7,6,2,4,3,1]=>[2,2,1,1,1,1]=>20
[5,8,7,6,2,1,4,3]=>[2,2,2,1,1]=>28
[5,8,7,6,4,2,3,1]=>[2,2,1,1,1,1]=>20
[5,8,7,6,4,2,1,3]=>[2,2,1,1,1,1]=>20
[5,8,7,6,4,1,3,2]=>[2,2,1,1,1,1]=>20
[5,8,7,6,4,3,1,2]=>[2,2,1,1,1,1]=>20
[7,2,1,5,6,4,3,8]=>[4,2,1,1]=>90
[1,4,6,7,3,8,2,5]=>[5,2,1]=>64
[6,4,5,7,1,3,8,2]=>[4,2,1,1]=>90
[6,3,5,1,7,4,8,2]=>[4,2,1,1]=>90
[6,2,1,5,7,4,8,3]=>[4,2,1,1]=>90
[3,2,1,5,7,4,8,6]=>[4,3,1]=>70
[2,4,6,7,3,8,1,5]=>[5,2,1]=>64
[1,4,6,7,3,8,5,2]=>[5,2,1]=>64
[1,5,6,7,8,3,4,2]=>[5,2,1]=>64
[2,5,6,7,8,3,1,4]=>[5,2,1]=>64
[3,2,1,6,7,8,4,5]=>[4,3,1]=>70
[5,2,1,6,7,8,4,3]=>[4,2,2]=>56
[5,3,6,1,7,8,4,2]=>[4,2,2]=>56
[1,5,6,7,8,3,2,4]=>[5,2,1]=>64
[6,4,5,7,2,1,8,3]=>[4,2,1,1]=>90
[5,4,6,7,2,8,3,1]=>[4,2,1,1]=>90
[6,3,4,2,1,7,8,5]=>[4,2,1,1]=>90
[4,3,6,2,7,8,5,1]=>[4,2,1,1]=>90
[3,4,6,7,2,8,5,1]=>[5,2,1]=>64
[4,2,1,5,7,3,8,6]=>[4,3,1]=>70
[1,5,6,7,8,2,4,3]=>[5,2,1]=>64
[1,5,6,7,8,4,2,3]=>[5,2,1]=>64
[3,4,6,7,1,8,5,2]=>[5,2,1]=>64
[4,3,6,1,7,8,5,2]=>[4,2,2]=>56
[2,1,4,3,6,5,8,7,9]=>[5,4]=>42
[2,4,1,3,6,5,8,7,9]=>[5,4]=>42
[2,4,1,6,3,5,8,7,9]=>[5,4]=>42
[2,4,1,6,3,8,5,7,9]=>[5,4]=>42
[2,4,1,6,3,7,5,9,8]=>[5,4]=>42
[2,4,1,5,3,7,6,9,8]=>[5,4]=>42
[2,3,1,5,4,7,6,9,8]=>[5,4]=>42
[1,3,2,5,4,7,6,9,8]=>[5,4]=>42
[2,4,1,3,6,5,8,7,10,9]=>[5,5]=>42
[2,4,6,1,3,5,8,7,9]=>[5,4]=>42
[2,4,1,6,3,5,8,7,10,9]=>[5,5]=>42
[2,4,1,6,8,3,5,7,9]=>[5,4]=>42
[2,4,1,6,3,8,5,7,10,9]=>[5,5]=>42
[2,4,1,6,3,8,9,5,7]=>[5,4]=>42
[2,4,1,6,3,8,5,10,7,9]=>[5,5]=>42
[2,4,1,6,3,7,5,8,9]=>[6,3]=>48
[2,4,1,6,3,8,5,9,7,10]=>[6,4]=>90
[2,4,1,5,3,8,6,9,7]=>[5,4]=>42
[2,4,1,6,3,7,5,9,8,10]=>[6,4]=>90
[2,3,1,6,4,7,5,9,8]=>[5,4]=>42
[2,4,1,5,3,7,6,9,8,10]=>[6,4]=>90
[1,4,2,5,3,7,6,9,8]=>[5,4]=>42
[2,3,1,5,4,7,6,9,8,10]=>[6,4]=>90
[1,3,2,5,4,7,6,9,8,10]=>[6,4]=>90
[7,1,2,3,4,5,6,8,9]=>[8,1]=>8
[1,4,3,6,2,5,7,8]=>[5,2,1]=>64
[1,4,3,7,2,5,6,8]=>[5,2,1]=>64
[1,4,3,7,6,8,2,5]=>[4,2,2]=>56
[1,4,3,7,5,8,2,6]=>[4,3,1]=>70
[1,4,3,7,2,6,5,8]=>[4,2,2]=>56
[1,5,3,7,4,8,2,6]=>[4,3,1]=>70
[1,3,2,6,5,8,4,7]=>[4,3,1]=>70
[1,5,4,8,2,6,3,7]=>[4,2,2]=>56
[1,5,4,8,3,7,2,6]=>[3,2,2,1]=>70
[1,2,3,6,5,8,4,7]=>[5,2,1]=>64
[6,8,2,4,5,7,1,3]=>[4,2,2]=>56
[3,7,8,4,5,2,6,1]=>[4,2,1,1]=>90
[7,8,1,4,5,3,6,2]=>[4,2,1,1]=>90
[3,8,7,4,1,6,5,2]=>[3,2,1,1,1]=>64
[4,8,3,6,1,5,7,2]=>[3,2,2,1]=>70
[5,8,3,1,6,4,7,2]=>[3,2,2,1]=>70
[5,8,1,4,7,6,3,2]=>[3,2,1,1,1]=>64
[7,5,1,8,6,2,4,3]=>[3,2,2,1]=>70
[7,4,1,8,2,6,3,5]=>[4,2,2]=>56
[7,1,8,4,2,6,3,5]=>[4,2,2]=>56
[1,6,3,8,5,2,4,7]=>[4,2,2]=>56
[6,1,3,8,5,2,4,7]=>[4,2,2]=>56
[7,2,8,4,1,6,5,3]=>[3,2,2,1]=>70
[7,2,8,3,6,5,1,4]=>[3,2,2,1]=>70
[7,2,8,3,6,1,5,4]=>[3,2,2,1]=>70
[7,1,8,2,3,6,5,4]=>[4,2,1,1]=>90
[1,5,2,3,8,4,7,6]=>[5,2,1]=>64
[5,1,2,3,8,4,7,6]=>[5,2,1]=>64
[6,2,8,1,3,5,4,7]=>[4,2,2]=>56
[2,6,3,8,7,1,5,4]=>[3,2,2,1]=>70
[2,5,1,3,8,4,7,6]=>[4,3,1]=>70
[2,4,8,1,3,7,6,5]=>[3,3,1,1]=>56
[2,4,8,3,7,6,1,5]=>[3,2,2,1]=>70
[2,5,4,1,3,8,7,6]=>[3,3,2]=>42
[1,4,8,2,3,7,6,5]=>[4,2,1,1]=>90
[6,3,8,1,5,2,4,7]=>[4,2,2]=>56
[5,3,8,1,2,4,7,6]=>[4,2,2]=>56
[1,5,4,8,2,7,6,3]=>[3,2,2,1]=>70
[6,5,1,2,8,7,4,3]=>[3,2,2,1]=>70
[5,3,1,6,4,2,8,7]=>[3,3,2]=>42
[5,1,6,2,8,7,4,3]=>[3,3,1,1]=>56
[1,4,2,5,8,7,6,3]=>[4,2,1,1]=>90
[3,6,2,8,7,5,1,4]=>[3,2,2,1]=>70
[4,2,6,1,8,7,3,5]=>[3,3,2]=>42
[4,3,1,5,8,2,7,6]=>[3,3,2]=>42
[3,4,8,7,1,2,6,5]=>[3,3,1,1]=>56
[3,4,8,1,7,2,6,5]=>[3,3,1,1]=>56
[1,3,4,8,7,2,6,5]=>[4,2,1,1]=>90
[7,8,3,5,4,1,6,2]=>[3,2,2,1]=>70
[4,3,7,5,8,6,1,2]=>[3,3,2]=>42
[4,2,7,1,8,3,6,5]=>[3,3,2]=>42
[1,7,6,5,3,8,4,2]=>[3,2,1,1,1]=>64
[2,7,6,5,3,8,1,4]=>[3,2,1,1,1]=>64
[1,7,6,5,2,4,8,3]=>[4,1,1,1,1]=>35
[3,7,6,4,8,5,1,2]=>[3,2,2,1]=>70
[5,7,6,3,8,4,1,2]=>[3,2,2,1]=>70
[5,1,6,2,4,8,3,7]=>[4,3,1]=>70
[4,7,6,5,1,2,8,3]=>[3,3,1,1]=>56
[6,1,3,5,4,8,7,2]=>[4,2,1,1]=>90
[1,2,6,3,4,8,7,5]=>[5,2,1]=>64
[6,1,4,2,8,3,5,7]=>[5,2,1]=>64
[4,7,1,6,2,3,8,5]=>[4,3,1]=>70
[1,2,6,7,4,8,5,3]=>[5,2,1]=>64
[3,1,6,7,4,2,8,5]=>[4,3,1]=>70
[4,7,6,8,3,5,1,2]=>[3,2,2,1]=>70
[2,7,6,5,1,4,3,8]=>[3,2,1,1,1]=>64
[6,3,2,1,7,4,8,5]=>[3,3,1,1]=>56
[4,2,1,7,3,5,8,6]=>[4,3,1]=>70
[8,4,1,5,2,7,6,3]=>[3,3,1,1]=>56
[8,2,5,1,3,7,6,4]=>[3,3,1,1]=>56
[4,7,2,5,3,1,8,6]=>[3,3,1,1]=>56
[7,5,4,3,2,1,8,6]=>[2,2,1,1,1,1]=>20
[5,7,4,3,2,8,1,6]=>[3,2,1,1,1]=>64
[1,7,6,2,4,8,3,5]=>[4,2,1,1]=>90
[2,7,3,6,4,8,1,5]=>[4,2,1,1]=>90
[6,2,7,5,3,8,1,4]=>[3,3,1,1]=>56
[7,1,8,5,3,6,4,2]=>[3,2,2,1]=>70
[5,8,3,2,7,1,6,4]=>[2,2,2,2]=>14
[8,7,2,6,1,5,4,3]=>[2,2,1,1,1,1]=>20
[1,8,5,7,4,3,6,2]=>[3,2,1,1,1]=>64
[1,8,5,7,2,4,6,3]=>[4,2,1,1]=>90
[3,8,6,1,7,2,5,4]=>[3,3,1,1]=>56
[7,2,8,5,6,1,4,3]=>[3,2,2,1]=>70
[6,3,7,5,8,2,1,4]=>[3,2,2,1]=>70
[3,7,2,6,8,4,1,5]=>[3,3,1,1]=>56
[3,6,5,8,1,4,2,7]=>[3,3,1,1]=>56
[2,6,5,8,4,1,3,7]=>[3,3,1,1]=>56
[6,5,4,8,3,2,1,7]=>[2,2,1,1,1,1]=>20
[6,3,5,1,8,4,2,7]=>[3,3,1,1]=>56
[8,4,1,5,7,3,6,2]=>[3,3,1,1]=>56
[6,3,7,4,8,5,2,1]=>[3,3,1,1]=>56
[4,7,2,5,8,6,3,1]=>[3,3,1,1]=>56
[6,3,1,8,4,7,5,2]=>[3,2,2,1]=>70
[6,5,3,8,7,4,1,2]=>[2,2,2,2]=>14
[5,4,8,1,7,6,2,3]=>[3,2,2,1]=>70
[5,2,8,1,7,3,6,4]=>[3,2,2,1]=>70
[6,4,7,8,1,5,3,2]=>[3,2,2,1]=>70
[2,5,8,7,1,3,6,4]=>[3,3,1,1]=>56
[5,3,8,7,2,1,6,4]=>[2,2,2,2]=>14
[8,3,7,6,1,5,4,2]=>[2,2,1,1,1,1]=>20
[8,2,7,6,5,1,4,3]=>[2,2,1,1,1,1]=>20
[4,3,8,7,6,2,1,5]=>[2,2,2,1,1]=>28
[2,4,8,7,6,1,3,5]=>[3,3,1,1]=>56
[3,5,8,7,2,6,1,4]=>[3,2,2,1]=>70
[4,7,3,8,6,5,1,2]=>[3,2,2,1]=>70
[7,5,8,6,4,3,2,1]=>[2,2,1,1,1,1]=>20
[5,8,7,3,6,4,2,1]=>[2,2,1,1,1,1]=>20
[4,8,7,6,2,5,3,1]=>[2,2,1,1,1,1]=>20
[3,8,7,6,5,1,4,2]=>[2,2,1,1,1,1]=>20
[2,8,7,6,5,4,1,3]=>[2,2,1,1,1,1]=>20
[3,4,1,2,5,6,7,8,9]=>[7,2]=>27
[3,2,1,4,5,6,7,8,9]=>[7,1,1]=>28
[4,3,2,1,5,6,7,8,9]=>[6,1,1,1]=>56
[5,6,7,8,1,2,3,4,9]=>[5,4]=>42
[5,4,3,2,1,6,7,8,9]=>[5,1,1,1,1]=>70
[6,5,4,3,2,1,7,8,9]=>[4,1,1,1,1,1]=>56
[7,6,5,4,3,2,1,8,9]=>[3,1,1,1,1,1,1]=>28
[3,2,1,4,5,6,7,8,9,10]=>[8,1,1]=>36
[4,3,2,1,5,6,7,8,9,10]=>[7,1,1,1]=>84
[5,4,3,2,1,6,7,8,9,10]=>[6,1,1,1,1]=>126
[6,5,4,3,2,1,7,8,9,10]=>[5,1,1,1,1,1]=>126
[7,6,5,4,3,2,1,8,9,10]=>[4,1,1,1,1,1,1]=>84
[8,7,6,5,4,3,2,1,9,10]=>[3,1,1,1,1,1,1,1]=>36
[3,6,5,1,2,4,8,7]=>[4,3,1]=>70
[3,7,5,8,2,4,1,6]=>[3,3,1,1]=>56
[3,8,5,7,2,4,1,6]=>[3,3,1,1]=>56
[5,1,7,8,4,3,2,6]=>[3,3,1,1]=>56
[5,1,2,6,4,3,8,7]=>[4,3,1]=>70
[6,1,2,5,4,3,8,7]=>[4,2,1,1]=>90
[5,1,2,4,6,3,8,7]=>[5,2,1]=>64
[4,1,2,6,5,3,8,7]=>[4,3,1]=>70
[4,1,5,7,8,3,2,6]=>[4,3,1]=>70
[4,1,5,8,7,3,2,6]=>[3,3,1,1]=>56
[4,7,1,8,3,6,2,5]=>[3,3,2]=>42
[4,1,7,8,5,2,3,6]=>[4,3,1]=>70
[5,1,7,4,8,2,3,6]=>[4,3,1]=>70
[7,5,3,8,1,4,2,6]=>[3,2,2,1]=>70
[2,1,5,8,7,3,4,6]=>[4,3,1]=>70
[5,1,8,4,7,2,3,6]=>[4,2,2]=>56
[4,1,8,7,5,2,3,6]=>[4,2,1,1]=>90
[4,7,1,6,3,2,8,5]=>[3,3,1,1]=>56
[6,1,2,3,7,5,8,4]=>[5,2,1]=>64
[7,1,2,3,8,6,5,4]=>[4,2,1,1]=>90
[7,1,2,3,5,8,6,4]=>[5,2,1]=>64
[6,8,1,4,3,7,2,5]=>[3,2,2,1]=>70
[8,7,3,2,4,1,6,5]=>[3,2,1,1,1]=>64
[2,1,7,3,4,8,6,5]=>[4,3,1]=>70
[7,8,3,2,4,1,6,5]=>[3,2,2,1]=>70
[6,7,1,4,3,8,2,5]=>[3,3,1,1]=>56
[8,1,2,3,5,7,6,4]=>[5,1,1,1]=>35
[8,1,2,3,6,7,5,4]=>[5,1,1,1]=>35
[7,1,2,3,6,8,5,4]=>[5,1,1,1]=>35
[7,1,2,3,8,5,6,4]=>[5,2,1]=>64
[8,1,2,3,7,5,6,4]=>[5,1,1,1]=>35
[8,1,2,3,6,5,7,4]=>[5,1,1,1]=>35
[7,1,8,5,4,3,2,6]=>[3,2,1,1,1]=>64
[7,8,2,6,3,4,1,5]=>[4,2,1,1]=>90
[6,8,2,7,3,4,1,5]=>[4,2,1,1]=>90
[6,7,2,8,3,4,1,5]=>[4,3,1]=>70
[3,8,7,1,4,2,6,5]=>[3,3,1,1]=>56
[3,7,8,1,4,2,6,5]=>[3,3,2]=>42
[3,6,8,1,4,2,7,5]=>[3,3,2]=>42
[3,5,7,8,2,4,1,6]=>[4,3,1]=>70
[3,6,7,1,4,2,8,5]=>[4,3,1]=>70
[7,6,2,8,3,1,4,5]=>[4,2,1,1]=>90
[8,6,2,7,3,1,4,5]=>[4,2,1,1]=>90
[8,1,7,5,4,3,2,6]=>[3,1,1,1,1,1]=>21
[8,1,7,4,5,3,2,6]=>[4,1,1,1,1]=>35
[5,8,3,7,1,4,2,6]=>[3,2,2,1]=>70
[2,1,7,3,4,6,8,5]=>[5,2,1]=>64
[6,7,3,2,4,1,8,5]=>[3,3,1,1]=>56
[8,7,2,4,3,6,1,5]=>[3,2,1,1,1]=>64
[7,1,2,3,5,6,8,4]=>[6,1,1]=>21
[6,1,2,3,8,7,4,5]=>[5,2,1]=>64
[5,1,2,3,7,8,6,4]=>[5,2,1]=>64
[5,1,2,3,8,7,6,4]=>[4,2,1,1]=>90
[5,1,2,3,8,6,7,4]=>[5,2,1]=>64
[6,1,2,3,5,8,7,4]=>[5,2,1]=>64
[8,6,2,4,3,1,7,5]=>[3,2,1,1,1]=>64
[7,6,3,2,4,8,1,5]=>[3,2,1,1,1]=>64
[2,1,6,3,4,8,7,5]=>[4,3,1]=>70
[8,6,3,2,4,7,1,5]=>[3,2,1,1,1]=>64
[7,6,2,4,3,1,8,5]=>[3,2,1,1,1]=>64
[6,1,2,3,5,7,8,4]=>[6,1,1]=>21
[5,1,2,3,6,8,7,4]=>[5,2,1]=>64
[1,3,8,5,4,2,7,6]=>[4,2,1,1]=>90
[2,4,8,1,7,3,6,5]=>[3,3,1,1]=>56
[3,4,8,5,7,6,1,2]=>[4,2,1,1]=>90
[7,1,4,2,6,3,5,8]=>[5,2,1]=>64
[6,8,1,4,7,2,3,5]=>[4,2,2]=>56
[1,6,4,2,8,3,5,7]=>[5,2,1]=>64
[1,6,3,8,5,4,2,7]=>[4,2,1,1]=>90
[6,8,1,7,3,5,4,2]=>[3,2,1,1,1]=>64
[7,1,3,6,5,4,2,8]=>[4,1,1,1,1]=>35
[7,3,1,6,5,4,2,8]=>[3,2,1,1,1]=>64
[7,1,2,3,6,5,4,8]=>[5,1,1,1]=>35
[6,8,1,2,7,3,5,4]=>[4,2,1,1]=>90
[1,5,8,2,7,6,3,4]=>[4,2,1,1]=>90
[5,1,8,2,7,6,3,4]=>[4,2,1,1]=>90
[5,8,2,7,6,3,4,1]=>[3,2,1,1,1]=>64
[6,8,2,1,7,4,3,5]=>[3,2,2,1]=>70
[2,1,6,3,8,5,4,7]=>[4,3,1]=>70
[2,5,3,8,7,4,6,1]=>[4,2,1,1]=>90
[3,5,8,7,1,4,2,6]=>[3,3,1,1]=>56
[5,3,8,4,1,7,6,2]=>[3,2,2,1]=>70
[4,2,8,7,6,3,5,1]=>[3,2,1,1,1]=>64
[4,2,8,7,6,5,3,1]=>[2,2,1,1,1,1]=>20
[4,1,8,7,6,5,3,2]=>[2,2,1,1,1,1]=>20
[4,3,8,7,6,5,1,2]=>[2,2,2,1,1]=>28
[5,8,7,4,6,1,2,3]=>[3,2,2,1]=>70
[5,6,3,1,2,4,8,7]=>[4,3,1]=>70
[5,6,1,2,4,3,8,7]=>[4,3,1]=>70
[4,5,8,1,7,2,3,6]=>[4,3,1]=>70
[1,3,2,5,8,7,4,6]=>[4,3,1]=>70
[3,5,1,8,7,4,6,2]=>[3,3,1,1]=>56
[3,5,1,8,7,2,6,4]=>[3,3,1,1]=>56
[4,5,8,3,1,7,2,6]=>[3,3,2]=>42
[3,4,8,7,6,2,1,5]=>[3,2,1,1,1]=>64
[3,1,4,8,7,6,2,5]=>[3,3,1,1]=>56
[3,4,8,7,6,5,1,2]=>[3,2,1,1,1]=>64
[1,2,7,5,8,6,4,3]=>[4,2,1,1]=>90
[7,1,4,8,2,6,5,3]=>[3,2,2,1]=>70
[6,8,1,3,7,5,2,4]=>[3,2,2,1]=>70
[3,7,8,1,2,6,5,4]=>[3,3,1,1]=>56
[1,3,7,8,2,6,5,4]=>[4,2,1,1]=>90
[2,3,7,8,1,6,5,4]=>[4,2,1,1]=>90
[2,7,8,1,3,6,5,4]=>[3,3,1,1]=>56
[8,1,2,6,7,3,5,4]=>[4,2,1,1]=>90
[8,1,2,6,7,5,3,4]=>[4,2,1,1]=>90
[8,2,5,7,1,3,6,4]=>[3,3,1,1]=>56
[2,8,1,6,7,3,5,4]=>[3,3,1,1]=>56
[2,6,8,3,7,1,5,4]=>[3,2,2,1]=>70
[2,8,6,4,7,1,5,3]=>[3,2,2,1]=>70
[6,8,3,4,1,7,5,2]=>[3,2,2,1]=>70
[6,8,3,7,4,1,5,2]=>[3,2,2,1]=>70
[2,6,8,3,7,5,1,4]=>[3,2,2,1]=>70
[2,8,1,6,7,5,3,4]=>[3,3,1,1]=>56
[8,2,5,7,1,6,3,4]=>[3,3,1,1]=>56
[8,4,7,2,3,6,1,5]=>[3,2,2,1]=>70
[8,5,7,4,2,6,1,3]=>[2,2,2,1,1]=>28
[8,3,5,7,4,1,6,2]=>[3,2,2,1]=>70
[8,5,2,4,7,1,6,3]=>[3,2,2,1]=>70
[8,2,3,5,7,1,6,4]=>[4,2,1,1]=>90
[8,2,4,7,3,6,1,5]=>[3,2,2,1]=>70
[8,2,7,1,4,6,3,5]=>[3,3,1,1]=>56
[8,7,1,2,4,6,3,5]=>[4,2,1,1]=>90
[8,7,1,4,6,2,3,5]=>[4,2,1,1]=>90
[8,4,7,1,3,6,2,5]=>[3,2,2,1]=>70
[1,6,8,3,7,2,5,4]=>[3,2,2,1]=>70
[8,3,5,7,1,2,6,4]=>[3,3,1,1]=>56
[5,8,7,1,3,6,2,4]=>[3,2,2,1]=>70
[8,5,4,7,1,6,2,3]=>[3,2,2,1]=>70
[8,5,4,7,1,2,6,3]=>[3,2,2,1]=>70
[8,5,1,4,7,2,6,3]=>[3,2,2,1]=>70
[1,4,6,8,2,7,5,3]=>[4,2,1,1]=>90
[1,6,5,8,2,7,4,3]=>[3,2,2,1]=>70
[8,5,6,3,1,7,4,2]=>[3,2,2,1]=>70
[5,6,2,8,1,7,4,3]=>[3,2,2,1]=>70
[1,8,4,5,7,2,6,3]=>[4,2,1,1]=>90
[5,8,7,3,6,1,2,4]=>[3,2,2,1]=>70
[8,3,5,7,1,6,2,4]=>[3,3,1,1]=>56
[1,6,8,3,7,5,2,4]=>[3,2,2,1]=>70
[6,3,8,2,7,5,1,4]=>[2,2,2,2]=>14
[6,8,4,2,7,1,5,3]=>[2,2,2,2]=>14
[8,6,4,7,3,1,5,2]=>[2,2,2,1,1]=>28
[8,4,5,7,3,1,6,2]=>[3,2,2,1]=>70
[8,4,2,5,7,1,6,3]=>[3,2,2,1]=>70
[8,3,4,7,2,6,1,5]=>[3,2,2,1]=>70
[8,7,1,3,4,6,2,5]=>[4,2,1,1]=>90
[8,3,7,2,4,6,1,5]=>[3,2,2,1]=>70
[2,8,4,5,7,1,6,3]=>[4,2,1,1]=>90
[8,7,3,4,5,1,6,2]=>[4,2,1,1]=>90
[8,7,4,5,2,6,1,3]=>[3,2,1,1,1]=>64
[5,8,7,2,3,6,1,4]=>[3,2,2,1]=>70
[8,7,2,3,4,6,1,5]=>[4,2,1,1]=>90
[8,7,2,3,6,1,4,5]=>[4,2,1,1]=>90
[1,3,2,8,5,4,7,6]=>[4,3,1]=>70
[4,2,8,5,3,7,1,6]=>[3,3,1,1]=>56
[5,2,1,8,4,3,7,6]=>[3,3,2]=>42
[6,2,8,4,3,7,5,1]=>[3,2,2,1]=>70
[7,2,8,4,3,1,6,5]=>[3,2,2,1]=>70
[7,3,4,8,2,1,6,5]=>[3,2,2,1]=>70
[6,3,4,8,2,7,5,1]=>[3,2,2,1]=>70
[5,3,4,1,8,2,7,6]=>[3,3,2]=>42
[8,1,4,5,2,3,7,6]=>[4,3,1]=>70
[8,1,5,4,3,2,7,6]=>[3,2,1,1,1]=>64
[3,5,4,2,8,1,7,6]=>[3,2,2,1]=>70
[4,5,3,2,8,7,1,6]=>[3,2,2,1]=>70
[6,4,3,2,8,7,5,1]=>[2,2,2,1,1]=>28
[6,5,3,2,1,7,8,4]=>[3,2,1,1,1]=>64
[5,6,3,2,7,8,4,1]=>[4,2,1,1]=>90
[4,1,6,3,2,7,8,5]=>[4,3,1]=>70
[3,6,4,2,7,8,1,5]=>[4,2,1,1]=>90
[8,1,6,4,3,7,2,5]=>[3,2,1,1,1]=>64
[8,1,7,4,3,6,5,2]=>[3,2,1,1,1]=>64
[2,7,4,1,3,6,5,8]=>[4,3,1]=>70
[3,7,4,2,6,1,5,8]=>[4,2,1,1]=>90
[4,1,7,3,2,6,5,8]=>[4,2,2]=>56
[5,7,3,2,6,4,8,1]=>[3,2,2,1]=>70
[6,7,3,2,5,4,1,8]=>[3,2,2,1]=>70
[7,6,3,2,1,5,4,8]=>[3,2,1,1,1]=>64
[4,7,5,6,2,3,8,1]=>[4,2,1,1]=>90
[3,1,7,5,6,2,4,8]=>[4,3,1]=>70
[2,7,5,6,1,3,4,8]=>[4,3,1]=>70
[2,6,5,7,1,3,8,4]=>[4,3,1]=>70
[4,6,5,7,2,8,1,3]=>[4,2,1,1]=>90
[5,6,4,7,2,8,3,1]=>[4,2,1,1]=>90
[6,5,4,1,7,2,8,3]=>[3,3,1,1]=>56
[7,5,4,6,2,1,8,3]=>[3,2,1,1,1]=>64
[6,4,5,7,1,8,2,3]=>[4,3,1]=>70
[5,4,6,1,7,8,2,3]=>[4,3,1]=>70
[8,1,5,6,7,2,3,4]=>[4,3,1]=>70
[2,1,4,6,8,7,3,5]=>[4,3,1]=>70
[3,4,6,8,7,1,2,5]=>[4,3,1]=>70
[4,3,1,6,8,7,2,5]=>[3,3,2]=>42
[5,3,6,8,7,2,4,1]=>[3,2,2,1]=>70
[6,3,5,1,8,7,2,4]=>[3,3,2]=>42
[7,3,5,8,6,2,1,4]=>[3,2,2,1]=>70
[7,2,8,5,6,3,1,4]=>[3,2,2,1]=>70
[6,2,8,5,1,7,3,4]=>[3,3,2]=>42
[4,2,1,8,6,7,3,5]=>[3,3,2]=>42
[1,3,2,8,6,7,4,5]=>[4,3,1]=>70
[2,3,8,6,7,1,4,5]=>[4,3,1]=>70
[8,1,3,2,6,7,4,5]=>[4,3,1]=>70
[2,3,8,7,1,6,5,4]=>[3,2,1,1,1]=>64
[4,2,8,7,6,1,5,3]=>[2,2,2,1,1]=>28
[5,2,8,7,6,4,1,3]=>[2,2,2,1,1]=>28
[7,2,1,8,6,5,4,3]=>[2,2,2,1,1]=>28
[7,3,6,1,8,5,4,2]=>[3,2,1,1,1]=>64
[6,3,7,8,5,4,2,1]=>[3,2,1,1,1]=>64
[5,3,7,8,6,4,1,2]=>[3,2,2,1]=>70
[4,3,1,7,8,6,5,2]=>[3,2,2,1]=>70
[3,4,7,8,6,1,5,2]=>[4,2,1,1]=>90
[8,1,5,7,6,2,4,3]=>[3,2,1,1,1]=>64
[3,5,7,6,8,1,4,2]=>[4,2,1,1]=>90
[4,5,7,6,8,3,1,2]=>[4,2,1,1]=>90
[5,4,1,7,6,8,3,2]=>[3,2,2,1]=>70
[6,4,7,5,8,3,2,1]=>[3,2,1,1,1]=>64
[7,4,6,5,1,8,3,2]=>[3,2,1,1,1]=>64
[7,5,6,4,3,1,8,2]=>[3,2,1,1,1]=>64
[6,5,1,7,4,3,8,2]=>[3,2,1,1,1]=>64
[4,6,7,5,3,8,1,2]=>[4,2,1,1]=>90
[3,6,7,5,1,4,8,2]=>[4,2,1,1]=>90
[8,1,6,7,5,4,2,3]=>[3,2,1,1,1]=>64
[8,1,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>7
[2,7,6,1,5,4,3,8]=>[3,2,1,1,1]=>64
[3,7,6,5,1,4,2,8]=>[3,2,1,1,1]=>64
[4,7,6,5,3,1,2,8]=>[3,2,1,1,1]=>64
[8,6,4,3,1,5,7,2]=>[3,2,1,1,1]=>64
[8,6,4,1,5,2,7,3]=>[3,3,1,1]=>56
[8,6,5,1,3,2,7,4]=>[3,2,1,1,1]=>64
[8,6,3,1,7,2,4,5]=>[4,2,1,1]=>90
[8,7,3,1,5,2,4,6]=>[4,2,1,1]=>90
[5,3,1,7,2,4,6,8]=>[5,2,1]=>64
[8,7,1,2,4,5,3,6]=>[5,1,1,1]=>35
[8,6,1,2,4,7,3,5]=>[4,2,1,1]=>90
[8,5,1,2,6,7,3,4]=>[4,3,1]=>70
[8,5,1,6,4,2,7,3]=>[3,3,1,1]=>56
[8,5,1,3,6,4,7,2]=>[4,2,1,1]=>90
[8,6,1,5,3,4,7,2]=>[4,1,1,1,1]=>35
[8,6,1,5,2,4,7,3]=>[4,1,1,1,1]=>35
[8,6,1,2,5,7,3,4]=>[4,2,1,1]=>90
[8,6,1,2,7,4,3,5]=>[4,2,1,1]=>90
[8,7,1,2,5,4,3,6]=>[4,1,1,1,1]=>35
[5,1,4,2,3,8,6,7]=>[5,2,1]=>64
[5,1,4,2,7,3,6,8]=>[5,2,1]=>64
[7,1,5,8,2,6,3,4]=>[4,2,2]=>56
[5,7,8,1,2,4,6,3]=>[4,3,1]=>70
[5,7,8,1,3,4,6,2]=>[4,3,1]=>70
[5,8,1,7,3,4,6,2]=>[4,2,1,1]=>90
[8,1,5,7,2,4,6,3]=>[4,2,1,1]=>90
[8,4,1,2,7,6,3,5]=>[4,2,1,1]=>90
[1,4,2,3,8,7,5,6]=>[5,2,1]=>64
[1,4,2,7,6,3,5,8]=>[5,2,1]=>64
[6,1,2,8,7,5,3,4]=>[4,2,1,1]=>90
[6,1,2,4,8,7,5,3]=>[4,2,1,1]=>90
[3,1,8,4,6,7,5,2]=>[4,2,1,1]=>90
[3,1,7,6,4,8,5,2]=>[3,3,1,1]=>56
[7,1,2,4,6,8,5,3]=>[5,1,1,1]=>35
[7,1,2,6,8,5,3,4]=>[4,2,1,1]=>90
[6,1,2,7,8,5,3,4]=>[4,3,1]=>70
[6,1,2,7,4,8,5,3]=>[4,3,1]=>70
[3,1,6,4,7,8,5,2]=>[4,3,1]=>70
[5,7,1,3,8,4,6,2]=>[4,3,1]=>70
[5,7,1,8,4,2,6,3]=>[3,3,2]=>42
[7,1,5,3,2,8,6,4]=>[3,2,2,1]=>70
[7,1,4,5,2,8,6,3]=>[4,2,2]=>56
[4,7,3,1,5,8,6,2]=>[3,3,2]=>42
[4,8,7,3,1,5,6,2]=>[3,2,2,1]=>70
[8,1,7,4,5,2,6,3]=>[4,2,1,1]=>90
[8,1,7,5,3,2,6,4]=>[3,2,1,1,1]=>64
[8,3,7,1,2,6,4,5]=>[4,2,1,1]=>90
[3,1,2,8,4,7,5,6]=>[5,2,1]=>64
[3,1,2,8,6,4,5,7]=>[5,2,1]=>64
[3,1,7,2,6,4,5,8]=>[5,2,1]=>64
[1,4,2,3,8,6,5,7]=>[5,2,1]=>64
[1,4,2,3,8,5,7,6]=>[5,2,1]=>64
[5,8,1,7,2,4,6,3]=>[4,2,1,1]=>90
[5,8,1,3,4,7,6,2]=>[4,2,1,1]=>90
[3,1,8,6,4,7,5,2]=>[3,3,1,1]=>56
[8,1,2,6,7,4,5,3]=>[4,2,1,1]=>90
[6,1,2,8,7,3,5,4]=>[4,2,1,1]=>90
[1,2,3,5,8,4,7,6]=>[5,2,1]=>64
[1,2,3,5,8,6,4,7]=>[6,1,1]=>21
[7,1,2,8,3,6,5,4]=>[4,2,1,1]=>90
[7,1,2,8,6,4,5,3]=>[4,2,1,1]=>90
[3,1,7,8,4,6,5,2]=>[3,3,1,1]=>56
[3,1,8,7,6,4,5,2]=>[3,2,1,1,1]=>64
[8,1,2,7,4,6,5,3]=>[4,1,1,1,1]=>35
[8,1,2,7,3,6,5,4]=>[4,1,1,1,1]=>35
[1,2,3,5,8,7,4,6]=>[5,2,1]=>64
[1,2,3,6,8,5,4,7]=>[5,2,1]=>64
[7,5,6,3,1,4,2,8]=>[3,2,2,1]=>70
[7,5,8,3,1,4,2,6]=>[3,2,2,1]=>70
[7,8,5,3,1,4,2,6]=>[3,2,2,1]=>70
[7,8,5,3,1,6,2,4]=>[3,2,2,1]=>70
[7,8,5,3,1,6,4,2]=>[2,2,2,2]=>14
[7,5,8,3,4,1,6,2]=>[3,2,2,1]=>70
[7,5,6,3,4,1,8,2]=>[3,2,2,1]=>70
[7,5,6,3,1,2,8,4]=>[3,3,1,1]=>56
[7,5,3,6,1,2,8,4]=>[3,3,1,1]=>56
[7,5,3,1,4,2,6,8]=>[4,2,1,1]=>90
[7,5,3,1,6,4,8,2]=>[3,2,2,1]=>70
[7,5,3,6,4,1,8,2]=>[3,2,2,1]=>70
[7,5,3,6,4,8,1,2]=>[3,2,2,1]=>70
[7,5,3,8,4,6,1,2]=>[3,2,2,1]=>70
[7,5,3,1,8,4,6,2]=>[3,2,2,1]=>70
[7,5,3,1,8,2,6,4]=>[3,2,2,1]=>70
[7,5,3,1,6,4,2,8]=>[3,2,2,1]=>70
[7,5,3,1,8,4,2,6]=>[3,2,2,1]=>70
[7,5,3,1,8,6,2,4]=>[3,2,2,1]=>70
[7,5,3,8,6,1,4,2]=>[2,2,2,2]=>14
[7,5,3,8,6,4,1,2]=>[2,2,2,2]=>14
[7,5,8,3,6,1,4,2]=>[2,2,2,2]=>14
[7,5,8,3,1,6,4,2]=>[2,2,2,2]=>14
[7,5,3,6,1,4,2,8]=>[3,2,2,1]=>70
[7,5,3,8,4,1,2,6]=>[3,2,2,1]=>70
[7,5,8,6,3,1,2,4]=>[3,2,2,1]=>70
[7,5,8,6,3,4,1,2]=>[2,2,2,2]=>14
[7,5,6,8,3,1,4,2]=>[3,2,2,1]=>70
[7,5,3,4,1,8,2,6]=>[3,3,1,1]=>56
[7,5,6,3,1,8,2,4]=>[3,3,1,1]=>56
[7,5,6,3,1,8,4,2]=>[3,2,2,1]=>70
[7,5,6,3,8,1,4,2]=>[3,2,2,1]=>70
[7,5,6,3,8,4,1,2]=>[3,2,2,1]=>70
[7,5,3,6,1,8,4,2]=>[3,2,2,1]=>70
[7,5,3,1,2,8,4,6]=>[4,2,1,1]=>90
[7,5,3,1,2,8,6,4]=>[3,2,2,1]=>70
[7,5,3,1,4,8,6,2]=>[3,2,2,1]=>70
[7,5,3,4,8,1,6,2]=>[3,2,2,1]=>70
[7,5,3,4,1,6,8,2]=>[4,2,1,1]=>90
[7,5,3,1,4,6,8,2]=>[4,2,1,1]=>90
[3,6,2,5,4,1,8,7]=>[3,3,1,1]=>56
[3,5,2,8,4,7,6,1]=>[3,3,1,1]=>56
[5,4,7,3,2,8,6,1]=>[3,2,1,1,1]=>64
[5,4,8,3,2,7,6,1]=>[2,2,2,1,1]=>28
[6,4,5,3,2,1,8,7]=>[3,2,1,1,1]=>64
[5,3,2,6,4,1,8,7]=>[3,3,1,1]=>56
[4,5,8,3,2,7,6,1]=>[3,2,2,1]=>70
[4,7,6,3,8,5,2,1]=>[3,2,1,1,1]=>64
[4,8,6,3,7,5,2,1]=>[3,2,1,1,1]=>64
[4,8,5,3,2,7,6,1]=>[3,2,1,1,1]=>64
[5,8,4,3,2,7,6,1]=>[2,2,2,1,1]=>28
[5,3,2,8,4,7,6,1]=>[3,2,2,1]=>70
[2,1,5,8,4,7,6,3]=>[3,3,1,1]=>56
[5,3,2,7,4,8,6,1]=>[3,3,1,1]=>56
[5,7,4,3,2,8,6,1]=>[3,2,1,1,1]=>64
[4,7,5,3,2,8,6,1]=>[3,2,1,1,1]=>64
[4,7,8,3,6,5,2,1]=>[3,2,1,1,1]=>64
[4,6,8,3,7,5,2,1]=>[3,2,1,1,1]=>64
[7,6,4,3,8,5,2,1]=>[2,2,1,1,1,1]=>20
[7,3,2,6,8,5,4,1]=>[3,2,1,1,1]=>64
[2,1,8,6,7,5,4,3]=>[3,2,1,1,1]=>64
[8,3,2,6,7,5,4,1]=>[3,2,1,1,1]=>64
[8,6,4,3,7,5,2,1]=>[2,2,1,1,1,1]=>20
[8,5,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>7
[8,4,5,3,2,7,6,1]=>[3,2,1,1,1]=>64
[8,4,7,3,6,5,2,1]=>[2,2,1,1,1,1]=>20
[8,4,6,3,7,5,2,1]=>[3,2,1,1,1]=>64
[7,4,6,3,8,5,2,1]=>[3,2,1,1,1]=>64
[3,7,2,6,8,5,4,1]=>[3,2,1,1,1]=>64
[3,8,2,6,7,5,4,1]=>[3,2,1,1,1]=>64
[3,8,2,5,4,7,6,1]=>[3,3,1,1]=>56
[3,7,2,8,6,5,4,1]=>[3,2,1,1,1]=>64
[3,6,2,8,7,5,4,1]=>[3,2,1,1,1]=>64
[6,4,7,3,8,5,2,1]=>[3,2,1,1,1]=>64
[6,4,8,3,7,5,2,1]=>[2,2,2,1,1]=>28
[7,4,8,3,6,5,2,1]=>[2,2,2,1,1]=>28
[7,4,5,3,2,8,6,1]=>[3,2,1,1,1]=>64
[7,5,4,3,2,8,6,1]=>[2,2,1,1,1,1]=>20
[7,3,2,5,4,8,6,1]=>[3,3,1,1]=>56
[2,1,7,5,4,8,6,3]=>[3,3,1,1]=>56
[7,3,2,8,6,5,4,1]=>[2,2,2,1,1]=>28
[7,8,4,3,6,5,2,1]=>[2,2,2,1,1]=>28
[6,8,5,7,4,3,2,1]=>[2,2,1,1,1,1]=>20
[6,8,4,3,7,5,2,1]=>[2,2,2,1,1]=>28
[6,3,2,8,7,5,4,1]=>[2,2,2,1,1]=>28
[6,3,2,7,8,5,4,1]=>[3,2,2,1]=>70
[6,7,4,3,8,5,2,1]=>[3,2,1,1,1]=>64
[2,3,1,4,5,6,7,8,9]=>[8,1]=>8
[2,3,4,1,5,6,7,8,9]=>[8,1]=>8
[2,3,4,5,1,6,7,8,9]=>[8,1]=>8
[2,3,4,5,6,1,7,8,9]=>[8,1]=>8
[2,3,1,4,5,6,7,8,9,10]=>[9,1]=>9
[2,4,3,1,5,6,7,8,9]=>[7,1,1]=>28
[2,3,4,1,5,6,7,8,9,10]=>[9,1]=>9
[2,3,4,5,1,6,7,8,9,10]=>[9,1]=>9
[2,3,4,5,6,1,7,8,9,10]=>[9,1]=>9
[2,3,4,5,6,7,1,8,9,10]=>[9,1]=>9
[2,3,4,5,6,8,7,1,9]=>[7,1,1]=>28
[2,3,4,5,6,7,8,1,9,10]=>[9,1]=>9
[2,3,4,5,6,7,9,8,1]=>[7,1,1]=>28
[4,6,8,3,5,7,1,2]=>[3,3,2]=>42
[6,8,1,2,4,5,7,3]=>[5,2,1]=>64
[3,5,8,2,4,7,1,6]=>[3,3,2]=>42
[8,3,5,2,4,1,6,7]=>[4,2,1,1]=>90
[4,2,5,7,3,6,1,8]=>[4,3,1]=>70
[4,5,2,8,3,1,6,7]=>[4,3,1]=>70
[4,2,5,8,3,7,1,6]=>[3,3,2]=>42
[2,1,6,8,4,7,3,5]=>[3,3,2]=>42
[1,2,5,8,3,6,7,4]=>[5,2,1]=>64
[5,3,6,8,4,7,1,2]=>[3,3,2]=>42
[1,6,5,8,2,4,7,3]=>[4,2,1,1]=>90
[3,1,2,6,8,5,7,4]=>[4,3,1]=>70
[1,4,3,8,2,6,7,5]=>[4,2,2]=>56
[5,4,8,3,2,1,6,7]=>[3,2,1,1,1]=>64
[5,4,3,7,2,6,1,8]=>[3,2,1,1,1]=>64
[4,3,6,2,7,5,1,8]=>[4,2,1,1]=>90
[4,6,3,2,1,8,5,7]=>[3,3,1,1]=>56
[4,1,7,3,2,5,8,6]=>[4,3,1]=>70
[4,3,1,7,8,2,6,5]=>[3,3,2]=>42
[3,5,1,2,7,8,6,4]=>[4,3,1]=>70
[7,5,1,4,8,2,6,3]=>[3,2,2,1]=>70
[5,4,7,3,8,6,1,2]=>[3,2,2,1]=>70
[5,8,4,7,6,3,1,2]=>[2,2,2,1,1]=>28
[5,8,7,1,4,2,6,3]=>[3,2,2,1]=>70
[8,3,5,1,2,7,6,4]=>[3,3,1,1]=>56
[4,8,3,1,7,2,6,5]=>[3,2,2,1]=>70
[1,8,4,3,5,2,7,6]=>[4,2,1,1]=>90
[4,6,3,1,5,2,8,7]=>[3,3,2]=>42
[4,7,3,6,5,2,1,8]=>[3,2,1,1,1]=>64
[5,3,7,6,4,2,1,8]=>[3,2,1,1,1]=>64
[1,6,3,4,2,8,7,5]=>[4,2,2]=>56
[1,8,3,6,2,7,5,4]=>[4,2,1,1]=>90
[1,6,8,7,4,2,5,3]=>[3,2,2,1]=>70
[6,4,8,7,5,3,1,2]=>[2,2,2,1,1]=>28
[7,6,4,3,8,5,1,2]=>[2,2,2,1,1]=>28
[1,7,6,2,8,4,5,3]=>[4,2,1,1]=>90
[7,1,3,2,6,8,5,4]=>[4,2,1,1]=>90
[1,5,3,2,7,4,8,6]=>[4,3,1]=>70
[6,3,2,1,8,5,4,7]=>[3,2,2,1]=>70
[6,5,3,2,7,4,1,8]=>[3,2,1,1,1]=>64
[5,2,6,3,7,4,1,8]=>[4,3,1]=>70
[2,8,5,3,1,6,4,7]=>[4,2,1,1]=>90
[2,1,7,3,8,5,4,6]=>[4,3,1]=>70
[1,6,2,3,7,8,5,4]=>[5,2,1]=>64
[1,6,7,2,8,4,5,3]=>[4,3,1]=>70
[5,7,1,8,2,4,6,3]=>[4,3,1]=>70
[5,1,2,7,8,3,6,4]=>[4,3,1]=>70
[2,4,1,7,8,6,3,5]=>[4,3,1]=>70
[4,2,1,7,3,8,5,6]=>[4,3,1]=>70
[6,2,8,4,3,1,5,7]=>[4,2,1,1]=>90
[7,3,2,1,8,4,5,6]=>[4,2,1,1]=>90
[7,8,3,2,5,6,1,4]=>[3,2,2,1]=>70
[7,1,8,2,4,5,6,3]=>[5,2,1]=>64
[8,7,6,1,2,4,5,3]=>[4,1,1,1,1]=>35
[8,3,7,6,2,1,4,5]=>[3,2,1,1,1]=>64
[3,2,8,7,5,1,4,6]=>[3,2,2,1]=>70
[8,3,6,5,2,1,4,7]=>[3,2,1,1,1]=>64
[7,6,3,5,2,4,1,8]=>[3,2,1,1,1]=>64
[7,4,6,2,5,3,1,8]=>[3,2,1,1,1]=>64
[8,2,4,1,6,5,3,7]=>[4,2,1,1]=>90
[4,2,8,1,7,5,3,6]=>[3,2,2,1]=>70
[8,2,4,1,7,6,3,5]=>[3,3,1,1]=>56
[8,7,1,5,6,2,4,3]=>[3,2,1,1,1]=>64
[8,5,7,3,6,4,1,2]=>[2,2,2,1,1]=>28
[6,8,3,7,5,4,1,2]=>[2,2,2,1,1]=>28
[8,1,6,7,5,2,4,3]=>[3,2,1,1,1]=>64
[8,1,2,6,4,3,7,5]=>[4,2,1,1]=>90
[2,8,1,7,5,4,3,6]=>[3,2,1,1,1]=>64
[2,5,1,8,6,4,3,7]=>[4,2,1,1]=>90
[5,7,2,6,4,3,1,8]=>[3,2,1,1,1]=>64
[6,2,7,5,4,3,1,8]=>[3,2,1,1,1]=>64
[2,1,8,6,5,4,3,7]=>[3,2,1,1,1]=>64
[1,2,7,5,4,3,8,6]=>[4,2,1,1]=>90
[1,7,2,4,3,8,6,5]=>[4,2,2]=>56
[1,7,2,8,3,6,5,4]=>[4,2,1,1]=>90
[1,7,8,6,5,2,4,3]=>[3,2,1,1,1]=>64
[7,3,8,6,5,4,1,2]=>[2,2,2,1,1]=>28
[1,8,7,6,5,2,4,3]=>[3,1,1,1,1,1]=>21
[8,1,7,3,2,6,5,4]=>[3,2,1,1,1]=>64
[5,1,4,3,2,8,7,6]=>[3,2,2,1]=>70
[8,6,5,3,2,1,7,4]=>[2,2,1,1,1,1]=>20
[8,6,3,2,1,7,4,5]=>[3,2,1,1,1]=>64
[8,6,5,4,1,7,2,3]=>[3,2,1,1,1]=>64
[8,6,5,1,7,3,2,4]=>[3,2,1,1,1]=>64
[8,6,1,7,4,3,2,5]=>[3,2,1,1,1]=>64
[4,6,3,2,7,5,1,8]=>[4,2,1,1]=>90
[1,4,3,7,2,5,8,6]=>[4,3,1]=>70
[7,4,8,3,1,6,2,5]=>[3,2,2,1]=>70
[7,1,5,8,3,2,6,4]=>[3,2,2,1]=>70
[5,7,4,1,8,2,6,3]=>[3,3,2]=>42
[5,7,4,3,1,8,6,2]=>[3,2,2,1]=>70
[1,8,7,2,5,4,6,3]=>[4,1,1,1,1]=>35
[1,8,5,3,7,2,6,4]=>[3,2,2,1]=>70
[4,3,1,8,7,5,2,6]=>[3,2,2,1]=>70
[1,4,8,6,3,5,2,7]=>[4,2,1,1]=>90
[7,4,6,3,5,2,1,8]=>[3,2,1,1,1]=>64
[1,3,5,6,8,4,2,7]=>[5,2,1]=>64
[3,5,4,8,7,1,2,6]=>[3,3,2]=>42
[3,1,4,6,8,7,2,5]=>[4,3,1]=>70
[1,6,3,8,7,2,5,4]=>[3,2,2,1]=>70
[1,6,2,4,8,7,5,3]=>[4,2,1,1]=>90
[8,4,1,6,7,5,3,2]=>[3,2,1,1,1]=>64
[7,1,6,4,8,5,2,3]=>[3,2,2,1]=>70
[7,3,6,8,5,1,2,4]=>[3,3,1,1]=>56
[1,3,7,2,6,8,4,5]=>[4,3,1]=>70
[3,6,5,2,8,1,4,7]=>[3,3,1,1]=>56
[3,6,5,7,2,4,1,8]=>[4,2,1,1]=>90
[4,2,6,3,8,1,5,7]=>[4,3,1]=>70
[4,2,6,7,3,5,1,8]=>[4,3,1]=>70
[3,6,2,4,7,5,1,8]=>[4,3,1]=>70
[3,6,2,4,1,8,5,7]=>[4,3,1]=>70
[7,3,8,2,1,6,4,5]=>[3,2,2,1]=>70
[7,3,5,2,1,8,6,4]=>[3,2,2,1]=>70
[8,7,6,4,3,1,5,2]=>[2,2,1,1,1,1]=>20
[8,7,6,4,1,5,2,3]=>[3,2,1,1,1]=>64
[3,8,7,2,1,4,6,5]=>[3,2,2,1]=>70
[3,8,2,7,1,5,4,6]=>[3,2,2,1]=>70
[3,6,8,2,1,5,4,7]=>[3,3,2]=>42
[2,4,8,1,6,5,3,7]=>[4,2,1,1]=>90
[4,2,8,1,5,7,3,6]=>[3,3,2]=>42
[8,5,7,6,1,4,2,3]=>[3,2,1,1,1]=>64
[8,6,1,7,3,5,4,2]=>[3,2,1,1,1]=>64
[8,6,1,7,5,4,2,3]=>[3,2,1,1,1]=>64
[1,6,2,8,7,3,5,4]=>[4,2,1,1]=>90
[1,8,2,4,6,7,3,5]=>[5,2,1]=>64
[2,8,5,4,7,1,3,6]=>[3,3,1,1]=>56
[2,1,5,8,6,4,3,7]=>[4,2,1,1]=>90
[7,2,5,6,4,3,1,8]=>[4,1,1,1,1]=>35
[1,2,5,7,8,4,3,6]=>[5,2,1]=>64
[1,2,7,4,8,6,3,5]=>[4,2,2]=>56
[1,2,7,8,3,6,5,4]=>[4,2,1,1]=>90
[7,1,8,6,3,5,4,2]=>[3,2,1,1,1]=>64
[1,8,7,6,3,5,2,4]=>[3,2,1,1,1]=>64
[1,8,7,4,6,3,2,5]=>[3,2,1,1,1]=>64
[7,1,6,4,2,3,5,8]=>[5,1,1,1]=>35
[8,6,2,4,7,3,5,1]=>[3,2,1,1,1]=>64
[8,6,2,4,5,7,3,1]=>[4,1,1,1,1]=>35
[7,1,4,6,5,8,3,2]=>[4,1,1,1,1]=>35
[7,1,2,3,8,5,4,6]=>[5,2,1]=>64
[7,1,5,4,3,8,2,6]=>[3,2,1,1,1]=>64
[7,1,5,4,6,2,8,3]=>[4,2,1,1]=>90
[6,5,8,7,2,3,1,4]=>[3,2,2,1]=>70
[6,5,7,8,2,4,1,3]=>[3,2,2,1]=>70
[3,4,7,2,5,8,1,6]=>[4,3,1]=>70
[4,3,8,1,2,7,5,6]=>[4,2,2]=>56
[2,8,3,1,5,6,4,7]=>[5,2,1]=>64
[3,8,7,1,5,4,2,6]=>[3,2,1,1,1]=>64
[3,4,1,5,7,6,2,8]=>[5,2,1]=>64
[2,8,6,1,5,3,7,4]=>[3,3,1,1]=>56
[7,6,5,1,3,8,2,4]=>[3,2,1,1,1]=>64
[6,7,5,2,1,3,8,4]=>[3,3,1,1]=>56
[4,7,5,2,8,1,6,3]=>[3,2,2,1]=>70
[7,3,8,4,1,5,2,6]=>[4,2,2]=>56
[7,2,3,4,1,6,5,8]=>[5,2,1]=>64
[4,2,8,3,6,1,5,7]=>[4,2,2]=>56
[6,8,5,7,2,1,3,4]=>[3,2,2,1]=>70
[4,8,5,2,7,1,3,6]=>[3,3,1,1]=>56
[6,3,5,2,1,7,4,8]=>[4,2,1,1]=>90
[3,6,5,4,2,8,1,7]=>[3,2,1,1,1]=>64
[1,6,4,7,2,5,3,8]=>[4,2,2]=>56
[1,6,4,8,2,5,3,7]=>[4,2,2]=>56
[1,6,5,8,2,4,3,7]=>[4,2,1,1]=>90
[1,6,8,2,4,3,7,5]=>[4,2,2]=>56
[1,6,2,4,3,7,8,5]=>[5,2,1]=>64
[1,5,6,2,4,7,3,8]=>[5,2,1]=>64
[1,5,6,2,4,7,8,3]=>[5,2,1]=>64
[1,5,8,2,4,7,3,6]=>[4,2,2]=>56
[1,5,7,2,4,8,3,6]=>[4,3,1]=>70
[1,6,5,7,2,4,3,8]=>[4,2,1,1]=>90
[1,6,7,2,4,3,8,5]=>[4,3,1]=>70
[1,5,6,7,2,4,8,3]=>[5,2,1]=>64
[1,5,8,2,4,6,7,3]=>[5,2,1]=>64
[1,5,7,2,4,6,8,3]=>[5,2,1]=>64
[1,5,7,8,3,2,4,6]=>[4,3,1]=>70
[1,5,8,3,2,4,6,7]=>[5,2,1]=>64
[1,5,6,2,4,8,3,7]=>[4,3,1]=>70
[1,7,6,2,8,3,4,5]=>[5,2,1]=>64
[1,7,3,4,2,8,6,5]=>[4,2,2]=>56
[1,6,2,4,3,8,7,5]=>[4,2,2]=>56
[1,5,6,2,4,8,7,3]=>[4,3,1]=>70
[1,5,8,7,3,2,4,6]=>[4,2,1,1]=>90
[1,4,2,3,5,8,7,6]=>[5,2,1]=>64
[1,5,2,3,4,8,7,6]=>[5,2,1]=>64
[1,6,5,2,3,8,7,4]=>[4,2,2]=>56
[1,7,4,2,8,6,5,3]=>[3,2,2,1]=>70
[1,7,6,5,2,8,4,3]=>[3,2,1,1,1]=>64
[1,6,7,5,2,3,8,4]=>[4,3,1]=>70
[1,7,5,2,8,4,3,6]=>[4,2,1,1]=>90
[1,7,5,6,2,8,3,4]=>[4,3,1]=>70
[1,5,7,6,2,4,8,3]=>[4,2,1,1]=>90
[1,5,8,3,2,4,7,6]=>[4,2,2]=>56
[1,6,5,2,3,7,4,8]=>[5,2,1]=>64
[1,6,5,2,3,7,8,4]=>[5,2,1]=>64
[1,6,8,4,2,3,7,5]=>[4,2,2]=>56
[1,7,4,6,2,8,3,5]=>[4,3,1]=>70
[1,7,3,5,2,8,4,6]=>[4,3,1]=>70
[1,6,8,5,2,3,7,4]=>[4,2,2]=>56
[1,6,4,2,3,7,8,5]=>[5,2,1]=>64
[1,6,4,2,3,7,5,8]=>[5,2,1]=>64
[1,5,8,6,2,4,7,3]=>[4,2,1,1]=>90
[1,5,7,3,2,4,8,6]=>[4,3,1]=>70
[1,7,3,4,2,8,5,6]=>[5,2,1]=>64
[1,7,4,2,8,5,3,6]=>[4,2,2]=>56
[1,6,7,4,2,3,8,5]=>[4,3,1]=>70
[1,6,4,2,3,8,5,7]=>[5,2,1]=>64
[1,7,6,4,2,8,5,3]=>[3,2,2,1]=>70
[1,7,5,2,8,6,4,3]=>[3,2,2,1]=>70
[1,6,4,2,3,8,7,5]=>[4,2,2]=>56
[3,7,5,6,1,4,8,2]=>[4,2,1,1]=>90
[3,5,4,1,6,7,8,2]=>[5,2,1]=>64
[1,7,6,4,3,5,8,2]=>[4,1,1,1,1]=>35
[8,4,1,3,7,2,5,6]=>[4,2,1,1]=>90
[4,7,1,3,8,2,5,6]=>[4,3,1]=>70
[4,7,8,1,2,6,5,3]=>[3,3,1,1]=>56
[1,8,6,4,2,7,5,3]=>[3,2,2,1]=>70
[8,7,1,3,6,2,5,4]=>[3,2,1,1,1]=>64
[1,8,4,3,7,2,5,6]=>[4,2,1,1]=>90
[2,4,3,7,8,6,1,5]=>[4,2,2]=>56
[5,7,6,8,3,2,1,4]=>[3,2,1,1,1]=>64
[8,1,4,3,7,2,5,6]=>[4,2,1,1]=>90
[8,2,3,4,7,6,1,5]=>[4,2,1,1]=>90
[4,2,3,8,5,6,1,7]=>[5,2,1]=>64
[8,2,3,7,5,6,1,4]=>[4,2,1,1]=>90
[3,7,4,8,5,2,1,6]=>[4,2,1,1]=>90
[1,4,8,3,6,2,5,7]=>[4,2,2]=>56
[7,5,8,6,3,2,1,4]=>[2,2,2,1,1]=>28
[6,5,8,7,3,2,1,4]=>[2,2,2,1,1]=>28
[2,5,3,8,7,6,1,4]=>[3,2,2,1]=>70
[1,8,7,3,6,2,5,4]=>[3,2,1,1,1]=>64
[6,8,7,5,3,2,1,4]=>[2,2,1,1,1,1]=>20
[5,7,6,8,3,4,1,2]=>[3,2,2,1]=>70
[1,7,4,6,5,8,2,3]=>[4,2,1,1]=>90
[1,6,2,7,5,8,3,4]=>[4,3,1]=>70
[1,8,4,6,5,7,2,3]=>[4,2,1,1]=>90
[7,8,1,5,2,4,3,6]=>[4,2,1,1]=>90
[1,7,2,8,5,6,3,4]=>[4,2,2]=>56
[5,7,6,8,1,4,2,3]=>[3,3,1,1]=>56
[7,8,5,6,1,3,2,4]=>[3,2,2,1]=>70
[1,3,2,7,6,8,4,5]=>[4,3,1]=>70
[1,7,6,8,2,4,3,5]=>[4,2,1,1]=>90
[7,8,1,6,2,4,3,5]=>[4,2,1,1]=>90
[7,8,1,4,2,6,3,5]=>[4,2,2]=>56
[7,8,1,4,2,5,3,6]=>[4,2,2]=>56
[7,8,2,1,4,3,6,5]=>[3,3,2]=>42
[4,3,6,5,8,7,1,2]=>[3,3,2]=>42
[3,4,1,5,6,7,8,9,2]=>[7,2]=>27
[3,4,5,1,6,7,8,9,2]=>[7,2]=>27
[3,4,5,6,7,1,8,9,2]=>[7,2]=>27
[3,4,5,6,7,8,1,9,2]=>[7,2]=>27
[3,1,2,5,6,7,8,9,4]=>[7,2]=>27
[3,4,1,5,6,7,8,9,10,2]=>[8,2]=>35
[3,4,5,6,1,7,8,9,10,2]=>[8,2]=>35
[3,4,5,6,7,1,2,9,8]=>[6,3]=>48
[3,4,5,6,7,8,1,2,9]=>[7,2]=>27
[3,4,5,6,7,8,9,1,10,2]=>[8,2]=>35
[1,6,2,3,8,7,4,5]=>[5,2,1]=>64
[1,7,4,3,2,8,6,5]=>[3,2,2,1]=>70
[1,4,7,6,2,5,8,3]=>[4,2,1,1]=>90
[1,2,6,5,3,7,4,8]=>[5,2,1]=>64
[1,2,6,5,3,7,8,4]=>[5,2,1]=>64
[1,3,7,5,2,6,8,4]=>[5,2,1]=>64
[1,3,7,4,2,6,8,5]=>[5,2,1]=>64
[1,2,6,4,3,7,8,5]=>[5,2,1]=>64
[1,2,6,4,3,7,5,8]=>[5,2,1]=>64
[1,4,7,3,2,5,8,6]=>[4,3,1]=>70
[1,4,3,2,5,8,6,7]=>[5,2,1]=>64
[1,5,3,2,4,8,6,7]=>[5,2,1]=>64
[1,7,5,3,2,8,6,4]=>[3,2,2,1]=>70
[1,5,3,2,4,8,7,6]=>[4,2,2]=>56
[7,6,5,4,3,1,8,2]=>[2,2,1,1,1,1]=>20
[6,8,5,4,3,2,1,7]=>[2,2,1,1,1,1]=>20
[7,1,5,4,3,8,6,2]=>[3,2,1,1,1]=>64
[2,8,5,4,3,7,1,6]=>[3,2,1,1,1]=>64
[1,8,7,6,5,4,3,10,9,2]=>[3,2,1,1,1,1,1]=>160
[7,6,1,4,3,8,5,2]=>[3,2,1,1,1]=>64
[3,8,5,4,7,2,1,6]=>[3,2,1,1,1]=>64
[7,6,5,1,3,8,4,2]=>[3,2,1,1,1]=>64
[1,8,3,4,7,2,6,5]=>[4,2,1,1]=>90
[7,5,8,4,3,2,1,6]=>[2,2,1,1,1,1]=>20
[8,4,7,5,2,6,1,3]=>[3,2,1,1,1]=>64
[5,4,6,8,2,1,7,3]=>[3,2,2,1]=>70
[8,4,6,5,2,1,7,3]=>[3,2,1,1,1]=>64
[4,8,7,5,6,1,3,2]=>[3,2,1,1,1]=>64
[2,7,5,1,8,4,3,6]=>[3,3,1,1]=>56
[5,1,8,7,4,2,3,6]=>[4,2,1,1]=>90
[2,8,6,7,4,3,5,1]=>[3,2,1,1,1]=>64
[3,6,5,2,4,1,8,7]=>[3,3,1,1]=>56
[5,2,3,6,4,1,8,7]=>[4,3,1]=>70
[6,1,4,5,3,2,8,7]=>[4,2,1,1]=>90
[3,8,7,1,4,6,5,2]=>[3,2,1,1,1]=>64
[5,7,1,2,4,3,8,6]=>[4,3,1]=>70
[4,3,7,6,8,2,5,1]=>[3,2,2,1]=>70
[5,3,6,8,1,7,2,4]=>[3,3,2]=>42
[3,2,6,8,5,7,1,4]=>[3,3,2]=>42
[6,3,7,2,4,8,5,1]=>[3,3,1,1]=>56
[7,4,8,6,5,2,1,3]=>[2,2,2,1,1]=>28
[7,1,8,2,5,4,3,6]=>[4,2,1,1]=>90
[2,5,3,7,4,1,8,6]=>[4,3,1]=>70
[3,6,4,7,5,1,8,2]=>[4,2,2]=>56
[8,4,7,6,2,3,1,5]=>[3,2,1,1,1]=>64
[8,4,7,1,2,5,6,3]=>[4,2,1,1]=>90
[4,2,8,7,3,5,6,1]=>[4,2,1,1]=>90
[8,1,7,4,2,5,6,3]=>[4,2,1,1]=>90
[7,4,3,8,2,5,6,1]=>[3,2,1,1,1]=>64
[6,4,1,5,8,2,7,3]=>[3,3,2]=>42
[2,5,8,7,3,6,1,4]=>[3,2,2,1]=>70
[2,1,5,8,7,4,6,3]=>[3,3,1,1]=>56
[8,3,5,6,7,4,1,2]=>[4,2,1,1]=>90
[7,4,3,2,8,5,6,1]=>[3,2,1,1,1]=>64
[4,2,7,1,8,5,6,3]=>[3,3,2]=>42
[4,1,7,2,8,5,6,3]=>[4,3,1]=>70
[2,4,8,7,3,5,6,1]=>[4,2,1,1]=>90
[4,7,8,3,1,5,6,2]=>[3,3,2]=>42
[3,4,7,2,8,5,6,1]=>[4,3,1]=>70
[3,7,1,4,8,5,6,2]=>[4,3,1]=>70
[7,2,3,4,8,5,6,1]=>[5,2,1]=>64
[6,1,8,5,2,7,4,3]=>[3,2,2,1]=>70
[2,1,7,4,5,8,6,3]=>[4,3,1]=>70
[2,1,8,3,6,7,5,4]=>[4,2,1,1]=>90
[8,2,1,6,4,7,5,3]=>[3,3,1,1]=>56
[7,8,2,6,4,1,5,3]=>[3,2,2,1]=>70
[2,6,3,5,8,7,1,4]=>[4,2,2]=>56
[7,6,2,1,5,8,4,3]=>[3,2,1,1,1]=>64
[4,5,2,7,6,1,8,3]=>[4,2,2]=>56
[5,1,6,8,4,7,2,3]=>[3,3,2]=>42
[3,6,8,7,5,2,1,4]=>[3,2,1,1,1]=>64
[7,4,8,6,5,2,3,1]=>[2,2,2,1,1]=>28
[8,1,6,4,7,3,2,5]=>[3,2,1,1,1]=>64
[7,6,4,1,2,3,8,5]=>[4,2,1,1]=>90
[2,6,4,8,5,3,7,1]=>[4,2,1,1]=>90
[7,3,5,8,4,2,1,6]=>[3,2,1,1,1]=>64
[3,2,5,8,4,1,7,6]=>[3,3,2]=>42
[8,4,7,1,5,2,3,6]=>[4,2,1,1]=>90
[4,8,7,5,6,1,2,3]=>[3,3,1,1]=>56
[6,1,4,8,7,3,5,2]=>[3,2,2,1]=>70
[7,2,8,4,3,5,6,1]=>[4,2,1,1]=>90
[4,7,8,1,3,5,6,2]=>[4,3,1]=>70
[8,7,3,4,1,5,6,2]=>[4,2,1,1]=>90
[4,8,2,7,3,5,6,1]=>[4,2,1,1]=>90
[3,1,8,7,2,5,6,4]=>[4,2,1,1]=>90
[3,8,1,7,2,5,6,4]=>[4,2,1,1]=>90
[8,2,3,7,1,5,6,4]=>[4,2,1,1]=>90
[6,4,8,7,1,3,2,5]=>[3,2,2,1]=>70
[2,8,4,6,7,3,1,5]=>[4,2,1,1]=>90
[4,3,8,2,7,6,1,5]=>[2,2,2,2]=>14
[6,8,4,2,1,3,7,5]=>[3,2,2,1]=>70
[7,8,2,4,3,5,6,1]=>[4,2,1,1]=>90
[2,8,3,7,1,5,6,4]=>[4,2,1,1]=>90
[8,1,2,7,3,5,6,4]=>[5,1,1,1]=>35
[6,4,1,3,2,8,5,7]=>[4,2,1,1]=>90
[5,3,8,6,2,1,4,7]=>[3,2,2,1]=>70
[4,6,5,2,8,3,1,7]=>[3,3,1,1]=>56
[4,3,7,5,1,8,2,6]=>[3,3,2]=>42
[6,8,5,2,7,4,3,1]=>[2,2,2,1,1]=>28
[7,2,5,4,3,8,1,6]=>[3,2,1,1,1]=>64
[3,6,8,1,4,5,2,7]=>[4,3,1]=>70
[6,8,1,2,4,5,3,7]=>[5,2,1]=>64
[8,1,6,2,4,5,3,7]=>[5,1,1,1]=>35
[3,8,6,1,2,5,4,7]=>[4,2,1,1]=>90
[5,8,1,6,2,3,4,7]=>[5,2,1]=>64
[4,1,6,5,8,2,3,7]=>[4,3,1]=>70
[4,3,8,6,2,5,1,7]=>[3,2,2,1]=>70
[8,3,6,1,4,5,2,7]=>[4,2,1,1]=>90
[2,3,6,8,4,5,1,7]=>[5,2,1]=>64
[2,7,5,4,3,8,1,6]=>[3,2,1,1,1]=>64
[6,3,8,7,4,2,5,1]=>[3,2,1,1,1]=>64
[5,8,4,3,7,6,1,2]=>[2,2,2,2]=>14
[8,7,4,3,1,6,2,5]=>[3,2,1,1,1]=>64
[1,7,4,3,8,6,2,5]=>[3,2,2,1]=>70
[7,1,5,3,4,8,2,6]=>[4,2,1,1]=>90
[2,8,6,1,7,4,5,3]=>[3,3,1,1]=>56
[4,8,6,5,7,2,1,3]=>[3,2,1,1,1]=>64
[4,7,6,8,2,1,5,3]=>[3,2,2,1]=>70
[6,1,8,7,4,3,5,2]=>[3,2,1,1,1]=>64
[8,5,4,3,1,6,7,2]=>[3,2,1,1,1]=>64
[1,5,8,6,3,4,7,2]=>[4,2,1,1]=>90
[2,5,8,6,3,4,7,1]=>[4,2,1,1]=>90
[4,1,3,8,5,6,7,2]=>[5,2,1]=>64
[6,5,8,4,3,1,7,2]=>[2,2,2,1,1]=>28
[4,6,5,2,8,1,7,3]=>[3,2,2,1]=>70
[7,2,8,1,3,6,4,5]=>[4,2,2]=>56
[1,8,5,2,3,6,7,4]=>[5,2,1]=>64
[1,8,3,2,5,6,7,4]=>[5,2,1]=>64
[2,8,3,1,5,6,7,4]=>[5,2,1]=>64
[4,8,3,2,5,6,7,1]=>[4,2,1,1]=>90
[8,2,3,1,5,6,7,4]=>[5,2,1]=>64
[2,1,8,3,5,6,7,4]=>[5,2,1]=>64
[1,4,8,2,3,6,7,5]=>[5,2,1]=>64
[3,1,2,7,8,6,4,5]=>[4,3,1]=>70
[7,5,1,8,2,4,3,6]=>[4,2,1,1]=>90
[3,5,8,1,2,4,7,6]=>[4,3,1]=>70
[4,5,8,1,2,3,7,6]=>[4,3,1]=>70
[4,2,7,1,8,6,3,5]=>[3,3,2]=>42
[3,8,4,1,2,6,7,5]=>[4,3,1]=>70
[5,4,8,2,3,6,7,1]=>[4,2,1,1]=>90
[5,8,3,6,7,4,1,2]=>[3,2,2,1]=>70
[2,3,1,6,8,4,7,5]=>[4,3,1]=>70
[2,4,3,7,1,8,5,6]=>[4,3,1]=>70
[1,4,7,3,2,8,5,6]=>[4,3,1]=>70
[2,7,1,4,3,8,5,6]=>[4,3,1]=>70
[2,4,1,8,6,3,7,5]=>[4,3,1]=>70
[8,4,1,3,6,2,7,5]=>[4,2,1,1]=>90
[6,8,5,1,7,2,3,4]=>[4,2,2]=>56
[7,3,6,5,8,2,1,4]=>[3,2,1,1,1]=>64
[7,6,3,5,8,2,1,4]=>[3,2,1,1,1]=>64
[4,5,8,7,3,6,1,2]=>[3,2,2,1]=>70
[3,5,2,8,6,1,7,4]=>[4,2,2]=>56
[8,2,5,6,1,4,7,3]=>[4,2,1,1]=>90
[8,6,5,4,1,2,7,3]=>[3,2,1,1,1]=>64
[2,6,1,8,3,7,5,4]=>[3,3,1,1]=>56
[4,7,1,6,2,8,5,3]=>[3,3,1,1]=>56
[6,1,5,3,8,7,2,4]=>[3,2,2,1]=>70
[2,8,6,3,7,1,5,4]=>[3,2,2,1]=>70
[7,6,1,5,8,2,3,4]=>[4,2,1,1]=>90
[3,6,8,5,1,2,7,4]=>[3,3,2]=>42
[6,5,2,4,8,1,7,3]=>[3,2,2,1]=>70
[5,1,4,8,2,6,7,3]=>[4,2,2]=>56
[4,8,2,5,1,6,7,3]=>[4,2,2]=>56
[3,4,8,5,2,6,7,1]=>[5,1,1,1]=>35
[4,2,1,8,5,6,7,3]=>[4,2,2]=>56
[1,5,4,8,2,6,7,3]=>[4,2,2]=>56
[7,2,1,5,8,6,3,4]=>[3,3,2]=>42
[2,8,4,5,1,6,7,3]=>[5,2,1]=>64
[5,4,8,3,7,6,1,2]=>[2,2,2,2]=>14
[3,1,5,8,6,2,7,4]=>[4,3,1]=>70
[6,3,4,8,5,1,7,2]=>[4,2,2]=>56
[5,3,4,8,1,6,7,2]=>[4,2,2]=>56
[7,6,1,2,8,3,5,4]=>[4,2,1,1]=>90
[7,5,8,4,1,2,6,3]=>[3,2,2,1]=>70
[7,5,8,4,6,1,3,2]=>[2,2,2,1,1]=>28
[6,5,4,8,7,1,3,2]=>[2,2,2,1,1]=>28
[6,5,4,8,1,2,7,3]=>[3,2,2,1]=>70
[7,5,1,6,2,3,8,4]=>[4,3,1]=>70
[7,5,1,6,8,2,4,3]=>[3,3,1,1]=>56
[6,5,4,1,8,2,7,3]=>[3,2,2,1]=>70
[6,5,4,7,1,2,8,3]=>[3,3,1,1]=>56
[6,5,4,7,8,1,3,2]=>[3,2,1,1,1]=>64
[6,5,3,7,1,4,2,8]=>[3,2,2,1]=>70
[6,5,3,1,8,4,2,7]=>[3,2,2,1]=>70
[7,5,1,4,8,3,2,6]=>[3,2,1,1,1]=>64
[8,1,6,4,7,3,5,2]=>[3,2,1,1,1]=>64
[7,5,1,4,8,3,6,2]=>[3,2,1,1,1]=>64
[6,5,3,7,1,4,8,2]=>[3,2,2,1]=>70
[6,4,3,1,5,8,7,2]=>[3,2,2,1]=>70
[7,4,1,5,3,8,6,2]=>[3,3,1,1]=>56
[8,1,5,4,3,7,6,2]=>[3,2,1,1,1]=>64
[8,1,5,4,3,7,2,6]=>[3,2,1,1,1]=>64
[7,4,1,5,3,8,2,6]=>[3,3,1,1]=>56
[7,4,1,5,3,2,6,8]=>[4,2,1,1]=>90
[8,1,5,4,3,2,6,7]=>[4,1,1,1,1]=>35
[8,1,6,4,2,5,3,7]=>[4,2,1,1]=>90
[6,5,3,1,2,7,4,8]=>[4,2,1,1]=>90
[6,5,3,8,1,4,2,7]=>[3,2,2,1]=>70
[7,6,8,1,4,3,2,5]=>[3,2,1,1,1]=>64
[8,1,7,2,5,4,3,6]=>[4,1,1,1,1]=>35
[8,1,7,2,5,4,6,3]=>[4,1,1,1,1]=>35
[7,6,1,2,5,4,8,3]=>[4,1,1,1,1]=>35
[6,5,3,8,1,4,7,2]=>[3,2,2,1]=>70
[6,5,3,1,2,7,8,4]=>[4,2,1,1]=>90
[7,5,1,4,2,6,8,3]=>[4,2,1,1]=>90
[8,1,6,4,2,5,7,3]=>[4,2,1,1]=>90
[7,4,1,5,3,2,8,6]=>[3,3,1,1]=>56
[6,4,3,1,5,2,8,7]=>[3,3,1,1]=>56
[6,4,3,1,5,7,2,8]=>[4,2,1,1]=>90
[7,4,1,5,3,6,2,8]=>[4,2,1,1]=>90
[8,1,5,4,3,6,2,7]=>[4,1,1,1,1]=>35
[8,1,5,4,3,6,7,2]=>[4,1,1,1,1]=>35
[7,4,1,5,3,6,8,2]=>[4,2,1,1]=>90
[6,4,3,1,5,7,8,2]=>[4,2,1,1]=>90
[6,7,3,8,4,5,1,2]=>[3,3,2]=>42
[4,7,5,6,1,8,2,3]=>[4,3,1]=>70
[4,7,5,6,3,8,1,2]=>[4,2,1,1]=>90
[4,8,3,6,5,7,1,2]=>[3,2,2,1]=>70
[5,6,4,7,1,8,2,3]=>[4,3,1]=>70
[5,6,1,8,4,7,2,3]=>[3,3,2]=>42
[3,6,4,5,1,8,2,7]=>[4,3,1]=>70
[2,8,3,6,1,5,4,7]=>[4,2,1,1]=>90
[7,8,1,5,3,6,2,4]=>[3,2,2,1]=>70
[1,8,3,6,2,7,4,5]=>[4,3,1]=>70
[1,7,3,6,4,8,2,5]=>[4,2,1,1]=>90
[6,7,1,5,3,8,2,4]=>[3,3,1,1]=>56
[6,7,5,8,1,4,2,3]=>[3,3,1,1]=>56
[5,8,6,7,2,3,1,4]=>[3,3,1,1]=>56
[6,7,2,8,1,4,3,5]=>[3,3,2]=>42
[3,4,2,7,5,6,1,8]=>[5,2,1]=>64
[2,3,1,8,4,7,5,6]=>[5,2,1]=>64
[7,8,2,6,1,4,3,5]=>[3,2,2,1]=>70
[2,8,6,7,1,4,3,5]=>[3,3,1,1]=>56
[2,8,1,4,3,7,5,6]=>[4,3,1]=>70
[3,7,2,5,4,6,1,8]=>[4,2,1,1]=>90
[4,5,2,7,3,6,1,8]=>[4,3,1]=>70
[4,5,1,8,2,7,3,6]=>[4,3,1]=>70
[3,4,1,8,6,7,2,5]=>[4,3,1]=>70
[3,4,2,5,1,8,6,7]=>[5,2,1]=>64
[4,5,2,8,1,6,3,7]=>[4,2,2]=>56
[4,5,3,6,1,8,2,7]=>[4,3,1]=>70
[8,6,3,7,5,1,2,4]=>[3,2,2,1]=>70
[7,6,2,8,3,5,1,4]=>[3,2,2,1]=>70
[7,6,2,3,8,5,1,4]=>[3,2,2,1]=>70
[8,4,2,1,7,6,3,5]=>[3,2,2,1]=>70
[8,5,7,2,1,4,3,6]=>[3,2,2,1]=>70
[5,8,7,3,1,4,2,6]=>[3,2,2,1]=>70
[5,8,7,3,1,4,6,2]=>[3,2,2,1]=>70
[8,5,7,2,1,4,6,3]=>[3,2,2,1]=>70
[8,4,2,1,3,7,6,5]=>[3,2,2,1]=>70
[8,4,3,1,7,2,6,5]=>[3,2,2,1]=>70
[8,5,1,3,2,7,6,4]=>[3,2,2,1]=>70
[5,2,8,6,4,1,3,7]=>[3,2,2,1]=>70
[8,4,7,5,1,6,2,3]=>[3,3,1,1]=>56
[8,4,7,5,1,2,3,6]=>[4,2,1,1]=>90
[8,3,2,6,5,1,4,7]=>[3,2,2,1]=>70
[4,8,6,3,5,1,2,7]=>[3,2,2,1]=>70
[4,8,7,3,1,5,2,6]=>[3,2,2,1]=>70
[8,7,3,1,4,2,6,5]=>[3,3,1,1]=>56
[8,7,3,1,2,6,4,5]=>[4,2,1,1]=>90
[8,7,3,1,2,4,6,5]=>[4,2,1,1]=>90
[8,3,2,1,4,7,6,5]=>[3,2,2,1]=>70
[8,3,2,1,7,4,6,5]=>[3,2,2,1]=>70
[8,4,7,2,1,5,6,3]=>[3,2,2,1]=>70
[8,7,2,1,6,3,4,5]=>[4,2,1,1]=>90
[3,6,5,4,1,2,8,7]=>[3,3,1,1]=>56
[3,8,5,6,7,4,1,2]=>[4,2,1,1]=>90
[4,7,5,8,6,2,1,3]=>[3,2,2,1]=>70
[2,5,7,8,6,3,4,1]=>[4,2,1,1]=>90
[4,8,5,7,6,3,1,2]=>[3,2,1,1,1]=>64
[4,6,3,2,1,5,8,7]=>[3,3,1,1]=>56
[6,2,1,5,3,4,8,7]=>[4,3,1]=>70
[5,8,1,3,7,6,4,2]=>[3,2,1,1,1]=>64
[4,7,2,3,6,1,8,5]=>[4,2,2]=>56
[3,7,4,2,8,1,5,6]=>[4,2,1,1]=>90
[4,2,6,8,5,7,3,1]=>[3,3,1,1]=>56
[6,4,2,7,3,8,5,1]=>[3,3,1,1]=>56
[8,1,6,7,5,3,4,2]=>[3,2,1,1,1]=>64
[2,1,5,8,7,6,3,4]=>[3,3,1,1]=>56
[2,1,4,7,6,3,8,5]=>[4,3,1]=>70
[6,4,7,8,5,3,2,1]=>[3,2,1,1,1]=>64
[4,1,3,7,6,2,8,5]=>[4,2,2]=>56
[8,5,1,6,3,2,7,4]=>[3,3,1,1]=>56
[6,3,7,1,5,2,8,4]=>[3,3,2]=>42
[3,2,6,8,4,7,5,1]=>[3,3,1,1]=>56
[8,4,6,1,3,2,5,7]=>[4,2,1,1]=>90
[4,2,8,6,7,3,1,5]=>[3,3,1,1]=>56
[7,4,3,8,2,1,5,6]=>[3,2,1,1,1]=>64
[4,7,5,8,1,6,3,2]=>[3,2,2,1]=>70
[6,4,3,2,7,8,1,5]=>[3,2,1,1,1]=>64
[4,2,5,1,6,7,8,3]=>[5,2,1]=>64
[2,4,8,5,7,1,3,6]=>[4,3,1]=>70
[3,7,1,4,6,8,5,2]=>[4,2,1,1]=>90
[7,8,2,5,6,1,4,3]=>[3,2,2,1]=>70
[2,4,3,8,7,5,6,1]=>[4,2,1,1]=>90
[2,6,7,3,5,1,8,4]=>[4,2,2]=>56
[7,6,8,4,2,5,3,1]=>[2,2,2,1,1]=>28
[8,5,7,1,6,3,2,4]=>[3,2,1,1,1]=>64
[6,5,7,2,8,4,3,1]=>[3,2,1,1,1]=>64
[3,4,8,6,5,2,1,7]=>[4,1,1,1,1]=>35
[2,7,6,1,4,5,8,3]=>[4,2,1,1]=>90
[6,5,8,2,1,7,3,4]=>[3,2,2,1]=>70
[7,4,3,5,1,6,8,2]=>[4,2,1,1]=>90
[4,1,6,3,5,8,7,2]=>[4,3,1]=>70
[6,2,5,8,4,3,7,1]=>[3,2,1,1,1]=>64
[8,6,7,1,5,4,3,2]=>[2,2,1,1,1,1]=>20
[2,1,6,5,8,4,7,3]=>[3,3,1,1]=>56
[2,1,6,8,5,4,3,7]=>[3,3,1,1]=>56
[4,1,8,5,6,2,3,7]=>[4,3,1]=>70
[2,6,4,8,7,3,5,1]=>[3,2,2,1]=>70
[6,2,8,4,3,5,1,7]=>[4,2,1,1]=>90
[4,8,2,7,6,1,3,5]=>[3,2,2,1]=>70
[3,1,8,2,7,5,4,6]=>[4,2,1,1]=>90
[3,8,1,2,6,7,4,5]=>[4,3,1]=>70
[5,8,4,3,2,7,1,6]=>[2,2,2,1,1]=>28
[7,4,8,6,3,2,5,1]=>[2,2,2,1,1]=>28
[5,8,4,7,2,1,3,6]=>[3,2,2,1]=>70
[2,1,8,4,3,7,5,6]=>[4,3,1]=>70
[6,3,8,2,4,5,7,1]=>[4,2,1,1]=>90
[5,8,4,2,3,6,1,7]=>[4,2,1,1]=>90
[5,8,2,4,3,1,6,7]=>[4,2,1,1]=>90
[2,8,3,1,6,4,5,7]=>[5,2,1]=>64
[8,2,1,3,4,7,5,6]=>[5,2,1]=>64
[1,4,8,2,6,3,5,7]=>[5,2,1]=>64
[1,2,7,3,5,4,8,6]=>[5,2,1]=>64
[1,2,3,8,4,5,7,6]=>[6,1,1]=>21
[1,2,8,3,4,5,7,6]=>[6,1,1]=>21
[1,3,8,2,6,4,5,7]=>[5,2,1]=>64
[1,5,7,2,3,6,4,8]=>[5,2,1]=>64
[1,7,2,3,5,4,8,6]=>[5,2,1]=>64
[1,3,8,2,4,5,7,6]=>[5,2,1]=>64
[1,2,3,8,4,6,7,5]=>[6,1,1]=>21
[1,8,2,3,5,4,6,7]=>[6,1,1]=>21
[1,7,8,2,3,6,4,5]=>[5,2,1]=>64
[1,6,7,8,2,3,5,4]=>[4,3,1]=>70
[1,7,8,2,5,3,6,4]=>[4,2,2]=>56
[1,7,8,2,4,5,3,6]=>[5,2,1]=>64
[1,2,8,3,6,4,5,7]=>[6,1,1]=>21
[1,8,2,3,6,4,5,7]=>[6,1,1]=>21
[1,2,8,3,5,4,6,7]=>[6,1,1]=>21
[1,2,7,8,3,6,4,5]=>[5,2,1]=>64
[1,5,2,7,8,3,6,4]=>[4,3,1]=>70
[1,3,2,8,4,6,7,5]=>[5,2,1]=>64
[1,8,2,3,4,6,7,5]=>[6,1,1]=>21
[1,7,8,2,4,3,6,5]=>[4,2,2]=>56
[6,7,3,1,5,2,8,4]=>[3,3,2]=>42
[6,8,3,1,5,2,7,4]=>[3,3,2]=>42
[6,7,4,5,1,2,8,3]=>[3,3,2]=>42
[6,7,5,4,1,2,8,3]=>[3,3,1,1]=>56
[6,4,7,5,1,2,8,3]=>[3,3,2]=>42
[6,3,8,1,5,2,7,4]=>[3,3,2]=>42
[5,6,8,4,1,7,2,3]=>[3,3,2]=>42
[4,6,8,5,7,1,2,3]=>[3,3,2]=>42
[4,5,8,6,7,1,2,3]=>[4,3,1]=>70
[5,4,8,6,1,7,2,3]=>[3,3,2]=>42
[5,3,8,1,6,7,2,4]=>[3,3,2]=>42
[5,4,7,6,1,8,2,3]=>[3,3,2]=>42
[4,8,6,5,7,1,2,3]=>[3,3,1,1]=>56
[4,6,5,7,8,1,2,3]=>[4,3,1]=>70
[5,7,4,6,1,8,2,3]=>[3,3,2]=>42
[5,8,4,6,1,7,2,3]=>[3,3,2]=>42
[5,8,3,1,6,7,2,4]=>[3,3,2]=>42
[5,7,3,1,6,8,2,4]=>[3,3,2]=>42
[5,6,3,1,7,8,2,4]=>[4,3,1]=>70
[5,8,3,1,7,6,2,4]=>[3,2,2,1]=>70
[5,7,4,8,1,6,2,3]=>[3,3,2]=>42
[5,4,6,8,1,7,2,3]=>[3,3,2]=>42
[4,8,6,7,5,1,2,3]=>[3,3,1,1]=>56
[5,2,1,7,8,6,3,4]=>[3,3,2]=>42
[5,3,8,1,7,6,2,4]=>[3,2,2,1]=>70
[5,4,8,7,1,6,2,3]=>[3,2,2,1]=>70
[4,6,8,7,5,1,2,3]=>[3,3,1,1]=>56
[4,7,8,6,5,1,2,3]=>[3,3,1,1]=>56
[4,8,7,6,5,1,2,3]=>[3,2,1,1,1]=>64
[2,5,4,7,3,6,1,8]=>[4,2,1,1]=>90
[2,4,6,3,7,5,1,8]=>[5,2,1]=>64
[4,2,7,3,6,5,1,8]=>[4,2,1,1]=>90
[4,2,6,3,1,5,8,7]=>[4,3,1]=>70
[2,5,3,1,6,4,8,7]=>[4,3,1]=>70
[2,5,3,7,6,4,1,8]=>[4,2,1,1]=>90
[2,6,5,3,7,4,1,8]=>[4,2,1,1]=>90
[4,2,7,6,3,5,1,8]=>[4,2,1,1]=>90
[2,7,5,3,6,4,1,8]=>[4,2,1,1]=>90
[2,6,3,7,5,4,1,8]=>[4,2,1,1]=>90
[1,7,5,2,3,8,4,6]=>[5,2,1]=>64
[2,1,3,7,5,4,8,6]=>[4,3,1]=>70
[2,3,1,8,6,5,4,7]=>[4,2,1,1]=>90
[2,5,3,1,8,6,4,7]=>[4,2,2]=>56
[4,2,8,3,1,6,5,7]=>[4,2,2]=>56
[8,3,2,6,4,1,5,7]=>[4,2,1,1]=>90
[3,6,8,2,1,4,5,7]=>[4,3,1]=>70
[1,5,2,8,3,4,7,6]=>[5,2,1]=>64
[1,2,6,3,8,7,4,5]=>[5,2,1]=>64
[1,2,8,3,6,4,7,5]=>[5,2,1]=>64
[1,2,7,6,3,4,8,5]=>[5,2,1]=>64
[2,1,3,8,7,5,4,6]=>[4,2,1,1]=>90
[1,2,3,8,6,4,7,5]=>[5,2,1]=>64
[1,2,3,7,4,8,6,5]=>[5,2,1]=>64
[1,2,7,6,3,8,4,5]=>[5,2,1]=>64
[1,2,3,6,4,8,7,5]=>[5,2,1]=>64
[1,2,3,7,6,4,8,5]=>[5,2,1]=>64
[2,6,3,1,8,5,4,7]=>[4,2,2]=>56
[2,1,3,8,5,4,7,6]=>[4,3,1]=>70
[7,1,8,4,2,3,5,6]=>[5,2,1]=>64
[2,1,8,4,3,5,7,6]=>[4,3,1]=>70
[4,2,6,3,1,8,5,7]=>[4,3,1]=>70
[5,4,2,8,3,1,6,7]=>[4,2,1,1]=>90
[3,5,8,2,4,1,6,7]=>[4,3,1]=>70
[2,5,4,8,3,1,6,7]=>[4,2,1,1]=>90
[4,2,1,8,3,5,7,6]=>[4,2,2]=>56
[1,8,7,4,2,3,5,6]=>[5,1,1,1]=>35
[1,5,2,8,7,3,4,6]=>[5,2,1]=>64
[1,2,7,3,6,4,8,5]=>[5,2,1]=>64
[1,2,8,6,3,7,4,5]=>[5,2,1]=>64
[1,2,7,3,8,6,4,5]=>[5,2,1]=>64
[1,2,3,8,4,7,6,5]=>[5,1,1,1]=>35
[1,2,7,3,4,8,6,5]=>[5,2,1]=>64
[1,2,6,3,8,4,7,5]=>[5,2,1]=>64
[1,5,2,3,8,7,4,6]=>[5,2,1]=>64
[4,2,1,8,3,7,5,6]=>[4,2,2]=>56
[8,3,2,1,7,4,5,6]=>[4,2,1,1]=>90
[1,8,4,2,7,3,5,6]=>[5,2,1]=>64
[1,2,8,6,3,4,7,5]=>[5,2,1]=>64
[1,2,7,3,8,4,6,5]=>[5,2,1]=>64
[1,2,3,8,7,4,6,5]=>[5,1,1,1]=>35
[1,2,3,8,7,6,4,5]=>[5,1,1,1]=>35
[3,8,5,7,2,6,4,1]=>[3,2,1,1,1]=>64
[3,4,8,6,1,2,5,7]=>[4,3,1]=>70
[2,4,8,1,5,7,6,3]=>[4,2,1,1]=>90
[2,4,8,1,3,5,7,6]=>[4,3,1]=>70
[3,5,7,6,2,4,8,1]=>[4,2,1,1]=>90
[4,8,6,7,1,2,3,5]=>[4,3,1]=>70
[3,8,5,7,1,6,4,2]=>[3,2,1,1,1]=>64
[3,4,8,6,2,1,5,7]=>[4,2,1,1]=>90
[5,8,6,7,3,4,2,1]=>[3,2,1,1,1]=>64
[5,8,6,7,2,1,3,4]=>[3,3,1,1]=>56
[5,8,6,7,2,1,4,3]=>[3,2,2,1]=>70
[4,3,1,7,5,2,8,6]=>[3,3,2]=>42
[4,3,8,5,1,6,7,2]=>[4,2,2]=>56
[4,8,6,7,1,5,3,2]=>[3,2,1,1,1]=>64
[5,8,6,7,1,4,3,2]=>[3,2,1,1,1]=>64
[4,2,3,8,5,1,6,7]=>[5,2,1]=>64
[3,2,4,8,6,1,5,7]=>[4,2,2]=>56
[3,2,5,7,6,1,4,8]=>[4,2,2]=>56
[4,3,8,5,2,6,7,1]=>[4,2,1,1]=>90
[3,8,4,7,2,5,1,6]=>[4,2,1,1]=>90
[4,1,2,6,7,5,3,8]=>[5,2,1]=>64
[4,1,7,5,2,8,6,3]=>[3,3,2]=>42
[5,8,6,7,4,1,2,3]=>[3,3,1,1]=>56
[5,8,6,7,4,1,3,2]=>[3,2,1,1,1]=>64
[5,8,6,7,3,1,4,2]=>[3,2,2,1]=>70
[4,8,6,7,3,1,5,2]=>[3,2,2,1]=>70
[4,1,6,7,5,3,8,2]=>[4,2,1,1]=>90
[5,8,6,7,4,2,1,3]=>[3,2,1,1,1]=>64
[5,8,6,7,4,3,1,2]=>[3,2,1,1,1]=>64
[3,8,7,6,1,4,2,5]=>[3,2,1,1,1]=>64
[5,1,8,3,6,7,2,4]=>[4,2,2]=>56
[3,6,1,4,7,8,5,2]=>[4,3,1]=>70
[1,6,8,4,7,5,2,3]=>[3,2,2,1]=>70
[6,8,1,3,5,7,2,4]=>[4,2,2]=>56
[3,8,1,6,5,4,2,7]=>[3,2,1,1,1]=>64
[6,1,7,3,8,4,2,5]=>[4,3,1]=>70
[3,1,7,6,5,8,4,2]=>[3,2,1,1,1]=>64
[7,4,1,6,8,2,5,3]=>[3,3,1,1]=>56
[6,1,3,2,7,8,4,5]=>[4,3,1]=>70
[1,8,6,2,5,3,4,7]=>[5,1,1,1]=>35
[4,7,2,6,8,1,5,3]=>[3,2,2,1]=>70
[8,7,3,6,4,5,2,1]=>[3,1,1,1,1,1]=>21
[2,7,4,1,6,8,3,5]=>[4,3,1]=>70
[1,8,6,4,5,2,3,7]=>[4,2,1,1]=>90
[6,4,1,2,7,5,8,3]=>[4,2,2]=>56
[4,3,7,8,5,1,6,2]=>[3,3,2]=>42
[5,4,8,2,7,6,1,3]=>[2,2,2,2]=>14
[5,8,2,6,3,4,1,7]=>[4,2,1,1]=>90
[4,1,7,5,8,6,2,3]=>[3,3,2]=>42
[5,1,7,8,4,3,6,2]=>[3,3,1,1]=>56
[1,4,3,5,7,8,2,6]=>[5,2,1]=>64
[1,5,2,7,4,3,8,6]=>[4,3,1]=>70
[2,8,5,6,4,3,1,7]=>[4,1,1,1,1]=>35
[1,8,6,5,4,3,2,7]=>[3,1,1,1,1,1]=>21
[6,1,5,2,8,4,7,3]=>[4,2,1,1]=>90
[4,6,1,8,5,7,2,3]=>[3,3,2]=>42
[4,7,1,2,8,5,6,3]=>[4,3,1]=>70
[1,4,7,2,8,5,6,3]=>[4,3,1]=>70
[1,7,3,5,8,6,2,4]=>[4,2,2]=>56
[7,3,5,8,6,1,2,4]=>[3,3,2]=>42
[3,6,8,1,5,7,2,4]=>[3,3,2]=>42
[3,4,6,5,8,1,7,2]=>[4,2,2]=>56
[6,8,1,5,7,2,3,4]=>[4,2,2]=>56
[7,1,2,5,8,6,3,4]=>[4,2,2]=>56
[1,7,2,5,8,6,3,4]=>[4,2,2]=>56
[1,7,6,8,2,3,5,4]=>[4,2,1,1]=>90
[7,6,8,1,2,3,5,4]=>[4,2,1,1]=>90
[2,7,1,5,8,6,3,4]=>[3,3,2]=>42
[2,4,7,1,8,5,6,3]=>[4,3,1]=>70
[4,7,5,8,3,1,6,2]=>[3,2,2,1]=>70
[4,7,2,1,8,5,6,3]=>[3,3,2]=>42
[7,6,8,2,1,3,5,4]=>[3,2,2,1]=>70
[1,2,7,6,8,3,5,4]=>[4,2,1,1]=>90
[3,7,6,8,2,1,5,4]=>[3,2,2,1]=>70
[7,4,2,1,6,8,5,3]=>[3,2,2,1]=>70
[6,7,4,1,8,5,3,2]=>[3,2,2,1]=>70
[6,7,4,3,1,8,5,2]=>[3,2,2,1]=>70
[2,7,4,1,6,8,5,3]=>[4,2,1,1]=>90
[2,3,7,6,8,1,5,4]=>[4,2,1,1]=>90
[7,4,2,6,8,5,1,3]=>[3,2,2,1]=>70
[7,3,2,5,8,6,1,4]=>[3,2,2,1]=>70
[3,1,7,6,8,2,5,4]=>[3,3,1,1]=>56
[3,7,6,8,1,2,5,4]=>[3,3,1,1]=>56
[1,3,7,6,8,2,5,4]=>[4,2,1,1]=>90
[1,7,4,2,6,8,5,3]=>[4,2,1,1]=>90
[7,4,1,2,6,8,5,3]=>[4,2,1,1]=>90
[7,1,4,2,8,5,6,3]=>[4,2,2]=>56
[7,1,8,2,5,4,6,3]=>[4,2,1,1]=>90
[7,3,8,4,6,1,5,2]=>[3,2,2,1]=>70
[7,2,8,1,6,4,5,3]=>[3,2,2,1]=>70
[7,1,6,8,5,4,2,3]=>[3,2,1,1,1]=>64
[7,1,2,6,8,5,4,3]=>[4,1,1,1,1]=>35
[1,7,2,6,8,5,4,3]=>[4,1,1,1,1]=>35
[1,7,6,8,3,2,5,4]=>[3,2,2,1]=>70
[7,6,8,3,1,2,5,4]=>[3,2,2,1]=>70
[7,1,5,8,6,3,2,4]=>[3,2,2,1]=>70
[7,2,5,8,6,3,1,4]=>[3,2,2,1]=>70
[3,6,7,1,8,5,4,2]=>[4,2,1,1]=>90
[7,2,6,8,5,4,1,3]=>[3,2,1,1,1]=>64
[7,6,8,2,3,1,5,4]=>[3,2,2,1]=>70
[2,7,6,8,3,1,5,4]=>[3,2,2,1]=>70
[2,7,1,6,8,5,4,3]=>[3,2,1,1,1]=>64
[6,7,3,1,8,5,4,2]=>[3,2,2,1]=>70
[6,7,1,8,5,4,3,2]=>[3,2,1,1,1]=>64
[7,2,1,6,8,5,4,3]=>[3,2,1,1,1]=>64
[7,6,8,3,2,1,5,4]=>[2,2,2,1,1]=>28
[4,7,8,5,6,1,3,2]=>[3,2,2,1]=>70
[4,6,5,8,7,1,3,2]=>[3,2,2,1]=>70
[5,6,4,8,1,2,7,3]=>[3,3,2]=>42
[8,1,5,6,7,2,4,3]=>[4,2,1,1]=>90
[6,4,5,1,8,2,7,3]=>[3,3,2]=>42
[5,4,6,7,1,2,8,3]=>[4,3,1]=>70
[4,3,6,7,2,1,5,8]=>[4,2,1,1]=>90
[5,3,6,7,1,4,2,8]=>[4,2,2]=>56
[8,1,4,6,7,3,2,5]=>[4,2,1,1]=>90
[8,1,3,6,7,4,5,2]=>[4,2,1,1]=>90
[7,2,1,6,8,4,5,3]=>[3,3,1,1]=>56
[5,2,6,7,1,4,8,3]=>[4,2,2]=>56
[4,2,6,7,3,1,8,5]=>[4,3,1]=>70
[6,2,4,1,5,8,7,3]=>[4,2,2]=>56
[7,2,1,5,4,8,6,3]=>[3,3,1,1]=>56
[8,1,4,5,3,7,2,6]=>[4,2,1,1]=>90
[7,3,1,5,4,8,2,6]=>[3,3,1,1]=>56
[6,3,4,1,5,8,2,7]=>[4,3,1]=>70
[5,3,4,2,1,8,6,7]=>[4,2,1,1]=>90
[4,3,5,2,7,1,6,8]=>[4,2,1,1]=>90
[5,6,3,8,1,4,2,7]=>[3,3,2]=>42
[8,1,7,2,4,5,6,3]=>[5,1,1,1]=>35
[7,6,1,2,4,5,8,3]=>[5,1,1,1]=>35
[4,7,8,2,3,1,6,5]=>[3,3,2]=>42
[5,6,2,8,1,4,7,3]=>[3,3,2]=>42
[6,5,2,1,3,7,8,4]=>[4,2,1,1]=>90
[7,5,1,3,2,6,8,4]=>[4,2,1,1]=>90
[8,1,6,3,2,5,7,4]=>[4,2,1,1]=>90
[7,4,1,3,5,2,8,6]=>[4,2,1,1]=>90
[5,4,2,3,1,6,8,7]=>[4,2,1,1]=>90
[7,3,1,4,5,6,2,8]=>[5,2,1]=>64
[8,1,4,3,5,6,2,7]=>[5,1,1,1]=>35
[6,2,3,1,5,7,8,4]=>[5,2,1]=>64
[7,8,4,2,1,6,5,3]=>[2,2,2,2]=>14
[7,8,4,2,1,5,6,3]=>[3,2,2,1]=>70
[7,8,3,4,6,2,1,5]=>[3,2,2,1]=>70
[6,2,3,8,7,5,1,4]=>[3,2,2,1]=>70
[6,2,3,7,8,5,1,4]=>[4,2,2]=>56
[5,2,6,3,8,1,7,4]=>[3,3,2]=>42
[6,4,3,8,7,5,1,2]=>[2,2,2,2]=>14
[6,2,4,1,7,3,5,8]=>[4,3,1]=>70
[4,5,6,8,3,2,1,7]=>[4,2,1,1]=>90
[5,6,1,4,2,3,7,8]=>[5,2,1]=>64
[5,6,8,4,3,7,1,2]=>[3,2,2,1]=>70
[4,6,5,8,3,2,1,7]=>[3,2,1,1,1]=>64
[6,2,3,4,5,8,1,7]=>[5,2,1]=>64
[5,1,4,3,6,2,8,7]=>[4,2,1,1]=>90
[5,1,4,3,7,2,8,6]=>[4,2,1,1]=>90
[5,1,4,3,8,2,7,6]=>[3,2,2,1]=>70
[5,6,2,4,1,7,8,3]=>[4,2,2]=>56
[5,7,2,4,1,8,6,3]=>[3,3,2]=>42
[6,1,4,2,7,8,5,3]=>[4,2,2]=>56
[5,2,7,4,1,6,8,3]=>[4,2,2]=>56
[5,1,6,3,4,2,7,8]=>[5,2,1]=>64
[4,8,6,5,3,2,1,7]=>[3,1,1,1,1,1]=>21
[4,8,5,6,3,2,1,7]=>[4,1,1,1,1]=>35
[5,4,7,8,3,2,1,6]=>[3,2,1,1,1]=>64
[5,4,8,7,3,2,1,6]=>[2,2,2,1,1]=>28
[4,7,6,8,3,2,1,5]=>[3,2,1,1,1]=>64
[5,1,8,4,2,3,6,7]=>[5,2,1]=>64
[5,1,7,4,2,3,6,8]=>[5,2,1]=>64
[5,8,1,3,4,2,6,7]=>[5,2,1]=>64
[4,8,7,6,3,2,1,5]=>[2,2,1,1,1,1]=>20
[4,8,2,6,3,7,5,1]=>[3,3,1,1]=>56
[4,3,8,1,6,2,5,7]=>[4,2,2]=>56
[4,3,8,7,2,5,1,6]=>[3,2,2,1]=>70
[5,8,4,3,7,1,6,2]=>[2,2,2,2]=>14
[6,8,1,2,4,3,5,7]=>[5,2,1]=>64
[5,8,7,1,3,4,2,6]=>[4,2,1,1]=>90
[4,3,8,2,7,5,6,1]=>[3,2,2,1]=>70
[1,4,3,8,2,6,5,7]=>[4,2,2]=>56
[4,3,2,8,1,6,5,7]=>[3,2,2,1]=>70
[4,1,3,8,2,6,5,7]=>[4,2,2]=>56
[3,7,8,1,5,4,2,6]=>[3,3,1,1]=>56
[7,3,8,1,5,4,6,2]=>[3,2,2,1]=>70
[3,4,8,1,6,2,5,7]=>[4,3,1]=>70
[3,4,2,1,8,6,5,7]=>[4,2,2]=>56
[3,6,7,8,4,1,2,5]=>[4,3,1]=>70
[4,1,7,8,5,3,2,6]=>[3,3,1,1]=>56
[4,3,1,8,2,6,5,7]=>[4,2,2]=>56
[2,6,8,4,7,3,1,5]=>[3,2,2,1]=>70
[7,6,2,8,3,5,4,1]=>[3,2,1,1,1]=>64
[3,2,4,8,1,6,5,7]=>[4,2,2]=>56
[2,4,8,3,6,1,5,7]=>[4,2,2]=>56
[7,4,1,8,5,2,6,3]=>[3,3,2]=>42
[1,3,2,4,8,6,5,7]=>[5,2,1]=>64
[3,1,2,4,8,6,5,7]=>[5,2,1]=>64
[3,1,4,8,2,6,5,7]=>[4,3,1]=>70
[3,7,4,8,5,1,2,6]=>[4,2,2]=>56
[6,7,2,8,3,5,4,1]=>[3,3,1,1]=>56
[2,1,3,4,8,6,5,7]=>[5,2,1]=>64
[1,2,3,4,8,6,5,7]=>[6,1,1]=>21
[4,8,3,6,2,1,5,7]=>[3,2,2,1]=>70
[3,5,8,2,6,1,4,7]=>[4,2,2]=>56
[3,6,5,8,2,4,1,7]=>[3,3,1,1]=>56
[5,3,8,7,2,4,6,1]=>[3,2,2,1]=>70
[2,8,4,5,7,3,6,1]=>[4,2,1,1]=>90
[2,4,5,7,3,8,1,6]=>[5,2,1]=>64
[6,2,4,5,8,3,1,7]=>[4,2,1,1]=>90
[4,8,1,2,5,6,3,7]=>[5,2,1]=>64
[8,1,3,5,2,6,4,7]=>[5,2,1]=>64
[5,2,1,6,3,8,4,7]=>[4,3,1]=>70
[6,2,5,1,8,4,3,7]=>[3,3,1,1]=>56
[3,6,1,5,8,4,2,7]=>[3,3,1,1]=>56
[6,1,4,5,8,3,2,7]=>[4,2,1,1]=>90
[5,6,4,8,1,3,2,7]=>[3,3,1,1]=>56
[6,5,4,3,8,2,1,7]=>[2,2,1,1,1,1]=>20
[5,4,3,7,2,8,1,6]=>[3,2,1,1,1]=>64
[5,8,4,3,7,2,6,1]=>[2,2,2,1,1]=>28
[4,6,8,3,7,2,5,1]=>[3,2,2,1]=>70
[7,4,6,3,2,8,1,5]=>[3,2,1,1,1]=>64
[1,4,3,6,2,7,8,5]=>[5,2,1]=>64
[1,5,4,3,7,2,8,6]=>[4,2,1,1]=>90
[4,7,8,5,3,1,2,6]=>[3,3,1,1]=>56
[5,7,3,4,1,2,8,6]=>[3,3,2]=>42
[8,5,4,7,6,2,1,3]=>[2,2,2,1,1]=>28
[8,5,7,4,3,6,1,2]=>[2,2,2,1,1]=>28
[4,3,8,1,6,7,5,2]=>[3,2,2,1]=>70
[4,7,8,3,6,1,5,2]=>[3,2,2,1]=>70
[5,3,8,6,7,4,1,2]=>[3,2,2,1]=>70
[1,3,8,6,4,7,5,2]=>[4,2,1,1]=>90
[8,6,2,7,4,1,5,3]=>[3,2,2,1]=>70
[7,6,2,1,4,3,8,5]=>[3,3,1,1]=>56
[7,6,1,3,4,2,8,5]=>[4,2,1,1]=>90
[1,5,7,3,2,6,8,4]=>[4,2,2]=>56
[1,6,7,3,2,5,8,4]=>[4,2,2]=>56
[3,2,6,8,5,7,4,1]=>[3,3,1,1]=>56
[5,8,2,3,6,7,4,1]=>[4,2,1,1]=>90
[7,5,2,3,1,6,8,4]=>[4,2,1,1]=>90
[1,6,4,7,2,3,8,5]=>[4,3,1]=>70
[3,1,7,5,2,8,4,6]=>[4,3,1]=>70
[2,5,7,4,1,8,3,6]=>[4,3,1]=>70
[4,2,6,1,7,8,3,5]=>[4,3,1]=>70
[4,2,7,6,3,8,1,5]=>[3,3,1,1]=>56
[6,4,8,7,2,3,5,1]=>[3,2,2,1]=>70
[3,2,6,8,7,4,5,1]=>[3,3,1,1]=>56
[3,2,7,4,1,6,8,5]=>[4,2,2]=>56
[6,3,2,1,7,8,4,5]=>[3,3,1,1]=>56
[3,7,1,8,4,2,5,6]=>[4,3,1]=>70
[4,2,1,3,7,5,8,6]=>[4,3,1]=>70
[8,1,3,7,4,2,6,5]=>[4,2,1,1]=>90
[8,4,3,7,6,2,1,5]=>[2,2,2,1,1]=>28
[8,3,5,2,7,6,1,4]=>[3,2,2,1]=>70
[3,6,2,8,7,1,5,4]=>[3,2,2,1]=>70
[7,3,2,8,1,6,5,4]=>[2,2,2,2]=>14
[3,8,7,2,6,5,4,1]=>[2,2,1,1,1,1]=>20
[4,2,7,8,6,1,5,3]=>[3,2,2,1]=>70
[6,8,2,4,7,1,5,3]=>[3,2,2,1]=>70
[5,2,1,8,7,3,6,4]=>[3,2,2,1]=>70
[8,2,1,6,3,7,5,4]=>[3,3,1,1]=>56
[6,8,3,1,7,5,2,4]=>[3,2,2,1]=>70
[5,8,1,6,7,2,4,3]=>[3,3,1,1]=>56
[6,2,8,1,5,7,4,3]=>[3,2,2,1]=>70
[5,7,8,2,6,1,4,3]=>[3,2,2,1]=>70
[8,7,2,5,6,4,3,1]=>[3,1,1,1,1,1]=>21
[8,6,7,5,2,4,3,1]=>[2,2,1,1,1,1]=>20
[7,2,6,8,1,5,4,3]=>[3,2,1,1,1]=>64
[1,2,7,8,5,6,4,3]=>[4,2,1,1]=>90
[7,4,8,1,6,2,5,3]=>[3,2,2,1]=>70
[3,7,1,8,2,6,5,4]=>[3,3,1,1]=>56
[2,1,7,3,8,6,5,4]=>[3,3,1,1]=>56
[8,2,1,7,6,5,4,3]=>[2,2,1,1,1,1]=>20
[8,1,4,7,6,5,3,2]=>[3,1,1,1,1,1]=>21
[8,6,7,5,1,4,3,2]=>[2,2,1,1,1,1]=>20
[7,8,6,5,4,1,3,2]=>[2,2,1,1,1,1]=>20
[5,8,4,3,2,1,6,7]=>[3,2,1,1,1]=>64
[6,4,7,3,2,1,8,5]=>[3,2,1,1,1]=>64
[5,8,3,6,2,1,4,7]=>[3,2,2,1]=>70
[5,3,7,6,2,1,4,8]=>[3,2,2,1]=>70
[5,8,4,2,6,1,3,7]=>[3,2,2,1]=>70
[4,8,7,2,5,1,3,6]=>[3,2,2,1]=>70
[4,8,3,2,5,1,7,6]=>[3,2,2,1]=>70
[4,3,7,2,5,1,8,6]=>[3,3,1,1]=>56
[6,4,2,7,5,1,3,8]=>[3,2,2,1]=>70
[6,2,7,8,5,1,3,4]=>[3,3,2]=>42
[5,2,7,6,8,1,3,4]=>[3,3,2]=>42
[4,2,7,6,5,1,3,8]=>[3,2,2,1]=>70
[2,8,7,6,5,1,3,4]=>[3,2,1,1,1]=>64
[6,5,4,3,1,7,8,2]=>[3,2,1,1,1]=>64
[6,4,7,3,1,5,8,2]=>[3,2,2,1]=>70
[5,4,7,3,1,8,6,2]=>[3,2,2,1]=>70
[5,4,3,6,1,8,7,2]=>[3,2,2,1]=>70
[5,3,7,6,1,4,8,2]=>[3,2,2,1]=>70
[4,3,7,6,1,5,8,2]=>[3,2,2,1]=>70
[3,8,7,6,1,4,5,2]=>[3,2,1,1,1]=>64
[4,8,7,2,1,5,3,6]=>[3,2,2,1]=>70
[5,8,3,2,1,4,7,6]=>[3,2,2,1]=>70
[3,8,7,2,1,4,5,6]=>[4,2,1,1]=>90
[5,8,2,6,1,4,3,7]=>[3,2,2,1]=>70
[6,4,2,7,1,5,3,8]=>[3,2,2,1]=>70
[3,2,7,6,1,4,5,8]=>[4,2,2]=>56
[5,8,4,1,6,7,3,2]=>[3,2,2,1]=>70
[6,4,7,1,5,8,3,2]=>[3,2,2,1]=>70
[4,8,7,1,5,6,3,2]=>[3,2,1,1,1]=>64
[4,8,3,1,5,6,7,2]=>[4,2,2]=>56
[5,8,2,1,6,4,3,7]=>[3,2,2,1]=>70
[3,8,2,1,5,4,6,7]=>[4,2,2]=>56
[6,2,7,1,5,4,3,8]=>[3,2,2,1]=>70
[5,2,7,1,6,4,3,8]=>[3,2,2,1]=>70
[3,2,7,1,5,4,6,8]=>[4,2,2]=>56
[2,8,7,1,5,4,3,6]=>[3,2,1,1,1]=>64
[6,4,1,7,5,8,3,2]=>[3,2,2,1]=>70
[5,4,1,6,7,8,3,2]=>[4,2,1,1]=>90
[6,3,1,7,5,4,8,2]=>[3,2,2,1]=>70
[5,3,1,6,7,4,8,2]=>[4,2,2]=>56
[4,3,1,6,5,7,8,2]=>[4,2,2]=>56
[2,8,1,6,5,4,3,7]=>[3,2,1,1,1]=>64
[6,1,7,8,5,4,3,2]=>[3,2,1,1,1]=>64
[4,1,7,6,5,8,3,2]=>[3,2,1,1,1]=>64
[4,5,8,1,2,6,3,7]=>[4,3,1]=>70
[1,4,5,7,2,6,3,8]=>[5,2,1]=>64
[1,7,3,5,6,2,4,8]=>[5,2,1]=>64
[8,1,3,5,7,2,4,6]=>[4,3,1]=>70
[3,6,8,1,7,2,4,5]=>[4,3,1]=>70
[3,4,5,6,8,1,7,2]=>[5,2,1]=>64
[4,5,8,2,6,7,1,3]=>[4,2,2]=>56
[8,2,3,5,6,7,1,4]=>[5,2,1]=>64
[1,7,2,3,5,4,6,8]=>[6,1,1]=>21
[8,1,2,3,5,4,6,7]=>[6,1,1]=>21
[2,7,8,1,3,5,4,6]=>[4,3,1]=>70
[2,7,8,3,5,6,1,4]=>[4,2,2]=>56
[2,4,5,7,8,1,6,3]=>[5,2,1]=>64
[4,5,8,1,7,6,3,2]=>[3,2,1,1,1]=>64
[4,5,8,7,2,1,6,3]=>[3,2,2,1]=>70
[8,7,3,5,6,2,1,4]=>[3,2,1,1,1]=>64
[8,7,2,1,3,5,4,6]=>[4,2,1,1]=>90
[3,6,8,7,2,1,5,4]=>[3,2,2,1]=>70
[8,6,4,1,7,5,3,2]=>[2,2,2,1,1]=>28
[7,6,4,3,1,8,5,2]=>[2,2,2,1,1]=>28
[2,3,6,7,8,1,5,4]=>[5,2,1]=>64
[3,6,8,1,2,5,4,7]=>[4,3,1]=>70
[1,3,6,7,2,5,4,8]=>[5,2,1]=>64
[7,4,1,8,5,2,3,6]=>[4,2,2]=>56
[7,1,4,2,8,3,6,5]=>[4,2,2]=>56
[7,1,8,2,5,3,6,4]=>[4,2,2]=>56
[8,1,7,5,4,2,3,6]=>[4,1,1,1,1]=>35
[1,7,2,6,5,4,3,8]=>[4,1,1,1,1]=>35
[1,7,6,3,2,5,4,8]=>[4,2,1,1]=>90
[8,6,3,1,2,5,4,7]=>[4,2,1,1]=>90
[8,1,7,6,3,2,4,5]=>[4,1,1,1,1]=>35
[8,2,5,7,6,3,1,4]=>[3,2,1,1,1]=>64
[3,6,8,1,7,5,4,2]=>[3,2,1,1,1]=>64
[8,2,6,7,5,4,1,3]=>[3,2,1,1,1]=>64
[2,7,8,6,3,1,5,4]=>[3,2,2,1]=>70
[2,7,8,1,6,5,4,3]=>[3,2,1,1,1]=>64
[7,3,1,8,6,5,4,2]=>[2,2,2,1,1]=>28
[8,7,2,1,6,5,4,3]=>[2,2,1,1,1,1]=>20
[8,7,6,3,2,1,5,4]=>[2,2,1,1,1,1]=>20
[2,1,8,6,3,7,4,5]=>[4,3,1]=>70
[8,6,1,5,2,7,4,3]=>[3,2,1,1,1]=>64
[8,5,1,7,4,2,6,3]=>[3,2,2,1]=>70
[2,1,7,5,4,3,8,6]=>[3,3,1,1]=>56
[2,1,7,8,3,6,5,4]=>[3,3,1,1]=>56
[2,1,4,8,5,7,3,6]=>[4,3,1]=>70
[8,5,3,1,6,2,4,7]=>[4,2,1,1]=>90
[6,4,1,5,2,3,8,7]=>[4,3,1]=>70
[8,3,7,5,2,6,1,4]=>[3,2,1,1,1]=>64
[5,3,7,4,6,8,1,2]=>[4,2,2]=>56
[5,8,3,7,6,2,1,4]=>[2,2,2,1,1]=>28
[4,2,6,3,8,5,1,7]=>[4,3,1]=>70
[5,8,2,1,7,6,4,3]=>[2,2,2,1,1]=>28
[8,3,2,4,1,7,5,6]=>[4,2,1,1]=>90
[7,2,8,1,4,6,5,3]=>[3,2,2,1]=>70
[6,8,1,4,5,3,2,7]=>[4,2,1,1]=>90
[8,2,6,1,4,7,3,5]=>[3,3,1,1]=>56
[8,3,5,6,1,7,4,2]=>[4,2,1,1]=>90
[8,7,3,6,5,1,4,2]=>[2,2,1,1,1,1]=>20
[2,7,4,3,6,1,8,5]=>[4,2,1,1]=>90
[3,4,7,2,8,1,5,6]=>[4,3,1]=>70
[4,2,3,5,8,1,6,7]=>[5,2,1]=>64
[3,8,4,7,1,6,5,2]=>[3,2,1,1,1]=>64
[8,3,4,5,7,6,1,2]=>[4,2,1,1]=>90
[3,2,4,5,6,8,1,7]=>[5,2,1]=>64
[5,6,8,1,4,2,7,3]=>[3,3,2]=>42
[1,5,7,8,4,6,2,3]=>[4,2,2]=>56
[1,3,5,7,8,6,2,4]=>[5,2,1]=>64
[3,5,7,8,6,1,2,4]=>[4,3,1]=>70
[3,5,1,6,8,2,7,4]=>[4,3,1]=>70
[3,1,5,6,8,2,7,4]=>[4,3,1]=>70
[2,3,5,6,8,1,7,4]=>[5,2,1]=>64
[5,6,4,8,2,1,7,3]=>[3,2,2,1]=>70
[5,1,6,3,8,4,7,2]=>[4,3,1]=>70
[2,5,1,6,8,3,7,4]=>[4,3,1]=>70
[5,1,2,6,8,3,7,4]=>[4,3,1]=>70
[5,7,1,8,6,2,3,4]=>[4,3,1]=>70
[1,5,2,7,8,6,3,4]=>[4,3,1]=>70
[1,6,7,5,2,8,3,4]=>[4,3,1]=>70
[6,1,7,5,2,8,3,4]=>[4,3,1]=>70
[2,6,7,5,1,8,3,4]=>[4,3,1]=>70
[5,7,2,8,6,1,3,4]=>[3,3,2]=>42
[3,5,7,8,6,2,1,4]=>[4,2,1,1]=>90
[5,1,7,8,6,3,4,2]=>[3,3,1,1]=>56
[5,1,3,7,8,6,4,2]=>[4,2,1,1]=>90
[5,2,7,8,4,6,1,3]=>[3,3,2]=>42
[3,2,5,7,8,6,1,4]=>[4,2,2]=>56
[6,2,7,5,1,8,3,4]=>[3,3,2]=>42
[1,2,6,7,5,8,3,4]=>[5,2,1]=>64
[6,2,7,5,4,1,8,3]=>[3,2,2,1]=>70
[6,7,5,2,4,1,8,3]=>[3,2,2,1]=>70
[6,7,2,5,3,8,1,4]=>[3,3,1,1]=>56
[6,7,4,5,2,1,8,3]=>[3,2,2,1]=>70
[5,1,7,8,6,4,3,2]=>[3,2,1,1,1]=>64
[2,5,7,8,6,3,1,4]=>[4,2,1,1]=>90
[5,1,7,8,6,3,2,4]=>[3,3,1,1]=>56
[6,3,7,5,1,8,2,4]=>[3,3,2]=>42
[1,6,7,5,3,8,2,4]=>[4,2,1,1]=>90
[1,6,7,5,4,2,8,3]=>[4,2,1,1]=>90
[6,7,5,1,4,2,8,3]=>[3,3,1,1]=>56
[5,7,8,6,4,1,2,3]=>[3,3,1,1]=>56
[4,1,7,2,6,5,8,3]=>[4,2,1,1]=>90
[2,4,7,1,5,6,8,3]=>[5,2,1]=>64
[6,7,4,1,5,2,8,3]=>[3,3,2]=>42
[1,6,7,4,5,2,8,3]=>[4,2,2]=>56
[1,6,3,7,5,8,2,4]=>[4,2,2]=>56
[6,3,1,7,5,8,2,4]=>[3,3,2]=>42
[2,5,3,7,8,6,1,4]=>[4,2,2]=>56
[6,7,5,4,2,1,8,3]=>[3,2,1,1,1]=>64
[6,3,2,7,5,8,1,4]=>[3,2,2,1]=>70
[6,7,4,2,5,1,8,3]=>[3,2,2,1]=>70
[6,2,7,4,5,1,8,3]=>[4,2,2]=>56
[6,2,3,7,5,8,1,4]=>[4,2,2]=>56
[2,7,6,1,3,8,5,4]=>[3,3,1,1]=>56
[7,3,5,1,8,2,6,4]=>[3,3,2]=>42
[7,3,5,1,8,2,4,6]=>[4,3,1]=>70
[3,7,5,1,8,6,2,4]=>[3,3,2]=>42
[2,6,7,4,1,8,3,5]=>[4,3,1]=>70
[3,6,5,1,8,4,7,2]=>[3,3,1,1]=>56
[3,6,5,1,8,4,2,7]=>[3,3,1,1]=>56
[4,6,1,5,8,7,3,2]=>[3,3,1,1]=>56
[7,5,1,6,2,8,4,3]=>[3,3,1,1]=>56
[2,3,4,7,8,1,6,5]=>[5,2,1]=>64
[6,8,5,4,3,2,7,1]=>[2,2,1,1,1,1]=>20
[8,9,6,5,4,3,2,1,7]=>[2,2,1,1,1,1,1]=>27
[6,8,5,4,3,7,2,1]=>[2,2,1,1,1,1]=>20
[5,8,4,3,2,1,7,6]=>[2,2,2,1,1]=>28
[6,5,4,3,1,8,7,2]=>[2,2,2,1,1]=>28
[8,7,5,4,3,1,6,2]=>[2,2,1,1,1,1]=>20
[11,10,9,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,1,1,1]=>10
[8,3,4,6,2,1,5,7]=>[4,2,1,1]=>90
[3,5,6,2,1,8,4,7]=>[4,3,1]=>70
[3,5,2,6,8,4,1,7]=>[4,3,1]=>70
[7,5,3,2,8,4,1,6]=>[3,2,1,1,1]=>64
[7,5,3,2,8,4,6,1]=>[3,2,1,1,1]=>64
[2,4,5,7,3,8,6,1]=>[5,2,1]=>64
[4,2,5,6,8,3,1,7]=>[4,3,1]=>70
[4,2,8,1,5,6,3,7]=>[4,2,2]=>56
[2,5,6,1,8,4,3,7]=>[4,3,1]=>70
[5,3,6,8,1,4,2,7]=>[3,3,2]=>42
[4,5,6,8,1,3,2,7]=>[4,3,1]=>70
[1,4,5,6,8,3,2,7]=>[5,2,1]=>64
[4,5,6,3,8,2,1,7]=>[4,2,1,1]=>90
[4,5,3,7,2,8,6,1]=>[4,2,1,1]=>90
[6,4,7,3,2,8,5,1]=>[3,2,1,1,1]=>64
[6,1,4,7,3,2,8,5]=>[4,2,1,1]=>90
[1,7,8,4,5,3,2,6]=>[4,2,1,1]=>90
[5,1,7,3,8,4,2,6]=>[4,3,1]=>70
[2,5,1,7,4,3,8,6]=>[4,3,1]=>70
[2,5,7,4,1,8,6,3]=>[4,2,2]=>56
[5,3,7,1,4,8,6,2]=>[3,3,2]=>42
[6,4,3,1,7,8,5,2]=>[3,2,2,1]=>70
[6,4,1,7,3,8,5,2]=>[3,3,1,1]=>56
[5,6,3,7,8,4,2,1]=>[4,2,1,1]=>90
[5,1,6,3,7,8,4,2]=>[4,3,1]=>70
[5,6,1,3,7,8,4,2]=>[4,3,1]=>70
[5,6,1,7,8,3,4,2]=>[4,3,1]=>70
[1,6,3,7,4,8,5,2]=>[4,3,1]=>70
[6,7,2,4,1,8,5,3]=>[3,3,2]=>42
[6,7,2,1,4,3,8,5]=>[3,3,2]=>42
[6,4,7,3,1,2,8,5]=>[3,3,1,1]=>56
[5,6,3,1,2,7,8,4]=>[4,3,1]=>70
[5,6,1,3,2,7,8,4]=>[4,3,1]=>70
[5,6,3,2,1,7,8,4]=>[4,2,1,1]=>90
[2,5,6,3,7,8,4,1]=>[5,2,1]=>64
[2,5,6,3,1,7,8,4]=>[5,2,1]=>64
[2,6,4,7,3,1,8,5]=>[4,2,1,1]=>90
[6,3,7,2,8,4,5,1]=>[3,3,1,1]=>56
[6,3,7,2,8,4,1,5]=>[3,3,1,1]=>56
[6,3,2,7,1,8,4,5]=>[3,3,1,1]=>56
[7,5,3,2,1,8,4,6]=>[3,2,1,1,1]=>64
[7,3,8,4,2,1,5,6]=>[4,2,1,1]=>90
[4,7,2,1,3,8,6,5]=>[3,3,2]=>42
[1,3,7,8,6,4,2,5]=>[4,2,1,1]=>90
[7,3,8,4,6,2,1,5]=>[3,2,2,1]=>70
[5,7,3,8,2,1,6,4]=>[3,2,2,1]=>70
[6,3,7,8,5,2,1,4]=>[3,2,2,1]=>70
[4,6,2,7,8,5,3,1]=>[4,2,1,1]=>90
[4,6,2,1,7,8,5,3]=>[4,2,2]=>56
[7,4,5,8,1,2,6,3]=>[3,3,2]=>42
[2,5,1,7,3,8,6,4]=>[4,3,1]=>70
[6,7,2,1,3,8,5,4]=>[3,3,2]=>42
[5,1,6,7,8,2,4,3]=>[4,3,1]=>70
[6,3,7,1,8,5,2,4]=>[3,3,2]=>42
[6,2,1,7,3,8,5,4]=>[3,3,2]=>42
[6,2,7,1,8,5,4,3]=>[3,2,2,1]=>70
[6,3,1,7,8,5,4,2]=>[3,2,2,1]=>70
[4,1,3,6,8,2,5,7]=>[4,3,1]=>70
[4,2,3,6,8,1,5,7]=>[4,3,1]=>70
[5,3,2,1,8,4,7,6]=>[3,2,2,1]=>70
[3,6,5,8,2,1,7,4]=>[3,2,2,1]=>70
[4,5,2,1,3,8,7,6]=>[3,3,2]=>42
[3,2,6,4,5,8,1,7]=>[4,3,1]=>70
[2,4,6,5,8,1,3,7]=>[4,3,1]=>70
[1,6,2,4,5,8,3,7]=>[5,2,1]=>64
[5,3,2,1,6,8,4,7]=>[3,3,1,1]=>56
[6,2,4,5,8,1,3,7]=>[4,3,1]=>70
[1,3,4,6,5,8,2,7]=>[5,2,1]=>64
[1,6,3,4,5,8,2,7]=>[5,2,1]=>64
[3,4,1,8,5,2,7,6]=>[4,3,1]=>70
[2,8,4,1,7,6,3,5]=>[3,3,1,1]=>56
[8,1,4,2,7,3,6,5]=>[4,2,1,1]=>90
[1,5,3,2,8,7,4,6]=>[4,2,2]=>56
[8,2,1,7,5,3,4,6]=>[4,2,1,1]=>90
[1,7,6,4,5,8,3,2]=>[4,1,1,1,1]=>35
[5,8,7,4,1,2,6,3]=>[3,2,2,1]=>70
[5,8,7,4,6,2,1,3]=>[2,2,2,1,1]=>28
[3,4,2,5,8,6,7,1]=>[5,2,1]=>64
[4,1,3,5,6,8,7,2]=>[5,2,1]=>64
[2,4,8,6,7,1,3,5]=>[4,3,1]=>70
[4,3,6,2,8,1,7,5]=>[3,2,2,1]=>70
[3,7,4,8,2,1,6,5]=>[3,2,2,1]=>70
[2,3,5,8,6,7,1,4]=>[5,2,1]=>64
[3,2,5,6,8,7,1,4]=>[4,2,2]=>56
[2,1,8,5,6,7,3,4]=>[4,3,1]=>70
[1,2,8,3,5,6,7,4]=>[6,1,1]=>21
[4,2,3,7,1,8,6,5]=>[4,2,2]=>56
[3,2,6,4,8,1,7,5]=>[3,3,2]=>42
[8,2,1,6,7,3,4,5]=>[4,3,1]=>70
[2,7,8,5,4,1,3,6]=>[3,3,1,1]=>56
[1,7,5,3,8,4,2,6]=>[4,2,1,1]=>90
[4,7,5,3,1,2,8,6]=>[3,3,1,1]=>56
[7,2,4,8,5,3,1,6]=>[4,2,1,1]=>90
[4,8,3,1,2,7,6,5]=>[3,2,2,1]=>70
[3,5,2,7,4,1,8,6]=>[4,3,1]=>70
[8,4,2,3,7,1,5,6]=>[4,2,1,1]=>90
[2,8,4,7,1,3,5,6]=>[4,3,1]=>70
[8,2,4,6,7,1,3,5]=>[4,3,1]=>70
[4,8,2,3,6,7,1,5]=>[4,2,2]=>56
[3,5,2,7,6,1,8,4]=>[4,2,2]=>56
[1,6,3,2,5,8,7,4]=>[4,2,2]=>56
[5,8,3,2,1,6,7,4]=>[3,2,2,1]=>70
[5,8,7,3,4,6,2,1]=>[3,2,1,1,1]=>64
[5,8,2,7,4,1,6,3]=>[3,2,2,1]=>70
[5,1,4,2,8,7,6,3]=>[3,2,2,1]=>70
[4,7,6,5,8,2,1,3]=>[3,2,1,1,1]=>64
[5,3,7,1,6,2,8,4]=>[3,3,2]=>42
[5,2,6,8,7,1,3,4]=>[3,3,2]=>42
[6,3,2,1,8,5,7,4]=>[3,2,2,1]=>70
[2,7,5,4,1,8,6,3]=>[3,2,2,1]=>70
[4,2,5,6,8,7,1,3]=>[4,2,2]=>56
[1,8,4,2,5,6,7,3]=>[5,2,1]=>64
[3,8,4,1,5,6,7,2]=>[5,2,1]=>64
[4,2,8,5,6,7,1,3]=>[4,2,2]=>56
[5,2,4,7,1,8,6,3]=>[4,2,2]=>56
[5,3,4,7,1,8,6,2]=>[4,2,2]=>56
[8,6,4,1,3,2,5,7]=>[4,1,1,1,1]=>35
[8,1,3,6,5,2,4,7]=>[4,2,1,1]=>90
[8,1,4,3,6,5,2,7]=>[4,2,1,1]=>90
[3,6,5,2,1,8,7,4]=>[3,2,2,1]=>70
[8,3,2,4,6,5,1,7]=>[4,2,1,1]=>90
[8,4,2,1,6,5,3,7]=>[3,2,2,1]=>70
[8,4,1,2,6,5,3,7]=>[4,2,1,1]=>90
[8,6,4,2,1,5,3,7]=>[3,2,1,1,1]=>64
[8,3,6,4,1,5,2,7]=>[4,2,1,1]=>90
[8,2,6,3,4,5,1,7]=>[5,1,1,1]=>35
[1,3,4,8,5,7,2,6]=>[5,2,1]=>64
[5,8,4,7,6,2,3,1]=>[2,2,2,1,1]=>28
[1,3,4,7,5,8,2,6]=>[5,2,1]=>64
[1,3,5,2,4,8,7,6]=>[4,3,1]=>70
[2,6,5,1,3,8,7,4]=>[3,3,2]=>42
[4,7,1,6,5,8,3,2]=>[3,2,1,1,1]=>64
[5,4,8,7,6,3,1,2]=>[2,2,2,1,1]=>28
[2,8,5,1,4,7,6,3]=>[3,3,1,1]=>56
[4,3,1,5,8,6,7,2]=>[4,2,2]=>56
[4,1,3,5,8,6,7,2]=>[5,2,1]=>64
[6,5,3,8,4,7,1,2]=>[3,2,2,1]=>70
[5,4,2,1,6,8,7,3]=>[3,2,2,1]=>70
[6,8,4,3,2,7,1,5]=>[2,2,2,1,1]=>28
[3,4,7,8,2,1,6,5]=>[4,2,2]=>56
[5,1,3,2,8,6,7,4]=>[4,2,2]=>56
[5,3,1,2,8,6,7,4]=>[4,2,2]=>56
[5,2,3,1,6,8,7,4]=>[4,2,2]=>56
[5,3,2,1,8,6,7,4]=>[3,2,2,1]=>70
[5,2,1,3,6,8,7,4]=>[4,2,2]=>56
[2,4,7,3,8,1,6,5]=>[4,2,2]=>56
[6,3,8,2,7,4,1,5]=>[3,2,2,1]=>70
[8,2,1,3,6,4,7,5]=>[4,3,1]=>70
[3,5,1,7,8,4,2,6]=>[4,3,1]=>70
[2,7,4,5,8,3,1,6]=>[4,2,1,1]=>90
[1,8,4,3,7,2,6,5]=>[3,2,2,1]=>70
[3,4,8,7,2,1,6,5]=>[3,2,2,1]=>70
[5,4,7,8,3,6,2,1]=>[3,2,1,1,1]=>64
[6,4,3,8,7,2,1,5]=>[2,2,2,1,1]=>28
[6,3,8,7,4,1,2,5]=>[3,2,2,1]=>70
[3,5,7,2,4,8,1,6]=>[4,3,1]=>70
[8,4,7,2,3,1,5,6]=>[4,2,1,1]=>90
[8,4,7,1,3,2,5,6]=>[4,2,1,1]=>90
[8,4,7,2,1,3,5,6]=>[4,2,1,1]=>90
[8,6,4,2,1,3,7,5]=>[3,2,1,1,1]=>64
[8,6,4,1,3,2,7,5]=>[3,2,1,1,1]=>64
[8,6,4,2,3,1,7,5]=>[3,2,1,1,1]=>64
[3,5,7,2,6,1,8,4]=>[4,2,2]=>56
[6,1,3,8,5,7,2,4]=>[4,2,2]=>56
[5,8,3,2,6,7,1,4]=>[3,2,2,1]=>70
[4,8,5,3,6,2,7,1]=>[4,1,1,1,1]=>35
[2,8,1,5,4,7,6,3]=>[3,3,1,1]=>56
[1,5,8,7,4,6,2,3]=>[3,2,2,1]=>70
[2,1,7,6,4,5,8,3]=>[4,2,1,1]=>90
[1,7,2,4,6,5,8,3]=>[5,1,1,1]=>35
[3,5,1,7,6,8,2,4]=>[4,3,1]=>70
[5,8,2,6,1,3,7,4]=>[3,3,2]=>42
[6,3,5,8,7,2,1,4]=>[3,2,2,1]=>70
[2,5,7,8,4,1,6,3]=>[4,2,2]=>56
[4,2,8,1,5,6,7,3]=>[4,2,2]=>56
[4,1,5,2,6,8,7,3]=>[4,3,1]=>70
[3,4,5,1,6,8,7,2]=>[5,2,1]=>64
[4,2,8,5,1,6,7,3]=>[4,2,2]=>56
[4,1,8,5,2,6,7,3]=>[4,3,1]=>70
[2,7,1,8,5,4,6,3]=>[3,3,1,1]=>56
[5,8,6,2,1,3,7,4]=>[3,3,1,1]=>56
[8,2,4,1,5,6,7,3]=>[5,2,1]=>64
[4,6,3,5,8,1,7,2]=>[3,3,2]=>42
[1,7,8,3,5,4,6,2]=>[4,2,1,1]=>90
[3,4,5,1,8,6,7,2]=>[5,2,1]=>64
[3,8,1,4,5,6,7,2]=>[5,2,1]=>64
[3,4,5,7,8,2,6,1]=>[5,2,1]=>64
[3,4,6,2,8,5,1,7]=>[4,3,1]=>70
[3,4,6,8,1,5,2,7]=>[4,3,1]=>70
[3,4,7,2,1,8,6,5]=>[4,2,2]=>56
[3,4,8,2,1,5,6,7]=>[5,2,1]=>64
[3,5,2,7,8,4,6,1]=>[4,3,1]=>70
[3,5,6,2,8,4,1,7]=>[4,3,1]=>70
[3,5,6,8,4,1,2,7]=>[4,3,1]=>70
[3,5,7,2,4,8,6,1]=>[4,3,1]=>70
[3,5,7,2,8,4,6,1]=>[4,3,1]=>70
[3,5,7,8,4,1,6,2]=>[4,2,2]=>56
[3,6,2,1,8,5,4,7]=>[3,3,2]=>42
[3,6,7,2,8,5,4,1]=>[4,2,1,1]=>90
[3,6,8,2,4,5,1,7]=>[4,3,1]=>70
[3,7,2,1,4,8,6,5]=>[3,3,2]=>42
[3,7,2,8,4,5,6,1]=>[4,3,1]=>70
[3,8,2,1,4,5,6,7]=>[5,2,1]=>64
[4,1,5,6,7,8,3,2]=>[5,2,1]=>64
[4,1,6,3,7,8,5,2]=>[4,3,1]=>70
[4,1,6,3,8,5,2,7]=>[4,3,1]=>70
[4,1,6,7,3,8,5,2]=>[4,3,1]=>70
[4,1,7,3,2,8,6,5]=>[3,3,2]=>42
[4,1,8,3,2,5,6,7]=>[5,2,1]=>64
[4,5,2,6,8,1,3,7]=>[4,3,1]=>70
[4,5,7,3,8,1,6,2]=>[4,2,2]=>56
[4,5,8,3,2,1,6,7]=>[4,2,1,1]=>90
[4,6,2,7,8,5,1,3]=>[4,2,2]=>56
[4,6,7,3,2,8,5,1]=>[4,2,1,1]=>90
[4,7,2,8,3,5,6,1]=>[4,3,1]=>70
[4,7,8,3,2,5,6,1]=>[3,3,1,1]=>56
[4,8,2,3,1,5,6,7]=>[5,2,1]=>64
[5,1,2,6,8,4,3,7]=>[4,3,1]=>70
[5,6,2,3,8,4,1,7]=>[4,3,1]=>70
[5,6,2,7,8,4,1,3]=>[4,2,2]=>56
[5,6,8,3,4,2,1,7]=>[3,3,1,1]=>56
[5,7,2,3,4,8,6,1]=>[4,3,1]=>70
[5,7,8,3,4,2,6,1]=>[3,3,1,1]=>56
[5,8,2,3,4,1,6,7]=>[5,2,1]=>64
[6,1,2,3,7,8,5,4]=>[5,2,1]=>64
[6,1,2,3,8,5,4,7]=>[5,2,1]=>64
[6,1,2,7,8,5,4,3]=>[4,2,1,1]=>90
[6,1,7,3,8,5,4,2]=>[3,3,1,1]=>56
[6,1,7,8,4,5,3,2]=>[3,3,1,1]=>56
[6,1,8,3,4,5,2,7]=>[5,2,1]=>64
[6,7,2,3,8,5,4,1]=>[3,3,1,1]=>56
[6,7,2,8,4,5,3,1]=>[3,3,1,1]=>56
[7,1,2,3,4,8,6,5]=>[5,2,1]=>64
[7,1,2,8,4,5,6,3]=>[5,2,1]=>64
[7,1,8,3,4,5,6,2]=>[5,2,1]=>64
[6,4,1,8,2,3,7,5]=>[4,2,2]=>56
[5,8,1,2,4,3,7,6]=>[4,2,2]=>56
[1,3,5,7,2,6,4,8]=>[5,2,1]=>64
[3,5,8,6,1,2,4,7]=>[4,3,1]=>70
[3,1,6,8,2,4,7,5]=>[4,3,1]=>70
[3,6,2,8,1,5,7,4]=>[3,3,2]=>42
[2,6,1,3,8,4,7,5]=>[4,3,1]=>70
[1,7,5,2,3,4,6,8]=>[6,1,1]=>21
[2,7,5,1,3,8,4,6]=>[4,3,1]=>70
[8,2,5,7,4,6,1,3]=>[3,2,2,1]=>70
[8,2,1,3,7,6,4,5]=>[4,2,1,1]=>90
[8,2,5,1,3,7,4,6]=>[4,3,1]=>70
[8,2,7,5,3,1,6,4]=>[3,2,1,1,1]=>64
[8,2,6,5,4,7,1,3]=>[3,2,1,1,1]=>64
[7,6,5,2,4,8,1,3]=>[3,2,1,1,1]=>64
[7,8,2,5,3,1,6,4]=>[3,2,2,1]=>70
[7,1,8,6,3,2,4,5]=>[4,2,1,1]=>90
[6,8,1,5,3,2,4,7]=>[4,2,1,1]=>90
[1,6,7,5,3,2,4,8]=>[4,2,1,1]=>90
[6,5,1,2,4,8,3,7]=>[4,2,1,1]=>90
[7,8,1,6,4,2,3,5]=>[4,2,1,1]=>90
[8,4,1,2,5,6,3,7]=>[5,2,1]=>64
[1,7,3,6,5,2,4,8]=>[4,2,1,1]=>90
[8,1,3,7,2,6,4,5]=>[4,2,1,1]=>90
[7,3,2,6,5,1,8,4]=>[3,2,2,1]=>70
[7,8,4,2,5,6,1,3]=>[3,2,2,1]=>70
[8,2,7,4,5,6,1,3]=>[4,2,1,1]=>90
[8,2,3,6,5,1,7,4]=>[4,2,1,1]=>90
[2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]=>8
[1,8,7,6,5,3,2,4]=>[3,1,1,1,1,1]=>21
[2,8,7,6,3,4,5,1]=>[4,1,1,1,1]=>35
[1,8,7,6,5,2,3,4]=>[4,1,1,1,1]=>35
[2,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]=>9
[7,2,8,6,5,4,1,3]=>[2,2,2,1,1]=>28
[7,2,8,5,4,6,1,3]=>[3,2,2,1]=>70
[6,3,2,8,5,1,7,4]=>[3,2,2,1]=>70
[8,4,7,2,5,6,3,1]=>[3,2,1,1,1]=>64
[6,8,5,4,3,1,7,2]=>[2,2,2,1,1]=>28
[5,8,6,4,1,3,7,2]=>[3,2,1,1,1]=>64
[4,8,6,1,5,3,7,2]=>[3,2,1,1,1]=>64
[3,6,1,8,5,2,7,4]=>[3,3,2]=>42
[3,4,1,2,8,6,7,5]=>[4,3,1]=>70
[6,8,3,5,4,1,7,2]=>[3,2,2,1]=>70
[7,2,5,8,3,6,1,4]=>[3,2,2,1]=>70
[1,7,5,6,3,4,2,8]=>[4,2,1,1]=>90
[7,2,6,8,5,3,1,4]=>[3,2,1,1,1]=>64
[7,6,3,8,5,2,1,4]=>[2,2,2,1,1]=>28
[7,2,6,4,8,3,1,5]=>[3,2,1,1,1]=>64
[1,5,7,4,2,6,3,8]=>[4,2,2]=>56
[4,2,3,1,7,8,5,6]=>[4,3,1]=>70
[5,2,8,4,1,7,6,3]=>[3,2,2,1]=>70
[8,6,3,4,7,2,5,1]=>[3,2,1,1,1]=>64
[6,8,3,4,5,1,7,2]=>[4,2,2]=>56
[1,6,3,2,5,8,4,7]=>[4,3,1]=>70
[8,3,2,1,5,4,7,6]=>[3,3,1,1]=>56
[6,3,7,1,5,8,4,2]=>[3,2,2,1]=>70
[2,5,1,8,4,3,7,6]=>[3,3,2]=>42
[6,2,5,4,8,1,3,7]=>[3,3,1,1]=>56
[4,3,1,6,5,8,2,7]=>[3,3,2]=>42
[1,3,5,4,6,8,2,7]=>[5,2,1]=>64
[6,1,3,4,5,8,2,7]=>[5,2,1]=>64
[8,3,4,1,5,2,7,6]=>[4,3,1]=>70
[7,5,4,2,6,8,3,1]=>[3,2,1,1,1]=>64
[8,2,6,4,1,7,3,5]=>[3,3,1,1]=>56
[7,3,8,4,5,2,1,6]=>[4,2,1,1]=>90
[7,2,5,1,8,4,3,6]=>[3,3,1,1]=>56
[1,7,3,2,5,4,8,6]=>[4,3,1]=>70
[8,7,2,1,5,3,4,6]=>[4,2,1,1]=>90
[3,6,1,5,8,7,4,2]=>[3,3,1,1]=>56
[8,3,6,4,5,1,7,2]=>[4,2,1,1]=>90
[5,4,6,8,1,2,7,3]=>[3,3,2]=>42
[6,4,7,2,3,5,8,1]=>[4,2,1,1]=>90
[6,8,4,1,3,5,7,2]=>[4,2,1,1]=>90
[3,4,7,8,6,2,5,1]=>[4,2,1,1]=>90
[4,1,3,5,7,8,6,2]=>[5,2,1]=>64
[6,5,1,8,4,7,3,2]=>[3,2,1,1,1]=>64
[5,3,1,8,4,7,6,2]=>[3,2,2,1]=>70
[8,2,7,4,6,1,3,5]=>[3,3,1,1]=>56
[4,7,3,2,8,1,6,5]=>[3,2,2,1]=>70
[6,3,1,4,7,2,8,5]=>[4,3,1]=>70
[8,7,3,6,1,5,2,4]=>[3,2,1,1,1]=>64
[7,4,3,6,8,2,5,1]=>[3,2,1,1,1]=>64
[2,4,7,3,8,5,6,1]=>[4,3,1]=>70
[2,8,6,1,5,7,3,4]=>[3,3,1,1]=>56
[7,8,2,5,4,3,1,6]=>[3,2,1,1,1]=>64
[1,8,3,4,2,7,6,5]=>[4,2,1,1]=>90
[8,5,3,7,4,2,6,1]=>[3,2,1,1,1]=>64
[5,7,3,2,4,1,8,6]=>[3,3,1,1]=>56
[2,8,3,4,7,1,5,6]=>[5,2,1]=>64
[4,1,3,6,7,8,2,5]=>[5,2,1]=>64
[1,7,6,3,2,5,8,4]=>[4,2,1,1]=>90
[3,8,1,5,6,2,7,4]=>[4,3,1]=>70
[8,2,5,6,1,7,4,3]=>[4,2,1,1]=>90
[7,1,5,2,8,6,4,3]=>[3,2,2,1]=>70
[6,5,4,8,7,2,1,3]=>[2,2,2,1,1]=>28
[1,8,6,4,5,2,7,3]=>[4,2,1,1]=>90
[1,8,5,3,6,2,7,4]=>[4,2,1,1]=>90
[3,6,2,1,7,5,8,4]=>[4,2,2]=>56
[2,5,4,1,8,7,6,3]=>[3,2,2,1]=>70
[4,7,2,6,5,8,1,3]=>[3,2,2,1]=>70
[6,8,1,4,2,7,3,5]=>[4,2,2]=>56
[6,3,4,7,1,8,2,5]=>[4,3,1]=>70
[3,4,7,8,2,5,6,1]=>[4,3,1]=>70
[1,8,2,4,5,6,7,3]=>[6,1,1]=>21
[5,2,4,1,6,8,7,3]=>[4,2,2]=>56
[3,2,5,7,6,1,8,4]=>[4,2,2]=>56
[4,3,5,6,1,8,7,2]=>[4,2,2]=>56
[5,3,4,1,7,6,8,2]=>[4,2,2]=>56
[3,1,4,6,5,7,8,2]=>[5,2,1]=>64
[1,4,7,3,5,6,8,2]=>[5,2,1]=>64
[1,3,2,7,5,8,6,4]=>[4,3,1]=>70
[1,3,2,7,5,8,4,6]=>[4,3,1]=>70
[1,3,2,8,5,7,4,6]=>[4,3,1]=>70
[1,5,2,4,8,7,3,6]=>[4,2,2]=>56
[1,2,6,4,8,7,3,5]=>[4,2,2]=>56
[1,2,7,8,5,6,3,4]=>[4,2,2]=>56
[1,3,8,2,6,7,4,5]=>[4,3,1]=>70
[1,6,7,8,2,5,3,4]=>[4,3,1]=>70
[1,5,7,8,2,3,6,4]=>[4,3,1]=>70
[1,5,2,7,8,4,6,3]=>[4,3,1]=>70
[1,3,6,2,4,8,7,5]=>[4,3,1]=>70
[1,6,7,3,4,8,5,2]=>[4,3,1]=>70
[1,5,3,7,4,8,6,2]=>[4,3,1]=>70
[2,8,4,1,5,3,7,6]=>[4,3,1]=>70
[1,3,8,4,2,7,6,5]=>[4,2,1,1]=>90
[1,2,7,4,8,3,6,5]=>[4,2,2]=>56
[1,2,6,4,8,3,7,5]=>[4,2,2]=>56
[1,5,2,4,8,3,7,6]=>[4,2,2]=>56
[1,8,3,5,2,7,4,6]=>[4,3,1]=>70
[1,3,8,6,2,7,4,5]=>[4,3,1]=>70
[1,2,6,8,5,3,7,4]=>[4,2,2]=>56
[1,6,7,8,5,2,3,4]=>[4,3,1]=>70
[1,5,7,8,6,2,3,4]=>[4,3,1]=>70
[1,4,7,6,8,2,3,5]=>[4,3,1]=>70
[1,2,7,8,6,5,3,4]=>[4,2,1,1]=>90
[5,2,6,7,3,4,8,1]=>[4,3,1]=>70
[5,2,4,7,6,3,8,1]=>[4,2,1,1]=>90
[5,6,2,1,7,8,3,4]=>[4,3,1]=>70
[5,6,2,1,4,8,7,3]=>[3,3,2]=>42
[2,6,1,4,5,8,7,3]=>[4,3,1]=>70
[5,4,2,7,6,3,8,1]=>[3,2,2,1]=>70
[2,3,7,6,4,5,8,1]=>[5,1,1,1]=>35
[2,6,1,7,5,8,3,4]=>[4,3,1]=>70
[2,6,1,7,4,8,5,3]=>[4,3,1]=>70
[5,1,2,7,8,4,3,6]=>[4,3,1]=>70
[2,6,1,7,4,8,3,5]=>[4,3,1]=>70
[3,6,4,1,7,8,2,5]=>[4,3,1]=>70
[5,4,6,1,3,8,7,2]=>[3,3,1,1]=>56
[3,6,4,1,5,8,7,2]=>[4,2,2]=>56
[2,6,1,5,4,8,7,3]=>[3,3,1,1]=>56
[2,6,1,4,7,8,5,3]=>[4,3,1]=>70
[5,1,2,4,8,6,7,3]=>[5,2,1]=>64
[5,1,2,4,8,7,3,6]=>[4,2,2]=>56
[5,1,2,4,8,7,6,3]=>[4,2,1,1]=>90
[1,2,3,8,5,4,7,6]=>[5,2,1]=>64
[4,3,1,2,8,5,7,6]=>[4,2,2]=>56
[2,1,5,3,8,6,4,7]=>[4,3,1]=>70
[1,2,3,8,5,6,4,7]=>[6,1,1]=>21
[1,2,3,8,6,4,5,7]=>[6,1,1]=>21
[1,2,3,8,6,5,4,7]=>[5,1,1,1]=>35
[1,2,3,8,5,4,6,7]=>[6,1,1]=>21
[2,6,1,5,4,8,3,7]=>[3,3,1,1]=>56
[5,1,2,4,8,6,3,7]=>[5,2,1]=>64
[5,1,2,4,8,3,7,6]=>[4,2,2]=>56
[5,6,3,1,4,8,2,7]=>[3,3,2]=>42
[2,5,4,3,1,8,6,7]=>[4,2,1,1]=>90
[5,4,6,3,1,8,7,2]=>[3,2,2,1]=>70
[3,6,4,5,1,8,7,2]=>[4,2,2]=>56
[3,6,5,4,1,8,7,2]=>[3,2,2,1]=>70
[5,2,6,1,7,8,4,3]=>[4,2,2]=>56
[5,1,6,2,8,7,3,4]=>[4,3,1]=>70
[2,1,3,7,8,6,4,5]=>[4,3,1]=>70
[2,1,3,7,8,5,6,4]=>[4,3,1]=>70
[5,2,4,1,7,8,6,3]=>[4,2,2]=>56
[4,3,1,2,8,6,7,5]=>[4,2,2]=>56
[5,1,4,2,8,6,7,3]=>[4,2,2]=>56
[2,1,3,6,8,5,7,4]=>[4,3,1]=>70
[1,2,3,8,6,7,4,5]=>[5,2,1]=>64
[1,2,3,8,7,5,4,6]=>[5,1,1,1]=>35
[1,2,3,8,7,4,5,6]=>[6,1,1]=>21
[1,2,3,8,5,7,4,6]=>[5,2,1]=>64
[2,1,3,6,8,7,4,5]=>[4,3,1]=>70
[5,4,1,2,8,7,6,3]=>[3,2,2,1]=>70
[3,1,6,2,8,7,5,4]=>[3,3,1,1]=>56
[1,2,3,4,5,9,6,7,8]=>[8,1]=>8
[1,2,3,4,9,5,6,7,8]=>[8,1]=>8
[1,2,3,9,4,5,6,7,8]=>[8,1]=>8
[1,2,9,3,4,5,6,7,8]=>[8,1]=>8
[1,2,3,4,5,6,7,10,8,9]=>[9,1]=>9
[1,2,3,4,5,9,7,6,8]=>[7,1,1]=>28
[1,2,3,4,5,6,10,7,8,9]=>[9,1]=>9
[1,2,3,4,9,6,5,7,8]=>[7,1,1]=>28
[1,2,3,4,5,10,6,7,8,9]=>[9,1]=>9
[1,2,3,9,5,4,6,7,8]=>[7,1,1]=>28
[1,2,3,4,10,5,6,7,8,9]=>[9,1]=>9
[1,8,3,4,2,5,6,7]=>[6,1,1]=>21
[1,2,9,4,3,5,6,7,8]=>[7,1,1]=>28
[1,2,3,10,4,5,6,7,8,9]=>[9,1]=>9
[1,8,4,3,2,5,6,7]=>[5,1,1,1]=>35
[1,9,3,2,4,5,6,7,8]=>[7,1,1]=>28
[1,2,10,3,4,5,6,7,8,9]=>[9,1]=>9
[8,4,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>7
[8,5,7,4,6,3,2,1]=>[2,2,1,1,1,1]=>20
[8,5,7,3,6,4,2,1]=>[2,2,1,1,1,1]=>20
[8,1,7,4,6,5,3,2]=>[3,1,1,1,1,1]=>21
[8,2,7,3,6,5,4,1]=>[3,1,1,1,1,1]=>21
[8,5,7,2,6,4,3,1]=>[2,2,1,1,1,1]=>20
[8,4,7,1,6,5,3,2]=>[2,2,1,1,1,1]=>20
[8,3,7,1,6,5,4,2]=>[2,2,1,1,1,1]=>20
[8,2,7,1,6,5,4,3]=>[2,2,1,1,1,1]=>20
[8,1,7,6,5,3,4,2]=>[3,1,1,1,1,1]=>21
[8,3,7,6,5,2,4,1]=>[2,2,1,1,1,1]=>20
[8,4,7,6,5,2,3,1]=>[2,2,1,1,1,1]=>20
[8,5,7,6,4,2,3,1]=>[2,2,1,1,1,1]=>20
[8,6,7,5,4,1,3,2]=>[2,2,1,1,1,1]=>20
[8,3,7,6,5,1,4,2]=>[2,2,1,1,1,1]=>20
[6,8,1,4,2,5,3,7]=>[4,2,2]=>56
[7,8,2,5,3,6,1,4]=>[3,2,2,1]=>70
[6,8,2,5,4,7,1,3]=>[3,2,2,1]=>70
[2,5,3,7,6,8,1,4]=>[4,2,2]=>56
[2,6,1,4,3,7,5,8]=>[4,3,1]=>70
[2,6,3,7,4,8,1,5]=>[4,3,1]=>70
[4,8,2,6,3,7,1,5]=>[3,3,1,1]=>56
[4,8,1,5,2,6,3,7]=>[4,3,1]=>70
[4,8,3,7,1,5,2,6]=>[3,2,2,1]=>70
[6,8,5,7,1,3,2,4]=>[3,2,2,1]=>70
[4,7,1,3,2,6,5,8]=>[4,2,2]=>56
[3,7,5,8,1,4,2,6]=>[3,3,1,1]=>56
[3,7,6,8,2,5,1,4]=>[3,2,2,1]=>70
[4,7,5,8,2,6,1,3]=>[3,2,2,1]=>70
[3,7,5,8,2,6,1,4]=>[3,2,2,1]=>70
[3,6,5,8,4,7,1,2]=>[3,2,2,1]=>70
[2,6,5,8,3,7,1,4]=>[3,2,2,1]=>70
[2,6,3,7,1,5,4,8]=>[4,2,2]=>56
[7,6,4,2,8,5,3,1]=>[2,2,2,1,1]=>28
[6,8,4,3,7,2,1,5]=>[2,2,2,1,1]=>28
[6,7,4,3,5,1,8,2]=>[3,2,2,1]=>70
[6,7,3,5,4,8,2,1]=>[3,2,1,1,1]=>64
[7,6,3,5,8,2,4,1]=>[3,2,1,1,1]=>64
[7,6,4,2,5,1,8,3]=>[3,2,1,1,1]=>64
[7,6,3,8,2,4,1,5]=>[3,2,1,1,1]=>64
[6,3,8,4,7,2,1,5]=>[3,2,2,1]=>70
[6,2,8,4,1,7,5,3]=>[3,2,2,1]=>70
[6,2,7,4,1,5,3,8]=>[4,2,2]=>56
[6,3,4,7,5,8,2,1]=>[4,2,1,1]=>90
[6,3,5,7,8,4,2,1]=>[4,1,1,1,1]=>35
[5,6,8,3,7,2,1,4]=>[3,2,2,1]=>70
[4,6,8,3,5,7,2,1]=>[3,3,1,1]=>56
[5,3,8,2,4,1,6,7]=>[4,2,1,1]=>90
[4,8,3,6,2,5,7,1]=>[3,2,2,1]=>70
[4,7,8,3,5,6,2,1]=>[3,3,1,1]=>56
[6,4,3,5,8,2,1,7]=>[3,2,1,1,1]=>64
[6,3,5,8,7,2,4,1]=>[3,2,2,1]=>70
[5,8,3,7,2,6,4,1]=>[2,2,2,1,1]=>28
[5,8,4,2,3,1,6,7]=>[4,2,1,1]=>90
[5,8,4,2,3,1,7,6]=>[3,2,2,1]=>70
[6,4,5,3,8,2,1,7]=>[3,2,1,1,1]=>64
[6,4,8,5,3,7,2,1]=>[3,2,1,1,1]=>64
[6,4,3,8,5,7,2,1]=>[3,2,1,1,1]=>64
[6,4,2,8,5,3,1,7]=>[3,2,2,1]=>70
[5,6,3,4,8,2,1,7]=>[3,3,1,1]=>56
[6,4,2,5,1,7,3,8]=>[4,2,1,1]=>90
[5,3,7,2,4,1,6,8]=>[4,2,1,1]=>90
[4,5,8,3,6,7,2,1]=>[4,2,1,1]=>90
[4,5,8,3,7,2,6,1]=>[3,2,2,1]=>70
[5,3,6,8,2,1,4,7]=>[3,3,1,1]=>56
[5,3,6,7,1,8,2,4]=>[4,3,1]=>70
[4,6,3,5,7,8,2,1]=>[4,2,1,1]=>90
[4,5,7,3,6,8,2,1]=>[4,2,1,1]=>90
[5,7,4,8,6,3,2,1]=>[3,2,1,1,1]=>64
[3,5,6,7,2,8,4,1]=>[5,2,1]=>64
[3,2,5,4,7,6,9,8,1]=>[4,4,1]=>84
[3,4,5,6,7,8,9,2,1]=>[7,1,1]=>28
[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,2]=>42
[3,4,5,6,7,8,9,10,2,1]=>[8,1,1]=>36
[1,6,2,5,3,4,8,7]=>[5,2,1]=>64
[1,3,8,2,4,6,5,7]=>[5,2,1]=>64
[1,7,2,3,6,4,8,5]=>[5,2,1]=>64
[1,6,8,2,5,3,7,4]=>[4,2,2]=>56
[1,8,2,5,3,4,7,6]=>[5,2,1]=>64
[1,8,2,3,6,4,7,5]=>[5,2,1]=>64
[1,3,5,2,8,4,7,6]=>[4,3,1]=>70
[1,2,7,3,5,4,6,8]=>[6,1,1]=>21
[1,8,2,7,3,4,6,5]=>[5,1,1,1]=>35
[1,5,8,2,3,7,4,6]=>[5,2,1]=>64
[1,6,8,2,3,5,4,7]=>[5,2,1]=>64
[5,3,6,1,2,4,8,7]=>[4,3,1]=>70
[7,1,5,8,4,2,3,6]=>[4,2,1,1]=>90
[8,1,5,7,4,2,3,6]=>[4,2,1,1]=>90
[7,1,4,5,8,2,3,6]=>[4,3,1]=>70
[7,4,1,6,2,8,3,5]=>[4,3,1]=>70
[8,4,1,7,2,6,3,5]=>[4,2,1,1]=>90
[8,1,4,7,5,2,3,6]=>[4,2,1,1]=>90
[8,1,5,4,7,2,3,6]=>[4,2,1,1]=>90
[2,1,7,5,8,3,4,6]=>[4,3,1]=>70
[7,1,5,4,8,2,3,6]=>[4,2,1,1]=>90
[7,1,4,8,5,2,3,6]=>[4,2,2]=>56
[6,4,1,7,2,3,8,5]=>[4,3,1]=>70
[7,8,3,1,2,4,6,5]=>[4,2,2]=>56
[8,7,1,6,4,2,3,5]=>[4,1,1,1,1]=>35
[8,6,1,7,4,2,3,5]=>[4,2,1,1]=>90
[7,6,1,8,4,2,3,5]=>[4,2,1,1]=>90
[7,3,8,1,2,4,6,5]=>[4,2,2]=>56
[8,3,7,1,2,4,6,5]=>[4,2,1,1]=>90
[8,3,6,1,2,4,7,5]=>[4,3,1]=>70
[8,3,7,5,1,2,4,6]=>[4,2,1,1]=>90
[7,3,6,1,2,4,8,5]=>[4,3,1]=>70
[6,7,1,8,4,2,3,5]=>[4,3,1]=>70
[6,8,1,7,4,2,3,5]=>[4,2,1,1]=>90
[7,1,8,5,4,2,3,6]=>[4,2,1,1]=>90
[7,1,8,4,5,2,3,6]=>[4,2,2]=>56
[2,1,7,8,5,3,4,6]=>[4,3,1]=>70
[7,6,3,1,2,4,8,5]=>[4,2,1,1]=>90
[6,1,2,3,8,7,5,4]=>[4,2,1,1]=>90
[6,8,1,4,2,3,7,5]=>[4,2,2]=>56
[6,8,3,1,2,7,4,5]=>[4,2,2]=>56
[6,7,3,1,2,8,4,5]=>[4,3,1]=>70
[6,7,1,4,2,3,8,5]=>[4,3,1]=>70
[4,3,6,8,5,7,1,2]=>[3,3,2]=>42
[1,3,6,8,7,4,2,5]=>[4,2,1,1]=>90
[2,6,1,5,8,3,4,7]=>[4,3,1]=>70
[5,7,1,6,8,4,3,2]=>[3,2,1,1,1]=>64
[8,3,6,4,7,2,5,1]=>[3,2,1,1,1]=>64
[1,7,8,4,6,2,5,3]=>[3,2,2,1]=>70
[2,7,3,1,5,8,4,6]=>[4,3,1]=>70
[2,7,4,6,8,1,3,5]=>[4,3,1]=>70
[2,7,5,8,6,4,1,3]=>[3,2,2,1]=>70
[8,2,6,7,5,4,3,1]=>[3,1,1,1,1,1]=>21
[3,4,2,7,8,1,6,5]=>[4,2,2]=>56
[4,1,7,3,8,5,2,6]=>[4,3,1]=>70
[3,6,1,4,5,8,2,7]=>[4,3,1]=>70
[1,6,7,4,5,3,8,2]=>[4,2,1,1]=>90
[6,1,7,3,5,4,8,2]=>[4,2,1,1]=>90
[1,4,7,2,8,5,3,6]=>[4,3,1]=>70
[5,6,8,7,2,4,1,3]=>[3,2,2,1]=>70
[6,8,5,7,1,2,4,3]=>[3,2,2,1]=>70
[8,2,4,3,7,5,6,1]=>[4,2,1,1]=>90
[6,8,2,1,5,7,3,4]=>[3,3,2]=>42
[2,7,8,1,4,6,3,5]=>[3,3,2]=>42
[4,8,2,5,7,1,6,3]=>[3,2,2,1]=>70
[4,1,6,8,5,3,7,2]=>[3,3,1,1]=>56
[5,2,6,4,8,3,1,7]=>[3,3,1,1]=>56
[6,7,1,3,4,5,8,2]=>[5,2,1]=>64
[1,7,3,2,4,8,5,6]=>[5,2,1]=>64
[6,3,4,2,8,7,5,1]=>[3,2,2,1]=>70
[4,3,8,7,5,2,6,1]=>[3,2,1,1,1]=>64
[6,8,7,4,2,3,5,1]=>[3,2,1,1,1]=>64
[3,6,4,5,2,8,7,1]=>[4,2,1,1]=>90
[8,6,1,3,5,4,2,7]=>[4,1,1,1,1]=>35
[5,3,8,6,1,2,4,7]=>[4,2,2]=>56
[2,5,6,3,4,8,7,1]=>[4,3,1]=>70
[2,5,3,6,8,7,4,1]=>[4,2,1,1]=>90
[4,8,7,3,5,2,6,1]=>[3,2,1,1,1]=>64
[3,8,7,2,6,4,5,1]=>[3,2,1,1,1]=>64
[6,3,5,4,8,7,2,1]=>[3,2,1,1,1]=>64
[4,3,8,6,1,5,2,7]=>[3,2,2,1]=>70
[4,7,6,2,5,3,8,1]=>[3,2,1,1,1]=>64
[7,5,2,6,8,1,4,3]=>[3,2,2,1]=>70
[8,5,2,7,1,4,3,6]=>[3,2,2,1]=>70
[1,8,5,3,6,2,4,7]=>[4,2,1,1]=>90
[5,1,7,2,4,3,8,6]=>[4,3,1]=>70
[1,5,3,4,8,6,2,7]=>[5,2,1]=>64
[5,4,1,3,8,6,2,7]=>[4,2,1,1]=>90
[5,1,8,6,3,4,2,7]=>[4,2,1,1]=>90
[4,5,2,8,3,7,6,1]=>[3,3,1,1]=>56
[8,2,3,7,6,4,5,1]=>[4,1,1,1,1]=>35
[5,8,2,4,7,6,3,1]=>[3,2,1,1,1]=>64
[6,8,2,5,3,4,7,1]=>[4,2,1,1]=>90
[7,2,5,6,4,8,1,3]=>[4,2,1,1]=>90
[1,6,7,4,8,2,3,5]=>[4,3,1]=>70
[7,1,3,5,8,2,6,4]=>[4,2,2]=>56
[8,2,1,3,5,6,7,4]=>[5,2,1]=>64
[6,3,1,4,7,5,8,2]=>[4,2,2]=>56
[4,1,3,8,2,6,7,5]=>[4,2,2]=>56
[2,8,3,6,7,5,4,1]=>[4,1,1,1,1]=>35
[3,1,7,2,8,5,4,6]=>[4,3,1]=>70
[3,6,1,4,7,2,8,5]=>[4,3,1]=>70
[1,5,8,4,7,2,3,6]=>[4,2,2]=>56
[7,1,3,6,2,8,4,5]=>[4,3,1]=>70
[6,2,7,4,5,8,1,3]=>[4,2,2]=>56
[2,1,8,4,5,7,3,6]=>[4,3,1]=>70
[1,8,5,7,3,2,4,6]=>[4,2,1,1]=>90
[2,1,8,5,4,3,6,7]=>[4,2,1,1]=>90
[2,7,4,1,5,3,8,6]=>[4,3,1]=>70
[7,4,8,6,2,3,1,5]=>[3,2,2,1]=>70
[2,7,1,4,6,3,8,5]=>[4,3,1]=>70
[4,7,5,6,8,1,3,2]=>[4,2,1,1]=>90
[7,1,3,2,8,5,4,6]=>[4,2,2]=>56
[2,8,5,4,1,3,6,7]=>[4,2,1,1]=>90
[5,1,7,4,2,3,8,6]=>[4,3,1]=>70
[3,8,6,5,1,4,2,7]=>[3,2,1,1,1]=>64
[1,3,4,8,6,5,2,7]=>[5,1,1,1]=>35
[4,1,8,6,5,3,2,7]=>[3,2,1,1,1]=>64
[4,8,5,2,7,3,6,1]=>[3,3,1,1]=>56
[7,2,8,5,3,6,4,1]=>[3,2,2,1]=>70
[5,2,8,4,3,7,6,1]=>[3,2,2,1]=>70
[8,4,7,5,2,3,6,1]=>[3,2,1,1,1]=>64
[7,5,2,8,4,6,1,3]=>[3,2,2,1]=>70
[5,7,4,3,6,2,8,1]=>[3,2,1,1,1]=>64
[6,7,5,1,2,8,3,4]=>[4,3,1]=>70
[5,2,6,8,3,4,7,1]=>[4,3,1]=>70
[7,6,2,4,5,8,3,1]=>[4,1,1,1,1]=>35
[3,6,8,4,7,2,5,1]=>[3,2,2,1]=>70
[7,6,3,8,4,2,5,1]=>[3,2,1,1,1]=>64
[2,6,3,8,4,7,5,1]=>[4,2,1,1]=>90
[7,2,3,6,5,8,4,1]=>[4,1,1,1,1]=>35
[6,2,7,5,8,3,1,4]=>[3,3,1,1]=>56
[2,8,3,6,4,5,7,1]=>[5,1,1,1]=>35
[2,1,5,6,8,3,7,4]=>[4,3,1]=>70
[5,8,1,2,6,4,7,3]=>[4,2,1,1]=>90
[1,6,8,3,2,7,4,5]=>[4,2,2]=>56
[6,5,7,2,8,4,1,3]=>[3,2,2,1]=>70
[7,5,1,2,8,4,6,3]=>[4,2,1,1]=>90
[5,4,8,3,6,2,7,1]=>[3,2,1,1,1]=>64
[5,8,2,7,4,3,6,1]=>[3,2,1,1,1]=>64
[6,4,5,8,2,7,3,1]=>[3,2,2,1]=>70
[5,7,3,6,4,8,2,1]=>[3,2,1,1,1]=>64
[1,5,6,4,8,2,7,3]=>[4,2,2]=>56
[3,1,5,6,4,8,7,2]=>[4,3,1]=>70
[3,5,1,6,4,7,8,2]=>[5,2,1]=>64
[1,2,6,4,3,8,5,7]=>[5,2,1]=>64
[1,2,6,3,5,8,7,4]=>[5,2,1]=>64
[2,3,5,1,8,4,7,6]=>[4,3,1]=>70
[2,3,6,1,8,5,4,7]=>[4,3,1]=>70
[1,2,7,3,6,8,5,4]=>[5,1,1,1]=>35
[2,3,6,1,8,5,7,4]=>[4,3,1]=>70
[1,2,5,8,4,7,3,6]=>[4,2,2]=>56
[1,2,6,8,5,4,3,7]=>[4,2,1,1]=>90
[1,3,5,8,2,4,7,6]=>[4,3,1]=>70
[1,4,6,8,3,2,5,7]=>[4,3,1]=>70
[1,3,7,5,6,8,2,4]=>[5,2,1]=>64
[1,2,6,7,3,8,5,4]=>[5,2,1]=>64
[3,1,5,7,6,8,4,2]=>[4,2,1,1]=>90
[3,5,4,6,8,2,7,1]=>[4,2,1,1]=>90
[2,3,6,5,8,7,1,4]=>[4,2,2]=>56
[1,2,7,5,6,8,4,3]=>[5,1,1,1]=>35
[3,1,6,7,5,8,4,2]=>[4,2,1,1]=>90
[4,6,2,7,5,8,3,1]=>[4,2,1,1]=>90
[3,5,7,4,8,2,6,1]=>[4,2,1,1]=>90
[2,4,7,6,8,3,5,1]=>[4,2,1,1]=>90
[1,4,6,8,3,5,7,2]=>[4,3,1]=>70
[1,3,5,8,2,7,4,6]=>[4,3,1]=>70
[1,2,5,8,4,7,6,3]=>[4,2,1,1]=>90
[1,2,5,8,7,4,3,6]=>[4,2,1,1]=>90
[1,3,5,8,7,2,4,6]=>[4,3,1]=>70
[5,7,1,2,8,6,4,3]=>[3,3,1,1]=>56
[6,4,5,7,2,8,1,3]=>[4,2,1,1]=>90
[5,3,4,7,2,8,1,6]=>[4,2,1,1]=>90
[3,2,7,4,6,8,1,5]=>[4,2,2]=>56
[5,3,6,2,7,1,4,8]=>[4,2,1,1]=>90
[2,6,3,4,7,1,5,8]=>[5,2,1]=>64
[2,7,3,4,5,8,1,6]=>[5,2,1]=>64
[3,7,4,5,6,8,1,2]=>[5,2,1]=>64
[2,5,7,3,6,8,1,4]=>[4,2,2]=>56
[4,7,6,2,3,8,1,5]=>[3,3,1,1]=>56
[7,3,5,2,4,8,1,6]=>[3,3,1,1]=>56
[7,6,2,4,5,8,1,3]=>[4,2,1,1]=>90
[6,5,2,3,4,8,1,7]=>[4,2,1,1]=>90
[5,3,1,2,8,4,7,6]=>[4,2,2]=>56
[6,5,2,3,7,1,4,8]=>[4,2,1,1]=>90
[5,2,1,7,3,4,6,8]=>[5,2,1]=>64
[5,2,1,8,3,4,6,7]=>[5,2,1]=>64
[6,3,2,8,4,5,7,1]=>[4,2,1,1]=>90
[7,3,1,2,8,4,6,5]=>[4,2,2]=>56
[6,4,1,3,8,5,7,2]=>[4,2,1,1]=>90
[6,2,3,1,8,4,7,5]=>[4,2,2]=>56
[8,3,5,2,7,1,4,6]=>[3,3,1,1]=>56
[8,6,2,4,7,1,5,3]=>[3,2,2,1]=>70
[8,5,2,3,6,1,4,7]=>[4,2,1,1]=>90
[8,2,1,7,3,4,5,6]=>[5,2,1]=>64
[8,6,3,7,2,4,5,1]=>[3,2,1,1,1]=>64
[7,1,6,2,3,4,5,8]=>[6,1,1]=>21
[8,2,7,3,4,5,6,1]=>[5,1,1,1]=>35
[8,1,6,2,3,4,5,7]=>[6,1,1]=>21
[8,1,7,3,4,5,6,2]=>[5,1,1,1]=>35
[8,6,1,7,2,4,5,3]=>[4,2,1,1]=>90
[8,1,5,7,2,3,6,4]=>[4,2,1,1]=>90
[1,7,5,8,2,3,6,4]=>[4,2,2]=>56
[7,2,1,8,3,4,5,6]=>[5,2,1]=>64
[7,3,8,2,4,5,6,1]=>[4,2,1,1]=>90
[7,2,8,3,4,5,6,1]=>[5,2,1]=>64
[1,7,8,3,4,5,6,2]=>[5,2,1]=>64
[1,4,5,8,3,6,7,2]=>[5,2,1]=>64
[2,5,7,1,8,3,6,4]=>[4,3,1]=>70
[6,2,7,1,8,4,5,3]=>[3,3,2]=>42
[4,7,1,3,8,5,6,2]=>[4,3,1]=>70
[1,6,2,8,4,5,7,3]=>[5,2,1]=>64
[4,1,3,6,8,2,7,5]=>[4,2,2]=>56
[5,3,4,6,8,2,7,1]=>[4,2,1,1]=>90
[4,6,3,8,7,1,2,5]=>[3,3,2]=>42
[6,4,5,8,7,1,2,3]=>[3,3,2]=>42
[5,3,4,8,7,1,2,6]=>[3,3,2]=>42
[3,2,8,7,1,4,6,5]=>[3,2,2,1]=>70
[3,1,8,7,2,4,6,5]=>[4,2,1,1]=>90
[5,3,7,6,1,2,4,8]=>[4,2,2]=>56
[1,8,3,7,2,4,5,6]=>[5,2,1]=>64
[3,8,1,7,2,4,5,6]=>[5,2,1]=>64
[6,8,2,3,5,1,4,7]=>[4,2,2]=>56
[4,7,8,2,6,1,3,5]=>[3,3,2]=>42
[6,2,8,7,1,4,5,3]=>[3,2,2,1]=>70
[3,8,7,1,4,5,6,2]=>[4,2,1,1]=>90
[2,8,6,1,3,4,5,7]=>[5,2,1]=>64
[2,7,6,1,3,4,5,8]=>[5,2,1]=>64
[1,7,6,2,3,4,5,8]=>[6,1,1]=>21
[1,8,6,2,3,4,5,7]=>[6,1,1]=>21
[2,8,7,3,4,5,6,1]=>[5,1,1,1]=>35
[3,8,7,2,4,5,6,1]=>[4,2,1,1]=>90
[7,8,3,6,2,4,5,1]=>[3,2,2,1]=>70
[1,5,8,7,2,3,6,4]=>[4,2,1,1]=>90
[8,7,6,1,3,4,5,2]=>[4,1,1,1,1]=>35
[3,4,7,2,5,1,8,6]=>[4,3,1]=>70
[1,2,8,3,7,5,4,6]=>[5,1,1,1]=>35
[1,6,3,8,7,4,2,5]=>[4,2,1,1]=>90
[4,3,8,1,2,6,7,5]=>[4,2,2]=>56
[1,2,3,4,5,10,9,8,7,6]=>[6,1,1,1,1]=>126
[3,1,2,4,5,6,7,8,9]=>[8,1]=>8
[2,4,1,3,5,6,7,8,9]=>[7,2]=>27
[2,3,5,1,4,6,7,8,9]=>[7,2]=>27
[2,3,4,6,1,5,7,8,9]=>[7,2]=>27
[2,3,4,5,7,1,6,8,9]=>[7,2]=>27
[2,3,4,5,6,8,1,7,9]=>[7,2]=>27
[3,6,8,7,1,2,5,4]=>[3,3,1,1]=>56
[6,5,7,2,4,8,1,3]=>[3,2,2,1]=>70
[3,4,1,6,5,8,7,2]=>[4,3,1]=>70
[3,5,1,2,4,8,7,6]=>[4,3,1]=>70
[3,7,5,2,1,4,6,8]=>[4,2,1,1]=>90
[3,8,5,2,7,4,1,6]=>[3,3,1,1]=>56
[5,2,8,4,7,3,1,6]=>[3,2,2,1]=>70
[5,2,7,4,1,3,6,8]=>[4,2,2]=>56
[4,3,5,1,2,8,7,6]=>[3,3,2]=>42
[3,1,4,6,2,8,7,5]=>[4,3,1]=>70
[1,4,6,5,2,8,7,3]=>[4,2,2]=>56
[3,4,5,6,1,8,7,2]=>[5,2,1]=>64
[3,4,5,8,7,2,1,6]=>[4,2,1,1]=>90
[1,4,7,2,6,3,5,8]=>[5,2,1]=>64
[8,4,7,5,2,1,6,3]=>[3,2,1,1,1]=>64
[8,1,4,7,2,3,6,5]=>[4,2,1,1]=>90
[1,8,5,7,3,4,6,2]=>[4,2,1,1]=>90
[6,3,5,1,7,4,2,8]=>[4,2,1,1]=>90
[6,1,4,8,7,3,2,5]=>[3,2,2,1]=>70
[6,4,8,5,7,1,2,3]=>[3,3,2]=>42
[5,4,8,1,6,3,2,7]=>[3,2,2,1]=>70
[1,4,8,6,3,7,2,5]=>[4,2,1,1]=>90
[5,4,7,6,3,8,1,2]=>[3,2,2,1]=>70
[4,6,3,7,5,8,1,2]=>[4,2,2]=>56
[4,1,3,5,8,6,2,7]=>[5,2,1]=>64
[5,7,4,3,8,1,2,6]=>[3,3,1,1]=>56
[1,4,8,3,7,6,5,2]=>[3,2,1,1,1]=>64
[4,3,8,2,1,6,5,7]=>[3,2,2,1]=>70
[3,8,4,2,7,1,5,6]=>[4,2,1,1]=>90
[3,1,2,5,7,6,4,8]=>[5,2,1]=>64
[1,8,2,7,6,5,4,3]=>[3,1,1,1,1,1]=>21
[3,8,1,6,7,5,4,2]=>[3,2,1,1,1]=>64
[3,7,2,6,8,5,1,4]=>[3,2,2,1]=>70
[7,2,3,8,5,6,1,4]=>[4,2,2]=>56
[8,2,1,7,5,6,4,3]=>[3,2,1,1,1]=>64
[8,1,3,6,5,7,4,2]=>[4,1,1,1,1]=>35
[8,2,4,3,6,1,5,7]=>[4,2,1,1]=>90
[1,7,8,5,4,3,6,2]=>[3,2,1,1,1]=>64
[1,8,4,5,3,2,6,7]=>[5,1,1,1]=>35
[7,8,5,4,3,1,6,2]=>[2,2,2,1,1]=>28
[7,1,6,3,4,2,5,8]=>[5,1,1,1]=>35
[6,8,7,1,4,2,5,3]=>[3,2,2,1]=>70
[3,6,1,4,2,7,5,8]=>[4,3,1]=>70
[3,4,1,8,5,7,6,2]=>[4,2,1,1]=>90
[3,6,5,1,2,8,4,7]=>[4,3,1]=>70
[3,8,5,6,7,2,1,4]=>[4,2,1,1]=>90
[8,1,7,6,2,4,3,5]=>[4,1,1,1,1]=>35
[8,5,6,1,4,2,3,7]=>[4,2,1,1]=>90
[8,6,5,4,7,1,3,2]=>[2,2,1,1,1,1]=>20
[1,6,4,5,7,2,3,8]=>[5,2,1]=>64
[8,3,6,1,7,2,4,5]=>[4,3,1]=>70
[1,8,6,5,7,3,4,2]=>[3,2,1,1,1]=>64
[1,7,5,3,6,8,4,2]=>[4,2,1,1]=>90
[7,4,1,6,5,8,3,2]=>[3,2,1,1,1]=>64
[4,1,5,8,7,6,3,2]=>[3,2,1,1,1]=>64
[1,2,5,8,6,7,3,4]=>[5,2,1]=>64
[4,2,1,5,8,7,3,6]=>[3,3,2]=>42
[5,2,4,6,1,7,3,8]=>[5,2,1]=>64
[1,5,3,6,8,7,4,2]=>[4,2,1,1]=>90
[3,5,4,6,1,8,2,7]=>[4,3,1]=>70
[3,1,5,7,6,8,2,4]=>[4,3,1]=>70
[1,4,5,6,8,7,2,3]=>[5,2,1]=>64
[1,4,6,3,7,2,8,5]=>[5,2,1]=>64
[3,7,2,6,5,4,1,8]=>[3,2,1,1,1]=>64
[3,2,6,4,7,5,1,8]=>[4,3,1]=>70
[8,1,3,6,2,7,5,4]=>[4,2,1,1]=>90
[1,2,4,7,3,8,6,5]=>[5,2,1]=>64
[3,1,8,6,2,7,5,4]=>[3,3,1,1]=>56
[5,6,1,8,2,7,4,3]=>[3,3,1,1]=>56
[4,2,7,8,1,6,5,3]=>[3,2,2,1]=>70
[3,2,8,6,1,7,5,4]=>[3,2,2,1]=>70
[7,2,8,1,6,5,4,3]=>[2,2,2,1,1]=>28
[2,8,7,1,6,5,4,3]=>[2,2,1,1,1,1]=>20
[3,8,7,1,6,5,4,2]=>[2,2,1,1,1,1]=>20
[4,8,7,5,1,6,3,2]=>[3,2,1,1,1]=>64
[6,7,8,5,1,4,3,2]=>[3,2,1,1,1]=>64
[5,6,3,8,4,1,7,2]=>[3,3,2]=>42
[7,3,8,5,4,1,6,2]=>[3,2,2,1]=>70
[3,4,8,6,5,1,7,2]=>[4,2,1,1]=>90
[1,4,6,2,3,8,7,5]=>[4,3,1]=>70
[5,6,7,1,2,8,4,3]=>[4,3,1]=>70
[2,7,1,3,8,6,5,4]=>[3,3,1,1]=>56
[5,6,8,1,2,7,4,3]=>[3,3,1,1]=>56
[2,1,3,7,4,8,6,5]=>[4,3,1]=>70
[4,2,7,3,6,8,1,5]=>[4,2,2]=>56
[5,3,6,4,2,8,1,7]=>[3,3,1,1]=>56
[4,1,5,3,8,2,7,6]=>[3,3,2]=>42
[5,2,6,4,7,3,1,8]=>[4,2,1,1]=>90
[2,6,3,4,7,5,1,8]=>[5,2,1]=>64
[2,6,3,5,4,8,1,7]=>[4,2,1,1]=>90
[2,7,4,3,5,8,1,6]=>[4,2,1,1]=>90
[7,3,6,4,2,8,1,5]=>[3,2,1,1,1]=>64
[7,6,4,5,2,8,1,3]=>[3,2,1,1,1]=>64
[5,4,3,1,8,2,7,6]=>[3,2,2,1]=>70
[6,5,4,2,7,3,1,8]=>[3,2,1,1,1]=>64
[5,4,1,7,2,6,3,8]=>[4,2,2]=>56
[5,4,1,8,3,2,6,7]=>[4,2,1,1]=>90
[6,5,2,8,3,4,7,1]=>[4,2,1,1]=>90
[7,4,2,1,8,3,6,5]=>[3,2,2,1]=>70
[6,5,3,4,8,2,7,1]=>[3,2,1,1,1]=>64
[6,1,5,3,8,2,7,4]=>[3,2,2,1]=>70
[4,6,3,1,8,2,7,5]=>[3,3,2]=>42
[5,8,4,2,7,3,1,6]=>[3,2,2,1]=>70
[8,2,6,4,7,3,1,5]=>[3,2,1,1,1]=>64
[8,6,2,5,7,4,1,3]=>[3,2,1,1,1]=>64
[8,5,3,2,6,4,1,7]=>[3,2,1,1,1]=>64
[8,3,1,7,2,5,4,6]=>[4,2,1,1]=>90
[7,5,2,6,4,3,1,8]=>[3,2,1,1,1]=>64
[7,1,6,2,5,4,3,8]=>[4,1,1,1,1]=>35
[8,1,7,3,5,6,4,2]=>[4,1,1,1,1]=>35
[8,6,1,7,4,5,2,3]=>[3,2,2,1]=>70
[8,1,3,7,2,6,5,4]=>[3,2,1,1,1]=>64
[1,7,6,8,3,2,4,5]=>[4,2,1,1]=>90
[7,1,5,8,4,2,6,3]=>[3,2,2,1]=>70
[7,3,8,4,5,2,6,1]=>[4,2,1,1]=>90
[7,2,8,5,3,4,6,1]=>[4,2,1,1]=>90
[6,1,8,4,3,2,5,7]=>[4,2,1,1]=>90
[6,1,7,4,2,5,3,8]=>[4,2,2]=>56
[1,2,7,3,4,6,5,8]=>[6,1,1]=>21
[1,7,8,4,3,5,6,2]=>[4,2,1,1]=>90
[1,6,2,8,3,5,7,4]=>[5,2,1]=>64
[2,6,1,7,3,5,4,8]=>[4,3,1]=>70
[3,1,5,8,4,2,6,7]=>[4,3,1]=>70
[4,3,1,6,8,2,7,5]=>[3,3,2]=>42
[5,7,4,8,3,2,1,6]=>[3,2,1,1,1]=>64
[5,4,8,2,7,3,1,6]=>[3,2,2,1]=>70
[5,2,8,7,3,4,1,6]=>[4,2,1,1]=>90
[6,4,7,5,3,2,1,8]=>[3,2,1,1,1]=>64
[1,8,3,7,6,2,4,5]=>[4,2,1,1]=>90
[5,8,3,2,6,4,1,7]=>[3,2,2,1]=>70
[6,8,2,4,7,5,1,3]=>[3,2,2,1]=>70
[7,3,8,2,6,4,1,5]=>[3,2,2,1]=>70
[4,6,8,2,7,3,1,5]=>[3,3,1,1]=>56
[2,6,8,7,3,4,1,5]=>[4,2,1,1]=>90
[7,2,8,6,3,5,1,4]=>[3,2,2,1]=>70
[6,8,1,7,2,5,4,3]=>[3,2,1,1,1]=>64
[3,8,7,4,5,6,1,2]=>[4,2,1,1]=>90
[2,8,6,4,3,5,1,7]=>[4,1,1,1,1]=>35
[2,7,6,3,5,4,1,8]=>[4,1,1,1,1]=>35
[1,7,6,5,2,4,3,8]=>[4,1,1,1,1]=>35
[1,8,6,5,3,2,4,7]=>[4,1,1,1,1]=>35
[3,8,7,4,6,2,5,1]=>[3,2,1,1,1]=>64
[5,8,3,7,6,2,4,1]=>[2,2,2,1,1]=>28
[7,1,8,6,5,2,3,4]=>[4,2,1,1]=>90
[8,4,7,5,3,2,1,6]=>[3,1,1,1,1,1]=>21
[8,7,2,5,4,3,1,6]=>[3,1,1,1,1,1]=>21
[6,8,3,2,5,4,7,1]=>[3,2,2,1]=>70
[1,5,7,8,4,3,6,2]=>[4,2,1,1]=>90
[6,3,8,1,5,4,7,2]=>[3,2,2,1]=>70
[6,2,1,8,5,4,7,3]=>[3,2,2,1]=>70
[2,6,5,7,4,1,3,8]=>[4,2,1,1]=>90
[2,5,4,7,1,8,6,3]=>[4,2,2]=>56
[5,2,1,8,7,6,4,3]=>[2,2,2,1,1]=>28
[4,8,6,7,5,3,1,2]=>[3,2,1,1,1]=>64
[6,5,4,8,2,1,7,3]=>[2,2,2,1,1]=>28
[5,8,4,7,2,6,3,1]=>[2,2,2,1,1]=>28
[5,8,3,2,7,6,4,1]=>[2,2,2,1,1]=>28
[5,2,1,4,3,6,7,8]=>[5,2,1]=>64
[3,5,7,4,2,6,1,8]=>[4,2,1,1]=>90
[4,2,1,6,5,3,7,8]=>[4,2,2]=>56
[4,2,1,5,7,6,3,8]=>[4,2,2]=>56
[3,5,4,7,1,6,2,8]=>[4,2,2]=>56
[4,3,5,1,6,8,7,2]=>[4,2,2]=>56
[4,3,1,2,6,5,8,7,10,9]=>[5,4,1]=>288
[2,4,6,8,1,3,5,7,9]=>[5,4]=>42
[8,7,6,5,4,3,2,10,1,9]=>[2,2,1,1,1,1,1,1]=>35
[6,5,4,10,3,9,2,8,1,7]=>[2,2,2,2,1,1]=>90
[6,5,4,3,2,8,10,1,7,9]=>[3,3,1,1,1,1]=>225
[4,8,3,7,2,6,10,1,5,9]=>[3,3,2,2]=>252
[4,3,2,6,8,10,1,5,7,9]=>[4,4,1,1]=>300
[2,1,7,3,8,4,6,5]=>[4,3,1]=>70
[4,1,8,2,7,3,6,5]=>[4,2,1,1]=>90
[4,1,7,2,8,3,6,5]=>[4,3,1]=>70
[7,1,3,2,8,4,6,5]=>[4,2,2]=>56
[7,1,8,2,4,3,6,5]=>[4,2,2]=>56
[8,1,7,2,5,3,6,4]=>[4,2,1,1]=>90
[7,1,5,2,8,3,6,4]=>[4,2,2]=>56
[5,1,7,2,8,3,6,4]=>[4,3,1]=>70
[5,1,8,2,7,3,6,4]=>[4,2,1,1]=>90
[5,1,8,2,4,3,7,6]=>[4,2,2]=>56
[8,1,6,2,4,3,7,5]=>[4,2,1,1]=>90
[6,1,8,2,4,3,7,5]=>[4,2,2]=>56
[6,1,8,2,5,3,7,4]=>[4,2,2]=>56
[8,1,6,2,5,3,7,4]=>[4,2,1,1]=>90
[8,1,6,2,7,3,5,4]=>[4,2,1,1]=>90
[6,1,8,2,7,3,5,4]=>[4,2,1,1]=>90
[6,1,7,2,8,3,5,4]=>[4,3,1]=>70
[6,1,7,2,5,3,8,4]=>[4,3,1]=>70
[6,1,7,2,4,3,8,5]=>[4,3,1]=>70
[5,1,6,2,4,3,8,7]=>[4,3,1]=>70
[7,1,5,2,4,3,8,6]=>[4,2,1,1]=>90
[7,1,6,2,4,3,8,5]=>[4,2,1,1]=>90
[7,1,6,2,5,3,8,4]=>[4,2,1,1]=>90
[7,1,6,2,8,3,5,4]=>[4,2,1,1]=>90
[7,1,8,2,6,3,5,4]=>[4,2,1,1]=>90
[1,8,2,7,5,4,6,3]=>[4,1,1,1,1]=>35
[1,8,2,7,4,3,5,6]=>[5,1,1,1]=>35
[1,8,6,4,7,2,3,5]=>[4,2,1,1]=>90
[1,8,4,2,6,3,5,7]=>[5,2,1]=>64
[7,4,8,1,5,2,3,6]=>[4,2,2]=>56
[7,5,8,3,2,4,1,6]=>[3,2,1,1,1]=>64
[1,8,5,4,3,6,2,7]=>[4,1,1,1,1]=>35
[1,8,5,4,3,7,2,6]=>[3,2,1,1,1]=>64
[1,8,4,2,5,3,7,6]=>[4,3,1]=>70
[7,4,8,2,1,3,5,6]=>[4,2,1,1]=>90
[7,5,4,8,2,3,6,1]=>[3,2,1,1,1]=>64
[5,1,7,4,2,6,8,3]=>[4,2,2]=>56
[4,1,6,3,2,5,8,7]=>[4,3,1]=>70
[6,5,4,3,7,1,8,2]=>[3,2,1,1,1]=>64
[6,5,1,7,3,8,2,4]=>[3,3,1,1]=>56
[6,3,2,8,5,7,1,4]=>[3,2,2,1]=>70
[6,5,4,3,8,2,7,1]=>[2,2,1,1,1,1]=>20
[6,5,4,3,8,7,1,2]=>[2,2,2,1,1]=>28
[7,6,3,8,5,4,1,2]=>[2,2,2,1,1]=>28
[5,4,8,2,1,7,3,6]=>[3,2,2,1]=>70
[6,4,2,8,5,1,3,7]=>[3,2,2,1]=>70
[7,6,4,8,5,1,2,3]=>[3,2,2,1]=>70
[7,2,8,6,3,1,4,5]=>[4,2,1,1]=>90
[7,2,8,6,1,5,3,4]=>[3,2,2,1]=>70
[2,1,7,8,3,6,4,5]=>[4,3,1]=>70
[6,4,1,7,8,2,3,5]=>[4,3,1]=>70
[4,1,5,3,2,8,6,7]=>[4,3,1]=>70
[6,3,1,7,8,5,2,4]=>[3,3,2]=>42
[6,5,4,2,7,8,3,1]=>[3,2,1,1,1]=>64
[4,3,1,5,2,6,8,7]=>[4,3,1]=>70
[5,4,2,1,6,7,8,3]=>[4,2,1,1]=>90
[5,4,3,1,6,7,8,2]=>[4,2,1,1]=>90
[7,8,3,1,2,5,6,4]=>[4,2,2]=>56
[7,8,2,1,3,5,4,6]=>[4,2,2]=>56
[5,2,3,7,1,8,6,4]=>[4,2,2]=>56
[2,5,3,6,1,8,7,4]=>[4,2,2]=>56
[2,6,7,3,1,8,4,5]=>[4,3,1]=>70
[6,2,8,3,1,7,4,5]=>[4,2,2]=>56
[3,2,5,7,1,8,4,6]=>[4,3,1]=>70
[4,3,1,2,7,8,6,5]=>[4,2,2]=>56
[5,3,4,7,8,6,1,2]=>[4,2,2]=>56
[5,1,3,7,2,6,8,4]=>[4,2,2]=>56
[5,2,4,7,8,1,6,3]=>[4,2,2]=>56
[4,3,5,7,6,8,1,2]=>[4,2,2]=>56
[3,4,2,1,8,7,5,6]=>[4,2,2]=>56
[7,6,5,8,2,1,4,3]=>[2,2,2,1,1]=>28
[8,5,4,3,2,1,7,6]=>[2,2,1,1,1,1]=>20
[8,6,5,4,3,2,1,9,7]=>[2,2,1,1,1,1,1]=>27
[7,6,5,4,3,2,1,9,8]=>[2,2,1,1,1,1,1]=>27
[7,6,5,4,1,8,3,2]=>[2,2,1,1,1,1]=>20
[7,6,5,8,4,1,3,2]=>[2,2,1,1,1,1]=>20
[7,8,4,5,9,2,3,6,10,1]=>[4,3,2,1]=>768
[7,8,1,3,2,4,5,6]=>[5,2,1]=>64
[7,8,4,1,5,2,3,6]=>[4,2,2]=>56
[4,6,7,1,5,2,3,8]=>[4,3,1]=>70
[3,2,5,6,1,4,7,8]=>[5,2,1]=>64
[3,5,2,6,1,4,7,8]=>[5,2,1]=>64
[3,5,4,6,7,8,1,2]=>[5,2,1]=>64
[1,5,3,6,2,4,7,8]=>[5,2,1]=>64
[2,5,4,6,7,1,3,8]=>[5,2,1]=>64
[2,6,7,4,5,1,3,8]=>[4,2,2]=>56
[4,2,5,6,7,1,3,8]=>[5,2,1]=>64
[6,1,7,3,2,4,5,8]=>[5,2,1]=>64
[7,3,2,5,4,1,6,8]=>[4,2,1,1]=>90
[7,3,5,4,2,1,6,8]=>[4,1,1,1,1]=>35
[7,3,5,2,4,1,6,8]=>[4,2,1,1]=>90
[7,6,5,2,1,4,3,8]=>[3,2,1,1,1]=>64
[1,3,6,7,5,2,8,4]=>[5,2,1]=>64
[7,3,4,1,6,2,5,8]=>[4,3,1]=>70
[7,3,4,1,6,5,2,8]=>[4,2,1,1]=>90
[7,3,4,1,5,6,2,8]=>[5,2,1]=>64
[7,3,2,5,1,6,4,8]=>[4,2,1,1]=>90
[7,6,5,4,1,3,2,8]=>[3,1,1,1,1,1]=>21
[7,3,4,1,5,2,6,8]=>[5,2,1]=>64
[1,3,6,7,2,5,8,4]=>[5,2,1]=>64
[1,7,4,6,2,8,5,3]=>[4,2,1,1]=>90
[4,3,1,7,2,6,8,5]=>[4,2,2]=>56
[5,6,1,4,7,3,8,2]=>[4,2,1,1]=>90
[5,3,2,1,7,4,8,6]=>[3,3,1,1]=>56
[1,3,4,5,8,7,2,6]=>[5,2,1]=>64
[6,3,4,5,8,1,7,2]=>[4,2,2]=>56
[2,4,5,1,6,8,7,3]=>[5,2,1]=>64
[3,1,2,5,6,8,7,4]=>[5,2,1]=>64
[4,3,2,5,6,8,1,7]=>[4,2,1,1]=>90
[3,7,5,4,6,8,1,2]=>[4,2,1,1]=>90
[3,1,4,6,5,8,2,7]=>[4,3,1]=>70
[2,3,4,5,8,6,1,7]=>[6,1,1]=>21
[2,3,4,5,8,1,7,6]=>[5,2,1]=>64
[3,1,4,6,5,8,7,2]=>[4,3,1]=>70
[3,7,5,4,6,8,2,1]=>[4,1,1,1,1]=>35
[5,6,1,4,7,2,8,3]=>[4,3,1]=>70
[4,3,1,7,5,6,8,2]=>[4,2,2]=>56
[4,3,1,7,6,5,8,2]=>[3,2,2,1]=>70
[3,1,4,6,7,8,5,2]=>[5,2,1]=>64
[1,4,5,2,6,8,7,3]=>[5,2,1]=>64
[3,7,5,2,6,8,1,4]=>[4,2,1,1]=>90
[3,7,5,2,6,8,4,1]=>[4,2,1,1]=>90
[5,6,1,2,7,4,8,3]=>[4,3,1]=>70
[6,3,5,2,4,7,8,1]=>[4,2,1,1]=>90
[5,3,2,1,4,7,8,6]=>[4,2,1,1]=>90
[5,3,1,4,2,7,8,6]=>[4,3,1]=>70
[5,3,1,2,4,7,8,6]=>[5,2,1]=>64
[7,1,5,2,6,8,4,3]=>[4,2,1,1]=>90
[7,1,5,2,6,8,3,4]=>[4,3,1]=>70
[1,7,4,6,5,8,3,2]=>[4,1,1,1,1]=>35
[2,7,4,6,1,8,3,5]=>[4,3,1]=>70
[2,7,4,6,1,8,5,3]=>[4,2,1,1]=>90
[2,3,6,7,1,5,8,4]=>[5,2,1]=>64
[2,3,6,7,5,1,8,4]=>[5,2,1]=>64
[4,3,2,6,7,1,8,5]=>[4,2,1,1]=>90
[7,3,2,5,6,8,1,4]=>[4,2,1,1]=>90
[7,1,5,4,6,8,2,3]=>[4,2,1,1]=>90
[2,7,4,6,5,8,1,3]=>[4,2,1,1]=>90
[7,3,4,5,8,6,1,2]=>[4,2,2]=>56
[7,3,4,5,8,1,6,2]=>[4,2,2]=>56
[7,3,4,5,8,1,2,6]=>[4,3,1]=>70
[1,3,4,5,8,6,2,7]=>[6,1,1]=>21
[1,3,4,5,8,2,7,6]=>[5,2,1]=>64
[6,3,4,5,8,2,1,7]=>[4,2,1,1]=>90
[6,3,4,5,8,2,7,1]=>[4,2,1,1]=>90
[7,3,4,5,8,6,2,1]=>[4,2,1,1]=>90
[2,7,4,6,5,8,3,1]=>[4,1,1,1,1]=>35
[7,1,5,4,6,8,3,2]=>[4,1,1,1,1]=>35
[7,3,2,5,6,8,4,1]=>[4,2,1,1]=>90
[5,7,4,6,1,8,3,2]=>[3,2,2,1]=>70
[6,3,4,5,8,1,2,7]=>[4,3,1]=>70
[7,3,4,5,8,2,1,6]=>[4,2,1,1]=>90
[7,3,4,5,8,2,6,1]=>[4,2,1,1]=>90
[4,8,6,1,7,5,2,3]=>[3,3,1,1]=>56
[4,7,8,2,6,1,5,3]=>[3,2,2,1]=>70
[7,6,4,2,8,3,5,1]=>[3,2,1,1,1]=>64
[8,6,4,2,7,5,3,1]=>[2,2,2,1,1]=>28
[8,4,7,3,6,5,1,2]=>[2,2,2,1,1]=>28
[8,4,6,1,7,5,3,2]=>[3,2,1,1,1]=>64
[6,4,7,1,8,3,2,5]=>[3,3,1,1]=>56
[7,4,8,3,6,1,5,2]=>[2,2,2,2]=>14
[6,12,5,11,4,10,3,9,2,8,1,7]=>[2,2,2,2,2,2]=>132
[6,2,1,7,3,5,4,8]=>[4,2,2]=>56
[2,1,8,6,3,5,4,7]=>[4,2,1,1]=>90
[2,1,7,3,5,8,6,4]=>[4,3,1]=>70
[2,7,3,1,5,4,6,8]=>[5,2,1]=>64
[2,6,3,1,4,8,5,7]=>[5,2,1]=>64
[4,2,1,8,3,6,7,5]=>[4,2,2]=>56
[2,1,8,6,3,5,7,4]=>[4,2,1,1]=>90
[6,2,1,7,3,5,8,4]=>[4,2,2]=>56
[2,7,3,1,4,8,5,6]=>[5,2,1]=>64
[3,2,1,6,4,5,7,8]=>[5,2,1]=>64
[3,2,1,5,7,8,4,6]=>[4,3,1]=>70
[2,1,7,3,6,8,4,5]=>[4,3,1]=>70
[2,7,3,1,5,6,8,4]=>[5,2,1]=>64
[2,4,7,5,1,6,8,3]=>[5,2,1]=>64
[4,3,7,5,6,1,8,2]=>[4,2,2]=>56
[4,3,6,8,5,1,7,2]=>[3,3,2]=>42
[2,6,1,8,3,5,7,4]=>[4,3,1]=>70
[2,1,6,8,3,7,4,5]=>[4,3,1]=>70
[2,1,8,3,5,7,4,6]=>[4,3,1]=>70
[3,2,1,5,6,8,4,7]=>[4,3,1]=>70
[3,2,1,5,7,4,6,8]=>[4,3,1]=>70
[2,1,7,3,6,4,5,8]=>[5,2,1]=>64
[2,1,6,3,5,8,4,7]=>[4,3,1]=>70
[8,2,4,1,7,5,6,3]=>[4,2,1,1]=>90
[3,8,4,7,5,1,6,2]=>[4,2,1,1]=>90
[8,4,3,6,1,7,5,2]=>[3,2,2,1]=>70
[8,2,1,7,3,5,4,6]=>[4,2,1,1]=>90
[2,6,1,8,3,5,4,7]=>[4,3,1]=>70
[2,7,3,1,5,6,4,8]=>[5,2,1]=>64
[2,4,7,5,1,6,3,8]=>[5,2,1]=>64
[8,2,4,1,7,5,3,6]=>[4,2,1,1]=>90
[5,8,6,3,1,7,4,2]=>[3,2,2,1]=>70
[2,4,7,1,8,5,3,6]=>[4,3,1]=>70
[2,4,8,5,1,6,3,7]=>[5,2,1]=>64
[6,2,1,7,3,4,8,5]=>[4,3,1]=>70
[6,2,1,7,8,3,5,4]=>[3,3,2]=>42
[2,7,1,8,3,5,6,4]=>[4,3,1]=>70
[2,1,8,3,6,4,5,7]=>[5,2,1]=>64
[3,2,1,6,7,4,5,8]=>[4,3,1]=>70
[3,2,1,7,4,5,6,8]=>[5,2,1]=>64
[3,2,1,6,8,4,5,7]=>[4,3,1]=>70
[2,1,8,3,7,4,5,6]=>[5,2,1]=>64
[2,1,8,3,6,7,4,5]=>[4,3,1]=>70
[2,4,8,5,1,6,7,3]=>[5,2,1]=>64
[4,3,8,5,6,1,7,2]=>[4,2,2]=>56
[3,2,1,8,4,5,6,7]=>[5,2,1]=>64
[1,6,8,3,7,2,4,5]=>[4,2,2]=>56
[3,8,1,5,7,2,4,6]=>[4,3,1]=>70
[1,2,6,8,4,7,3,5]=>[4,2,2]=>56
[6,1,5,8,2,4,7,3]=>[4,2,1,1]=>90
[1,2,4,8,3,6,7,5]=>[5,2,1]=>64
[4,1,2,7,8,3,6,5]=>[4,3,1]=>70
[3,5,7,4,8,6,1,2]=>[4,2,2]=>56
[5,3,8,4,7,6,1,2]=>[3,2,2,1]=>70
[8,7,1,2,5,4,6,3]=>[4,1,1,1,1]=>35
[5,8,1,2,3,7,6,4]=>[4,2,1,1]=>90
[1,2,8,4,3,5,7,6]=>[5,2,1]=>64
[1,2,5,3,7,6,4,8]=>[5,2,1]=>64
[6,1,2,8,7,4,5,3]=>[4,2,1,1]=>90
[7,1,6,2,8,4,5,3]=>[4,2,1,1]=>90
[1,2,6,3,8,5,4,7]=>[5,2,1]=>64
[1,2,8,5,3,6,4,7]=>[5,2,1]=>64
[1,2,7,3,8,5,4,6]=>[5,2,1]=>64
[4,1,2,7,8,6,3,5]=>[4,3,1]=>70
[1,6,2,8,4,3,5,7]=>[5,2,1]=>64
[1,6,4,2,7,3,5,8]=>[5,2,1]=>64
[1,8,6,3,2,4,5,7]=>[5,1,1,1]=>35
[1,7,3,2,8,4,5,6]=>[5,2,1]=>64
[3,1,7,8,6,2,4,5]=>[4,3,1]=>70
[1,8,7,2,4,5,6,3]=>[5,1,1,1]=>35
[1,8,7,3,5,6,2,4]=>[4,2,1,1]=>90
[1,3,2,8,7,4,5,6]=>[5,2,1]=>64
[1,8,3,2,6,4,5,7]=>[5,2,1]=>64
[1,7,6,3,2,4,5,8]=>[5,1,1,1]=>35
[1,2,8,4,3,7,5,6]=>[5,2,1]=>64
[8,5,1,7,2,4,6,3]=>[4,2,1,1]=>90
[5,3,8,7,4,6,1,2]=>[3,2,2,1]=>70
[3,8,6,4,7,5,1,2]=>[3,2,2,1]=>70
[6,1,8,2,7,4,5,3]=>[4,2,1,1]=>90
[1,2,5,3,8,6,4,7]=>[5,2,1]=>64
[1,2,7,5,3,6,4,8]=>[5,2,1]=>64
[1,2,6,3,7,5,4,8]=>[5,2,1]=>64
[1,2,3,7,5,4,8,6]=>[5,2,1]=>64
[3,7,4,8,6,5,1,2]=>[3,2,2,1]=>70
[1,8,2,7,6,4,5,3]=>[4,1,1,1,1]=>35
[2,8,7,6,5,1,4,3]=>[2,2,1,1,1,1]=>20
[7,1,6,3,2,5,4,8]=>[4,2,1,1]=>90
[2,7,6,3,1,5,8,4]=>[4,2,1,1]=>90
[1,8,4,3,6,5,2,7]=>[4,2,1,1]=>90
[1,8,4,6,5,3,2,7]=>[4,1,1,1,1]=>35
[7,4,2,1,6,5,3,8]=>[3,2,2,1]=>70
[7,6,1,4,3,5,2,8]=>[4,1,1,1,1]=>35
[7,4,1,3,5,2,6,8]=>[5,1,1,1]=>35
[7,3,1,2,4,6,5,8]=>[5,2,1]=>64
[1,8,6,3,4,5,2,7]=>[5,1,1,1]=>35
[1,8,6,7,4,2,5,3]=>[3,2,2,1]=>70
[3,6,2,1,4,8,5,7]=>[4,3,1]=>70
[3,1,7,2,4,6,8,5]=>[5,2,1]=>64
[3,4,7,1,5,2,8,6]=>[4,3,1]=>70
[3,6,7,4,1,5,8,2]=>[4,2,2]=>56
[4,3,2,7,1,5,8,6]=>[3,3,1,1]=>56
[3,1,2,8,6,5,4,7]=>[4,2,1,1]=>90
[5,4,8,6,1,2,3,7]=>[4,2,2]=>56
[5,6,8,7,4,3,1,2]=>[3,2,1,1,1]=>64
[1,8,2,7,4,3,6,5]=>[4,2,1,1]=>90
[6,5,8,2,3,7,1,4]=>[3,2,2,1]=>70
[6,4,8,5,3,1,7,2]=>[3,2,2,1]=>70
[5,7,8,6,1,3,2,4]=>[3,3,1,1]=>56
[2,4,8,1,6,3,7,5]=>[4,3,1]=>70
[3,1,2,8,6,4,7,5]=>[4,3,1]=>70
[5,3,2,6,4,8,1,7]=>[3,3,1,1]=>56
[4,1,6,3,5,8,2,7]=>[4,3,1]=>70
[2,4,5,3,8,6,1,7]=>[5,2,1]=>64
[1,8,5,3,2,7,6,4]=>[3,2,2,1]=>70
[1,8,4,5,2,6,7,3]=>[5,2,1]=>64
[4,1,2,7,6,5,8,3]=>[4,2,1,1]=>90
[2,4,1,6,7,8,5,3]=>[5,2,1]=>64
[1,8,4,3,6,2,7,5]=>[4,2,1,1]=>90
[5,6,7,3,2,8,1,4]=>[4,2,1,1]=>90
[2,5,7,3,6,8,4,1]=>[4,2,1,1]=>90
[5,3,2,1,4,8,6,7]=>[4,2,1,1]=>90
[5,3,1,4,2,8,6,7]=>[4,3,1]=>70
[7,6,1,3,8,5,4,2]=>[3,2,1,1,1]=>64
[3,4,7,8,1,2,6,5]=>[4,3,1]=>70
[3,6,7,8,1,4,5,2]=>[4,3,1]=>70
[3,6,2,8,1,5,4,7]=>[3,3,2]=>42
[2,3,6,8,5,1,4,7]=>[4,3,1]=>70
[3,1,6,4,8,2,5,7]=>[4,3,1]=>70
[7,3,2,6,8,5,1,4]=>[3,2,2,1]=>70
[7,3,5,8,4,6,1,2]=>[3,2,2,1]=>70
[7,5,2,8,4,1,6,3]=>[3,2,2,1]=>70
[7,4,5,8,2,1,3,6]=>[3,3,1,1]=>56
[1,8,5,2,4,6,3,7]=>[5,1,1,1]=>35
[1,8,4,2,3,5,7,6]=>[5,2,1]=>64
[6,4,2,8,3,5,1,7]=>[4,2,1,1]=>90
[6,3,4,8,2,5,7,1]=>[4,2,1,1]=>90
[7,5,4,8,3,6,2,1]=>[2,2,1,1,1,1]=>20
[2,7,4,8,5,3,6,1]=>[4,2,1,1]=>90
[7,1,5,4,8,3,6,2]=>[3,2,1,1,1]=>64
[7,3,2,5,8,4,6,1]=>[3,3,1,1]=>56
[8,4,6,3,7,2,5,1]=>[3,2,1,1,1]=>64
[7,4,6,3,8,5,1,2]=>[3,2,2,1]=>70
[2,5,6,8,3,4,1,7]=>[4,3,1]=>70
[8,4,6,2,7,5,3,1]=>[3,2,1,1,1]=>64
[8,5,6,7,2,4,3,1]=>[3,2,1,1,1]=>64
[2,5,6,8,4,3,1,7]=>[4,2,1,1]=>90
[2,5,7,8,4,1,3,6]=>[4,3,1]=>70
[6,5,7,8,4,1,3,2]=>[3,2,1,1,1]=>64
[7,5,6,8,2,4,1,3]=>[3,2,2,1]=>70
[7,4,6,2,8,5,1,3]=>[3,2,2,1]=>70
[4,3,2,6,8,5,1,7]=>[3,3,1,1]=>56
[3,5,6,8,2,4,1,7]=>[4,3,1]=>70
[3,5,6,8,4,2,1,7]=>[4,2,1,1]=>90
[2,6,7,8,1,4,5,3]=>[4,3,1]=>70
[3,6,7,8,1,4,2,5]=>[4,3,1]=>70
[3,5,7,8,2,1,4,6]=>[4,3,1]=>70
[2,6,7,8,1,4,3,5]=>[4,3,1]=>70
[6,5,7,8,3,1,4,2]=>[3,2,2,1]=>70
[2,5,7,8,3,1,4,6]=>[4,3,1]=>70
[2,4,7,3,8,1,5,6]=>[4,3,1]=>70
[6,4,7,3,8,1,5,2]=>[3,2,2,1]=>70
[6,4,7,3,8,1,2,5]=>[3,3,1,1]=>56
[7,4,6,3,8,2,1,5]=>[3,2,1,1,1]=>64
[6,3,2,5,4,8,1,7]=>[3,3,1,1]=>56
[6,4,5,2,3,8,1,7]=>[3,3,1,1]=>56
[6,4,5,3,2,8,1,7]=>[3,2,1,1,1]=>64
[5,4,6,3,8,2,1,7]=>[3,2,1,1,1]=>64
[5,4,7,3,8,1,6,2]=>[3,2,2,1]=>70
[2,5,7,8,3,1,6,4]=>[4,2,2]=>56
[4,5,7,8,3,1,2,6]=>[4,3,1]=>70
[4,5,6,8,2,3,1,7]=>[4,3,1]=>70
[5,4,6,2,8,3,1,7]=>[3,3,1,1]=>56
[5,3,2,6,8,4,1,7]=>[3,3,1,1]=>56
[5,4,7,2,8,1,3,6]=>[3,3,1,1]=>56
[4,5,7,8,2,1,3,6]=>[4,3,1]=>70
[4,6,7,8,1,3,2,5]=>[4,3,1]=>70
[4,6,7,8,1,3,5,2]=>[4,3,1]=>70
[2,6,7,8,1,3,5,4]=>[4,3,1]=>70
[2,6,7,8,1,5,3,4]=>[4,3,1]=>70
[4,6,7,8,1,5,2,3]=>[4,3,1]=>70
[4,6,7,8,1,2,5,3]=>[4,3,1]=>70
[4,5,7,8,2,1,6,3]=>[4,2,2]=>56
[5,4,7,2,8,1,6,3]=>[3,2,2,1]=>70
[5,3,2,7,8,1,6,4]=>[3,2,2,1]=>70
[4,3,2,7,8,1,6,5]=>[3,2,2,1]=>70
[3,5,7,8,2,1,6,4]=>[4,2,2]=>56
[3,6,7,8,1,2,5,4]=>[4,3,1]=>70
[3,6,7,8,1,5,2,4]=>[4,3,1]=>70
[3,6,7,8,1,5,4,2]=>[4,2,1,1]=>90
[2,6,7,8,1,5,4,3]=>[4,2,1,1]=>90
[2,3,4,5,6,7,8,9,10,1,11]=>[10,1]=>10
[3,4,5,6,7,8,9,1,2,10]=>[8,2]=>35
[2,4,5,6,7,8,1,3,9]=>[7,2]=>27
[1,4,5,6,7,8,2,9,3]=>[7,2]=>27
[1,4,5,6,7,8,9,10,2,3]=>[8,2]=>35
[1,3,4,5,6,7,8,9,10,11,2]=>[10,1]=>10
[4,2,7,1,5,3,8,6]=>[3,3,2]=>42
[4,2,8,6,1,5,3,7]=>[3,2,2,1]=>70
[3,2,6,7,5,1,4,8]=>[4,2,2]=>56
[2,7,1,3,5,4,8,6]=>[4,3,1]=>70
[4,7,2,1,5,8,6,3]=>[3,3,2]=>42
[7,2,1,3,5,8,6,4]=>[4,2,2]=>56
[2,3,6,4,7,1,5,8]=>[5,2,1]=>64
[1,3,4,8,2,7,5,6]=>[5,2,1]=>64
[3,1,4,8,2,6,7,5]=>[4,3,1]=>70
[8,3,1,6,2,5,7,4]=>[4,2,1,1]=>90
[4,8,6,2,1,5,7,3]=>[3,2,2,1]=>70
[4,8,3,6,5,1,7,2]=>[3,2,2,1]=>70
[6,4,7,3,5,1,8,2]=>[3,2,2,1]=>70
[6,4,7,5,1,8,2,3]=>[3,3,2]=>42
[3,6,1,7,5,8,2,4]=>[4,3,1]=>70
[7,3,5,1,6,8,2,4]=>[4,3,1]=>70
[4,7,3,5,6,1,8,2]=>[4,2,2]=>56
[3,4,6,8,5,1,7,2]=>[4,2,2]=>56
[4,6,8,2,1,5,7,3]=>[3,3,2]=>42
[6,8,2,1,3,5,7,4]=>[4,2,2]=>56
[1,8,2,3,5,7,4,6]=>[5,2,1]=>64
[2,7,3,6,1,4,5,8]=>[5,2,1]=>64
[2,6,1,3,5,8,4,7]=>[4,3,1]=>70
[7,3,2,5,6,1,4,8]=>[4,2,1,1]=>90
[4,7,5,2,6,1,3,8]=>[4,2,1,1]=>90
[4,6,2,8,1,5,3,7]=>[3,3,2]=>42
[8,4,1,2,7,5,3,6]=>[4,2,1,1]=>90
[4,5,6,2,7,1,3,8]=>[5,2,1]=>64
[8,5,1,2,6,3,4,7]=>[5,2,1]=>64
[1,6,2,7,4,8,3,5]=>[4,3,1]=>70
[6,2,1,7,8,5,3,4]=>[3,3,2]=>42
[6,7,3,8,4,1,5,2]=>[3,3,2]=>42
[2,7,8,4,1,5,6,3]=>[4,2,2]=>56
[2,7,1,8,5,6,3,4]=>[3,3,2]=>42
[8,2,5,1,6,7,3,4]=>[4,3,1]=>70
[8,2,4,5,1,6,7,3]=>[5,2,1]=>64
[3,8,4,5,6,1,7,2]=>[5,2,1]=>64
[4,5,8,3,7,6,1,2]=>[3,2,2,1]=>70
[4,2,8,3,7,1,6,5]=>[3,2,2,1]=>70
[7,2,3,4,8,1,6,5]=>[4,2,2]=>56
[7,2,3,8,5,1,6,4]=>[4,2,2]=>56
[7,2,3,5,8,1,4,6]=>[4,3,1]=>70
[7,8,2,3,6,1,4,5]=>[4,2,2]=>56
[2,6,4,8,1,3,7,5]=>[3,3,2]=>42
[7,6,5,1,2,3,8,4]=>[4,2,1,1]=>90
[7,8,5,4,1,2,6,3]=>[3,2,2,1]=>70
[7,6,5,1,2,4,8,3]=>[4,1,1,1,1]=>35
[7,6,5,1,3,2,8,4]=>[3,2,1,1,1]=>64
[7,6,5,1,3,4,2,8]=>[4,1,1,1,1]=>35
[7,2,3,4,5,1,8,6]=>[5,2,1]=>64
[2,6,4,3,1,5,8,7]=>[4,2,1,1]=>90
[3,5,8,4,1,2,7,6]=>[3,3,2]=>42
[3,5,8,4,1,6,7,2]=>[4,2,2]=>56
[3,6,4,2,1,7,8,5]=>[4,2,1,1]=>90
[2,6,4,5,1,3,7,8]=>[5,2,1]=>64
[7,6,5,1,8,2,4,3]=>[3,2,1,1,1]=>64
[7,6,5,1,8,3,2,4]=>[3,2,1,1,1]=>64
[7,6,5,1,4,8,2,3]=>[3,2,1,1,1]=>64
[2,5,6,4,1,7,8,3]=>[5,2,1]=>64
[7,8,5,4,1,6,3,2]=>[2,2,2,1,1]=>28
[2,5,6,4,1,7,3,8]=>[5,2,1]=>64
[7,6,5,1,8,3,4,2]=>[3,2,1,1,1]=>64
[7,6,5,1,8,4,2,3]=>[3,2,1,1,1]=>64
[4,1,7,6,2,8,5,3]=>[3,3,1,1]=>56
[7,8,6,2,1,3,5,4]=>[3,2,2,1]=>70
[3,7,6,1,2,8,4,5]=>[4,3,1]=>70
[2,6,5,3,1,4,8,7]=>[4,2,1,1]=>90
[4,6,1,5,3,2,8,7]=>[3,3,1,1]=>56
[3,6,1,4,2,5,8,7]=>[4,3,1]=>70
[2,6,4,5,7,8,1,3]=>[5,2,1]=>64
[8,7,1,6,5,2,4,3]=>[3,1,1,1,1,1]=>21
[7,2,5,6,8,1,3,4]=>[4,3,1]=>70
[6,1,3,4,2,8,7,5]=>[4,2,2]=>56
[2,4,5,6,1,8,7,3]=>[5,2,1]=>64
[8,4,1,6,5,7,3,2]=>[3,2,1,1,1]=>64
[2,8,3,4,7,5,1,6]=>[5,1,1,1]=>35
[6,8,2,7,4,3,5,1]=>[3,2,1,1,1]=>64
[4,7,8,5,1,6,3,2]=>[3,2,2,1]=>70
[8,2,6,4,7,3,5,1]=>[3,2,1,1,1]=>64
[4,8,6,1,7,3,2,5]=>[3,3,1,1]=>56
[8,7,3,2,1,5,4,6]=>[3,2,1,1,1]=>64
[3,8,5,1,7,2,4,6]=>[4,3,1]=>70
[6,8,7,1,3,2,4,5]=>[4,2,1,1]=>90
[2,5,1,8,7,4,6,3]=>[3,3,1,1]=>56
[3,7,1,8,4,5,6,2]=>[4,3,1]=>70
[6,2,3,8,4,7,5,1]=>[4,2,1,1]=>90
[8,6,4,3,1,7,2,5]=>[3,2,1,1,1]=>64
[8,3,7,4,6,1,2,5]=>[3,3,1,1]=>56
[7,1,3,8,6,4,5,2]=>[4,2,1,1]=>90
[2,3,5,8,6,7,4,1]=>[5,1,1,1]=>35
[7,4,2,1,8,6,5,3]=>[2,2,2,2]=>14
[4,6,7,2,5,8,3,1]=>[4,2,1,1]=>90
[7,6,2,5,3,8,1,4]=>[3,2,1,1,1]=>64
[6,2,1,3,4,8,7,5]=>[4,2,2]=>56
[6,5,4,2,8,3,1,7]=>[3,2,1,1,1]=>64
[5,4,3,1,8,7,2,6]=>[3,2,2,1]=>70
[6,1,4,3,8,5,2,7]=>[4,2,1,1]=>90
[4,7,6,2,8,1,5,3]=>[3,2,2,1]=>70
[6,4,5,1,7,8,3,2]=>[4,2,1,1]=>90
[4,2,3,1,7,8,6,5]=>[4,2,2]=>56
[3,4,2,1,8,6,7,5]=>[4,2,2]=>56
[2,7,6,8,1,5,3,4]=>[3,3,1,1]=>56
[6,4,5,8,3,1,2,7]=>[3,3,1,1]=>56
[8,1,3,2,5,6,7,4]=>[5,2,1]=>64
[3,6,8,1,5,2,4,7]=>[4,3,1]=>70
[3,2,8,7,4,5,1,6]=>[4,2,1,1]=>90
[6,3,8,5,7,4,2,1]=>[3,2,1,1,1]=>64
[7,4,6,8,5,1,2,3]=>[3,3,1,1]=>56
[2,1,4,8,7,5,3,6]=>[4,2,1,1]=>90
[2,1,6,8,3,7,5,4]=>[3,3,1,1]=>56
[3,6,8,2,4,1,5,7]=>[4,3,1]=>70
[6,2,8,1,7,5,4,3]=>[2,2,2,1,1]=>28
[2,6,5,4,8,1,3,7]=>[3,3,1,1]=>56
[6,5,3,4,8,1,7,2]=>[3,2,2,1]=>70
[8,4,3,2,5,1,7,6]=>[3,2,1,1,1]=>64
[4,2,8,1,5,3,6,7]=>[4,2,2]=>56
[5,1,8,2,6,4,3,7]=>[4,2,1,1]=>90
[7,4,8,6,2,1,3,5]=>[3,2,2,1]=>70
[4,6,2,8,3,7,5,1]=>[3,3,1,1]=>56
[2,1,5,8,3,6,4,7]=>[4,3,1]=>70
[2,8,5,3,6,7,1,4]=>[4,2,1,1]=>90
[7,8,5,6,4,1,3,2]=>[2,2,2,1,1]=>28
[5,8,4,1,6,3,7,2]=>[3,2,2,1]=>70
[4,8,1,3,5,7,6,2]=>[4,2,1,1]=>90
[3,8,1,4,5,6,2,7]=>[5,2,1]=>64
[7,6,8,3,5,1,4,2]=>[2,2,2,1,1]=>28
[8,9,6,7,4,5,2,3,1]=>[2,2,2,2,1]=>42
[5,3,8,7,6,1,4,2]=>[2,2,2,1,1]=>28
[6,5,8,4,7,1,3,2]=>[2,2,2,1,1]=>28
[6,7,4,2,5,3,1,8]=>[3,2,2,1]=>70
[7,6,4,8,3,1,5,2]=>[2,2,2,1,1]=>28
[7,4,8,5,6,1,3,2]=>[3,2,2,1]=>70
[7,4,2,5,6,3,1,8]=>[4,2,1,1]=>90
[4,2,7,5,6,3,1,8]=>[4,2,1,1]=>90
[3,4,7,5,6,2,1,8]=>[5,1,1,1]=>35
[4,7,3,5,6,2,1,8]=>[4,2,1,1]=>90
[3,7,2,5,6,4,1,8]=>[4,2,1,1]=>90
[7,8,3,5,6,1,4,2]=>[3,2,2,1]=>70
[1,6,8,5,2,7,4,3]=>[3,2,2,1]=>70
[6,2,8,5,1,7,4,3]=>[3,2,2,1]=>70
[6,7,4,8,2,1,5,3]=>[3,2,2,1]=>70
[3,2,7,8,6,1,5,4]=>[3,2,2,1]=>70
[6,8,4,1,2,3,7,5]=>[4,2,2]=>56
[4,1,8,5,6,3,2,7]=>[4,2,1,1]=>90
[1,8,2,5,6,4,3,7]=>[5,1,1,1]=>35
[6,1,8,5,3,7,4,2]=>[3,2,2,1]=>70
[3,8,1,5,2,7,6,4]=>[3,3,1,1]=>56
[8,2,1,5,3,7,6,4]=>[3,3,1,1]=>56
[1,5,2,4,6,7,8,3]=>[6,1,1]=>21
[4,1,5,3,6,7,8,2]=>[5,2,1]=>64
[8,1,6,5,3,7,2,4]=>[3,2,1,1,1]=>64
[7,1,4,6,3,2,8,5]=>[4,2,1,1]=>90
[3,2,6,4,1,7,8,5]=>[4,3,1]=>70
[7,6,4,3,1,2,8,5]=>[3,2,1,1,1]=>64
[8,6,3,5,1,7,2,4]=>[3,3,1,1]=>56
[4,5,3,1,6,7,8,2]=>[5,2,1]=>64
[3,5,2,1,6,7,8,4]=>[5,2,1]=>64
[5,2,3,1,6,7,8,4]=>[5,2,1]=>64
[1,5,3,2,6,7,8,4]=>[5,2,1]=>64
[8,4,6,5,1,7,2,3]=>[3,3,1,1]=>56
[7,5,4,6,1,2,8,3]=>[3,3,1,1]=>56
[3,2,5,6,1,7,8,4]=>[5,2,1]=>64
[3,2,8,7,6,1,4,5]=>[3,2,2,1]=>70
[6,8,4,7,2,1,3,5]=>[3,2,2,1]=>70
[3,8,7,5,6,1,2,4]=>[3,3,1,1]=>56
[8,2,7,5,6,1,3,4]=>[3,3,1,1]=>56
[4,8,6,5,1,7,3,2]=>[3,2,1,1,1]=>64
[1,7,4,6,2,3,8,5]=>[4,3,1]=>70
[7,6,4,2,1,5,8,3]=>[3,2,1,1,1]=>64
[5,7,4,6,1,3,8,2]=>[3,2,2,1]=>70
[8,6,4,7,3,1,2,5]=>[3,2,1,1,1]=>64
[5,2,4,3,7,1,8,6]=>[4,2,1,1]=>90
[3,5,4,2,7,1,8,6]=>[4,2,1,1]=>90
[8,6,4,1,3,5,2,7]=>[4,1,1,1,1]=>35
[6,7,4,1,5,3,8,2]=>[3,2,2,1]=>70
[7,5,4,1,2,6,8,3]=>[4,2,1,1]=>90
[1,7,4,2,3,6,8,5]=>[5,2,1]=>64
[1,8,2,5,3,7,6,4]=>[4,2,1,1]=>90
[6,8,1,5,4,7,3,2]=>[3,2,1,1,1]=>64
[8,2,1,5,6,4,3,7]=>[4,2,1,1]=>90
[3,8,1,5,6,4,2,7]=>[4,2,1,1]=>90
[6,8,4,1,2,5,3,7]=>[4,2,2]=>56
[3,2,8,1,6,5,4,7]=>[3,2,2,1]=>70
[3,2,6,1,5,7,8,4]=>[4,2,2]=>56
[7,6,4,1,5,2,8,3]=>[3,3,1,1]=>56
[8,6,1,5,4,7,2,3]=>[3,2,1,1,1]=>64
[3,5,1,4,6,7,8,2]=>[5,2,1]=>64
[5,2,1,4,6,7,8,3]=>[5,2,1]=>64
[5,4,1,3,6,7,8,2]=>[5,1,1,1]=>35
[8,4,1,5,3,7,2,6]=>[3,3,1,1]=>56
[7,5,4,1,3,2,8,6]=>[3,2,1,1,1]=>64
[3,2,5,1,4,7,8,6]=>[4,3,1]=>70
[7,1,4,3,5,2,8,6]=>[4,2,1,1]=>90
[8,1,3,5,4,7,2,6]=>[4,2,1,1]=>90
[5,1,3,4,6,7,8,2]=>[6,1,1]=>21
[8,3,2,6,1,4,7,5]=>[3,3,1,1]=>56
[2,6,1,3,8,7,5,4]=>[3,3,1,1]=>56
[2,6,8,1,5,7,4,3]=>[3,3,1,1]=>56
[2,7,1,6,4,8,3,5]=>[3,3,1,1]=>56
[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1]=>20
[8,3,2,7,1,6,5,4]=>[2,2,2,1,1]=>28
[3,7,1,8,6,5,4,2]=>[3,2,1,1,1]=>64
[3,6,8,5,1,4,7,2]=>[3,3,1,1]=>56
[7,3,6,2,1,4,5,8]=>[4,2,1,1]=>90
[7,4,2,8,1,6,5,3]=>[2,2,2,2]=>14
[8,7,5,3,2,1,6,4]=>[2,2,1,1,1,1]=>20
[7,5,2,6,3,1,4,8]=>[4,2,1,1]=>90
[6,8,4,5,2,1,7,3]=>[3,2,2,1]=>70
[4,6,8,5,1,7,3,2]=>[3,2,2,1]=>70
[4,7,5,1,3,8,6,2]=>[3,3,1,1]=>56
[5,1,7,6,4,2,8,3]=>[3,3,1,1]=>56
[5,1,8,7,6,4,3,2]=>[2,2,1,1,1,1]=>20
[8,5,2,1,7,6,4,3]=>[2,2,2,1,1]=>28
[8,5,2,1,6,3,7,4]=>[3,3,1,1]=>56
[5,1,8,6,3,2,7,4]=>[3,3,1,1]=>56
[8,4,2,5,7,3,1,6]=>[3,3,1,1]=>56
[5,4,8,2,7,3,6,1]=>[3,2,2,1]=>70
[5,4,8,7,3,6,1,2]=>[2,2,2,2]=>14
[6,3,7,2,4,8,1,5]=>[3,3,1,1]=>56
[5,7,4,2,8,1,3,6]=>[3,3,1,1]=>56
[6,5,2,7,1,3,8,4]=>[3,3,1,1]=>56
[8,6,5,4,2,1,7,3]=>[2,2,1,1,1,1]=>20
[6,4,7,3,1,8,2,5]=>[3,3,1,1]=>56
[7,5,8,4,6,3,2,1]=>[2,2,1,1,1,1]=>20
[6,5,4,3,2,1,9,8,7]=>[2,2,2,1,1,1]=>48
[5,4,3,2,1,9,8,7,6]=>[2,2,2,2,1]=>42
[3,2,1,5,4,7,6,9,8]=>[4,4,1]=>84
[2,1,4,3,5,6,7,8,9]=>[7,2]=>27
[7,6,5,4,3,2,1,10,9,8]=>[2,2,2,1,1,1,1]=>75
[3,2,1,5,4,7,6,9,8,10]=>[5,4,1]=>288
[5,6,3,7,4,2,1,8]=>[4,2,1,1]=>90
[7,6,3,8,5,1,4,2]=>[2,2,2,1,1]=>28
[6,4,8,1,3,2,5,7]=>[4,2,1,1]=>90
[7,4,8,6,3,1,5,2]=>[2,2,2,2]=>14
[4,2,7,6,5,3,1,8]=>[3,2,1,1,1]=>64
[3,7,2,4,6,5,1,8]=>[4,2,1,1]=>90
[8,1,3,4,5,2,6,7]=>[6,1,1]=>21
[1,6,8,4,2,5,3,7]=>[4,2,2]=>56
[6,2,8,4,1,5,7,3]=>[4,2,2]=>56
[6,7,4,8,5,1,2,3]=>[3,3,2]=>42
[3,2,7,8,5,1,6,4]=>[3,3,2]=>42
[3,2,8,1,5,4,6,7]=>[4,2,2]=>56
[6,1,4,8,5,3,7,2]=>[4,2,1,1]=>90
[1,4,8,5,2,6,7,3]=>[5,2,1]=>64
[6,1,8,4,3,7,2,5]=>[3,2,2,1]=>70
[3,7,1,4,2,5,8,6]=>[4,3,1]=>70
[7,2,1,4,3,5,6,8]=>[5,2,1]=>64
[4,1,5,3,6,8,2,7]=>[4,3,1]=>70
[6,1,8,5,3,2,7,4]=>[3,2,2,1]=>70
[7,1,4,6,3,8,5,2]=>[4,2,1,1]=>90
[3,2,6,4,1,8,7,5]=>[3,3,2]=>42
[7,6,4,3,1,8,2,5]=>[3,2,1,1,1]=>64
[3,5,2,1,8,7,6,4]=>[3,2,2,1]=>70
[1,5,3,2,8,6,4,7]=>[4,2,2]=>56
[5,4,2,1,7,8,6,3]=>[3,2,2,1]=>70
[8,2,7,6,5,1,3,4]=>[3,2,1,1,1]=>64
[8,6,2,7,1,4,5,3]=>[3,2,2,1]=>70
[1,7,3,6,2,8,5,4]=>[4,2,1,1]=>90
[7,6,3,2,1,8,5,4]=>[2,2,2,1,1]=>28
[8,6,3,7,4,1,2,5]=>[3,2,2,1]=>70
[5,2,3,4,7,1,8,6]=>[5,2,1]=>64
[8,6,3,1,4,5,7,2]=>[4,2,1,1]=>90
[6,7,3,1,5,4,2,8]=>[3,2,2,1]=>70
[5,8,3,1,2,4,7,6]=>[4,2,2]=>56
[8,1,3,2,4,5,6,7]=>[6,1,1]=>21
[8,4,1,7,2,3,6,5]=>[4,2,1,1]=>90
[8,2,1,6,5,4,7,3]=>[3,2,1,1,1]=>64
[3,8,1,5,6,4,7,2]=>[4,2,1,1]=>90
[6,8,4,1,2,5,7,3]=>[4,2,2]=>56
[3,2,8,1,6,5,7,4]=>[3,2,2,1]=>70
[7,6,4,1,5,2,3,8]=>[4,2,1,1]=>90
[8,6,1,5,4,7,3,2]=>[3,1,1,1,1,1]=>21
[3,5,1,4,6,7,2,8]=>[5,2,1]=>64
[5,2,1,4,7,6,3,8]=>[4,2,2]=>56
[4,5,8,2,1,3,7,6]=>[3,3,2]=>42
[5,8,2,3,1,4,6,7]=>[5,2,1]=>64
[4,2,1,3,5,8,7,6]=>[4,2,2]=>56
[5,4,1,3,6,2,8,7]=>[4,2,1,1]=>90
[8,5,4,1,3,6,2,7]=>[4,1,1,1,1]=>35
[3,2,5,1,4,6,8,7]=>[4,3,1]=>70
[8,1,4,3,5,6,7,2]=>[5,1,1,1]=>35
[7,1,3,5,4,6,2,8]=>[5,1,1,1]=>35
[5,1,3,4,6,2,7,8]=>[6,1,1]=>21
[4,1,3,2,5,7,6,8]=>[5,2,1]=>64
[3,1,4,2,6,5,8,7,9]=>[5,4]=>42
[3,1,5,2,6,4,8,7,9]=>[5,4]=>42
[3,1,5,2,4,7,6,9,8]=>[5,4]=>42
[3,1,2,5,4,7,6,9,8]=>[5,4]=>42
[3,1,4,2,6,5,8,7,10,9]=>[5,5]=>42
[4,1,5,2,6,3,8,7,9]=>[5,4]=>42
[3,1,6,2,7,4,8,5,9]=>[5,4]=>42
[3,1,5,2,7,4,9,6,8,10]=>[6,4]=>90
[1,3,5,2,4,7,6,9,8]=>[5,4]=>42
[3,1,2,5,4,7,6,9,8,10]=>[6,4]=>90
[4,6,7,3,1,5,2,8]=>[4,2,2]=>56
[6,8,1,3,5,2,7,4]=>[4,2,2]=>56
[6,8,3,1,4,5,7,2]=>[4,2,2]=>56
[7,5,1,8,2,3,6,4]=>[4,2,2]=>56
[5,3,8,4,2,6,7,1]=>[4,2,1,1]=>90
[4,5,7,2,3,6,8,1]=>[4,3,1]=>70
[2,6,3,4,7,5,8,1]=>[5,2,1]=>64
[7,3,1,4,8,5,6,2]=>[4,2,2]=>56
[6,4,2,8,7,1,5,3]=>[2,2,2,2]=>14
[7,2,4,8,1,5,3,6]=>[4,2,2]=>56
[4,6,3,1,7,8,5,2]=>[4,2,2]=>56
[5,3,1,6,7,8,4,2]=>[4,2,2]=>56
[4,1,6,2,7,8,5,3]=>[4,3,1]=>70
[2,1,3,4,8,7,5,6]=>[5,2,1]=>64
[4,5,6,7,8,9,1,2,3]=>[6,3]=>48
[4,5,6,7,8,9,2,3,1]=>[6,2,1]=>105
[5,6,7,8,9,1,2,3,4]=>[5,4]=>42
[6,7,8,9,2,3,4,5,1]=>[4,4,1]=>84
[4,5,6,7,8,9,10,1,2,3]=>[7,3]=>75
[4,5,6,7,8,9,10,2,3,1]=>[7,2,1]=>160
[5,6,7,8,9,10,1,2,3,4]=>[6,4]=>90
[8,9,10,5,6,7,2,3,4,1]=>[3,3,3,1]=>210
[4,8,3,7,6,5,1,2]=>[2,2,2,1,1]=>28
[6,3,8,7,5,4,1,2]=>[2,2,2,1,1]=>28
[5,3,8,7,6,4,1,2]=>[2,2,2,1,1]=>28
[2,8,7,6,1,5,4,3]=>[2,2,1,1,1,1]=>20
[5,2,8,7,6,1,4,3]=>[2,2,2,1,1]=>28
[6,2,8,7,5,1,4,3]=>[2,2,2,1,1]=>28
[7,8,2,6,5,1,4,3]=>[2,2,2,1,1]=>28
[6,1,8,7,5,4,3,2]=>[2,2,1,1,1,1]=>20
[3,1,8,7,6,5,4,2]=>[2,2,1,1,1,1]=>20
[7,8,2,6,1,5,4,3]=>[2,2,2,1,1]=>28
[6,2,8,7,1,5,4,3]=>[2,2,2,1,1]=>28
[4,2,8,1,7,6,5,3]=>[2,2,2,1,1]=>28
[4,8,2,7,6,1,5,3]=>[2,2,2,1,1]=>28
[3,8,7,2,1,6,5,4]=>[2,2,2,1,1]=>28
[6,5,8,7,1,4,3,2]=>[2,2,2,1,1]=>28
[4,8,1,7,6,5,3,2]=>[2,2,1,1,1,1]=>20
[5,4,1,8,7,6,3,2]=>[2,2,2,1,1]=>28
[6,4,8,1,7,5,3,2]=>[2,2,2,1,1]=>28
[7,8,4,1,6,5,3,2]=>[2,2,2,1,1]=>28
[7,8,3,1,6,5,4,2]=>[2,2,2,1,1]=>28
[6,3,8,1,7,5,4,2]=>[2,2,2,1,1]=>28
[5,3,1,8,7,6,4,2]=>[2,2,2,1,1]=>28
[7,8,2,1,6,5,4,3]=>[2,2,2,1,1]=>28
[6,5,3,1,8,7,4,2]=>[2,2,2,2]=>14
[6,4,3,1,8,7,5,2]=>[2,2,2,2]=>14
[7,5,2,1,8,6,4,3]=>[2,2,2,2]=>14
[5,4,2,1,8,7,6,3]=>[2,2,2,2]=>14
[7,3,2,1,8,6,5,4]=>[2,2,2,2]=>14
[6,3,2,1,8,7,5,4]=>[2,2,2,2]=>14
[9,7,5,3,1,10,8,6,4,2]=>[2,2,2,2,2]=>42
[6,1,4,2,3,5,8,7]=>[5,2,1]=>64
[8,6,1,4,2,3,5,7]=>[5,1,1,1]=>35
[6,8,1,4,2,3,5,7]=>[5,2,1]=>64
[8,1,4,2,3,6,5,7]=>[5,2,1]=>64
[4,1,8,2,3,6,5,7]=>[5,2,1]=>64
[8,2,3,6,1,4,5,7]=>[5,2,1]=>64
[6,2,3,8,1,4,5,7]=>[5,2,1]=>64
[4,6,2,3,8,1,5,7]=>[4,3,1]=>70
[4,8,2,3,6,1,5,7]=>[4,2,2]=>56
[8,2,3,6,4,1,5,7]=>[5,1,1,1]=>35
[8,4,3,6,2,1,5,7]=>[3,2,1,1,1]=>64
[6,2,3,8,4,1,5,7]=>[5,2,1]=>64
[8,4,2,3,6,1,5,7]=>[4,2,1,1]=>90
[6,4,2,3,8,1,5,7]=>[4,2,1,1]=>90
[2,6,4,3,8,1,5,7]=>[4,2,1,1]=>90
[2,8,4,3,6,1,5,7]=>[4,2,1,1]=>90
[2,6,3,8,4,1,5,7]=>[5,2,1]=>64
[6,3,8,4,2,1,5,7]=>[4,2,1,1]=>90
[2,6,3,8,1,4,5,7]=>[5,2,1]=>64
[2,8,3,6,1,4,5,7]=>[5,2,1]=>64
[8,3,6,4,2,1,5,7]=>[4,1,1,1,1]=>35
[2,8,3,6,4,1,5,7]=>[5,1,1,1]=>35
[8,3,6,2,4,1,5,7]=>[4,2,1,1]=>90
[8,3,6,2,1,4,5,7]=>[4,2,1,1]=>90
[6,2,1,3,8,4,5,7]=>[5,2,1]=>64
[8,2,1,3,6,4,5,7]=>[5,2,1]=>64
[6,3,8,2,4,1,5,7]=>[4,2,1,1]=>90
[6,2,4,3,8,1,5,7]=>[4,2,1,1]=>90
[3,6,4,7,8,5,1,2]=>[4,2,2]=>56
[6,4,8,5,3,7,1,2]=>[3,2,2,1]=>70
[1,6,5,2,4,8,7,3]=>[4,2,1,1]=>90
[4,8,5,3,1,6,2,7]=>[4,2,1,1]=>90
[6,1,8,7,4,2,3,5]=>[4,2,1,1]=>90
[1,3,6,8,7,5,2,4]=>[4,2,1,1]=>90
[1,8,2,5,4,7,6,3]=>[4,2,1,1]=>90
[7,1,2,4,5,8,6,3]=>[5,2,1]=>64
[1,6,3,7,8,5,2,4]=>[4,2,2]=>56
[4,6,2,3,7,8,1,5]=>[4,3,1]=>70
[4,6,3,7,1,2,8,5]=>[4,3,1]=>70
[7,3,2,4,5,1,8,6]=>[4,2,1,1]=>90
[7,8,4,2,6,3,1,5]=>[3,2,2,1]=>70
[4,2,6,3,8,7,1,5]=>[3,3,2]=>42
[5,8,2,7,4,3,1,6]=>[3,2,1,1,1]=>64
[6,4,3,5,2,8,1,7]=>[3,2,1,1,1]=>64
[6,1,7,2,8,3,9,4,10,5]=>[5,5]=>42
[6,1,7,8,9,10,2,3,4,5]=>[5,5]=>42
[7,1,8,2,9,3,10,4,11,5,12,6]=>[6,6]=>132
[3,8,1,7,5,6,4,2]=>[3,2,1,1,1]=>64
[8,2,5,7,3,6,4,1]=>[3,2,1,1,1]=>64
[1,8,6,7,5,3,4,2]=>[3,2,1,1,1]=>64
[8,2,6,7,5,3,4,1]=>[3,2,1,1,1]=>64
[1,5,8,7,2,6,4,3]=>[3,2,1,1,1]=>64
[5,4,8,6,2,3,7,1]=>[3,2,2,1]=>70
[2,7,6,1,3,5,4,8]=>[4,2,1,1]=>90
[6,4,1,8,2,5,7,3]=>[4,2,2]=>56
[2,8,6,1,3,5,4,7]=>[4,2,1,1]=>90
[4,1,3,6,5,8,7,2]=>[4,3,1]=>70
[2,1,6,3,5,8,7,4]=>[4,3,1]=>70
[2,4,1,3,8,5,7,6]=>[4,3,1]=>70
[2,4,1,3,5,8,7,6]=>[4,3,1]=>70
[2,6,1,3,5,8,7,4]=>[4,3,1]=>70
[4,6,1,3,5,8,7,2]=>[4,3,1]=>70
[6,1,4,3,5,8,7,2]=>[4,2,1,1]=>90
[6,4,1,3,5,8,7,2]=>[4,2,1,1]=>90
[6,2,1,3,5,8,7,4]=>[4,2,2]=>56
[4,2,1,3,6,5,7,8]=>[5,2,1]=>64
[4,2,1,6,3,5,7,8]=>[5,2,1]=>64
[6,2,1,8,3,5,7,4]=>[4,2,2]=>56
[6,2,1,3,8,5,7,4]=>[4,2,2]=>56
[6,1,4,3,8,5,7,2]=>[4,2,1,1]=>90
[1,6,4,3,8,5,7,2]=>[4,2,1,1]=>90
[8,1,4,3,6,5,7,2]=>[4,2,1,1]=>90
[8,4,1,3,6,5,7,2]=>[4,2,1,1]=>90
[8,2,1,3,6,5,7,4]=>[4,2,1,1]=>90
[8,2,1,6,3,5,7,4]=>[4,2,1,1]=>90
[8,2,1,4,3,5,7,6]=>[4,3,1]=>70
[6,2,1,4,3,5,7,8]=>[5,2,1]=>64
[8,2,4,1,3,5,7,6]=>[4,3,1]=>70
[8,2,6,1,3,5,7,4]=>[4,2,1,1]=>90
[8,4,6,1,3,5,7,2]=>[4,2,1,1]=>90
[8,4,1,6,3,5,7,2]=>[4,2,1,1]=>90
[8,1,4,6,3,5,7,2]=>[4,2,1,1]=>90
[1,8,4,6,3,5,7,2]=>[4,2,1,1]=>90
[1,6,4,8,3,5,7,2]=>[4,2,1,1]=>90
[6,4,1,8,3,5,7,2]=>[4,2,1,1]=>90
[6,4,8,1,3,5,7,2]=>[4,2,1,1]=>90
[6,2,8,1,3,5,7,4]=>[4,2,2]=>56
[4,2,8,1,3,5,7,6]=>[4,2,2]=>56
[2,6,8,1,3,5,7,4]=>[4,3,1]=>70
[4,6,8,1,3,5,7,2]=>[4,3,1]=>70
[4,6,1,8,3,5,7,2]=>[4,3,1]=>70
[4,1,6,8,3,5,7,2]=>[4,3,1]=>70
[1,4,6,3,8,5,7,2]=>[4,3,1]=>70
[4,6,1,3,8,5,7,2]=>[4,3,1]=>70
[2,4,1,8,3,5,7,6]=>[4,3,1]=>70
[2,1,6,8,3,5,7,4]=>[4,3,1]=>70
[4,1,3,6,8,5,7,2]=>[4,3,1]=>70
[1,4,3,6,8,5,7,2]=>[4,3,1]=>70
[4,1,3,8,6,5,7,2]=>[4,2,1,1]=>90
[2,1,8,3,6,5,7,4]=>[4,2,1,1]=>90
[2,1,6,4,3,5,7,8]=>[5,2,1]=>64
[2,6,1,4,3,5,7,8]=>[5,2,1]=>64
[2,8,1,4,3,5,7,6]=>[4,3,1]=>70
[2,8,1,6,3,5,7,4]=>[4,2,1,1]=>90
[4,8,1,3,6,5,7,2]=>[4,2,1,1]=>90
[1,4,8,3,6,5,7,2]=>[4,2,1,1]=>90
[1,4,8,6,3,5,7,2]=>[4,2,1,1]=>90
[4,1,8,6,3,5,7,2]=>[4,2,1,1]=>90
[4,8,1,6,3,5,7,2]=>[4,2,1,1]=>90
[4,8,6,1,3,5,7,2]=>[4,2,1,1]=>90
[2,8,6,1,3,5,7,4]=>[4,2,1,1]=>90
[2,8,4,1,3,5,7,6]=>[4,3,1]=>70
[2,6,4,1,3,5,7,8]=>[5,2,1]=>64
[4,6,2,1,3,5,7,8]=>[5,2,1]=>64
[6,8,1,4,3,5,7,2]=>[4,2,1,1]=>90
[6,1,8,4,3,5,7,2]=>[4,2,1,1]=>90
[1,6,8,4,3,5,7,2]=>[4,2,1,1]=>90
[1,8,6,4,3,5,7,2]=>[4,1,1,1,1]=>35
[8,1,6,4,3,5,7,2]=>[4,1,1,1,1]=>35
[8,6,1,4,3,5,7,2]=>[4,1,1,1,1]=>35
[8,6,4,1,3,5,7,2]=>[4,1,1,1,1]=>35
[8,6,2,1,3,5,7,4]=>[4,2,1,1]=>90
[8,4,2,1,3,5,7,6]=>[4,2,1,1]=>90
[7,8,6,5,2,1,4,3]=>[2,2,2,1,1]=>28
[5,7,4,1,8,6,3,2]=>[3,2,2,1]=>70
[5,6,4,2,8,3,7,1]=>[3,3,1,1]=>56
[5,6,4,2,7,3,1,8]=>[4,2,1,1]=>90
[5,7,1,4,6,3,2,8]=>[4,2,1,1]=>90
[5,8,1,4,6,3,7,2]=>[4,2,1,1]=>90
[3,6,7,4,5,8,2,1]=>[4,2,1,1]=>90
[3,5,7,4,6,8,2,1]=>[4,2,1,1]=>90
[6,8,4,1,7,2,5,3]=>[3,2,2,1]=>70
[5,4,6,1,7,8,3,2]=>[4,2,1,1]=>90
[5,6,4,1,8,7,3,2]=>[3,2,2,1]=>70
[3,5,8,4,6,7,2,1]=>[4,2,1,1]=>90
[3,6,8,4,5,7,2,1]=>[4,2,1,1]=>90
[3,7,8,4,5,6,2,1]=>[4,2,1,1]=>90
[6,8,1,4,5,3,7,2]=>[4,2,1,1]=>90
[6,7,1,4,5,3,2,8]=>[4,2,1,1]=>90
[3,7,1,5,4,6,2,8]=>[4,2,1,1]=>90
[3,8,1,5,4,6,7,2]=>[4,2,1,1]=>90
[3,7,1,5,4,6,8,2]=>[4,2,1,1]=>90
[6,7,1,4,5,3,8,2]=>[4,2,1,1]=>90
[5,7,1,4,6,3,8,2]=>[4,2,1,1]=>90
[5,6,4,2,7,3,8,1]=>[4,2,1,1]=>90
[5,4,7,2,8,3,1,6]=>[3,3,1,1]=>56
[5,4,7,2,8,3,6,1]=>[3,3,1,1]=>56
[5,6,4,2,8,3,1,7]=>[3,3,1,1]=>56
[5,8,1,4,6,3,2,7]=>[4,2,1,1]=>90
[3,8,1,5,4,6,2,7]=>[4,2,1,1]=>90
[3,6,1,5,4,2,7,8]=>[4,2,1,1]=>90
[3,6,1,5,4,8,2,7]=>[3,3,1,1]=>56
[6,8,3,1,4,2,5,7]=>[4,2,2]=>56
[7,3,8,1,4,2,5,6]=>[4,2,2]=>56
[6,7,3,1,4,2,8,5]=>[3,3,2]=>42
[3,6,1,5,4,7,8,2]=>[4,2,1,1]=>90
[3,4,1,2,7,6,5,8]=>[4,3,1]=>70
[3,4,1,2,6,8,7,5]=>[4,3,1]=>70
[6,8,3,1,4,7,2,5]=>[3,3,2]=>42
[6,4,7,2,8,5,1,3]=>[3,2,2,1]=>70
[5,8,1,4,7,3,2,6]=>[3,2,2,1]=>70
[7,8,1,4,5,3,2,6]=>[4,2,1,1]=>90
[3,8,1,5,4,7,2,6]=>[3,3,1,1]=>56
[3,6,1,5,4,8,7,2]=>[3,3,1,1]=>56
[3,6,1,5,4,7,2,8]=>[4,2,1,1]=>90
[6,7,3,1,4,2,5,8]=>[4,2,2]=>56
[6,8,3,1,4,2,7,5]=>[3,3,2]=>42
[7,8,3,1,4,6,2,5]=>[3,3,2]=>42
[7,8,4,2,6,5,1,3]=>[2,2,2,2]=>14
[6,5,8,7,3,4,2,1]=>[2,2,2,1,1]=>28
[7,8,3,1,4,6,5,2]=>[3,2,2,1]=>70
[6,7,3,1,4,5,2,8]=>[4,2,2]=>56
[3,7,1,5,4,2,6,8]=>[4,2,1,1]=>90
[3,8,1,5,4,2,7,6]=>[3,3,1,1]=>56
[5,8,1,4,7,3,6,2]=>[3,2,2,1]=>70
[6,8,4,2,7,5,3,1]=>[2,2,2,1,1]=>28
[6,4,7,2,8,5,3,1]=>[3,2,2,1]=>70
[6,3,7,1,4,8,5,2]=>[3,3,2]=>42
[6,8,3,1,4,7,5,2]=>[3,2,2,1]=>70
[3,7,1,5,4,8,6,2]=>[3,3,1,1]=>56
[3,4,1,2,8,5,7,6]=>[4,3,1]=>70
[3,4,1,2,5,8,7,6]=>[4,3,1]=>70
[3,7,1,5,4,2,8,6]=>[3,3,1,1]=>56
[6,7,3,1,4,5,8,2]=>[4,2,2]=>56
[7,3,8,1,4,5,2,6]=>[4,2,2]=>56
[7,3,8,1,4,5,6,2]=>[4,2,2]=>56
[6,8,3,1,4,5,2,7]=>[4,2,2]=>56
[3,8,1,5,4,2,6,7]=>[4,2,1,1]=>90
[8,5,7,4,3,2,1,6]=>[2,2,1,1,1,1]=>20
[9,7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1,1]=>8
[10,9,8,7,6,5,4,2,1,3]=>[2,1,1,1,1,1,1,1,1]=>9
[10,9,8,7,6,4,3,2,1,5]=>[2,1,1,1,1,1,1,1,1]=>9
[8,7,3,6,5,2,1,4]=>[2,2,1,1,1,1]=>20
[10,9,8,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,1,1,1]=>9
[6,5,8,4,3,2,1,7]=>[2,2,1,1,1,1]=>20
[8,4,7,6,3,2,1,5]=>[2,2,1,1,1,1]=>20
[5,8,7,4,3,2,1,6]=>[2,2,1,1,1,1]=>20
[10,8,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,1,1]=>9
[5,8,6,2,3,4,7,1]=>[4,2,1,1]=>90
[4,5,2,7,3,1,8,6]=>[4,3,1]=>70
[4,8,2,6,3,5,7,1]=>[4,2,1,1]=>90
[4,1,7,2,5,8,6,3]=>[4,3,1]=>70
[1,6,2,5,8,4,3,7]=>[4,2,1,1]=>90
[7,3,1,6,8,5,2,4]=>[3,3,1,1]=>56
[5,2,7,1,8,6,3,4]=>[3,3,2]=>42
[6,5,2,8,1,7,3,4]=>[3,2,2,1]=>70
[8,3,7,4,2,6,5,1]=>[3,2,1,1,1]=>64
[5,4,2,8,3,1,7,6]=>[3,2,2,1]=>70
[8,4,7,6,2,5,3,1]=>[2,2,1,1,1,1]=>20
[4,8,7,6,1,5,3,2]=>[2,2,1,1,1,1]=>20
[7,3,8,5,2,1,6,4]=>[3,2,2,1]=>70
[7,3,8,4,2,1,6,5]=>[3,2,2,1]=>70
[7,5,4,3,8,2,1,6]=>[2,2,1,1,1,1]=>20
[3,7,8,4,1,2,6,5]=>[3,3,2]=>42
[8,7,4,6,3,5,2,1]=>[2,2,1,1,1,1]=>20
[6,5,8,7,3,1,4,2]=>[2,2,2,2]=>14
[2,3,8,4,1,6,7,5]=>[5,2,1]=>64
[8,6,4,7,3,2,5,1]=>[2,2,1,1,1,1]=>20
[8,3,4,7,2,5,6,1]=>[4,2,1,1]=>90
[2,5,8,6,1,4,7,3]=>[4,2,1,1]=>90
[2,6,8,5,1,3,7,4]=>[3,3,2]=>42
[2,5,8,3,1,4,7,6]=>[4,2,2]=>56
[2,3,5,4,1,8,6,7]=>[5,2,1]=>64
[2,3,6,4,8,1,5,7]=>[5,2,1]=>64
[1,8,4,6,3,5,2,7]=>[4,2,1,1]=>90
[5,4,8,6,2,1,3,7]=>[3,2,2,1]=>70
[2,3,6,8,1,5,4,7]=>[4,3,1]=>70
[2,5,6,1,4,7,8,3]=>[5,2,1]=>64
[2,5,6,1,4,7,3,8]=>[5,2,1]=>64
[7,3,5,1,6,8,4,2]=>[4,2,1,1]=>90
[2,7,6,1,8,5,4,3]=>[3,2,1,1,1]=>64
[2,7,6,8,1,4,5,3]=>[3,3,1,1]=>56
[1,8,7,6,3,2,5,4]=>[3,2,1,1,1]=>64
[1,8,7,6,3,2,4,5]=>[4,1,1,1,1]=>35
[5,7,8,6,2,3,4,1]=>[3,3,1,1]=>56
[2,7,6,1,8,5,3,4]=>[3,3,1,1]=>56
[6,3,5,1,7,2,4,8]=>[4,3,1]=>70
[2,3,4,7,6,1,5,8]=>[5,2,1]=>64
[7,3,5,8,4,1,2,6]=>[3,3,1,1]=>56
[1,8,4,5,2,7,3,6]=>[4,3,1]=>70
[1,8,4,5,2,7,6,3]=>[4,2,1,1]=>90
[7,3,5,8,4,1,6,2]=>[3,2,2,1]=>70
[2,7,6,4,8,5,1,3]=>[3,2,2,1]=>70
[7,3,5,4,6,8,1,2]=>[4,2,1,1]=>90
[6,3,5,4,7,1,8,2]=>[4,2,1,1]=>90
[6,3,5,4,7,1,2,8]=>[4,2,1,1]=>90
[3,4,1,5,6,8,7,2]=>[5,2,1]=>64
[3,7,1,6,8,5,2,4]=>[3,3,1,1]=>56
[2,3,1,8,6,4,7,5]=>[4,3,1]=>70
[1,8,4,3,6,2,5,7]=>[4,2,1,1]=>90
[2,3,1,8,6,4,5,7]=>[5,2,1]=>64
[3,7,1,6,8,5,4,2]=>[3,2,1,1,1]=>64
[6,3,5,4,7,2,1,8]=>[4,1,1,1,1]=>35
[7,3,5,4,6,8,2,1]=>[4,1,1,1,1]=>35
[2,7,6,4,8,5,3,1]=>[3,2,1,1,1]=>64
[1,8,4,5,2,6,3,7]=>[5,2,1]=>64
[6,4,8,5,3,1,2,7]=>[3,2,2,1]=>70
[7,3,5,8,4,6,2,1]=>[3,2,1,1,1]=>64
[2,3,4,6,5,8,1,7]=>[5,2,1]=>64
[2,3,4,7,5,1,8,6]=>[5,2,1]=>64
[2,3,4,7,5,1,6,8]=>[6,1,1]=>21
[2,3,4,7,1,6,5,8]=>[5,2,1]=>64
[2,3,4,7,1,6,8,5]=>[5,2,1]=>64
[2,3,4,6,1,8,7,5]=>[5,2,1]=>64
[6,3,5,8,4,2,7,1]=>[3,2,1,1,1]=>64
[7,4,8,5,3,2,1,6]=>[3,2,1,1,1]=>64
[1,8,4,5,2,3,6,7]=>[5,2,1]=>64
[7,4,8,5,3,2,6,1]=>[3,2,1,1,1]=>64
[6,3,5,8,4,2,1,7]=>[3,2,1,1,1]=>64
[5,2,4,6,8,3,7,1]=>[4,2,1,1]=>90
[1,5,7,4,6,3,2,8]=>[4,2,1,1]=>90
[5,2,8,4,6,3,7,1]=>[4,2,1,1]=>90
[3,8,5,4,6,7,2,1]=>[4,1,1,1,1]=>35
[6,8,3,4,5,7,2,1]=>[4,2,1,1]=>90
[2,5,7,4,6,3,8,1]=>[4,2,1,1]=>90
[5,4,1,7,8,3,2,6]=>[3,3,1,1]=>56
[5,4,2,7,8,3,6,1]=>[3,3,1,1]=>56
[5,1,4,6,8,3,2,7]=>[4,2,1,1]=>90
[5,1,8,4,6,3,2,7]=>[4,2,1,1]=>90
[8,1,6,4,5,3,2,7]=>[4,1,1,1,1]=>35
[8,1,3,5,4,6,2,7]=>[5,1,1,1]=>35
[8,1,6,2,4,3,5,7]=>[5,1,1,1]=>35
[8,7,1,2,4,3,5,6]=>[5,1,1,1]=>35
[1,7,6,2,4,3,5,8]=>[5,1,1,1]=>35
[8,7,3,2,4,6,5,1]=>[3,2,1,1,1]=>64
[8,2,6,3,4,5,7,1]=>[5,1,1,1]=>35
[1,7,6,3,4,5,2,8]=>[5,1,1,1]=>35
[1,7,2,5,4,3,6,8]=>[5,1,1,1]=>35
[8,7,2,4,5,3,6,1]=>[4,1,1,1,1]=>35
[5,8,2,4,7,3,6,1]=>[3,2,2,1]=>70
[6,8,3,2,4,7,5,1]=>[3,2,2,1]=>70
[8,7,1,3,4,5,2,6]=>[5,1,1,1]=>35
[8,1,6,3,4,5,2,7]=>[5,1,1,1]=>35
[8,1,2,5,4,3,6,7]=>[5,1,1,1]=>35
[3,4,8,7,5,2,6,1]=>[4,1,1,1,1]=>35
[3,2,8,6,1,5,4,7]=>[3,2,2,1]=>70
[8,6,1,2,4,3,5,7]=>[5,1,1,1]=>35
[8,7,3,6,4,2,5,1]=>[3,1,1,1,1,1]=>21
[3,8,7,2,5,4,6,1]=>[3,2,1,1,1]=>64
[8,7,2,4,5,6,3,1]=>[4,1,1,1,1]=>35
[5,3,6,2,4,8,7,1]=>[3,3,1,1]=>56
[3,5,2,8,6,1,4,7]=>[4,2,2]=>56
[3,7,2,5,1,4,8,6]=>[3,3,2]=>42
[5,1,8,6,2,3,4,7]=>[5,2,1]=>64
[2,5,4,1,8,6,3,7]=>[4,2,2]=>56
[3,7,6,1,8,2,5,4]=>[3,3,1,1]=>56
[7,6,3,1,8,2,4,5]=>[4,2,1,1]=>90
[8,2,3,6,1,4,7,5]=>[4,3,1]=>70
[1,8,2,6,3,4,7,5]=>[5,2,1]=>64
[8,1,3,6,4,7,2,5]=>[4,2,1,1]=>90
[7,1,3,6,4,8,2,5]=>[4,2,1,1]=>90
[8,2,1,3,5,7,4,6]=>[4,3,1]=>70
[8,2,6,3,1,4,7,5]=>[4,2,1,1]=>90
[7,5,4,1,3,8,2,6]=>[3,2,1,1,1]=>64
[2,7,5,8,3,4,1,6]=>[4,2,1,1]=>90
[7,3,8,5,4,1,2,6]=>[3,2,2,1]=>70
[7,2,3,6,1,4,8,5]=>[4,3,1]=>70
[1,3,7,2,5,8,4,6]=>[4,3,1]=>70
[1,7,2,3,5,8,4,6]=>[5,2,1]=>64
[7,4,8,1,3,6,2,5]=>[3,2,2,1]=>70
[8,1,2,3,5,7,4,6]=>[5,2,1]=>64
[7,1,2,3,5,8,4,6]=>[5,2,1]=>64
[8,6,1,4,7,3,2,5]=>[3,2,1,1,1]=>64
[2,6,3,7,1,4,8,5]=>[4,3,1]=>70
[2,6,3,8,1,4,7,5]=>[4,2,2]=>56
[7,5,4,8,1,3,2,6]=>[3,2,1,1,1]=>64
[8,5,4,7,1,3,2,6]=>[3,2,1,1,1]=>64
[2,3,1,8,5,4,6,7]=>[5,2,1]=>64
[8,6,5,1,3,4,2,7]=>[4,1,1,1,1]=>35
[8,5,1,7,6,3,4,2]=>[3,2,1,1,1]=>64
[3,4,7,6,1,8,5,2]=>[4,2,1,1]=>90
[3,5,2,6,7,1,8,4]=>[5,2,1]=>64
[3,2,8,4,7,5,1,6]=>[4,2,1,1]=>90
[8,4,7,5,1,3,2,6]=>[3,2,1,1,1]=>64
[3,8,1,6,5,2,7,4]=>[3,3,1,1]=>56
[6,1,2,8,3,4,7,5]=>[5,2,1]=>64
[6,8,3,1,7,2,4,5]=>[4,2,2]=>56
[3,7,2,5,6,1,8,4]=>[4,2,2]=>56
[6,8,4,2,5,1,7,3]=>[3,2,2,1]=>70
[2,7,5,3,8,4,1,6]=>[4,2,1,1]=>90
[8,3,1,4,7,2,6,5]=>[3,3,1,1]=>56
[8,3,2,1,5,7,4,6]=>[3,3,1,1]=>56
[2,8,3,6,4,7,1,5]=>[4,2,1,1]=>90
[7,3,6,4,8,1,2,5]=>[3,3,1,1]=>56
[8,3,6,4,7,1,2,5]=>[3,3,1,1]=>56
[1,2,8,3,5,7,4,6]=>[5,2,1]=>64
[1,8,3,2,5,7,4,6]=>[4,3,1]=>70
[6,5,1,7,4,2,8,3]=>[3,3,1,1]=>56
[7,3,6,4,8,2,1,5]=>[3,2,1,1,1]=>64
[6,1,7,3,4,2,8,5]=>[4,3,1]=>70
[7,3,8,1,6,5,2,4]=>[3,2,2,1]=>70
[8,3,7,1,6,5,2,4]=>[3,2,1,1,1]=>64
[5,1,7,4,2,8,6,3]=>[3,3,2]=>42
[4,2,8,6,5,1,7,3]=>[3,2,2,1]=>70
[6,4,2,8,5,1,7,3]=>[3,2,2,1]=>70
[8,6,4,7,1,5,2,3]=>[3,2,2,1]=>70
[3,8,7,1,6,5,2,4]=>[3,2,1,1,1]=>64
[4,2,3,7,8,5,1,6]=>[4,3,1]=>70
[5,1,6,4,2,3,7,8]=>[5,2,1]=>64
[6,4,7,8,1,5,2,3]=>[3,3,2]=>42
[8,6,5,7,1,4,2,3]=>[3,2,1,1,1]=>64
[6,7,4,8,1,5,2,3]=>[3,3,2]=>42
[8,3,2,4,7,1,5,6]=>[4,2,1,1]=>90
[2,5,3,7,1,6,4,8]=>[4,2,2]=>56
[8,4,6,7,1,5,2,3]=>[3,3,1,1]=>56
[7,4,6,8,1,5,2,3]=>[3,3,1,1]=>56
[3,7,5,8,1,6,2,4]=>[3,3,2]=>42
[4,7,6,8,1,5,2,3]=>[3,3,1,1]=>56
[8,5,6,7,1,4,2,3]=>[3,3,1,1]=>56
[8,6,7,5,1,4,2,3]=>[3,2,1,1,1]=>64
[5,6,8,7,1,4,2,3]=>[3,3,1,1]=>56
[2,4,6,7,1,5,8,3]=>[5,2,1]=>64
[6,7,8,5,1,4,2,3]=>[3,3,1,1]=>56
[7,8,6,5,1,4,2,3]=>[3,2,1,1,1]=>64
[3,1,7,5,4,2,8,6]=>[3,3,1,1]=>56
[4,1,8,5,2,3,6,7]=>[5,2,1]=>64
[8,2,7,1,5,3,4,6]=>[4,2,1,1]=>90
[6,3,7,1,5,4,2,8]=>[3,2,2,1]=>70
[7,1,5,3,8,4,2,6]=>[4,2,1,1]=>90
[4,5,1,3,6,8,2,7]=>[4,3,1]=>70
[6,8,3,1,5,4,2,7]=>[3,2,2,1]=>70
[3,6,2,1,5,8,4,7]=>[3,3,2]=>42
[8,6,2,1,5,3,4,7]=>[4,2,1,1]=>90
[4,8,2,1,7,5,3,6]=>[3,2,2,1]=>70
[7,1,6,2,8,3,4,5]=>[5,2,1]=>64
[2,7,8,1,5,3,4,6]=>[4,3,1]=>70
[4,7,2,1,8,5,3,6]=>[3,3,2]=>42
[8,7,2,1,4,5,3,6]=>[4,2,1,1]=>90
[8,7,5,6,1,4,3,2]=>[2,2,1,1,1,1]=>20
[3,7,1,4,5,6,8,2]=>[5,2,1]=>64
[3,5,1,4,7,6,8,2]=>[4,3,1]=>70
[8,6,5,7,1,4,3,2]=>[2,2,1,1,1,1]=>20
[7,2,3,1,5,6,4,8]=>[5,2,1]=>64
[8,3,1,5,4,6,7,2]=>[4,2,1,1]=>90
[6,2,8,1,4,5,3,7]=>[4,2,2]=>56
[4,2,1,5,6,3,8,7]=>[4,3,1]=>70
[7,6,8,5,1,4,3,2]=>[2,2,1,1,1,1]=>20
[6,8,7,5,1,4,3,2]=>[2,2,1,1,1,1]=>20
[2,7,6,1,4,5,3,8]=>[4,2,1,1]=>90
[7,8,6,5,1,4,3,2]=>[2,2,1,1,1,1]=>20
[4,3,1,6,5,8,7,2]=>[3,3,2]=>42
[5,3,1,2,4,8,7,6]=>[4,2,2]=>56
[5,3,6,2,1,8,7,4]=>[3,2,2,1]=>70
[5,3,7,2,1,4,6,8]=>[4,2,1,1]=>90
[5,3,7,2,8,4,1,6]=>[3,3,1,1]=>56
[7,2,4,5,8,3,1,6]=>[4,2,1,1]=>90
[7,2,4,5,1,3,6,8]=>[5,2,1]=>64
[6,2,4,5,1,8,7,3]=>[4,2,2]=>56
[3,1,4,5,2,8,7,6]=>[4,3,1]=>70
[1,6,4,5,2,8,7,3]=>[4,2,2]=>56
[3,7,4,5,1,2,6,8]=>[5,2,1]=>64
[3,7,4,5,8,2,1,6]=>[4,2,1,1]=>90
[1,7,4,2,6,3,5,8]=>[5,2,1]=>64
[8,7,4,5,2,1,6,3]=>[3,2,1,1,1]=>64
[6,3,7,1,8,4,2,5]=>[3,3,2]=>42
[5,7,4,1,6,3,2,8]=>[3,2,2,1]=>70
[1,7,4,8,6,3,2,5]=>[3,2,2,1]=>70
[5,7,4,8,6,3,1,2]=>[3,2,2,1]=>70
[4,8,3,5,6,7,1,2]=>[4,2,2]=>56
[1,8,3,5,6,7,2,4]=>[5,2,1]=>64
[4,8,1,5,6,7,2,3]=>[4,3,1]=>70
[4,1,3,5,6,7,2,8]=>[6,1,1]=>21
[5,8,4,3,6,1,2,7]=>[3,2,2,1]=>70
[5,3,8,4,1,7,2,6]=>[3,3,2]=>42
[1,5,8,4,6,7,3,2]=>[4,2,1,1]=>90
[1,4,8,3,6,7,5,2]=>[4,2,1,1]=>90
[4,3,8,2,1,7,5,6]=>[3,2,2,1]=>70
[3,8,4,2,6,1,5,7]=>[4,2,1,1]=>90
[1,8,2,5,6,7,4,3]=>[5,1,1,1]=>35
[3,8,1,5,6,7,4,2]=>[4,2,1,1]=>90
[3,8,2,5,6,7,1,4]=>[4,2,2]=>56
[8,2,1,5,6,7,4,3]=>[4,2,1,1]=>90
[8,1,3,5,6,7,4,2]=>[5,1,1,1]=>35
[7,1,4,3,6,2,5,8]=>[4,2,1,1]=>90
[7,8,4,3,6,2,1,5]=>[2,2,2,1,1]=>28
[4,3,1,8,5,7,6,2]=>[3,2,2,1]=>70
[4,3,1,6,8,7,5,2]=>[3,2,2,1]=>70
[6,3,1,8,2,7,4,5]=>[4,2,2]=>56
[6,3,5,8,2,7,1,4]=>[3,2,2,1]=>70
[7,5,4,8,6,2,1,3]=>[2,2,2,1,1]=>28
[7,1,4,8,6,2,3,5]=>[4,2,2]=>56
[7,5,4,1,6,2,3,8]=>[4,2,1,1]=>90
[7,6,4,5,8,1,3,2]=>[3,2,1,1,1]=>64
[1,6,4,5,8,2,3,7]=>[4,3,1]=>70
[7,3,6,1,8,2,4,5]=>[4,3,1]=>70
[1,7,6,5,8,3,4,2]=>[3,2,1,1,1]=>64
[1,8,5,3,6,7,4,2]=>[4,2,1,1]=>90
[8,3,5,2,1,7,4,6]=>[3,3,1,1]=>56
[8,4,1,5,6,7,3,2]=>[4,2,1,1]=>90
[8,4,2,5,6,7,1,3]=>[4,2,1,1]=>90
[4,1,8,5,6,7,3,2]=>[4,2,1,1]=>90
[1,2,8,5,6,7,3,4]=>[5,2,1]=>64
[4,2,1,5,6,7,3,8]=>[5,2,1]=>64
[1,5,3,8,6,7,4,2]=>[4,2,1,1]=>90
[1,4,5,8,6,7,3,2]=>[5,1,1,1]=>35
[4,3,5,8,1,7,2,6]=>[3,3,2]=>42
[3,5,4,8,6,1,2,7]=>[4,2,2]=>56
[1,4,8,5,6,7,2,3]=>[5,2,1]=>64
[3,4,8,5,6,7,1,2]=>[5,2,1]=>64
[4,3,7,2,5,6,8,1]=>[4,2,1,1]=>90
[2,6,3,1,4,5,8,7]=>[5,2,1]=>64
[3,7,1,5,6,2,8,4]=>[4,3,1]=>70
[4,7,1,5,6,8,2,3]=>[4,3,1]=>70
[8,4,2,3,5,7,1,6]=>[4,2,1,1]=>90
[5,3,4,6,2,8,1,7]=>[4,2,1,1]=>90
[6,4,7,2,3,8,1,5]=>[3,3,1,1]=>56
[6,5,7,2,8,3,1,4]=>[3,3,1,1]=>56
[8,7,6,1,4,5,2,3]=>[3,2,1,1,1]=>64
[8,7,4,5,1,6,2,3]=>[3,3,1,1]=>56
[8,5,6,4,1,7,2,3]=>[3,3,1,1]=>56
[8,4,6,2,3,1,7,5]=>[3,3,1,1]=>56
[10,3,1,2,4,5,6,7,8,9]=>[8,1,1]=>36
[5,10,1,2,3,4,6,7,8,9]=>[8,2]=>35
[10,7,1,2,3,4,5,6,8,9]=>[8,1,1]=>36
[8,10,1,2,3,4,5,6,7,9]=>[8,2]=>35
[2,11,1,3,4,5,6,7,8,9,10]=>[9,2]=>44
[2,3,10,1,4,5,6,7,8,9]=>[8,2]=>35
[4,3,1,10,2,5,6,7,8,9]=>[7,2,1]=>160
[8,9,1,2,3,4,5,6,10,7]=>[7,3]=>75
[11,9,1,2,3,4,5,6,7,8,10]=>[9,1,1]=>45
[7,3,5,4,1,8,6,2]=>[3,2,2,1]=>70
[2,6,5,7,3,1,8,4]=>[4,2,1,1]=>90
[4,2,1,6,3,7,5,8]=>[4,3,1]=>70
[4,2,1,6,3,7,8,5]=>[4,3,1]=>70
[4,2,1,3,7,8,6,5]=>[4,2,2]=>56
[4,2,1,8,3,5,6,7]=>[5,2,1]=>64
[4,2,1,6,3,8,7,5]=>[3,3,2]=>42
[3,6,7,5,2,4,8,1]=>[4,2,1,1]=>90
[3,6,7,5,2,4,1,8]=>[4,2,1,1]=>90
[4,2,1,7,3,6,5,8]=>[4,2,2]=>56
[3,7,6,8,4,2,5,1]=>[3,2,1,1,1]=>64
[5,8,1,7,4,2,6,3]=>[3,2,2,1]=>70
[3,7,8,6,2,4,5,1]=>[3,3,1,1]=>56
[4,2,1,3,5,8,6,7]=>[5,2,1]=>64
[4,2,1,8,3,7,6,5]=>[3,2,2,1]=>70
[2,6,1,5,4,7,8,3]=>[4,2,1,1]=>90
[4,6,3,5,8,7,1,2]=>[3,3,2]=>42
[2,7,5,1,8,3,4,6]=>[4,3,1]=>70
[4,7,5,2,1,3,6,8]=>[4,2,1,1]=>90
[3,5,6,2,4,1,7,8]=>[5,2,1]=>64
[2,5,6,1,4,8,3,7]=>[4,3,1]=>70
[7,1,6,8,4,5,3,2]=>[3,2,1,1,1]=>64
[5,7,8,1,4,6,3,2]=>[3,3,1,1]=>56
[1,8,4,6,7,5,3,2]=>[4,1,1,1,1]=>35
[6,1,8,4,7,5,3,2]=>[3,2,1,1,1]=>64
[4,5,8,6,1,7,3,2]=>[4,2,1,1]=>90
[5,6,7,1,4,2,3,8]=>[4,3,1]=>70
[4,8,5,2,1,6,7,3]=>[4,2,1,1]=>90
[1,8,4,6,2,5,3,7]=>[4,2,1,1]=>90
[8,2,4,3,6,7,1,5]=>[4,2,1,1]=>90
[3,2,8,5,7,1,6,4]=>[3,2,2,1]=>70
[2,8,7,1,4,6,5,3]=>[3,2,1,1,1]=>64
[8,2,7,1,5,4,6,3]=>[3,2,1,1,1]=>64
[7,2,5,3,6,8,1,4]=>[4,2,1,1]=>90
[2,7,3,6,5,8,1,4]=>[4,2,1,1]=>90
[8,7,2,4,1,6,5,3]=>[3,2,1,1,1]=>64
[1,2,7,3,6,4,5,8]=>[6,1,1]=>21
[1,6,2,8,4,3,7,5]=>[4,2,2]=>56
[8,1,4,7,3,2,5,6]=>[4,2,1,1]=>90
[7,1,4,2,3,5,6,8]=>[6,1,1]=>21
[1,2,3,4,8,5,7,6]=>[6,1,1]=>21
[2,4,8,7,5,6,3,1]=>[4,1,1,1,1]=>35
[2,5,3,8,4,7,6,1]=>[4,2,1,1]=>90
[2,8,5,7,3,6,4,1]=>[3,2,1,1,1]=>64
[3,1,8,5,2,7,6,4]=>[3,3,1,1]=>56
[2,8,6,3,4,5,7,1]=>[5,1,1,1]=>35
[8,3,7,6,1,4,5,2]=>[3,2,1,1,1]=>64
[3,1,7,8,2,5,6,4]=>[4,3,1]=>70
[7,3,8,5,1,6,4,2]=>[3,2,2,1]=>70
[7,5,1,2,3,4,8,6]=>[5,2,1]=>64
[4,8,1,5,2,7,3,6]=>[4,3,1]=>70
[4,1,2,5,3,8,7,6]=>[4,3,1]=>70
[4,3,6,8,7,5,1,2]=>[3,2,2,1]=>70
[5,4,1,6,8,2,7,3]=>[3,3,2]=>42
[5,4,7,1,2,8,6,3]=>[3,3,2]=>42
[6,7,4,1,2,8,3,5]=>[4,3,1]=>70
[6,5,1,2,3,7,8,4]=>[5,2,1]=>64
[6,5,1,2,3,4,8,7]=>[5,2,1]=>64
[6,7,4,1,2,5,3,8]=>[4,2,2]=>56
[1,4,6,3,7,2,5,8]=>[5,2,1]=>64
[8,6,2,5,3,1,7,4]=>[3,2,1,1,1]=>64
[8,2,3,4,5,1,7,6]=>[5,2,1]=>64
[6,1,3,5,7,2,4,8]=>[5,2,1]=>64
[7,1,8,2,5,6,3,4]=>[4,2,2]=>56
[6,1,5,8,2,7,3,4]=>[4,2,2]=>56
[4,5,2,8,1,6,7,3]=>[4,2,2]=>56
[6,2,5,8,1,4,7,3]=>[3,3,1,1]=>56
[1,3,8,2,5,7,4,6]=>[4,3,1]=>70
[6,2,3,1,5,4,7,8]=>[5,2,1]=>64
[8,2,3,1,4,5,7,6]=>[5,2,1]=>64
[8,5,1,3,2,4,7,6]=>[4,2,1,1]=>90
[7,5,1,3,2,6,4,8]=>[4,2,1,1]=>90
[3,6,4,1,5,2,7,8]=>[5,2,1]=>64
[4,5,7,1,2,6,3,8]=>[4,3,1]=>70
[2,7,1,3,5,6,4,8]=>[5,2,1]=>64
[8,6,1,2,4,3,7,5]=>[4,2,1,1]=>90
[7,8,1,2,5,3,6,4]=>[4,2,2]=>56
[1,2,6,7,5,3,8,4]=>[5,2,1]=>64
[1,7,5,3,2,8,4,6]=>[4,2,1,1]=>90
[1,6,7,5,3,8,4,2]=>[4,2,1,1]=>90
[1,6,5,7,2,3,8,4]=>[4,3,1]=>70
[1,3,8,2,6,5,7,4]=>[4,2,1,1]=>90
[1,2,5,7,6,3,4,8]=>[5,2,1]=>64
[1,3,4,8,2,5,7,6]=>[5,2,1]=>64
[1,5,7,6,2,3,4,8]=>[5,2,1]=>64
[1,5,3,8,2,6,4,7]=>[4,2,2]=>56
[1,4,8,3,2,5,7,6]=>[4,2,2]=>56
[1,4,8,3,5,7,6,2]=>[4,2,1,1]=>90
[1,2,4,8,3,5,7,6]=>[5,2,1]=>64
[1,3,8,4,2,6,7,5]=>[5,2,1]=>64
[1,4,8,2,3,5,7,6]=>[5,2,1]=>64
[6,5,7,3,8,2,4,1]=>[3,2,1,1,1]=>64
[4,2,6,7,5,8,3,1]=>[4,2,1,1]=>90
[6,7,5,2,1,8,4,3]=>[3,2,2,1]=>70
[3,4,8,7,5,2,1,6]=>[4,1,1,1,1]=>35
[1,7,5,2,8,4,6,3]=>[4,2,1,1]=>90
[5,6,8,3,1,7,2,4]=>[3,3,2]=>42
[6,1,4,8,3,2,7,5]=>[3,2,2,1]=>70
[3,4,7,1,8,6,2,5]=>[4,3,1]=>70
[3,4,6,8,2,1,5,7]=>[4,3,1]=>70
[3,8,2,5,6,1,4,7]=>[4,2,2]=>56
[3,5,2,8,6,4,1,7]=>[4,2,1,1]=>90
[4,2,5,7,3,8,6,1]=>[4,3,1]=>70
[7,4,2,5,3,8,1,6]=>[3,3,1,1]=>56
[3,1,2,8,5,6,4,7]=>[5,2,1]=>64
[5,2,1,6,8,3,4,7]=>[4,3,1]=>70
[5,2,6,8,4,1,3,7]=>[3,3,2]=>42
[1,5,6,8,3,4,2,7]=>[4,3,1]=>70
[4,5,8,1,6,3,2,7]=>[4,2,1,1]=>90
[4,5,1,6,8,3,2,7]=>[4,3,1]=>70
[4,5,7,3,8,2,6,1]=>[4,2,1,1]=>90
[6,4,3,7,8,2,5,1]=>[3,2,1,1,1]=>64
[6,4,3,1,7,8,2,5]=>[3,3,1,1]=>56
[4,5,3,1,7,8,2,6]=>[4,3,1]=>70
[7,1,3,5,4,8,2,6]=>[4,2,1,1]=>90
[7,5,2,8,1,4,3,6]=>[3,2,2,1]=>70
[5,7,3,8,4,6,1,2]=>[3,3,2]=>42
[1,4,5,7,3,8,6,2]=>[5,2,1]=>64
[4,6,3,7,8,5,2,1]=>[4,2,1,1]=>90
[5,3,6,7,8,4,2,1]=>[4,2,1,1]=>90
[1,5,3,6,7,8,4,2]=>[5,2,1]=>64
[4,6,1,7,3,8,5,2]=>[4,3,1]=>70
[6,3,7,1,8,4,5,2]=>[3,3,2]=>42
[6,7,2,4,8,1,5,3]=>[3,3,2]=>42
[2,6,1,4,7,3,8,5]=>[4,3,1]=>70
[3,2,5,6,7,8,1,4]=>[5,2,1]=>64
[5,2,3,6,7,8,4,1]=>[5,2,1]=>64
[6,7,1,3,2,8,4,5]=>[4,3,1]=>70
[6,2,7,1,3,4,8,5]=>[4,3,1]=>70
[5,2,1,7,3,8,4,6]=>[4,3,1]=>70
[6,4,2,7,1,8,3,5]=>[3,3,1,1]=>56
[4,2,6,3,7,8,1,5]=>[4,3,1]=>70
[4,2,6,3,7,8,5,1]=>[4,3,1]=>70
[6,7,3,8,2,4,5,1]=>[3,3,1,1]=>56
[3,6,2,7,4,1,8,5]=>[4,3,1]=>70
[6,7,3,2,1,4,8,5]=>[3,3,1,1]=>56
[7,1,8,3,4,2,5,6]=>[5,2,1]=>64
[7,2,4,1,8,3,5,6]=>[4,3,1]=>70
[7,2,4,8,6,1,3,5]=>[3,3,2]=>42
[7,3,4,8,6,2,1,5]=>[3,2,2,1]=>70
[3,5,7,2,1,8,6,4]=>[4,2,2]=>56
[6,7,8,3,2,5,1,4]=>[3,2,2,1]=>70
[6,3,7,8,2,5,4,1]=>[3,2,2,1]=>70
[2,6,7,4,8,5,3,1]=>[4,2,1,1]=>90
[6,2,4,7,1,8,5,3]=>[4,2,2]=>56
[4,6,2,7,1,8,5,3]=>[4,2,2]=>56
[1,7,4,8,5,2,6,3]=>[4,2,2]=>56
[1,3,7,8,5,2,6,4]=>[4,2,2]=>56
[2,5,7,8,1,6,3,4]=>[4,3,1]=>70
[6,3,7,1,8,2,5,4]=>[3,3,2]=>42
[1,6,4,7,8,2,5,3]=>[4,2,2]=>56
[2,5,6,1,7,8,4,3]=>[5,2,1]=>64
[5,6,1,2,7,8,4,3]=>[4,3,1]=>70
[6,7,2,1,8,5,3,4]=>[3,3,2]=>42
[6,7,2,8,5,4,1,3]=>[3,2,2,1]=>70
[1,6,7,4,8,5,3,2]=>[4,2,1,1]=>90
[1,8,4,5,3,6,2,7]=>[5,1,1,1]=>35
[1,8,5,3,4,7,2,6]=>[4,2,1,1]=>90
[1,8,2,4,6,3,7,5]=>[5,2,1]=>64
[3,6,2,7,1,4,5,8]=>[4,3,1]=>70
[4,6,5,3,7,1,8,2]=>[4,2,1,1]=>90
[4,2,3,8,6,7,1,5]=>[4,2,2]=>56
[5,2,4,8,1,3,7,6]=>[3,3,2]=>42
[6,2,5,4,8,3,7,1]=>[3,2,1,1,1]=>64
[6,4,3,5,8,2,7,1]=>[3,2,1,1,1]=>64
[5,2,3,4,8,1,6,7]=>[5,2,1]=>64
[3,5,2,4,7,1,6,8]=>[4,3,1]=>70
[5,3,4,8,1,6,2,7]=>[4,2,2]=>56
[4,5,3,7,1,6,2,8]=>[4,2,2]=>56
[7,6,3,8,5,1,2,4]=>[3,2,2,1]=>70
[4,2,6,7,3,8,1,5]=>[4,3,1]=>70
[1,5,7,4,2,8,6,3]=>[4,2,2]=>56
[1,3,7,2,8,6,4,5]=>[4,3,1]=>70
[1,4,3,7,8,6,2,5]=>[4,2,2]=>56
[1,5,3,6,8,2,7,4]=>[4,2,2]=>56
[4,3,6,5,7,8,1,2]=>[4,2,2]=>56
[4,2,3,5,6,8,1,7]=>[5,2,1]=>64
[4,2,6,7,3,8,5,1]=>[4,3,1]=>70
[3,2,5,6,8,1,7,4]=>[4,2,2]=>56
[6,4,5,2,3,8,7,1]=>[3,3,1,1]=>56
[6,4,2,5,3,8,7,1]=>[3,3,1,1]=>56
[8,6,4,7,5,2,3,1]=>[2,2,2,1,1]=>28
[8,6,2,7,4,5,3,1]=>[3,2,1,1,1]=>64
[4,6,2,5,3,8,7,1]=>[3,3,1,1]=>56
[4,6,5,2,3,8,7,1]=>[3,3,1,1]=>56
[6,8,2,7,4,5,3,1]=>[3,2,1,1,1]=>64
[6,8,7,2,4,5,3,1]=>[3,2,1,1,1]=>64
[2,6,4,5,8,7,3,1]=>[4,2,1,1]=>90
[2,6,4,8,7,5,3,1]=>[3,2,1,1,1]=>64
[8,2,4,6,7,5,3,1]=>[4,1,1,1,1]=>35
[4,2,6,5,8,7,3,1]=>[3,3,1,1]=>56
[4,2,3,6,8,7,5,1]=>[4,2,1,1]=>90
[6,4,8,7,2,5,3,1]=>[2,2,2,1,1]=>28
[6,4,8,7,5,2,3,1]=>[2,2,2,1,1]=>28
[4,6,8,2,7,5,3,1]=>[3,2,1,1,1]=>64
[4,6,5,8,2,7,3,1]=>[3,2,2,1]=>70
[2,1,8,6,4,7,5,3]=>[3,3,1,1]=>56
[6,8,7,4,2,5,3,1]=>[2,2,2,1,1]=>28
[9,2,4,6,8,1,3,5,7]=>[4,4,1]=>84
[9,4,6,8,1,2,3,5,7]=>[5,3,1]=>162
[9,6,8,1,2,3,4,5,7]=>[6,2,1]=>105
[3,5,7,9,1,2,4,6,8]=>[5,4]=>42
[5,7,9,1,2,3,4,6,8]=>[6,3]=>48
[7,9,1,2,3,4,5,6,8]=>[7,2]=>27
[10,9,8,7,6,5,2,4,1,3]=>[2,2,1,1,1,1,1,1]=>35
[10,9,4,8,3,7,2,6,1,5]=>[2,2,2,2,1,1]=>90
[10,9,8,7,2,4,6,1,3,5]=>[3,3,1,1,1,1]=>225
[6,10,5,9,2,4,8,1,3,7]=>[3,3,2,2]=>252
[10,9,2,4,6,8,1,3,5,7]=>[4,4,1,1]=>300
[10,3,5,7,9,1,2,4,6,8]=>[5,4,1]=>288
[10,5,7,9,1,2,3,4,6,8]=>[6,3,1]=>315
[10,7,9,1,2,3,4,5,6,8]=>[7,2,1]=>160
[4,2,5,6,3,8,1,7]=>[4,3,1]=>70
[6,2,5,7,4,8,3,1]=>[4,1,1,1,1]=>35
[8,5,2,1,4,7,6,3]=>[3,2,2,1]=>70
[6,7,3,2,5,8,4,1]=>[3,2,2,1]=>70
[3,2,6,4,8,1,5,7]=>[4,3,1]=>70
[2,3,6,4,7,8,5,1]=>[5,2,1]=>64
[7,5,1,8,3,4,6,2]=>[4,2,1,1]=>90
[5,7,8,2,6,3,4,1]=>[3,3,1,1]=>56
[7,1,6,3,5,8,4,2]=>[4,1,1,1,1]=>35
[6,3,1,7,8,4,5,2]=>[3,3,2]=>42
[5,3,6,7,4,1,8,2]=>[4,2,2]=>56
[7,3,1,2,5,8,6,4]=>[4,2,2]=>56
[1,6,3,5,2,4,8,7]=>[4,3,1]=>70
[3,4,8,2,7,5,1,6]=>[4,2,1,1]=>90
[6,3,2,8,5,7,4,1]=>[3,2,2,1]=>70
[3,8,4,7,2,5,6,1]=>[4,2,1,1]=>90
[2,4,8,1,5,3,7,6]=>[4,3,1]=>70
[3,4,8,1,6,2,7,5]=>[4,3,1]=>70
[1,8,4,6,7,3,5,2]=>[4,2,1,1]=>90
[8,1,6,3,4,5,7,2]=>[5,1,1,1]=>35
[7,6,5,4,1,2,8,3]=>[3,2,1,1,1]=>64
[5,7,6,8,3,4,2,1]=>[3,2,1,1,1]=>64
[2,8,1,6,5,7,4,3]=>[3,2,1,1,1]=>64
[4,6,8,2,5,3,7,1]=>[3,3,1,1]=>56
[5,2,3,7,6,1,8,4]=>[4,2,2]=>56
[8,1,2,4,6,7,3,5]=>[5,2,1]=>64
[5,2,3,7,4,8,6,1]=>[4,3,1]=>70
[5,2,6,8,4,3,1,7]=>[3,3,1,1]=>56
[7,8,1,5,4,3,6,2]=>[3,2,1,1,1]=>64
[7,2,4,8,5,3,6,1]=>[4,2,1,1]=>90
[3,7,5,1,8,4,6,2]=>[3,3,1,1]=>56
[2,7,8,5,4,6,1,3]=>[3,2,2,1]=>70
[5,7,4,3,8,6,2,1]=>[3,2,1,1,1]=>64
[4,8,1,6,3,5,2,7]=>[4,2,1,1]=>90
[8,3,1,7,4,2,5,6]=>[4,2,1,1]=>90
[3,1,8,2,4,5,7,6]=>[5,2,1]=>64
[8,1,3,7,6,2,4,5]=>[4,2,1,1]=>90
[2,3,6,8,7,1,4,5]=>[4,3,1]=>70
[4,3,2,8,5,7,1,6]=>[3,2,2,1]=>70
[3,6,4,2,8,5,7,1]=>[4,2,1,1]=>90
[4,7,3,2,5,1,8,6]=>[3,3,1,1]=>56
[3,2,4,7,5,8,6,1]=>[4,3,1]=>70
[4,2,3,8,6,5,1,7]=>[4,2,1,1]=>90
[2,4,3,5,1,8,6,7]=>[5,2,1]=>64
[3,2,8,1,4,6,5,7]=>[4,2,2]=>56
[4,7,8,3,1,2,6,5]=>[3,3,2]=>42
[4,7,8,2,1,3,6,5]=>[3,3,2]=>42
[4,1,6,8,2,3,7,5]=>[4,3,1]=>70
[4,5,1,2,8,3,7,6]=>[4,3,1]=>70
[4,6,2,8,1,3,7,5]=>[3,3,2]=>42
[3,6,2,8,4,7,1,5]=>[3,3,2]=>42
[4,2,6,8,3,1,7,5]=>[3,3,2]=>42
[4,1,2,5,8,3,7,6]=>[4,3,1]=>70
[5,2,4,1,3,8,7,6]=>[3,3,2]=>42
[4,2,5,3,8,1,7,6]=>[3,3,2]=>42
[3,2,5,4,8,7,1,6]=>[3,3,2]=>42
[5,1,4,2,3,8,7,6]=>[4,2,2]=>56
[5,4,1,3,2,8,7,6]=>[3,2,2,1]=>70
[5,4,3,1,2,8,7,6]=>[3,2,2,1]=>70
[3,5,1,4,8,7,2,6]=>[3,3,2]=>42
[3,4,5,1,8,7,2,6]=>[4,3,1]=>70
[4,3,6,8,2,1,7,5]=>[3,2,2,1]=>70
[2,4,6,8,3,7,5,1]=>[4,2,1,1]=>90
[3,4,5,2,8,7,1,6]=>[4,2,2]=>56
[5,3,1,4,2,8,7,6]=>[3,3,2]=>42
[5,3,2,1,4,8,7,6]=>[3,2,2,1]=>70
[4,3,2,5,8,1,7,6]=>[3,2,2,1]=>70
[5,2,1,3,4,8,7,6]=>[4,2,2]=>56
[5,1,2,3,4,8,7,6]=>[5,2,1]=>64
[8,6,2,5,4,1,3,7]=>[3,2,1,1,1]=>64
[6,5,7,4,2,8,3,1]=>[3,2,1,1,1]=>64
[6,7,5,3,8,2,4,1]=>[3,2,1,1,1]=>64
[8,2,1,6,3,4,5,7]=>[5,2,1]=>64
[8,3,5,6,2,4,1,7]=>[4,2,1,1]=>90
[8,6,2,1,3,5,4,7]=>[4,2,1,1]=>90
[8,1,2,3,4,6,5,7]=>[6,1,1]=>21
[6,2,3,7,8,4,5,1]=>[4,3,1]=>70
[7,5,8,2,6,3,4,1]=>[3,2,2,1]=>70
[7,3,1,6,5,8,4,2]=>[3,2,1,1,1]=>64
[1,5,6,7,3,4,8,2]=>[5,2,1]=>64
[6,7,8,2,1,4,5,3]=>[3,3,2]=>42
[8,4,7,6,2,1,3,5]=>[3,2,1,1,1]=>64
[5,3,8,4,7,2,6,1]=>[3,2,2,1]=>70
[8,1,3,7,6,4,2,5]=>[4,1,1,1,1]=>35
[5,3,1,7,8,6,2,4]=>[3,3,2]=>42
[3,5,8,2,7,1,6,4]=>[3,2,2,1]=>70
[6,2,8,5,3,1,7,4]=>[3,2,2,1]=>70
[8,2,6,4,7,1,3,5]=>[3,3,1,1]=>56
[3,4,2,8,5,1,7,6]=>[4,2,2]=>56
[3,8,6,5,2,1,7,4]=>[3,2,1,1,1]=>64
[8,3,7,4,2,5,6,1]=>[4,1,1,1,1]=>35
[4,8,5,7,2,1,3,6]=>[3,3,1,1]=>56
[3,4,1,8,2,6,7,5]=>[4,3,1]=>70
[8,4,6,3,7,1,5,2]=>[3,2,2,1]=>70
[6,8,3,4,1,5,7,2]=>[4,2,2]=>56
[5,1,7,6,2,8,4,3]=>[3,3,1,1]=>56
[6,8,2,5,7,4,1,3]=>[3,2,2,1]=>70
[2,8,5,6,7,1,3,4]=>[4,3,1]=>70
[2,5,7,6,3,1,8,4]=>[4,2,1,1]=>90
[4,2,8,3,1,5,6,7]=>[5,2,1]=>64
[2,5,7,3,8,4,6,1]=>[4,3,1]=>70
[4,2,7,1,8,5,3,6]=>[3,3,2]=>42
[4,2,1,8,7,5,6,3]=>[3,2,2,1]=>70
[8,3,6,7,1,5,4,2]=>[3,2,1,1,1]=>64
[1,3,7,5,8,6,4,2]=>[4,2,1,1]=>90
[5,7,8,4,3,1,6,2]=>[3,2,2,1]=>70
[2,7,4,5,8,3,6,1]=>[4,2,1,1]=>90
[3,5,7,1,4,8,6,2]=>[4,3,1]=>70
[7,2,8,5,1,4,6,3]=>[3,2,2,1]=>70
[1,6,5,3,8,4,2,7]=>[4,2,1,1]=>90
[5,7,4,8,3,6,2,1]=>[3,2,1,1,1]=>64
[4,8,6,1,3,5,2,7]=>[4,2,1,1]=>90
[1,8,3,2,4,7,5,6]=>[5,2,1]=>64
[8,4,3,2,5,7,1,6]=>[3,2,1,1,1]=>64
[3,6,4,8,2,5,7,1]=>[4,2,1,1]=>90
[4,3,7,2,5,8,1,6]=>[3,3,1,1]=>56
[3,2,4,7,8,5,6,1]=>[4,3,1]=>70
[2,6,4,3,8,5,1,7]=>[4,2,1,1]=>90
[3,8,2,1,6,4,5,7]=>[4,2,2]=>56
[8,2,1,3,4,5,7,6]=>[5,2,1]=>64
[4,6,8,3,2,1,5,7]=>[3,3,1,1]=>56
[3,2,6,8,5,4,1,7]=>[3,3,1,1]=>56
[7,3,8,2,5,4,1,6]=>[3,2,2,1]=>70
[4,2,5,3,8,7,6,1]=>[3,3,1,1]=>56
[4,8,2,6,5,3,1,7]=>[3,2,1,1,1]=>64
[2,6,8,5,4,1,3,7]=>[3,3,1,1]=>56
[3,1,8,6,5,4,2,7]=>[3,2,1,1,1]=>64
[5,4,8,7,3,2,6,1]=>[2,2,2,1,1]=>28
[6,4,8,3,7,2,5,1]=>[2,2,2,1,1]=>28
[4,7,3,6,2,1,8,5]=>[3,2,2,1]=>70
[5,4,3,7,1,8,2,6]=>[3,3,1,1]=>56
[7,3,8,5,1,4,2,6]=>[3,2,2,1]=>70
[5,4,8,7,6,2,1,3]=>[2,2,2,1,1]=>28
[3,8,1,5,7,4,6,2]=>[3,3,1,1]=>56
[4,8,5,7,3,1,6,2]=>[3,2,2,1]=>70
[1,5,4,8,3,7,6,2]=>[3,2,2,1]=>70
[4,8,3,6,7,1,5,2]=>[3,2,2,1]=>70
[4,7,8,3,1,6,5,2]=>[3,2,2,1]=>70
[8,7,5,3,6,4,2,1]=>[2,2,1,1,1,1]=>20
[4,6,1,3,8,7,5,2]=>[3,3,1,1]=>56
[6,8,2,1,7,4,5,3]=>[3,2,2,1]=>70
[3,7,1,6,4,2,8,5]=>[3,3,1,1]=>56
[3,1,2,7,5,6,8,4]=>[5,2,1]=>64
[3,6,1,2,7,5,8,4]=>[4,3,1]=>70
[3,7,6,2,5,8,1,4]=>[3,2,2,1]=>70
[3,6,2,5,8,7,4,1]=>[3,3,1,1]=>56
[8,5,2,3,6,7,4,1]=>[4,2,1,1]=>90
[4,7,2,6,3,8,1,5]=>[3,3,1,1]=>56
[6,3,2,4,8,7,5,1]=>[3,2,2,1]=>70
[3,7,2,4,6,1,8,5]=>[4,2,2]=>56
[5,3,7,2,8,1,4,6]=>[3,3,1,1]=>56
[6,3,2,8,7,5,1,4]=>[2,2,2,2]=>14
[7,3,8,2,6,5,1,4]=>[2,2,2,2]=>14
[6,4,8,7,2,5,1,3]=>[2,2,2,2]=>14
[2,5,4,8,1,7,6,3]=>[3,2,2,1]=>70
[5,2,8,1,7,6,3,4]=>[3,2,2,1]=>70
[6,2,1,3,8,7,5,4]=>[3,2,2,1]=>70
[3,6,1,8,7,5,2,4]=>[3,3,1,1]=>56
[5,6,1,2,8,7,4,3]=>[3,3,1,1]=>56
[7,5,2,8,1,6,4,3]=>[2,2,2,2]=>14
[2,7,6,8,1,5,4,3]=>[3,2,1,1,1]=>64
[7,8,5,1,6,2,4,3]=>[3,2,2,1]=>70
[7,4,8,6,1,2,5,3]=>[3,2,2,1]=>70
[7,2,1,8,3,6,5,4]=>[3,2,2,1]=>70
[5,8,7,1,6,4,3,2]=>[2,2,1,1,1,1]=>20
[11,9,8,7,6,5,4,3,2,1,10]=>[2,1,1,1,1,1,1,1,1,1]=>10
[8,5,4,3,7,2,1,6]=>[2,2,1,1,1,1]=>20
[6,5,4,8,3,2,7,1]=>[2,2,1,1,1,1]=>20
[10,9,8,7,6,5,4,3,2,11,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[7,3,1,4,8,2,5,6]=>[4,3,1]=>70
[5,7,2,4,6,8,1,3]=>[4,2,2]=>56
[6,4,7,1,3,8,5,2]=>[3,3,1,1]=>56
[4,5,1,2,7,6,8,3]=>[4,3,1]=>70
[5,4,6,8,3,1,2,7]=>[3,3,1,1]=>56
[1,3,8,4,5,7,2,6]=>[5,2,1]=>64
[2,6,7,4,5,3,1,8]=>[4,2,1,1]=>90
[1,3,7,4,2,8,5,6]=>[5,2,1]=>64
[7,5,8,6,2,1,3,4]=>[3,2,2,1]=>70
[2,8,7,3,5,4,1,6]=>[4,1,1,1,1]=>35
[7,3,8,4,1,2,6,5]=>[3,3,2]=>42
[6,8,3,2,7,1,5,4]=>[2,2,2,2]=>14
[3,7,1,2,4,6,5,8]=>[5,2,1]=>64
[1,7,2,3,5,6,8,4]=>[6,1,1]=>21
[4,7,1,6,5,2,8,3]=>[3,3,1,1]=>56
[4,7,3,6,5,1,8,2]=>[3,2,2,1]=>70
[3,2,4,8,6,7,1,5]=>[4,2,2]=>56
[4,2,6,8,7,3,1,5]=>[3,3,1,1]=>56
[4,3,7,1,6,8,2,5]=>[3,3,2]=>42
[2,8,7,4,5,3,1,6]=>[4,1,1,1,1]=>35
[2,8,7,4,3,5,1,6]=>[4,1,1,1,1]=>35
[3,8,1,4,2,6,5,7]=>[4,3,1]=>70
[4,2,7,3,6,1,8,5]=>[4,2,2]=>56
[3,8,2,4,5,6,7,1]=>[5,2,1]=>64
[3,8,2,4,1,6,7,5]=>[4,2,2]=>56
[3,8,2,5,4,6,7,1]=>[4,2,1,1]=>90
[4,2,7,5,6,3,8,1]=>[4,2,1,1]=>90
[4,2,7,5,6,1,8,3]=>[4,2,2]=>56
[4,2,6,7,5,3,1,8]=>[4,2,1,1]=>90
[3,2,6,1,4,5,8,7]=>[4,3,1]=>70
[3,8,1,2,4,6,5,7]=>[5,2,1]=>64
[2,8,7,5,3,4,1,6]=>[4,1,1,1,1]=>35
[5,8,7,6,4,1,2,3]=>[3,2,1,1,1]=>64
[5,4,2,3,7,6,8,1]=>[4,2,1,1]=>90
[7,4,3,5,2,8,1,6]=>[3,2,1,1,1]=>64
[8,4,3,7,5,1,6,2]=>[3,2,2,1]=>70
[8,4,7,2,5,1,6,3]=>[3,2,2,1]=>70
[7,4,6,2,3,5,8,1]=>[4,2,1,1]=>90
[5,1,7,2,4,6,8,3]=>[5,2,1]=>64
[4,5,7,1,2,6,8,3]=>[4,3,1]=>70
[5,4,1,7,3,6,8,2]=>[4,2,1,1]=>90
[3,6,4,7,5,2,8,1]=>[4,2,1,1]=>90
[3,4,7,6,2,5,8,1]=>[4,2,1,1]=>90
[4,7,5,6,1,3,8,2]=>[4,2,1,1]=>90
[5,7,6,4,3,1,8,2]=>[3,2,1,1,1]=>64
[5,7,6,3,1,4,8,2]=>[3,2,2,1]=>70
[7,5,2,3,4,8,1,6]=>[4,2,1,1]=>90
[8,7,5,3,4,1,6,2]=>[3,2,1,1,1]=>64
[6,7,1,3,8,4,2,5]=>[4,3,1]=>70
[7,6,1,3,4,8,5,2]=>[4,2,1,1]=>90
[3,6,5,2,7,8,1,4]=>[4,2,1,1]=>90
[3,2,8,6,7,1,4,5]=>[3,3,2]=>42
[4,8,3,6,5,2,1,7]=>[3,2,1,1,1]=>64
[1,8,6,5,4,2,3,7]=>[4,1,1,1,1]=>35
[1,8,7,2,3,5,4,6]=>[5,1,1,1]=>35
[1,8,7,2,5,3,4,6]=>[5,1,1,1]=>35
[3,6,8,5,1,2,4,7]=>[4,3,1]=>70
[3,7,5,1,8,2,6,4]=>[3,3,2]=>42
[7,1,2,8,3,5,6,4]=>[5,2,1]=>64
[6,1,7,8,2,5,3,4]=>[4,3,1]=>70
[6,7,5,2,8,1,4,3]=>[3,2,2,1]=>70
[7,1,4,5,8,6,2,3]=>[4,2,2]=>56
[5,7,6,4,2,8,1,3]=>[3,2,1,1,1]=>64
[7,5,6,1,2,8,4,3]=>[3,3,1,1]=>56
[4,1,3,7,8,6,2,5]=>[4,2,2]=>56
[5,1,4,3,6,8,7,2]=>[4,2,1,1]=>90
[4,5,7,6,8,2,1,3]=>[4,2,1,1]=>90
[5,7,6,8,4,2,1,3]=>[3,2,1,1,1]=>64
[5,1,6,8,4,2,7,3]=>[3,3,2]=>42
[7,4,8,2,3,6,5,1]=>[3,2,2,1]=>70
[5,6,8,4,7,3,2,1]=>[3,2,1,1,1]=>64
[6,4,7,8,5,2,1,3]=>[3,2,2,1]=>70
[3,6,4,8,5,1,2,7]=>[4,2,2]=>56
[3,7,4,8,1,2,5,6]=>[4,3,1]=>70
[7,4,3,8,2,6,5,1]=>[2,2,2,1,1]=>28
[7,6,8,3,2,5,4,1]=>[2,2,2,1,1]=>28
[8,7,1,3,5,4,6,2]=>[4,1,1,1,1]=>35
[7,1,8,3,4,2,6,5]=>[4,2,2]=>56
[7,6,8,3,1,4,5,2]=>[3,2,2,1]=>70
[3,1,4,8,2,5,7,6]=>[4,3,1]=>70
[4,8,5,2,1,3,6,7]=>[4,2,1,1]=>90
[5,8,2,6,3,1,4,7]=>[4,2,1,1]=>90
[6,8,2,3,7,4,1,5]=>[4,2,1,1]=>90
[7,8,2,3,4,6,5,1]=>[4,2,1,1]=>90
[8,1,7,2,4,5,3,6]=>[5,1,1,1]=>35
[8,1,3,6,2,5,4,7]=>[4,2,1,1]=>90
[7,2,1,6,3,5,4,8]=>[4,2,1,1]=>90
[2,7,1,6,3,5,4,8]=>[4,2,1,1]=>90
[2,7,1,5,4,3,6,8]=>[4,2,1,1]=>90
[7,2,1,5,4,3,6,8]=>[4,2,1,1]=>90
[8,1,3,5,4,2,6,7]=>[5,1,1,1]=>35
[8,1,5,3,4,2,6,7]=>[5,1,1,1]=>35
[8,1,5,6,2,3,7,4]=>[4,3,1]=>70
[8,1,4,5,3,2,6,7]=>[5,1,1,1]=>35
[8,1,4,3,5,2,6,7]=>[5,1,1,1]=>35
[7,2,1,4,5,3,6,8]=>[5,2,1]=>64
[2,7,1,4,5,3,6,8]=>[5,2,1]=>64
[2,6,3,1,5,4,7,8]=>[5,2,1]=>64
[6,3,2,1,5,4,7,8]=>[4,2,1,1]=>90
[7,3,1,4,5,2,6,8]=>[5,2,1]=>64
[7,3,1,5,4,2,6,8]=>[4,2,1,1]=>90
[7,3,1,6,2,5,4,8]=>[4,2,1,1]=>90
[3,7,1,6,2,5,4,8]=>[4,2,1,1]=>90
[3,7,1,4,5,2,6,8]=>[5,2,1]=>64
[3,6,2,1,5,4,7,8]=>[4,2,2]=>56
[2,3,6,1,5,4,7,8]=>[5,2,1]=>64
[3,5,2,4,1,6,7,8]=>[5,2,1]=>64
[6,3,4,1,5,2,7,8]=>[5,2,1]=>64
[6,2,4,1,5,3,7,8]=>[5,2,1]=>64
[2,6,4,1,5,3,7,8]=>[5,2,1]=>64
[2,6,5,1,3,7,4,8]=>[4,3,1]=>70
[6,2,5,1,3,7,4,8]=>[4,3,1]=>70
[6,5,2,1,3,7,4,8]=>[4,2,1,1]=>90
[7,6,1,2,4,5,3,8]=>[5,1,1,1]=>35
[6,7,1,2,8,3,5,4]=>[4,3,1]=>70
[6,7,1,2,5,4,3,8]=>[4,2,1,1]=>90
[5,6,2,1,3,7,4,8]=>[4,3,1]=>70
[5,2,6,1,3,7,4,8]=>[4,3,1]=>70
[2,4,6,1,5,3,7,8]=>[5,2,1]=>64
[4,7,1,3,5,2,6,8]=>[5,2,1]=>64
[4,7,1,5,3,2,6,8]=>[4,2,1,1]=>90
[5,7,1,4,2,6,3,8]=>[4,2,2]=>56
[5,7,1,6,2,3,8,4]=>[4,3,1]=>70
[5,6,3,1,2,7,4,8]=>[4,3,1]=>70
[4,2,5,3,1,6,7,8]=>[5,2,1]=>64
[5,3,6,1,2,7,4,8]=>[4,3,1]=>70
[3,4,6,1,5,2,7,8]=>[5,2,1]=>64
[8,2,7,5,4,1,3,6]=>[3,2,1,1,1]=>64
[6,8,5,2,3,4,1,7]=>[4,2,1,1]=>90
[8,5,6,2,7,1,4,3]=>[3,2,2,1]=>70
[6,5,1,2,7,8,4,3]=>[4,2,1,1]=>90
[4,7,6,1,5,3,8,2]=>[3,2,1,1,1]=>64
[5,7,6,4,1,3,8,2]=>[3,2,1,1,1]=>64
[7,6,2,4,5,3,8,1]=>[4,1,1,1,1]=>35
[6,1,7,5,3,8,4,2]=>[3,3,1,1]=>56
[8,6,7,5,3,1,4,2]=>[2,2,2,1,1]=>28
[8,5,2,7,1,6,4,3]=>[2,2,2,1,1]=>28
[7,6,1,5,3,8,4,2]=>[3,2,1,1,1]=>64
[5,6,2,4,7,8,1,3]=>[4,2,2]=>56
[3,4,6,1,7,8,5,2]=>[5,2,1]=>64
[3,4,8,6,7,1,5,2]=>[4,2,1,1]=>90
[4,8,5,6,7,2,3,1]=>[4,2,1,1]=>90
[5,8,6,4,1,2,7,3]=>[3,3,1,1]=>56
[5,8,6,1,7,2,4,3]=>[3,3,1,1]=>56
[5,8,7,3,2,6,4,1]=>[2,2,2,1,1]=>28
[5,8,1,7,2,6,4,3]=>[3,2,1,1,1]=>64
[8,1,5,7,2,6,4,3]=>[3,2,1,1,1]=>64
[8,1,7,2,5,6,3,4]=>[4,2,1,1]=>90
[6,8,7,2,5,1,3,4]=>[3,2,2,1]=>70
[5,8,7,2,1,6,3,4]=>[3,2,2,1]=>70
[4,8,1,5,2,6,7,3]=>[4,3,1]=>70
[3,7,8,5,1,6,2,4]=>[3,3,2]=>42
[6,5,2,7,8,1,4,3]=>[3,2,2,1]=>70
[7,1,2,8,5,6,3,4]=>[4,2,2]=>56
[8,7,2,1,5,6,3,4]=>[3,3,1,1]=>56
[8,6,7,1,5,2,3,4]=>[4,2,1,1]=>90
[6,1,7,8,5,2,3,4]=>[4,3,1]=>70
[7,5,6,2,1,8,4,3]=>[3,2,2,1]=>70
[8,7,5,2,1,6,4,3]=>[2,2,2,1,1]=>28
[7,1,3,5,8,6,2,4]=>[4,2,2]=>56
[5,1,3,4,6,8,7,2]=>[5,2,1]=>64
[4,5,3,6,8,2,7,1]=>[4,2,1,1]=>90
[5,6,3,4,8,1,7,2]=>[3,3,2]=>42
[4,6,7,8,5,1,3,2]=>[4,2,1,1]=>90
[8,4,3,1,2,6,7,5]=>[4,2,1,1]=>90
[8,5,1,6,3,4,7,2]=>[4,2,1,1]=>90
[5,1,8,6,3,4,7,2]=>[4,2,1,1]=>90
[4,6,8,1,5,3,7,2]=>[3,3,1,1]=>56
[6,4,5,8,3,2,7,1]=>[3,2,1,1,1]=>64
[3,6,4,8,7,1,5,2]=>[3,2,2,1]=>70
[6,5,8,1,3,4,7,2]=>[4,2,1,1]=>90
[5,6,8,3,1,2,7,4]=>[3,3,2]=>42
[6,1,8,3,5,2,7,4]=>[4,2,2]=>56
[7,6,8,3,5,2,1,4]=>[2,2,2,1,1]=>28
[8,6,1,3,5,2,7,4]=>[4,2,1,1]=>90
[8,7,1,3,5,6,2,4]=>[4,2,1,1]=>90
[6,7,8,3,5,1,2,4]=>[3,3,2]=>42
[3,4,8,1,2,6,7,5]=>[4,3,1]=>70
[5,8,2,4,3,6,7,1]=>[4,2,1,1]=>90
[5,8,2,3,1,6,7,4]=>[4,2,2]=>56
[6,8,2,3,5,1,7,4]=>[4,2,2]=>56
[7,8,2,3,5,6,1,4]=>[4,2,2]=>56
[8,6,5,1,4,3,7,2]=>[3,1,1,1,1,1]=>21
[2,6,5,4,1,3,8,7]=>[3,3,1,1]=>56
[4,1,7,6,3,8,2,5]=>[3,3,1,1]=>56
[4,8,2,5,7,6,3,1]=>[3,2,1,1,1]=>64
[3,4,6,5,1,8,2,7]=>[4,3,1]=>70
[2,6,5,3,4,1,8,7]=>[4,2,1,1]=>90
[4,6,1,5,2,3,8,7]=>[4,3,1]=>70
[6,2,3,5,1,4,8,7]=>[4,3,1]=>70
[2,6,7,5,1,8,4,3]=>[4,2,1,1]=>90
[8,6,1,2,5,3,4,7]=>[5,1,1,1]=>35
[6,2,5,1,8,3,4,7]=>[4,3,1]=>70
[7,6,5,2,8,3,4,1]=>[3,2,1,1,1]=>64
[2,6,3,5,1,8,7,4]=>[4,2,2]=>56
[2,4,7,6,5,8,1,3]=>[4,2,1,1]=>90
[2,1,4,8,7,6,3,5]=>[3,3,1,1]=>56
[7,4,6,8,5,3,2,1]=>[3,1,1,1,1,1]=>21
[8,1,3,5,7,4,6,2]=>[4,2,1,1]=>90
[3,2,8,7,5,1,6,4]=>[3,2,2,1]=>70
[4,8,5,1,6,7,2,3]=>[4,3,1]=>70
[3,8,5,1,6,7,2,4]=>[4,3,1]=>70
[7,8,6,1,3,5,2,4]=>[3,2,2,1]=>70
[5,6,7,2,8,1,3,4]=>[4,3,1]=>70
[2,5,1,8,6,7,4,3]=>[4,2,1,1]=>90
[3,5,1,8,6,7,4,2]=>[4,2,1,1]=>90
[5,2,3,8,6,7,4,1]=>[4,2,1,1]=>90
[8,3,5,4,6,7,1,2]=>[4,2,1,1]=>90
[5,1,3,8,6,7,4,2]=>[4,2,1,1]=>90
[3,2,5,8,6,7,4,1]=>[4,2,1,1]=>90
[6,2,1,5,3,8,7,4]=>[3,3,2]=>42
[5,6,3,2,8,1,4,7]=>[3,3,1,1]=>56
[8,1,6,3,5,2,7,4]=>[4,2,1,1]=>90
[8,7,6,2,5,3,1,4]=>[3,1,1,1,1,1]=>21
[4,7,6,8,3,2,5,1]=>[3,2,1,1,1]=>64
[2,7,5,8,1,3,4,6]=>[4,3,1]=>70
[7,6,2,8,5,1,4,3]=>[2,2,2,1,1]=>28
[8,1,3,7,5,2,6,4]=>[4,2,1,1]=>90
[3,4,8,7,5,1,6,2]=>[4,2,1,1]=>90
[6,3,8,1,4,2,5,7]=>[4,2,2]=>56
[6,3,8,5,7,4,1,2]=>[3,2,2,1]=>70
[7,4,6,8,5,1,3,2]=>[3,2,1,1,1]=>64
[2,1,4,8,7,5,6,3]=>[4,2,1,1]=>90
[7,1,5,8,2,6,4,3]=>[3,2,2,1]=>70
[3,6,8,2,4,1,7,5]=>[3,3,2]=>42
[4,5,8,2,6,7,3,1]=>[4,2,1,1]=>90
[5,2,8,1,6,7,3,4]=>[3,3,2]=>42
[2,5,8,4,6,7,3,1]=>[4,2,1,1]=>90
[5,8,3,4,6,7,2,1]=>[4,2,1,1]=>90
[8,4,3,2,6,7,1,5]=>[3,2,1,1,1]=>64
[4,2,8,1,6,7,3,5]=>[3,3,2]=>42
[2,4,8,1,6,7,3,5]=>[4,3,1]=>70
[5,1,8,2,6,7,3,4]=>[4,3,1]=>70
[3,4,8,7,2,1,5,6]=>[4,2,1,1]=>90
[7,8,5,3,6,4,2,1]=>[2,2,2,1,1]=>28
[2,8,5,7,4,1,3,6]=>[3,3,1,1]=>56
[5,8,4,1,6,7,2,3]=>[3,3,2]=>42
[3,8,1,4,6,7,2,5]=>[4,3,1]=>70
[8,2,3,4,6,7,1,5]=>[5,2,1]=>64
[6,2,7,3,8,4,1,5]=>[4,3,1]=>70
[7,4,3,2,8,5,1,6]=>[3,2,1,1,1]=>64
[5,3,2,8,4,6,1,7]=>[4,2,1,1]=>90
[8,4,2,6,5,3,1,7]=>[3,2,1,1,1]=>64
[7,4,2,5,3,1,6,8]=>[4,2,1,1]=>90
[8,3,6,2,5,4,1,7]=>[3,2,1,1,1]=>64
[5,4,8,3,2,6,1,7]=>[3,2,1,1,1]=>64
[3,5,8,2,4,6,1,7]=>[4,3,1]=>70
[6,4,7,8,2,3,1,5]=>[3,3,1,1]=>56
[5,8,3,6,4,2,1,7]=>[3,2,1,1,1]=>64
[4,8,6,2,5,3,1,7]=>[3,2,1,1,1]=>64
[1,6,4,3,2,8,7,5]=>[3,2,2,1]=>70
[1,5,3,2,8,4,7,6]=>[4,2,2]=>56
[5,7,4,3,1,2,6,8]=>[4,2,1,1]=>90
[2,8,7,3,5,1,4,6]=>[4,2,1,1]=>90
[7,3,8,6,4,1,2,5]=>[3,2,2,1]=>70
[6,1,2,7,3,8,5,4]=>[4,3,1]=>70
[2,1,7,4,3,8,6,5]=>[3,3,2]=>42
[6,1,4,3,8,2,7,5]=>[3,2,2,1]=>70
[5,1,3,2,8,7,4,6]=>[4,2,2]=>56
[1,8,4,2,7,6,5,3]=>[3,2,1,1,1]=>64
[1,8,3,7,2,6,5,4]=>[3,2,1,1,1]=>64
[5,1,4,8,3,7,2,6]=>[3,2,2,1]=>70
[2,1,6,8,5,4,7,3]=>[3,3,1,1]=>56
[6,1,5,7,8,2,4,3]=>[4,2,1,1]=>90
[8,3,1,6,7,2,5,4]=>[3,3,1,1]=>56
[7,4,8,6,1,3,2,5]=>[3,2,2,1]=>70
[4,7,6,1,2,5,3,8]=>[4,2,1,1]=>90
[3,7,6,1,5,2,4,8]=>[4,2,1,1]=>90
[1,5,4,8,3,2,7,6]=>[3,2,2,1]=>70
[7,3,6,1,2,5,4,8]=>[4,2,1,1]=>90
[5,4,7,1,3,2,6,8]=>[4,2,1,1]=>90
[5,7,4,8,2,1,3,6]=>[3,3,1,1]=>56
[4,6,8,2,5,1,3,7]=>[3,3,2]=>42
[7,4,6,2,1,5,3,8]=>[3,2,2,1]=>70
[1,2,6,3,8,5,7,4]=>[5,2,1]=>64
[1,5,2,6,8,4,7,3]=>[4,3,1]=>70
[5,7,2,3,8,1,4,6]=>[4,3,1]=>70
[6,4,7,5,8,1,2,3]=>[3,3,2]=>42
[7,4,8,5,1,6,3,2]=>[3,2,2,1]=>70
[5,8,3,6,1,7,4,2]=>[3,2,2,1]=>70
[8,6,4,2,1,7,5,3]=>[2,2,2,1,1]=>28
[7,4,2,1,5,8,6,3]=>[3,2,2,1]=>70
[7,6,4,1,8,5,2,3]=>[3,2,2,1]=>70
[1,6,4,8,7,5,3,2]=>[3,2,1,1,1]=>64
[6,3,1,2,8,4,7,5]=>[4,2,2]=>56
[7,5,1,3,2,8,6,4]=>[3,2,2,1]=>70
[4,7,1,2,5,8,6,3]=>[4,3,1]=>70
[6,8,4,1,2,7,5,3]=>[3,2,2,1]=>70
[7,5,8,1,2,6,4,3]=>[3,2,2,1]=>70
[7,4,8,1,6,3,5,2]=>[3,2,2,1]=>70
[5,8,2,1,7,3,6,4]=>[3,2,2,1]=>70
[3,6,1,8,2,4,7,5]=>[4,3,1]=>70
[1,3,8,7,6,2,5,4]=>[3,2,1,1,1]=>64
[5,4,1,8,7,3,2,6]=>[3,2,2,1]=>70
[3,5,1,8,7,2,4,6]=>[4,3,1]=>70
[4,6,1,8,3,7,2,5]=>[3,3,2]=>42
[4,7,1,2,8,6,3,5]=>[4,3,1]=>70
[5,8,4,1,7,6,2,3]=>[3,2,2,1]=>70
[7,6,8,1,5,4,2,3]=>[3,2,1,1,1]=>64
[8,6,1,7,5,4,3,2]=>[2,2,1,1,1,1]=>20
[7,1,5,8,6,4,3,2]=>[3,2,1,1,1]=>64
[5,1,8,7,3,6,4,2]=>[3,2,1,1,1]=>64
[4,1,8,7,6,2,5,3]=>[3,2,1,1,1]=>64
[3,1,8,7,6,5,2,4]=>[3,2,1,1,1]=>64
[1,6,4,5,2,3,7,8]=>[5,2,1]=>64
[1,7,4,5,2,3,6,8]=>[5,2,1]=>64
[1,7,3,5,2,4,6,8]=>[5,2,1]=>64
[1,6,3,5,2,4,7,8]=>[5,2,1]=>64
[1,6,3,4,2,5,7,8]=>[6,1,1]=>21
[1,7,3,4,2,5,6,8]=>[6,1,1]=>21
[1,8,6,7,3,4,2,5]=>[4,2,1,1]=>90
[1,8,5,7,3,4,2,6]=>[4,2,1,1]=>90
[1,7,3,4,2,6,5,8]=>[5,2,1]=>64
[1,5,2,8,4,7,3,6]=>[4,2,2]=>56
[1,4,2,8,5,7,3,6]=>[4,3,1]=>70
[1,7,3,5,2,6,4,8]=>[5,2,1]=>64
[1,8,4,7,3,5,2,6]=>[4,2,1,1]=>90
[1,7,3,6,2,5,4,8]=>[4,2,1,1]=>90
[1,7,3,6,2,4,5,8]=>[5,2,1]=>64
[1,7,4,6,2,3,5,8]=>[5,2,1]=>64
[1,8,5,6,2,3,4,7]=>[5,2,1]=>64
[1,8,5,6,2,4,3,7]=>[4,2,1,1]=>90
[1,3,2,8,5,6,4,7]=>[5,2,1]=>64
[1,4,2,8,5,6,3,7]=>[5,2,1]=>64
[1,5,2,8,4,6,3,7]=>[5,2,1]=>64
[1,6,2,8,4,5,3,7]=>[5,2,1]=>64
[9,10,3,4,5,6,7,8,1,2]=>[6,2,2]=>225
[11,12,1,2,3,4,5,6,7,8,9,10]=>[10,2]=>54
[8,6,4,7,2,1,3,5]=>[3,2,1,1,1]=>64
[1,6,4,7,2,8,3,5]=>[4,3,1]=>70
[1,4,7,3,5,8,2,6]=>[4,3,1]=>70
[8,4,6,2,3,5,1,7]=>[4,2,1,1]=>90
[5,4,8,2,3,6,1,7]=>[4,2,1,1]=>90
[7,4,8,5,2,3,1,6]=>[3,2,2,1]=>70
[3,8,6,2,4,5,1,7]=>[4,2,1,1]=>90
[4,8,6,2,3,5,1,7]=>[4,2,1,1]=>90
[1,7,5,3,4,8,2,6]=>[4,2,1,1]=>90
[1,7,6,4,8,2,3,5]=>[4,2,1,1]=>90
[5,8,7,4,1,2,3,6]=>[4,2,1,1]=>90
[6,8,5,3,4,1,2,7]=>[3,2,2,1]=>70
[6,8,3,7,2,1,4,5]=>[3,2,2,1]=>70
[8,5,1,6,3,7,2,4]=>[3,3,1,1]=>56
[6,1,3,7,4,8,2,5]=>[4,3,1]=>70
[4,1,7,3,5,8,2,6]=>[4,3,1]=>70
[7,1,6,4,8,2,3,5]=>[4,2,1,1]=>90
[1,8,5,7,2,3,4,6]=>[5,2,1]=>64
[6,1,5,8,2,3,4,7]=>[5,2,1]=>64
[5,1,7,3,8,2,4,6]=>[4,3,1]=>70
[6,1,5,7,8,2,3,4]=>[4,3,1]=>70
[7,4,8,6,1,2,3,5]=>[4,2,2]=>56
[3,8,7,5,1,2,4,6]=>[4,2,1,1]=>90
[3,7,6,1,2,4,5,8]=>[5,2,1]=>64
[4,7,6,1,2,3,5,8]=>[5,2,1]=>64
[1,6,5,8,2,3,4,7]=>[5,2,1]=>64
[6,5,8,4,1,2,3,7]=>[4,2,1,1]=>90
[8,5,7,4,1,2,3,6]=>[4,2,1,1]=>90
[1,5,7,4,8,2,3,6]=>[4,3,1]=>70
[7,6,4,8,2,1,3,5]=>[3,2,1,1,1]=>64
[7,6,2,3,8,1,4,5]=>[4,2,1,1]=>90
[7,4,8,5,1,6,2,3]=>[3,3,2]=>42
[8,6,2,3,1,7,4,5]=>[4,2,1,1]=>90
[8,6,4,1,2,7,3,5]=>[4,2,1,1]=>90
[1,7,2,8,6,3,4,5]=>[5,2,1]=>64
[7,6,1,3,8,2,4,5]=>[4,2,1,1]=>90
[7,5,8,1,3,6,2,4]=>[3,2,2,1]=>70
[5,4,1,8,2,3,6,7]=>[5,2,1]=>64
[1,4,8,7,2,3,5,6]=>[5,2,1]=>64
[1,5,8,7,2,3,4,6]=>[5,2,1]=>64
[6,5,1,8,2,3,4,7]=>[5,2,1]=>64
[5,7,1,3,8,2,4,6]=>[4,3,1]=>70
[7,6,8,1,5,2,3,4]=>[4,2,1,1]=>90
[7,1,5,8,6,2,3,4]=>[4,2,2]=>56
[6,1,8,2,7,3,4,5]=>[5,2,1]=>64
[4,1,8,7,2,3,5,6]=>[5,2,1]=>64
[5,1,8,7,2,3,4,6]=>[5,2,1]=>64
[1,8,7,6,4,5,3,2]=>[3,1,1,1,1,1]=>21
[1,8,7,3,6,5,4,2]=>[3,1,1,1,1,1]=>21
[6,4,2,7,5,8,3,1]=>[3,2,2,1]=>70
[2,4,1,7,5,8,3,6]=>[4,3,1]=>70
[7,1,4,6,5,8,2,3]=>[4,2,1,1]=>90
[7,1,4,6,3,8,2,5]=>[4,2,1,1]=>90
[7,1,4,6,5,3,2,8]=>[4,1,1,1,1]=>35
[6,4,2,7,5,3,8,1]=>[3,2,2,1]=>70
[3,4,7,1,6,8,2,5]=>[4,3,1]=>70
[3,4,1,7,8,6,2,5]=>[4,3,1]=>70
[6,4,2,7,5,3,1,8]=>[3,2,2,1]=>70
[4,8,3,2,5,6,1,7]=>[4,2,1,1]=>90
[4,8,7,3,5,1,2,6]=>[3,2,2,1]=>70
[3,4,7,2,6,5,8,1]=>[4,2,1,1]=>90
[4,8,3,1,2,6,7,5]=>[4,2,2]=>56
[5,4,7,3,6,2,8,1]=>[3,2,1,1,1]=>64
[6,4,3,7,5,1,8,2]=>[3,2,2,1]=>70
[3,8,7,4,1,5,2,6]=>[4,2,1,1]=>90
[5,8,3,2,1,6,4,7]=>[3,2,2,1]=>70
[5,4,7,3,6,2,1,8]=>[3,2,1,1,1]=>64
[7,4,3,8,5,2,1,6]=>[3,2,1,1,1]=>64
[3,2,5,8,6,1,4,7]=>[4,2,2]=>56
[5,3,7,8,4,1,2,6]=>[3,3,2]=>42
[5,2,3,8,4,1,6,7]=>[5,2,1]=>64
[8,6,5,3,7,2,4,1]=>[2,2,1,1,1,1]=>20
[7,5,4,3,8,2,6,1]=>[2,2,1,1,1,1]=>20
[6,4,5,3,8,2,7,1]=>[3,2,1,1,1]=>64
[7,5,6,3,8,2,4,1]=>[3,2,1,1,1]=>64
[8,5,7,3,4,2,6,1]=>[3,2,1,1,1]=>64
[6,5,8,3,4,2,7,1]=>[3,2,1,1,1]=>64
[7,5,8,3,4,2,6,1]=>[3,2,1,1,1]=>64
[7,5,8,4,6,2,3,1]=>[2,2,2,1,1]=>28
[7,4,8,3,6,2,5,1]=>[2,2,2,1,1]=>28
[6,4,8,3,5,2,7,1]=>[3,2,1,1,1]=>64
[5,4,8,3,7,2,6,1]=>[2,2,2,1,1]=>28
[6,5,8,4,7,2,3,1]=>[2,2,2,1,1]=>28
[5,4,6,3,8,2,7,1]=>[3,2,1,1,1]=>64
[5,3,6,2,4,7,8,1]=>[4,2,1,1]=>90
[4,2,1,5,8,6,3,7]=>[4,2,2]=>56
[4,2,1,5,8,7,6,3]=>[3,2,2,1]=>70
[4,3,1,7,5,8,6,2]=>[3,3,2]=>42
[6,7,3,1,4,8,2,5]=>[3,3,2]=>42
[3,2,1,8,5,4,6,7]=>[4,2,2]=>56
[5,2,7,1,8,4,3,6]=>[3,3,2]=>42
[4,3,1,6,7,8,5,2]=>[4,2,2]=>56
[5,2,6,1,8,7,4,3]=>[3,2,2,1]=>70
[5,2,6,1,8,3,4,7]=>[4,3,1]=>70
[4,2,1,6,8,3,7,5]=>[3,3,2]=>42
[4,2,1,7,8,6,3,5]=>[3,3,2]=>42
[3,2,1,8,6,4,7,5]=>[3,3,2]=>42
[3,2,1,8,6,4,5,7]=>[4,2,2]=>56
[3,2,1,8,4,6,5,7]=>[4,2,2]=>56
[3,2,1,8,4,6,7,5]=>[4,2,2]=>56
[3,2,1,8,4,7,6,5]=>[3,2,2,1]=>70
[3,2,1,8,7,4,6,5]=>[3,2,2,1]=>70
[5,2,7,1,8,3,4,6]=>[4,3,1]=>70
[4,2,1,7,8,3,5,6]=>[4,3,1]=>70
[3,2,1,8,4,5,7,6]=>[4,2,2]=>56
[7,5,2,8,6,3,4,1]=>[3,2,2,1]=>70
[7,4,8,6,2,5,3,1]=>[2,2,2,1,1]=>28
[7,3,8,6,2,4,5,1]=>[3,2,2,1]=>70
[7,3,8,5,2,4,6,1]=>[3,2,2,1]=>70
[7,3,8,4,5,6,2,1]=>[4,2,1,1]=>90
[6,3,8,2,4,5,1,7]=>[4,2,1,1]=>90
[6,3,7,8,2,4,1,5]=>[3,3,1,1]=>56
[5,6,7,3,8,2,4,1]=>[4,2,1,1]=>90
[5,3,8,2,4,6,7,1]=>[4,2,1,1]=>90
[6,4,8,2,7,5,1,3]=>[2,2,2,2]=>14
[5,6,3,7,8,2,4,1]=>[4,2,1,1]=>90
[6,3,7,2,5,8,4,1]=>[3,2,2,1]=>70
[5,3,6,8,2,4,7,1]=>[3,3,1,1]=>56
[5,3,6,7,8,2,4,1]=>[4,2,1,1]=>90
[3,6,4,2,1,5,8,7]=>[4,2,1,1]=>90
[3,5,8,6,4,2,1,7]=>[4,1,1,1,1]=>35
[5,8,6,3,4,2,1,7]=>[3,2,1,1,1]=>64
[5,6,3,4,2,1,8,7]=>[3,3,1,1]=>56
[6,3,4,2,1,5,8,7]=>[4,2,1,1]=>90
[5,6,4,2,1,3,8,7]=>[3,3,1,1]=>56
[2,5,4,1,7,8,6,3]=>[4,2,2]=>56
[2,7,8,5,4,1,6,3]=>[3,2,2,1]=>70
[2,8,5,4,1,6,3,7]=>[4,2,1,1]=>90
[2,6,3,8,5,4,1,7]=>[4,2,1,1]=>90
[2,8,6,3,5,4,1,7]=>[4,1,1,1,1]=>35
[5,8,6,4,2,1,3,7]=>[3,2,1,1,1]=>64
[4,2,1,5,7,8,6,3]=>[4,2,2]=>56
[2,7,8,6,3,5,4,1]=>[3,2,1,1,1]=>64
[4,3,8,5,7,6,2,1]=>[3,2,1,1,1]=>64
[7,6,2,1,8,4,3,5]=>[3,2,2,1]=>70
[2,1,8,5,6,4,3,7]=>[4,2,1,1]=>90
[4,2,1,8,5,6,3,7]=>[4,2,2]=>56
[8,4,2,1,5,6,3,7]=>[4,2,1,1]=>90
[2,5,6,3,8,4,1,7]=>[4,3,1]=>70
[6,3,4,2,1,8,5,7]=>[4,2,1,1]=>90
[3,7,8,5,6,4,2,1]=>[3,2,1,1,1]=>64
[3,8,5,6,4,2,1,7]=>[4,1,1,1,1]=>35
[3,6,4,2,1,8,5,7]=>[4,2,1,1]=>90
[3,8,6,4,2,1,5,7]=>[4,1,1,1,1]=>35
[3,7,8,6,4,2,1,5]=>[3,2,1,1,1]=>64
[8,5,3,7,6,2,4,1]=>[2,2,2,1,1]=>28
[7,6,2,4,1,8,5,3]=>[3,2,2,1]=>70
[8,5,4,1,7,6,2,3]=>[3,2,2,1]=>70
[7,6,2,3,8,5,4,1]=>[3,2,1,1,1]=>64
[2,1,7,8,6,4,3,5]=>[3,3,1,1]=>56
[2,1,6,4,3,7,8,5]=>[4,3,1]=>70
[6,4,2,1,3,7,8,5]=>[4,2,1,1]=>90
[6,3,7,8,4,2,1,5]=>[3,3,1,1]=>56
[7,8,4,2,1,6,3,5]=>[3,2,2,1]=>70
[5,7,6,2,3,8,4,1]=>[3,3,1,1]=>56
[2,6,1,8,4,3,7,5]=>[3,3,2]=>42
[2,6,1,7,5,8,4,3]=>[4,2,1,1]=>90
[8,4,2,3,7,5,6,1]=>[4,2,1,1]=>90
[8,5,7,6,2,1,4,3]=>[2,2,2,1,1]=>28
[4,8,5,7,6,2,1,3]=>[3,2,1,1,1]=>64
[4,7,6,2,1,3,8,5]=>[3,3,1,1]=>56
[7,5,6,1,8,4,2,3]=>[3,3,1,1]=>56
[2,7,5,8,4,3,6,1]=>[3,2,1,1,1]=>64
[2,8,4,3,6,1,7,5]=>[4,2,1,1]=>90
[6,4,7,8,3,2,1,5]=>[3,2,1,1,1]=>64
[7,6,5,4,3,2,8,1,9]=>[3,1,1,1,1,1,1]=>28
[6,4,3,7,5,2,1,8]=>[3,2,1,1,1]=>64
[6,3,7,2,5,4,1,8]=>[3,2,2,1]=>70
[8,4,2,6,3,1,7,5]=>[3,3,1,1]=>56
[1,5,3,7,4,2,8,6]=>[4,3,1]=>70
[1,6,7,3,4,2,8,5]=>[4,3,1]=>70
[8,6,5,2,3,1,7,4]=>[3,2,1,1,1]=>64
[1,7,6,3,4,2,8,5]=>[4,2,1,1]=>90
[1,8,6,3,2,5,7,4]=>[4,2,1,1]=>90
[8,7,5,2,1,4,6,3]=>[3,2,1,1,1]=>64
[7,8,5,2,1,4,6,3]=>[3,2,2,1]=>70
[6,8,5,2,3,1,7,4]=>[3,2,2,1]=>70
[5,8,6,2,3,1,7,4]=>[3,3,1,1]=>56
[4,8,2,6,3,1,7,5]=>[3,3,1,1]=>56
[3,2,8,6,4,1,7,5]=>[3,3,1,1]=>56
[3,2,1,7,5,4,8,6]=>[3,3,2]=>42
[4,1,3,7,5,2,8,6]=>[4,3,1]=>70
[5,1,7,3,4,2,8,6]=>[4,3,1]=>70
[7,1,6,3,2,5,8,4]=>[4,2,1,1]=>90
[1,2,7,4,3,6,8,5]=>[5,2,1]=>64
[6,1,8,2,4,5,7,3]=>[5,2,1]=>64
[5,1,8,3,2,6,7,4]=>[4,2,2]=>56
[3,2,8,7,1,5,6,4]=>[3,2,2,1]=>70
[4,8,2,7,1,5,6,3]=>[3,2,2,1]=>70
[5,8,7,2,1,4,6,3]=>[3,2,2,1]=>70
[6,8,7,1,3,4,5,2]=>[4,2,1,1]=>90
[7,8,6,1,3,4,5,2]=>[4,2,1,1]=>90
[1,7,8,2,4,5,6,3]=>[5,2,1]=>64
[8,6,7,1,3,4,5,2]=>[4,2,1,1]=>90
[7,6,8,1,3,4,5,2]=>[4,2,1,1]=>90
[6,5,8,2,3,1,7,4]=>[3,2,2,1]=>70
[1,6,8,3,2,5,7,4]=>[4,2,2]=>56
[1,5,3,8,2,6,7,4]=>[4,2,2]=>56
[8,4,2,7,1,5,6,3]=>[3,2,2,1]=>70
[7,4,2,8,1,5,6,3]=>[3,2,2,1]=>70
[6,4,2,8,3,1,7,5]=>[3,2,2,1]=>70
[5,4,2,3,8,1,7,6]=>[3,2,2,1]=>70
[4,5,2,3,1,6,8,7]=>[4,3,1]=>70
[7,4,2,1,3,6,8,5]=>[4,2,1,1]=>90
[8,4,2,1,3,6,7,5]=>[4,2,1,1]=>90
[1,5,3,2,4,7,8,6]=>[5,2,1]=>64
[8,5,1,3,2,6,7,4]=>[4,2,1,1]=>90
[5,6,1,3,4,2,8,7]=>[4,3,1]=>70
[4,6,2,1,5,3,8,7]=>[3,3,2]=>42
[4,7,2,1,3,6,8,5]=>[4,2,2]=>56
[5,7,1,3,2,6,8,4]=>[4,2,2]=>56
[6,7,1,2,4,5,8,3]=>[5,2,1]=>64
[8,6,1,2,4,5,7,3]=>[5,1,1,1]=>35
[1,8,2,3,5,6,7,4]=>[6,1,1]=>21
[8,7,1,2,4,5,6,3]=>[5,1,1,1]=>35
[7,8,1,2,4,5,6,3]=>[5,2,1]=>64
[5,8,1,3,2,6,7,4]=>[4,2,2]=>56
[4,8,2,1,3,6,7,5]=>[4,2,2]=>56
[4,1,3,2,5,7,8,6]=>[5,2,1]=>64
[5,1,2,4,3,7,8,6]=>[5,2,1]=>64
[5,4,8,1,2,3,7,6]=>[4,2,2]=>56
[1,4,7,6,3,2,5,8]=>[4,2,1,1]=>90
[4,8,3,2,7,6,1,5]=>[2,2,2,2]=>14
[4,3,8,2,7,1,6,5]=>[2,2,2,2]=>14
[4,1,8,7,3,2,5,6]=>[4,2,1,1]=>90
[4,7,8,1,2,5,3,6]=>[4,3,1]=>70
[3,1,7,8,4,2,5,6]=>[4,3,1]=>70
[3,7,2,4,8,6,1,5]=>[3,3,2]=>42
[1,3,6,4,7,2,5,8]=>[5,2,1]=>64
[4,7,1,5,8,2,3,6]=>[4,3,1]=>70
[8,6,5,2,7,3,4,1]=>[3,2,1,1,1]=>64
[7,4,8,5,6,3,2,1]=>[3,2,1,1,1]=>64
[3,4,6,7,8,5,1,2]=>[5,2,1]=>64
[7,8,3,1,4,2,5,6]=>[4,2,2]=>56
[5,1,6,3,8,7,2,4]=>[3,3,2]=>42
[6,1,8,7,4,3,2,5]=>[3,2,1,1,1]=>64
[3,1,6,4,8,2,7,5]=>[3,3,2]=>42
[7,8,4,1,6,3,2,5]=>[3,2,2,1]=>70
[4,1,6,3,8,7,2,5]=>[3,3,2]=>42
[5,4,6,1,3,8,2,7]=>[3,3,1,1]=>56
[6,5,8,1,4,3,2,7]=>[3,2,1,1,1]=>64
[1,3,5,7,4,6,8,2]=>[5,2,1]=>64
[1,3,5,4,7,2,6,8]=>[5,2,1]=>64
[1,3,5,4,7,8,2,6]=>[5,2,1]=>64
[1,3,5,7,4,8,2,6]=>[5,2,1]=>64
[1,3,5,7,4,8,6,2]=>[5,2,1]=>64
[1,3,5,7,8,4,2,6]=>[5,2,1]=>64
[1,6,3,2,7,4,8,5]=>[4,3,1]=>70
[3,5,1,6,2,8,7,4]=>[4,3,1]=>70
[1,3,7,2,5,4,8,6]=>[4,3,1]=>70
[1,3,7,5,2,4,8,6]=>[4,3,1]=>70
[2,5,7,4,3,8,1,6]=>[4,2,1,1]=>90
[3,2,6,7,8,1,5,4]=>[4,2,2]=>56
[3,5,2,7,8,4,1,6]=>[4,3,1]=>70
[1,5,7,4,8,3,2,6]=>[4,2,1,1]=>90
[3,5,2,6,8,4,7,1]=>[4,3,1]=>70
[4,6,3,7,2,8,5,1]=>[4,2,1,1]=>90
[1,4,7,3,8,6,2,5]=>[4,2,2]=>56
[5,3,7,8,2,4,1,6]=>[3,3,1,1]=>56
[2,4,7,8,3,1,5,6]=>[4,3,1]=>70
[3,2,4,8,1,5,6,7]=>[5,2,1]=>64
[3,2,4,6,8,1,5,7]=>[4,3,1]=>70
[7,2,4,8,3,1,5,6]=>[4,2,1,1]=>90
[5,3,8,7,2,4,1,6]=>[3,2,2,1]=>70
[2,4,8,7,3,1,5,6]=>[4,2,1,1]=>90
[8,7,4,6,2,3,1,5]=>[3,2,1,1,1]=>64
[5,6,8,7,2,3,1,4]=>[3,3,1,1]=>56
[5,7,6,8,2,3,1,4]=>[3,3,1,1]=>56
[4,7,6,8,2,3,1,5]=>[3,3,1,1]=>56
[8,6,4,7,2,3,1,5]=>[3,2,1,1,1]=>64
[2,3,7,8,4,1,6,5]=>[4,2,2]=>56
[3,7,4,8,2,5,1,6]=>[4,2,1,1]=>90
[2,3,7,4,1,6,8,5]=>[5,2,1]=>64
[7,5,8,6,2,3,1,4]=>[3,2,2,1]=>70
[7,1,6,4,2,3,8,5]=>[4,2,1,1]=>90
[3,1,7,6,4,2,8,5]=>[3,3,1,1]=>56
[6,8,7,5,2,3,1,4]=>[3,2,1,1,1]=>64
[4,3,6,1,5,8,7,2]=>[3,3,2]=>42
[4,3,6,5,1,8,7,2]=>[3,3,2]=>42
[4,6,3,5,1,8,7,2]=>[3,3,2]=>42
[4,6,3,1,5,8,7,2]=>[3,3,2]=>42
[4,1,6,5,3,8,7,2]=>[3,3,1,1]=>56
[4,6,1,5,3,8,7,2]=>[3,3,1,1]=>56
[2,6,5,3,1,8,7,4]=>[3,2,2,1]=>70
[2,6,5,1,8,7,3,4]=>[3,3,2]=>42
[2,6,5,8,1,7,3,4]=>[3,3,2]=>42
[2,6,5,8,1,3,7,4]=>[3,3,2]=>42
[2,6,5,8,3,1,7,4]=>[3,2,2,1]=>70
[2,6,5,3,8,1,7,4]=>[3,2,2,1]=>70
[4,6,1,5,8,3,7,2]=>[3,3,1,1]=>56
[4,1,6,5,8,3,7,2]=>[3,3,1,1]=>56
[1,4,6,5,8,3,7,2]=>[4,2,1,1]=>90
[4,1,6,5,8,7,3,2]=>[3,3,1,1]=>56
[2,6,5,3,8,7,1,4]=>[3,2,2,1]=>70
[6,4,3,8,7,1,5,2]=>[2,2,2,2]=>14
[6,4,8,3,7,1,5,2]=>[2,2,2,2]=>14
[2,6,8,5,3,7,1,4]=>[3,2,2,1]=>70
[4,6,8,1,5,7,3,2]=>[3,3,1,1]=>56
[4,6,1,8,5,7,3,2]=>[3,3,1,1]=>56
[4,1,6,8,5,7,3,2]=>[3,3,1,1]=>56
[1,4,6,8,5,7,3,2]=>[4,2,1,1]=>90
[1,4,6,8,5,3,7,2]=>[4,2,1,1]=>90
[4,6,1,8,5,3,7,2]=>[3,3,1,1]=>56
[2,6,8,5,3,1,7,4]=>[3,2,2,1]=>70
[2,6,8,5,1,7,3,4]=>[3,3,2]=>42
[4,6,8,3,5,1,7,2]=>[3,3,2]=>42
[4,6,8,3,1,5,7,2]=>[3,3,2]=>42
[4,6,3,1,8,5,7,2]=>[3,3,2]=>42
[4,6,3,8,1,5,7,2]=>[3,3,2]=>42
[4,6,3,8,5,7,1,2]=>[3,3,2]=>42
[4,3,6,8,1,5,7,2]=>[3,3,2]=>42
[4,3,6,1,8,5,7,2]=>[3,3,2]=>42
[4,3,1,6,8,5,7,2]=>[3,3,2]=>42
[4,1,3,6,8,7,5,2]=>[4,2,1,1]=>90
[4,3,6,1,8,7,5,2]=>[3,2,2,1]=>70
[4,3,6,8,1,7,5,2]=>[3,2,2,1]=>70
[6,5,2,8,7,3,1,4]=>[3,2,2,1]=>70
[6,5,2,8,7,1,3,4]=>[3,2,2,1]=>70
[6,2,5,8,7,1,3,4]=>[3,3,2]=>42
[6,2,5,8,7,3,1,4]=>[3,2,2,1]=>70
[4,6,3,8,1,7,5,2]=>[3,2,2,1]=>70
[4,6,3,1,8,7,5,2]=>[3,2,2,1]=>70
[4,1,6,3,8,7,5,2]=>[3,3,1,1]=>56
[1,4,6,3,8,7,5,2]=>[4,2,1,1]=>90
[4,1,6,8,3,7,5,2]=>[3,3,1,1]=>56
[4,6,1,8,3,7,5,2]=>[3,3,1,1]=>56
[4,6,8,1,3,7,5,2]=>[3,3,1,1]=>56
[6,2,8,5,7,3,1,4]=>[3,2,2,1]=>70
[6,2,8,5,7,1,3,4]=>[3,3,2]=>42
[2,4,8,7,1,5,3,6]=>[4,2,1,1]=>90
[4,2,8,7,5,3,1,6]=>[3,2,1,1,1]=>64
[6,4,1,8,7,5,3,2]=>[2,2,2,1,1]=>28
[6,1,4,8,7,5,3,2]=>[3,2,1,1,1]=>64
[1,6,4,8,7,3,5,2]=>[3,2,2,1]=>70
[6,4,1,8,7,3,5,2]=>[3,2,2,1]=>70
[4,2,8,7,5,1,3,6]=>[3,2,2,1]=>70
[2,4,8,7,3,5,1,6]=>[4,2,1,1]=>90
[2,3,4,5,6,8,9,7,1]=>[7,1,1]=>28
[2,3,4,7,8,5,6,1]=>[5,2,1]=>64
[2,3,7,1,4,8,6,5]=>[4,3,1]=>70
[2,6,1,3,7,8,5,4]=>[4,3,1]=>70
[2,3,4,5,6,7,10,1,8,9]=>[8,2]=>35
[3,4,5,6,7,8,9,10,11,2,1]=>[9,1,1]=>45
[1,5,3,2,6,4,7,8]=>[5,2,1]=>64
[1,5,3,2,6,7,4,8]=>[5,2,1]=>64
[1,7,3,2,8,5,4,6]=>[4,2,2]=>56
[1,3,2,7,5,4,8,6]=>[4,3,1]=>70
[6,5,2,4,3,7,1,8]=>[4,1,1,1,1]=>35
[6,4,2,5,3,7,1,8]=>[4,2,1,1]=>90
[5,4,7,6,2,3,1,8]=>[3,2,2,1]=>70
[3,6,4,8,2,1,5,7]=>[4,2,1,1]=>90
[1,6,2,8,5,3,4,7]=>[5,2,1]=>64
[4,6,2,3,7,5,1,8]=>[4,3,1]=>70
[4,7,2,3,6,5,1,8]=>[4,2,1,1]=>90
[4,7,2,3,5,6,1,8]=>[5,2,1]=>64
[5,3,2,7,4,6,1,8]=>[4,2,1,1]=>90
[5,3,2,6,4,7,1,8]=>[4,2,1,1]=>90
[4,6,2,3,5,7,1,8]=>[5,2,1]=>64
[3,5,2,1,6,8,4,7]=>[4,3,1]=>70
[1,5,2,6,8,4,3,7]=>[4,3,1]=>70
[1,5,7,2,8,4,3,6]=>[4,3,1]=>70
[3,5,2,1,8,6,4,7]=>[4,2,2]=>56
[3,6,8,4,2,1,5,7]=>[4,2,1,1]=>90
[4,3,2,6,1,8,5,7]=>[3,3,1,1]=>56
[1,5,8,2,7,4,3,6]=>[4,2,1,1]=>90
[1,7,2,3,4,8,6,5]=>[5,2,1]=>64
[6,8,2,3,4,1,7,5]=>[4,2,2]=>56
[4,1,8,2,3,5,7,6]=>[5,2,1]=>64
[2,3,1,8,4,5,7,6]=>[5,2,1]=>64
[7,3,2,1,4,5,8,6]=>[4,2,1,1]=>90
[7,8,1,4,3,5,2,6]=>[4,2,1,1]=>90
[7,1,2,3,4,6,8,5]=>[6,1,1]=>21
[6,1,2,3,4,8,7,5]=>[5,2,1]=>64
[1,8,2,3,4,7,6,5]=>[5,1,1,1]=>35
[8,1,2,3,4,6,7,5]=>[6,1,1]=>21
[2,8,1,3,5,4,7,6]=>[4,3,1]=>70
[8,7,1,4,3,5,2,6]=>[4,1,1,1,1]=>35
[8,3,2,1,4,5,7,6]=>[4,2,1,1]=>90
[3,8,2,1,5,6,4,7]=>[4,2,2]=>56
[3,8,2,1,6,5,4,7]=>[3,2,2,1]=>70
[1,7,8,3,5,4,2,6]=>[4,2,1,1]=>90
[7,4,1,8,3,5,2,6]=>[4,2,1,1]=>90
[8,4,1,7,3,5,2,6]=>[4,2,1,1]=>90
[3,8,4,6,2,1,5,7]=>[4,2,1,1]=>90
[8,4,2,5,3,1,6,7]=>[4,2,1,1]=>90
[8,5,2,4,3,1,6,7]=>[4,1,1,1,1]=>35
[8,3,2,5,4,1,6,7]=>[4,2,1,1]=>90
[4,3,2,5,1,8,6,7]=>[4,2,1,1]=>90
[3,5,2,4,1,8,6,7]=>[4,3,1]=>70
[2,4,7,8,1,5,3,6]=>[4,3,1]=>70
[1,8,7,3,5,4,2,6]=>[4,1,1,1,1]=>35
[5,1,8,2,7,4,3,6]=>[4,2,1,1]=>90
[5,1,7,2,8,4,3,6]=>[4,3,1]=>70
[6,1,2,8,5,3,4,7]=>[5,2,1]=>64
[6,3,2,1,8,4,5,7]=>[4,2,1,1]=>90
[7,3,2,8,4,5,1,6]=>[4,2,1,1]=>90
[2,7,8,4,3,5,1,6]=>[4,2,1,1]=>90
[7,1,8,3,5,4,2,6]=>[4,2,1,1]=>90
[7,8,2,3,4,6,1,5]=>[4,2,2]=>56
[6,7,1,3,4,8,2,5]=>[4,3,1]=>70
[6,8,1,3,4,7,2,5]=>[4,2,2]=>56
[1,7,2,3,4,6,8,5]=>[6,1,1]=>21
[1,6,2,3,4,8,7,5]=>[5,2,1]=>64
[7,6,2,3,4,1,8,5]=>[4,2,1,1]=>90
[8,6,2,3,4,1,7,5]=>[4,2,1,1]=>90
[8,1,7,3,5,4,2,6]=>[4,1,1,1,1]=>35
[8,3,2,7,4,5,1,6]=>[4,2,1,1]=>90
[6,7,2,3,4,1,8,5]=>[4,3,1]=>70
[7,6,2,3,4,8,1,5]=>[4,2,1,1]=>90
[8,6,2,3,4,7,1,5]=>[4,2,1,1]=>90
[6,3,4,8,7,5,1,2]=>[3,2,2,1]=>70
[4,8,7,3,5,6,1,2]=>[3,2,2,1]=>70
[5,8,4,2,1,6,7,3]=>[3,2,2,1]=>70
[7,8,4,1,2,6,5,3]=>[3,2,2,1]=>70
[4,8,1,5,2,7,6,3]=>[3,3,1,1]=>56
[3,8,7,6,2,4,1,5]=>[3,2,1,1,1]=>64
[2,8,7,6,4,1,3,5]=>[3,2,1,1,1]=>64
[2,8,7,6,3,1,4,5]=>[4,1,1,1,1]=>35
[1,8,7,6,2,4,3,5]=>[4,1,1,1,1]=>35
[1,8,7,6,3,4,2,5]=>[4,1,1,1,1]=>35
[2,1,7,3,6,5,8,4]=>[4,2,1,1]=>90
[3,1,7,2,6,5,8,4]=>[4,2,1,1]=>90
[6,1,2,8,5,7,3,4]=>[4,2,2]=>56
[6,2,1,8,5,7,3,4]=>[3,3,2]=>42
[6,1,3,8,5,2,7,4]=>[4,2,2]=>56
[2,3,7,1,6,8,5,4]=>[4,2,1,1]=>90
[3,2,6,7,5,8,1,4]=>[4,2,2]=>56
[3,8,7,6,2,1,5,4]=>[2,2,2,1,1]=>28
[4,8,7,6,2,1,3,5]=>[3,2,1,1,1]=>64
[4,8,7,6,1,3,2,5]=>[3,2,1,1,1]=>64
[5,1,4,6,8,2,3,7]=>[4,3,1]=>70
[1,7,6,3,5,4,8,2]=>[4,1,1,1,1]=>35
[4,3,7,2,6,5,1,8]=>[3,2,2,1]=>70
[3,4,6,1,5,7,2,8]=>[5,2,1]=>64
[1,6,8,5,7,3,4,2]=>[3,2,2,1]=>70
[2,4,1,5,8,6,3,7]=>[5,2,1]=>64
[4,6,1,2,5,8,3,7]=>[4,3,1]=>70
[5,6,7,2,1,4,8,3]=>[4,2,2]=>56
[7,8,6,5,1,2,4,3]=>[3,2,1,1,1]=>64
[1,3,6,5,7,8,2,4]=>[5,2,1]=>64
[7,4,8,5,3,1,6,2]=>[3,2,2,1]=>70
[6,8,5,2,4,1,7,3]=>[3,2,2,1]=>70
[2,3,1,6,8,5,7,4]=>[4,3,1]=>70
[7,3,2,5,1,4,8,6]=>[3,3,1,1]=>56
[7,1,4,2,3,6,8,5]=>[5,2,1]=>64
[1,5,8,3,4,6,7,2]=>[5,2,1]=>64
[8,3,1,2,4,7,6,5]=>[4,2,1,1]=>90
[2,3,8,1,6,5,4,7]=>[4,2,1,1]=>90
[8,1,4,7,2,5,3,6]=>[4,2,1,1]=>90
[3,5,2,4,1,7,8,6]=>[4,3,1]=>70
[3,4,7,8,6,2,1,5]=>[4,2,1,1]=>90
[3,4,8,6,2,7,1,5]=>[4,2,1,1]=>90
[5,8,2,1,6,7,3,4]=>[3,3,2]=>42
[5,7,2,8,6,4,3,1]=>[3,2,1,1,1]=>64
[6,1,2,7,5,3,8,4]=>[4,3,1]=>70
[7,3,2,8,6,4,1,5]=>[3,2,2,1]=>70
[2,7,8,4,6,3,1,5]=>[3,2,2,1]=>70
[1,4,5,7,2,6,8,3]=>[5,2,1]=>64
[7,3,5,2,6,1,8,4]=>[4,2,1,1]=>90
[8,5,2,3,6,1,7,4]=>[4,2,1,1]=>90
[8,1,6,3,5,7,2,4]=>[4,2,1,1]=>90
[2,8,6,4,3,7,1,5]=>[3,2,1,1,1]=>64
[8,3,2,6,4,7,1,5]=>[3,3,1,1]=>56
[2,3,8,7,6,5,1,4]=>[3,2,1,1,1]=>64
[1,5,8,7,3,2,6,4]=>[3,2,2,1]=>70
[4,5,8,7,3,2,1,6]=>[3,2,1,1,1]=>64
[2,6,8,1,7,5,4,3]=>[3,2,1,1,1]=>64
[3,6,8,4,7,2,1,5]=>[3,2,2,1]=>70
[3,2,8,4,7,6,1,5]=>[3,2,2,1]=>70
[1,5,8,4,2,7,6,3]=>[3,2,2,1]=>70
[1,5,8,2,3,7,6,4]=>[4,2,1,1]=>90
[2,1,8,4,3,7,6,5]=>[3,3,1,1]=>56
[5,6,8,4,1,2,7,3]=>[3,3,2]=>42
[1,6,8,4,3,2,7,5]=>[3,2,2,1]=>70
[5,6,8,4,3,2,1,7]=>[3,2,1,1,1]=>64
[7,1,2,8,6,5,4,3]=>[3,2,1,1,1]=>64
[7,1,4,8,6,2,5,3]=>[3,2,2,1]=>70
[7,3,1,8,6,2,5,4]=>[3,2,2,1]=>70
[3,2,5,8,7,6,1,4]=>[3,2,2,1]=>70
[3,2,4,8,7,6,1,5]=>[3,2,2,1]=>70
[3,1,4,8,7,2,6,5]=>[3,3,1,1]=>56
[1,6,4,8,2,7,5,3]=>[3,2,2,1]=>70
[7,6,1,4,8,2,5,3]=>[3,2,2,1]=>70
[7,6,3,4,8,2,1,5]=>[3,2,1,1,1]=>64
[7,2,5,3,8,6,1,4]=>[3,2,2,1]=>70
[7,2,1,4,8,6,5,3]=>[3,2,2,1]=>70
[7,2,1,3,8,6,5,4]=>[3,2,2,1]=>70
[7,2,3,4,8,6,1,5]=>[4,2,2]=>56
[1,6,5,4,8,2,7,3]=>[3,2,2,1]=>70
[7,6,2,4,3,8,1,5]=>[3,2,1,1,1]=>64
[7,1,5,2,3,8,6,4]=>[4,2,2]=>56
[2,6,5,4,3,8,1,7]=>[3,2,1,1,1]=>64
[2,7,8,3,5,4,1,6]=>[4,2,1,1]=>90
[4,7,1,2,8,5,3,6]=>[4,3,1]=>70
[4,8,1,2,7,5,3,6]=>[4,2,1,1]=>90
[2,7,1,3,6,8,4,5]=>[4,3,1]=>70
[6,7,3,2,8,1,4,5]=>[3,3,1,1]=>56
[8,7,4,2,1,5,3,6]=>[3,2,1,1,1]=>64
[2,7,1,3,6,5,4,8]=>[4,2,1,1]=>90
[8,4,3,1,5,6,7,2]=>[4,2,1,1]=>90
[6,4,8,2,1,5,3,7]=>[3,2,2,1]=>70
[6,8,3,2,5,1,4,7]=>[3,2,2,1]=>70
[6,1,4,2,7,5,3,8]=>[4,2,2]=>56
[5,4,3,7,1,6,8,2]=>[3,2,2,1]=>70
[8,2,7,6,5,4,1,3]=>[2,2,1,1,1,1]=>20
[7,2,8,6,5,4,3,1]=>[2,2,1,1,1,1]=>20
[3,2,8,7,6,5,1,4]=>[2,2,2,1,1]=>28
[4,8,7,6,5,3,1,2]=>[2,2,1,1,1,1]=>20
[7,8,6,1,5,4,3,2]=>[2,2,1,1,1,1]=>20
[8,9,1,7,6,5,4,3,2]=>[2,2,1,1,1,1,1]=>27
[7,3,8,6,5,4,2,1]=>[2,2,1,1,1,1]=>20
[4,8,5,7,6,3,2,1]=>[3,1,1,1,1,1]=>21
[8,5,6,1,3,2,4,7]=>[4,2,1,1]=>90
[8,6,1,5,3,2,4,7]=>[4,1,1,1,1]=>35
[7,8,1,5,3,2,4,6]=>[4,2,1,1]=>90
[8,1,7,5,3,2,4,6]=>[4,1,1,1,1]=>35
[8,6,1,4,5,2,3,7]=>[4,2,1,1]=>90
[8,6,3,1,5,2,4,7]=>[4,2,1,1]=>90
[8,4,6,1,5,2,3,7]=>[4,2,1,1]=>90
[8,6,2,1,5,4,3,7]=>[3,2,1,1,1]=>64
[8,5,2,6,1,4,3,7]=>[3,2,2,1]=>70
[8,5,2,1,7,4,3,6]=>[3,2,2,1]=>70
[7,8,2,1,5,4,3,6]=>[3,2,2,1]=>70
[7,8,3,1,5,2,4,6]=>[4,2,2]=>56
[8,2,7,5,1,3,4,6]=>[4,2,1,1]=>90
[8,4,1,7,5,2,3,6]=>[4,2,1,1]=>90
[8,2,7,1,5,4,3,6]=>[3,2,1,1,1]=>64
[8,2,6,1,7,4,3,5]=>[3,3,1,1]=>56
[8,1,7,4,3,2,6,5]=>[3,2,1,1,1]=>64
[8,1,5,7,3,2,6,4]=>[3,2,2,1]=>70
[5,7,8,1,3,2,6,4]=>[3,3,2]=>42
[8,2,6,1,5,7,3,4]=>[3,3,1,1]=>56
[5,8,1,6,7,2,3,4]=>[4,3,1]=>70
[5,7,6,1,8,2,3,4]=>[4,3,1]=>70
[6,7,2,5,1,8,3,4]=>[3,3,2]=>42
[7,5,1,6,8,2,3,4]=>[4,3,1]=>70
[6,5,7,1,8,2,3,4]=>[4,3,1]=>70
[6,7,3,8,1,2,4,5]=>[4,3,1]=>70
[7,5,4,1,8,2,3,6]=>[4,2,1,1]=>90
[7,6,1,4,8,2,3,5]=>[4,2,1,1]=>90
[8,1,6,4,7,2,3,5]=>[4,2,1,1]=>90
[7,5,8,1,3,2,4,6]=>[4,2,1,1]=>90
[7,8,4,1,3,2,5,6]=>[4,2,1,1]=>90
[8,3,7,4,1,2,5,6]=>[4,2,1,1]=>90
[8,5,1,7,3,2,4,6]=>[4,2,1,1]=>90
[6,8,1,7,3,2,4,5]=>[4,2,1,1]=>90
[7,1,8,4,3,6,2,5]=>[3,2,2,1]=>70
[7,3,1,8,6,4,2,5]=>[3,2,2,1]=>70
[8,3,1,7,4,6,2,5]=>[3,3,1,1]=>56
[8,4,5,1,7,2,3,6]=>[4,3,1]=>70
[5,6,8,1,7,2,3,4]=>[4,3,1]=>70
[6,5,8,1,2,7,3,4]=>[4,2,2]=>56
[7,3,1,8,5,6,2,4]=>[3,3,2]=>42
[6,2,7,8,3,1,5,4]=>[3,3,2]=>42
[5,8,1,7,3,2,6,4]=>[3,2,2,1]=>70
[8,4,1,7,3,2,6,5]=>[3,2,2,1]=>70
[8,3,4,7,1,2,6,5]=>[3,3,1,1]=>56
[8,2,7,4,1,3,6,5]=>[3,3,1,1]=>56
[7,4,8,2,1,3,6,5]=>[3,2,2,1]=>70
[7,4,3,8,1,2,6,5]=>[3,2,2,1]=>70
[8,2,3,6,7,1,5,4]=>[4,2,1,1]=>90
[7,8,5,2,3,6,4,1]=>[3,2,2,1]=>70
[6,8,5,2,3,4,7,1]=>[4,2,1,1]=>90
[3,5,2,6,8,1,4,7]=>[4,3,1]=>70
[3,5,2,4,6,8,1,7]=>[4,3,1]=>70
[2,4,5,7,3,6,8,1]=>[5,2,1]=>64
[2,4,5,3,6,8,1,7]=>[5,2,1]=>64
[5,2,4,6,8,1,3,7]=>[4,3,1]=>70
[5,1,3,4,6,8,2,7]=>[5,2,1]=>64
[4,3,5,2,6,8,1,7]=>[4,2,1,1]=>90
[4,3,5,7,2,8,1,6]=>[4,2,1,1]=>90
[4,3,5,7,2,6,8,1]=>[4,2,1,1]=>90
[4,6,3,7,2,5,8,1]=>[4,2,1,1]=>90
[4,6,3,1,7,8,2,5]=>[4,3,1]=>70
[4,3,5,1,7,8,2,6]=>[4,3,1]=>70
[5,7,1,3,4,8,2,6]=>[4,3,1]=>70
[5,7,1,3,4,6,8,2]=>[5,2,1]=>64
[4,5,7,1,3,6,8,2]=>[4,3,1]=>70
[4,3,6,7,1,5,8,2]=>[4,2,2]=>56
[4,6,3,5,1,7,8,2]=>[4,2,2]=>56
[4,6,3,5,7,2,8,1]=>[4,2,1,1]=>90
[3,5,6,4,1,7,8,2]=>[5,2,1]=>64
[3,1,5,6,7,4,8,2]=>[5,2,1]=>64
[5,1,6,7,3,4,8,2]=>[4,3,1]=>70
[6,4,7,1,3,5,8,2]=>[4,2,1,1]=>90
[1,6,7,3,4,5,8,2]=>[5,2,1]=>64
[2,6,7,4,5,8,1,3]=>[4,2,2]=>56
[2,6,7,4,8,1,3,5]=>[4,3,1]=>70
[5,3,6,1,2,7,8,4]=>[4,3,1]=>70
[3,5,2,6,1,7,8,4]=>[5,2,1]=>64
[3,5,2,6,7,4,8,1]=>[5,2,1]=>64
[5,2,3,6,7,4,8,1]=>[5,2,1]=>64
[5,2,3,6,1,7,8,4]=>[5,2,1]=>64
[5,2,6,1,3,7,8,4]=>[4,3,1]=>70
[4,2,6,7,3,5,8,1]=>[4,3,1]=>70
[6,3,7,2,4,5,8,1]=>[4,2,1,1]=>90
[3,5,7,2,8,1,4,6]=>[4,3,1]=>70
[3,7,2,4,8,1,5,6]=>[4,3,1]=>70
[7,2,4,6,8,1,3,5]=>[4,3,1]=>70
[7,1,3,4,6,8,2,5]=>[5,2,1]=>64
[3,7,2,4,6,8,1,5]=>[4,2,2]=>56
[3,5,7,2,6,8,1,4]=>[4,2,2]=>56
[6,3,7,2,5,8,1,4]=>[3,2,2,1]=>70
[6,3,5,7,2,8,1,4]=>[4,2,1,1]=>90
[6,3,5,7,2,4,8,1]=>[4,2,1,1]=>90
[6,2,4,5,7,3,8,1]=>[5,1,1,1]=>35
[6,2,4,5,1,7,8,3]=>[5,2,1]=>64
[4,7,1,2,5,6,8,3]=>[5,2,1]=>64
[2,6,7,5,8,1,3,4]=>[4,3,1]=>70
[4,6,7,1,2,5,8,3]=>[4,3,1]=>70
[5,6,2,4,7,3,8,1]=>[4,2,1,1]=>90
[5,4,2,6,7,3,8,1]=>[4,2,1,1]=>90
[5,4,2,6,1,7,8,3]=>[4,2,1,1]=>90
[1,5,4,6,2,7,8,3]=>[5,2,1]=>64
[5,6,4,1,2,7,8,3]=>[4,3,1]=>70
[6,4,5,1,2,7,8,3]=>[4,3,1]=>70
[6,3,5,1,7,8,2,4]=>[4,3,1]=>70
[6,5,7,2,8,1,3,4]=>[3,3,1,1]=>56
[6,5,7,1,3,4,8,2]=>[4,2,1,1]=>90
[5,6,4,7,1,3,8,2]=>[4,2,1,1]=>90
[5,4,6,3,1,7,8,2]=>[4,2,1,1]=>90
[7,5,3,2,4,8,1,6]=>[3,2,1,1,1]=>64
[8,4,5,2,6,1,3,7]=>[4,2,1,1]=>90
[8,5,4,2,1,6,3,7]=>[3,2,1,1,1]=>64
[8,5,3,4,1,6,2,7]=>[4,2,1,1]=>90
[8,4,5,3,1,6,2,7]=>[4,2,1,1]=>90
[7,5,4,2,1,8,3,6]=>[3,2,1,1,1]=>64
[7,5,4,2,1,6,8,3]=>[3,2,1,1,1]=>64
[7,4,5,3,1,6,8,2]=>[4,2,1,1]=>90
[7,4,3,5,6,1,8,2]=>[4,2,1,1]=>90
[5,6,3,7,4,1,8,2]=>[4,2,2]=>56
[5,6,7,3,1,4,8,2]=>[4,2,2]=>56
[6,7,3,4,1,5,8,2]=>[4,2,2]=>56
[6,7,4,2,1,5,8,3]=>[3,2,2,1]=>70
[5,6,7,3,1,8,2,4]=>[4,3,1]=>70
[5,6,3,7,8,1,2,4]=>[4,3,1]=>70
[5,6,3,7,2,4,8,1]=>[4,2,1,1]=>90
[5,6,7,2,3,8,1,4]=>[4,3,1]=>70
[7,4,5,2,8,1,3,6]=>[3,3,1,1]=>56
[6,7,3,2,4,8,1,5]=>[3,3,1,1]=>56
[7,6,4,2,1,3,8,5]=>[3,2,1,1,1]=>64
[7,6,3,4,1,2,8,5]=>[3,3,1,1]=>56
[7,6,3,2,4,1,8,5]=>[3,2,1,1,1]=>64
[6,7,3,2,5,1,8,4]=>[3,2,2,1]=>70
[6,5,3,2,7,8,1,4]=>[3,2,1,1,1]=>64
[6,5,3,2,7,4,8,1]=>[3,2,1,1,1]=>64
[6,4,5,2,7,3,8,1]=>[4,2,1,1]=>90
[6,4,5,2,7,8,1,3]=>[4,2,1,1]=>90
[7,4,5,2,6,1,8,3]=>[4,2,1,1]=>90
[7,4,5,6,1,2,8,3]=>[4,3,1]=>70
[7,5,6,2,1,3,8,4]=>[3,3,1,1]=>56
[6,7,3,5,1,2,8,4]=>[3,3,2]=>42
[5,6,7,4,1,2,8,3]=>[4,3,1]=>70
[5,6,7,2,4,1,8,3]=>[4,2,2]=>56
[5,6,4,2,7,8,1,3]=>[4,2,1,1]=>90
[6,5,7,2,1,8,3,4]=>[3,3,1,1]=>56
[6,5,7,2,1,4,8,3]=>[3,2,2,1]=>70
[5,4,6,7,3,1,8,2]=>[4,2,1,1]=>90
[3,7,8,5,6,1,4,2]=>[3,2,2,1]=>70
[1,7,8,5,6,3,4,2]=>[3,2,2,1]=>70
[1,7,5,8,6,3,4,2]=>[3,2,2,1]=>70
[3,7,5,8,6,1,4,2]=>[3,2,2,1]=>70
[5,7,3,8,6,4,1,2]=>[3,2,2,1]=>70
[1,5,7,8,6,3,4,2]=>[4,2,1,1]=>90
[1,5,7,8,3,6,4,2]=>[4,2,1,1]=>90
[5,3,7,8,1,6,4,2]=>[3,2,2,1]=>70
[7,8,1,5,6,3,4,2]=>[3,2,2,1]=>70
[7,1,8,5,6,3,4,2]=>[3,2,2,1]=>70
[7,1,5,8,6,3,4,2]=>[3,2,2,1]=>70
[5,1,7,8,3,6,4,2]=>[3,3,1,1]=>56
[3,1,7,8,5,6,4,2]=>[3,3,1,1]=>56
[1,3,7,8,5,6,4,2]=>[4,2,1,1]=>90
[3,1,7,5,8,6,4,2]=>[3,3,1,1]=>56
[5,1,7,3,8,6,4,2]=>[3,3,1,1]=>56
[7,1,5,3,8,6,4,2]=>[3,2,2,1]=>70
[7,1,5,8,3,6,4,2]=>[3,2,2,1]=>70
[5,3,7,1,8,6,4,2]=>[3,2,2,1]=>70
[3,5,7,1,8,6,4,2]=>[4,2,1,1]=>90
[1,7,5,3,8,6,4,2]=>[3,2,2,1]=>70
[5,7,3,1,8,6,4,2]=>[3,2,2,1]=>70
[5,7,3,8,6,1,4,2]=>[3,2,2,1]=>70
[1,7,5,8,3,6,4,2]=>[3,2,2,1]=>70
[1,7,8,5,3,6,4,2]=>[3,2,2,1]=>70
[5,7,8,6,3,1,4,2]=>[3,2,2,1]=>70
[5,7,8,1,6,3,4,2]=>[3,3,1,1]=>56
[3,7,8,1,5,6,4,2]=>[3,3,1,1]=>56
[1,7,8,3,5,6,4,2]=>[4,2,1,1]=>90
[1,7,3,8,5,6,4,2]=>[4,2,1,1]=>90
[3,7,1,8,5,6,4,2]=>[3,3,1,1]=>56
[5,7,1,8,3,6,4,2]=>[3,3,1,1]=>56
[5,7,1,8,6,3,4,2]=>[3,3,1,1]=>56
[7,5,1,8,6,3,4,2]=>[3,2,2,1]=>70
[7,5,8,1,6,3,4,2]=>[3,2,2,1]=>70
[7,8,5,1,6,3,4,2]=>[3,2,2,1]=>70
[7,5,8,1,3,6,4,2]=>[3,2,2,1]=>70
[7,5,1,8,3,6,4,2]=>[3,2,2,1]=>70
[7,5,1,3,8,6,4,2]=>[3,2,2,1]=>70
[5,7,1,3,8,6,4,2]=>[3,3,1,1]=>56
[3,7,1,5,8,6,4,2]=>[3,3,1,1]=>56
[1,7,3,5,8,6,4,2]=>[4,2,1,1]=>90
[1,5,3,7,8,6,4,2]=>[4,2,1,1]=>90
[3,5,1,7,8,6,4,2]=>[4,2,1,1]=>90
[5,3,1,7,8,6,4,2]=>[3,2,2,1]=>70
[7,3,1,5,8,6,4,2]=>[3,2,2,1]=>70
[7,3,1,8,5,6,4,2]=>[3,2,2,1]=>70
[7,8,3,1,5,6,4,2]=>[3,2,2,1]=>70
[7,1,8,3,5,6,4,2]=>[4,2,1,1]=>90
[7,1,3,8,5,6,4,2]=>[4,2,1,1]=>90
[7,1,3,5,8,6,4,2]=>[4,2,1,1]=>90
[3,1,5,7,8,6,4,2]=>[4,2,1,1]=>90
[5,7,3,4,8,6,1,2]=>[3,3,2]=>42
[5,7,3,4,8,1,6,2]=>[3,3,2]=>42
[5,7,3,4,1,8,6,2]=>[3,3,2]=>42
[5,7,3,1,4,6,2,8]=>[4,2,2]=>56
[5,7,3,1,4,8,6,2]=>[3,3,2]=>42
[5,3,7,4,1,2,6,8]=>[4,2,2]=>56
[5,3,7,1,4,2,6,8]=>[4,2,2]=>56
[5,3,7,1,4,2,8,6]=>[3,3,2]=>42
[3,7,5,1,2,8,6,4]=>[3,3,2]=>42
[7,3,5,8,1,2,6,4]=>[3,3,2]=>42
[3,7,5,1,2,6,8,4]=>[4,3,1]=>70
[6,1,4,3,5,2,8,7]=>[4,2,1,1]=>90
[2,5,7,3,8,4,1,6]=>[4,3,1]=>70
[5,4,7,8,6,1,3,2]=>[3,2,2,1]=>70
[7,5,6,2,8,3,1,4]=>[3,3,1,1]=>56
[4,7,2,5,8,3,1,6]=>[3,3,1,1]=>56
[6,2,4,5,1,3,8,7]=>[4,3,1]=>70
[5,1,4,6,3,2,8,7]=>[4,2,1,1]=>90
[3,5,6,2,4,1,8,7]=>[4,3,1]=>70
[3,8,6,7,5,4,1,2]=>[3,2,1,1,1]=>64
[6,2,7,8,3,4,1,5]=>[4,3,1]=>70
[2,5,3,4,8,1,7,6]=>[4,2,2]=>56
[8,7,1,2,5,3,4,6]=>[5,1,1,1]=>35
[5,1,8,2,3,4,7,6]=>[5,2,1]=>64
[5,4,7,6,2,8,1,3]=>[3,2,2,1]=>70
[3,7,8,1,5,4,6,2]=>[3,3,1,1]=>56
[7,1,3,4,6,8,5,2]=>[5,1,1,1]=>35
[8,3,6,5,7,1,4,2]=>[3,2,1,1,1]=>64
[5,8,7,1,4,6,2,3]=>[3,2,2,1]=>70
[4,7,6,1,8,3,5,2]=>[3,3,1,1]=>56
[4,7,2,6,3,8,5,1]=>[3,3,1,1]=>56
[2,1,8,4,6,7,3,5]=>[4,3,1]=>70
[4,7,8,6,3,1,2,5]=>[3,3,1,1]=>56
[3,8,1,5,6,7,2,4]=>[4,3,1]=>70
[6,7,2,4,8,5,3,1]=>[3,3,1,1]=>56
[2,8,3,6,7,5,1,4]=>[4,2,1,1]=>90
[8,2,1,7,6,3,5,4]=>[3,2,1,1,1]=>64
[3,2,4,5,8,1,7,6]=>[4,2,2]=>56
[7,4,6,3,2,1,8,5]=>[3,2,1,1,1]=>64
[4,7,3,2,1,8,6,5]=>[3,2,2,1]=>70
[6,4,7,5,2,3,8,1]=>[3,2,2,1]=>70
[6,4,8,1,7,3,2,5]=>[3,2,2,1]=>70
[4,8,7,2,3,1,5,6]=>[4,2,1,1]=>90
[4,2,3,1,8,7,5,6]=>[4,2,2]=>56
[7,6,8,1,3,5,2,4]=>[3,2,2,1]=>70
[6,7,5,2,3,1,8,4]=>[3,3,1,1]=>56
[4,7,2,6,5,1,8,3]=>[3,2,2,1]=>70
[6,4,2,1,8,5,7,3]=>[3,2,2,1]=>70
[7,2,1,5,6,8,4,3]=>[4,2,1,1]=>90
[8,7,2,6,4,1,5,3]=>[3,2,1,1,1]=>64
[6,7,8,2,5,3,1,4]=>[3,3,1,1]=>56
[2,1,7,3,6,8,5,4]=>[4,2,1,1]=>90
[2,1,5,7,8,4,6,3]=>[4,3,1]=>70
[2,5,7,8,3,6,1,4]=>[4,2,2]=>56
[6,4,1,5,7,2,8,3]=>[4,3,1]=>70
[7,4,8,1,2,5,6,3]=>[4,2,2]=>56
[4,2,7,8,6,3,5,1]=>[3,3,1,1]=>56
[6,1,7,4,3,2,8,5]=>[3,3,1,1]=>56
[6,8,3,4,2,1,7,5]=>[3,2,2,1]=>70
[4,2,6,1,5,7,8,3]=>[4,2,2]=>56
[2,4,6,7,3,5,8,1]=>[5,2,1]=>64
[6,5,8,3,7,4,1,2]=>[2,2,2,2]=>14
[7,1,4,8,3,5,6,2]=>[4,2,1,1]=>90
[6,8,7,5,3,4,1,2]=>[2,2,2,1,1]=>28
[4,8,6,3,1,5,7,2]=>[3,2,2,1]=>70
[3,4,8,2,5,7,6,1]=>[4,2,1,1]=>90
[2,5,7,4,8,6,1,3]=>[4,2,2]=>56
[2,6,4,8,7,5,1,3]=>[3,2,2,1]=>70
[6,3,7,2,8,5,1,4]=>[3,2,2,1]=>70
[3,6,2,5,8,7,1,4]=>[3,3,2]=>42
[5,2,8,4,7,6,1,3]=>[3,2,2,1]=>70
[7,2,4,8,6,5,1,3]=>[3,2,2,1]=>70
[6,2,4,8,7,5,1,3]=>[3,2,2,1]=>70
[2,4,5,8,7,6,1,3]=>[4,2,1,1]=>90
[4,2,7,3,8,1,6,5]=>[3,3,2]=>42
[6,1,3,8,7,2,5,4]=>[3,2,2,1]=>70
[3,1,5,6,2,8,7,4]=>[4,3,1]=>70
[4,1,5,2,8,7,6,3]=>[3,3,1,1]=>56
[4,1,5,3,2,8,7,6]=>[3,3,2]=>42
[3,4,5,1,8,7,6,2]=>[4,2,1,1]=>90
[1,4,5,2,8,7,6,3]=>[4,2,1,1]=>90
[1,6,4,2,8,7,5,3]=>[3,2,2,1]=>70
[7,4,2,5,1,8,6,3]=>[3,2,2,1]=>70
[4,6,2,7,5,1,8,3]=>[4,2,2]=>56
[1,5,3,6,2,8,7,4]=>[4,2,2]=>56
[1,5,8,3,2,7,6,4]=>[3,2,2,1]=>70
[4,5,8,2,1,7,6,3]=>[3,2,2,1]=>70
[3,6,2,5,1,4,8,7]=>[3,3,2]=>42
[2,4,8,7,1,3,6,5]=>[3,3,1,1]=>56
[1,3,8,2,4,7,6,5]=>[4,2,1,1]=>90
[7,5,1,2,8,6,4,3]=>[3,2,2,1]=>70
[1,5,2,3,8,7,6,4]=>[4,2,1,1]=>90
[4,5,1,2,8,7,6,3]=>[3,3,1,1]=>56
[6,4,1,2,8,7,5,3]=>[3,2,2,1]=>70
[5,2,8,1,3,7,6,4]=>[3,2,2,1]=>70
[4,7,5,6,8,3,1,2]=>[4,2,1,1]=>90
[8,6,4,7,5,3,1,2]=>[2,2,2,1,1]=>28
[7,5,2,6,4,1,3,8]=>[3,2,2,1]=>70
[1,6,3,7,5,8,4,2]=>[4,2,1,1]=>90
[1,3,7,4,5,8,6,2]=>[5,2,1]=>64
[7,2,6,3,4,1,5,8]=>[5,1,1,1]=>35
[8,3,7,4,6,5,1,2]=>[3,2,1,1,1]=>64
[6,8,4,7,5,3,1,2]=>[2,2,2,1,1]=>28
[4,8,7,5,6,3,1,2]=>[3,2,1,1,1]=>64
[3,8,7,6,4,5,1,2]=>[3,2,1,1,1]=>64
[1,6,5,2,8,3,7,4]=>[4,2,2]=>56
[8,6,5,2,1,4,3,7]=>[3,2,1,1,1]=>64
[2,7,6,3,1,4,5,8]=>[5,1,1,1]=>35
[6,8,5,3,2,1,4,7]=>[3,2,1,1,1]=>64
[2,7,6,4,5,1,3,8]=>[4,2,1,1]=>90
[5,7,2,6,4,1,3,8]=>[3,2,2,1]=>70
[6,1,3,7,5,8,4,2]=>[4,2,1,1]=>90
[4,1,7,3,6,8,5,2]=>[4,2,1,1]=>90
[8,1,6,4,3,7,5,2]=>[3,2,1,1,1]=>64
[2,1,7,4,8,6,3,5]=>[3,3,2]=>42
[1,8,6,3,7,5,4,2]=>[3,2,1,1,1]=>64
[1,8,2,7,3,6,5,4]=>[4,1,1,1,1]=>35
[2,1,3,8,4,7,5,6]=>[5,2,1]=>64
[8,1,2,7,4,3,6,5]=>[4,2,1,1]=>90
[5,3,1,6,8,4,7,2]=>[3,3,2]=>42
[6,2,8,7,1,4,3,5]=>[3,2,2,1]=>70
[8,7,2,1,5,4,3,6]=>[3,2,1,1,1]=>64
[8,2,3,1,4,6,5,7]=>[5,2,1]=>64
[2,4,8,3,1,5,6,7]=>[5,2,1]=>64
[3,4,2,7,1,5,6,8]=>[5,2,1]=>64
[4,7,3,8,2,1,5,6]=>[3,3,1,1]=>56
[5,2,7,3,1,4,6,8]=>[5,2,1]=>64
[8,3,7,2,1,5,4,6]=>[3,2,2,1]=>70
[1,3,7,2,8,4,6,5]=>[4,3,1]=>70
[1,4,2,5,8,6,7,3]=>[5,2,1]=>64
[6,5,3,8,2,1,4,7]=>[3,2,1,1,1]=>64
[2,6,4,5,7,1,3,8]=>[5,2,1]=>64
[5,4,6,2,7,1,3,8]=>[4,2,1,1]=>90
[7,6,3,1,8,4,5,2]=>[3,2,2,1]=>70
[7,6,2,1,8,5,3,4]=>[3,2,2,1]=>70
[1,7,5,8,6,4,3,2]=>[3,2,1,1,1]=>64
[6,5,1,2,8,3,7,4]=>[4,2,2]=>56
[8,6,1,4,3,7,5,2]=>[3,2,1,1,1]=>64
[6,8,4,1,3,7,5,2]=>[3,2,2,1]=>70
[6,5,7,1,3,8,4,2]=>[3,3,1,1]=>56
[5,8,3,1,7,4,6,2]=>[3,2,2,1]=>70
[8,3,1,7,5,4,6,2]=>[3,2,1,1,1]=>64
[1,3,8,7,4,6,5,2]=>[4,1,1,1,1]=>35
[1,2,8,7,6,3,5,4]=>[4,1,1,1,1]=>35
[8,2,1,7,6,4,3,5]=>[3,2,1,1,1]=>64
[2,3,1,8,7,4,5,6]=>[5,2,1]=>64
[2,4,1,8,5,7,3,6]=>[4,3,1]=>70
[5,8,2,1,7,6,3,4]=>[3,2,2,1]=>70
[6,2,7,1,8,5,3,4]=>[3,3,2]=>42
[8,7,1,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>7
[7,1,8,3,6,5,4,2]=>[3,2,1,1,1]=>64
[4,1,8,7,5,6,3,2]=>[3,2,1,1,1]=>64
[8,1,2,3,4,5,9,6,7]=>[7,2]=>27
[8,1,2,3,4,9,5,6,7]=>[7,2]=>27
[8,1,2,9,3,4,5,6,7]=>[7,2]=>27
[8,1,9,2,3,4,5,6,7]=>[7,2]=>27
[9,1,2,3,4,5,6,10,7,8]=>[8,2]=>35
[4,1,2,3,8,9,5,6,7]=>[6,3]=>48
[2,1,8,9,3,4,5,6,7]=>[6,3]=>48
[3,5,8,7,2,6,4,1]=>[3,2,1,1,1]=>64
[5,8,2,7,1,6,4,3]=>[2,2,2,1,1]=>28
[2,1,6,4,5,8,3,7]=>[4,3,1]=>70
[8,6,3,7,5,2,1,4]=>[2,2,2,1,1]=>28
[4,6,3,8,5,2,1,7]=>[3,3,1,1]=>56
[4,6,3,7,5,2,8,1]=>[4,2,1,1]=>90
[3,5,7,8,2,6,1,4]=>[4,2,2]=>56
[7,2,3,4,6,8,5,1]=>[5,1,1,1]=>35
[4,8,3,7,5,1,6,2]=>[3,2,2,1]=>70
[5,2,3,4,8,7,1,6]=>[4,2,2]=>56
[5,2,3,4,6,8,1,7]=>[5,2,1]=>64
[4,2,8,5,7,6,1,3]=>[3,2,2,1]=>70
[3,7,6,4,5,1,8,2]=>[4,2,1,1]=>90
[4,8,3,7,5,2,1,6]=>[3,2,1,1,1]=>64
[8,7,3,6,5,1,2,4]=>[3,2,1,1,1]=>64
[4,2,7,5,8,6,3,1]=>[3,3,1,1]=>56
[5,8,1,7,3,6,4,2]=>[3,2,1,1,1]=>64
[5,2,7,8,4,6,3,1]=>[3,3,1,1]=>56
[5,2,8,3,7,6,1,4]=>[3,2,2,1]=>70
[8,2,7,3,1,6,4,5]=>[4,2,1,1]=>90
[6,2,3,4,8,5,1,7]=>[5,2,1]=>64
[6,2,3,4,1,8,5,7]=>[5,2,1]=>64
[7,2,3,4,1,8,6,5]=>[4,2,2]=>56
[7,2,3,4,1,5,8,6]=>[5,2,1]=>64
[1,2,3,4,8,7,5,6]=>[6,1,1]=>21
[1,2,8,5,3,4,6,7]=>[6,1,1]=>21
[1,8,4,2,3,5,6,7]=>[6,1,1]=>21
[8,6,7,4,1,5,3,2]=>[2,2,2,1,1]=>28
[4,8,6,7,5,1,3,2]=>[3,2,1,1,1]=>64
[7,1,8,4,6,5,2,3]=>[3,2,2,1]=>70
[8,7,1,5,4,6,2,3]=>[3,2,1,1,1]=>64
[8,5,7,1,4,6,3,2]=>[3,2,1,1,1]=>64
[6,4,8,5,1,7,3,2]=>[3,2,2,1]=>70
[8,7,5,1,4,6,2,3]=>[3,2,1,1,1]=>64
[8,7,2,5,1,4,6,3]=>[3,2,1,1,1]=>64
[1,6,4,8,5,2,7,3]=>[4,2,2]=>56
[8,7,1,4,2,5,6,3]=>[4,2,1,1]=>90
[3,8,7,1,2,5,6,4]=>[4,2,1,1]=>90
[2,3,8,5,7,1,6,4]=>[4,2,1,1]=>90
[3,5,8,7,1,6,2,4]=>[3,3,1,1]=>56
[2,3,8,6,7,5,1,4]=>[4,2,1,1]=>90
[4,1,8,6,2,7,5,3]=>[3,3,1,1]=>56
[5,7,1,8,2,6,3,4]=>[4,3,1]=>70
[2,8,7,1,5,6,3,4]=>[3,3,1,1]=>56
[1,3,8,5,7,2,6,4]=>[4,2,1,1]=>90
[1,8,3,7,2,5,6,4]=>[4,2,1,1]=>90
[2,8,7,1,3,5,6,4]=>[4,2,1,1]=>90
[7,1,8,2,3,5,6,4]=>[5,2,1]=>64
[8,6,3,7,4,1,5,2]=>[3,2,2,1]=>70
[4,2,8,6,7,5,1,3]=>[3,2,2,1]=>70
[8,4,2,7,5,6,1,3]=>[3,2,2,1]=>70
[4,8,3,6,1,7,5,2]=>[3,2,2,1]=>70
[8,3,4,7,5,1,6,2]=>[4,2,1,1]=>90
[8,3,7,4,5,1,6,2]=>[4,2,1,1]=>90
[8,7,4,2,5,6,1,3]=>[3,2,1,1,1]=>64
[8,7,5,1,6,2,3,4]=>[4,2,1,1]=>90
[8,7,2,4,1,5,6,3]=>[4,2,1,1]=>90
[4,8,6,1,7,2,5,3]=>[3,3,1,1]=>56
[4,7,1,8,2,6,5,3]=>[3,3,1,1]=>56
[4,2,8,6,7,1,5,3]=>[3,2,2,1]=>70
[8,7,4,1,2,5,6,3]=>[4,2,1,1]=>90
[8,2,7,1,6,3,4,5]=>[4,2,1,1]=>90
[8,2,7,1,3,6,4,5]=>[4,2,1,1]=>90
[2,8,3,6,7,1,5,4]=>[4,2,1,1]=>90
[8,7,2,1,3,5,6,4]=>[4,2,1,1]=>90
[1,8,7,2,3,6,4,5]=>[5,1,1,1]=>35
[1,8,7,2,6,3,4,5]=>[5,1,1,1]=>35
[8,2,7,3,6,1,4,5]=>[4,2,1,1]=>90
[1,8,7,3,6,2,4,5]=>[4,2,1,1]=>90
[1,8,2,7,6,3,4,5]=>[5,1,1,1]=>35
[8,2,7,4,1,5,6,3]=>[4,2,1,1]=>90
[8,2,1,7,5,6,3,4]=>[3,3,1,1]=>56
[8,7,3,1,5,6,2,4]=>[3,3,1,1]=>56
[2,8,7,3,5,6,1,4]=>[4,2,1,1]=>90
[8,3,1,6,7,5,2,4]=>[3,3,1,1]=>56
[8,5,2,1,6,7,4,3]=>[3,2,2,1]=>70
[1,5,2,8,6,7,4,3]=>[4,2,1,1]=>90
[1,2,8,6,7,5,3,4]=>[4,2,1,1]=>90
[1,8,3,6,7,5,2,4]=>[4,2,1,1]=>90
[8,2,3,6,7,5,1,4]=>[4,2,1,1]=>90
[8,3,7,2,5,6,1,4]=>[3,2,2,1]=>70
[8,1,3,7,5,6,2,4]=>[4,2,1,1]=>90
[8,4,1,2,7,5,6,3]=>[4,2,1,1]=>90
[8,1,4,2,6,7,5,3]=>[4,2,1,1]=>90
[1,2,8,6,7,3,5,4]=>[4,2,1,1]=>90
[8,1,2,7,3,6,4,5]=>[5,1,1,1]=>35
[8,1,7,3,6,2,4,5]=>[4,2,1,1]=>90
[8,1,7,2,6,3,4,5]=>[5,1,1,1]=>35
[8,1,7,2,3,6,4,5]=>[5,1,1,1]=>35
[8,1,3,7,2,5,6,4]=>[4,2,1,1]=>90
[1,8,3,6,7,2,5,4]=>[4,2,1,1]=>90
[1,7,8,2,3,6,5,4]=>[4,2,1,1]=>90
[8,3,7,1,2,5,6,4]=>[4,2,1,1]=>90
[8,7,1,2,3,6,4,5]=>[5,1,1,1]=>35
[3,1,8,5,7,4,2,6]=>[3,3,1,1]=>56
[8,3,5,7,4,2,6,1]=>[3,2,1,1,1]=>64
[8,3,6,2,4,5,7,1]=>[4,2,1,1]=>90
[8,4,2,7,6,1,3,5]=>[3,2,2,1]=>70
[4,8,1,7,6,3,2,5]=>[3,2,1,1,1]=>64
[3,7,1,8,6,2,5,4]=>[3,3,1,1]=>56
[3,1,6,8,7,5,2,4]=>[3,3,1,1]=>56
[6,3,8,7,5,2,4,1]=>[2,2,2,1,1]=>28
[7,8,5,2,1,4,3,6]=>[3,2,2,1]=>70
[7,5,2,3,1,4,8,6]=>[4,2,1,1]=>90
[5,7,1,3,4,6,2,8]=>[5,2,1]=>64
[8,4,6,2,1,3,7,5]=>[3,3,1,1]=>56
[5,4,8,7,3,1,2,6]=>[3,2,2,1]=>70
[6,8,3,7,2,5,4,1]=>[2,2,2,1,1]=>28
[5,4,6,8,2,3,7,1]=>[3,3,1,1]=>56
[5,7,4,2,8,3,6,1]=>[3,3,1,1]=>56
[6,4,7,2,1,8,3,5]=>[3,3,1,1]=>56
[6,5,3,4,1,2,8,7]=>[3,3,1,1]=>56
[6,8,5,4,1,3,2,7]=>[3,2,1,1,1]=>64
[9,6,7,5,4,3,2,1,8]=>[3,1,1,1,1,1,1]=>28
[6,4,2,8,1,5,7,3]=>[3,2,2,1]=>70
[6,3,7,8,2,5,1,4]=>[3,2,2,1]=>70
[7,3,5,6,4,2,1,8]=>[4,1,1,1,1]=>35
[4,8,6,7,5,3,2,1]=>[3,1,1,1,1,1]=>21
[6,3,8,7,2,4,1,5]=>[3,2,2,1]=>70
[5,3,8,7,2,6,4,1]=>[2,2,2,1,1]=>28
[5,3,7,8,6,2,4,1]=>[3,2,2,1]=>70
[6,5,2,4,3,7,8,1]=>[4,1,1,1,1]=>35
[5,4,6,2,8,7,1,3]=>[3,2,2,1]=>70
[5,7,3,8,6,2,4,1]=>[3,2,2,1]=>70
[5,4,6,8,2,7,1,3]=>[3,2,2,1]=>70
[5,7,8,2,6,4,1,3]=>[3,2,2,1]=>70
[1,7,4,8,6,2,3,5]=>[4,2,2]=>56
[3,6,2,5,7,8,1,4]=>[4,2,2]=>56
[5,2,7,4,6,8,1,3]=>[4,2,2]=>56
[5,3,6,7,1,8,4,2]=>[4,2,2]=>56
[4,2,5,6,7,1,8,3]=>[5,2,1]=>64
[8,1,3,6,7,2,4,5]=>[4,3,1]=>70
[8,1,4,2,7,5,3,6]=>[4,2,1,1]=>90
[1,7,5,2,8,6,3,4]=>[4,2,2]=>56
[1,5,8,4,2,6,3,7]=>[4,2,2]=>56
[3,5,7,4,1,6,8,2]=>[4,2,2]=>56
[3,5,7,1,2,6,4,8]=>[4,3,1]=>70
[4,5,1,8,2,3,7,6]=>[4,3,1]=>70
[4,7,1,8,2,6,3,5]=>[4,3,1]=>70
[7,5,1,2,3,8,6,4]=>[4,2,2]=>56
[6,7,1,3,2,5,4,8]=>[4,2,2]=>56
[7,8,2,4,3,5,1,6]=>[4,2,1,1]=>90
[7,8,2,4,1,5,3,6]=>[4,2,2]=>56
[6,7,2,4,3,5,1,8]=>[4,2,1,1]=>90
[2,5,1,6,4,7,3,8]=>[5,2,1]=>64
[3,6,5,7,4,8,1,2]=>[4,2,1,1]=>90
[6,7,5,8,1,3,2,4]=>[3,3,1,1]=>56
[4,5,1,3,2,7,6,8]=>[4,3,1]=>70
[4,6,5,7,1,3,2,8]=>[4,2,1,1]=>90
[4,6,1,3,2,7,5,8]=>[4,3,1]=>70
[4,5,2,3,1,7,6,8]=>[4,3,1]=>70
[4,6,5,7,3,8,1,2]=>[4,2,1,1]=>90
[3,4,2,6,1,7,5,8]=>[5,2,1]=>64
[3,6,2,7,5,4,8,1]=>[4,2,1,1]=>90
[4,6,1,7,3,8,2,5]=>[4,3,1]=>70
[3,5,2,7,6,4,8,1]=>[4,2,1,1]=>90
[1,5,7,2,8,3,6,4]=>[4,3,1]=>70
[2,5,7,3,1,8,4,6]=>[4,3,1]=>70
[2,1,5,6,8,4,3,7]=>[4,3,1]=>70
[1,3,7,2,8,5,4,6]=>[4,3,1]=>70
[4,6,2,7,1,8,3,5]=>[4,3,1]=>70
[2,1,5,6,8,4,7,3]=>[4,3,1]=>70
[2,1,5,6,8,7,3,4]=>[4,3,1]=>70
[3,6,5,2,7,8,4,1]=>[4,2,1,1]=>90
[6,2,4,7,5,8,3,1]=>[4,2,1,1]=>90
[1,5,7,8,4,2,6,3]=>[4,2,2]=>56
[3,7,4,1,8,6,2,5]=>[3,3,2]=>42
[4,2,5,7,3,1,8,6]=>[4,3,1]=>70
[4,5,6,1,8,7,3,2]=>[4,2,1,1]=>90
[4,6,3,2,1,7,5,8]=>[4,2,1,1]=>90
[4,3,5,7,6,1,8,2]=>[4,2,2]=>56
[4,3,2,6,1,7,5,8]=>[4,2,1,1]=>90
[5,3,2,1,6,4,7,8]=>[4,2,1,1]=>90
[5,3,1,6,2,7,4,8]=>[4,3,1]=>70
[5,1,6,3,2,7,4,8]=>[4,3,1]=>70
[4,6,1,7,5,3,2,8]=>[4,2,1,1]=>90
[5,3,6,4,2,1,7,8]=>[4,2,1,1]=>90
[5,3,2,6,4,1,7,8]=>[4,2,1,1]=>90
[5,2,1,6,3,7,4,8]=>[4,3,1]=>70
[5,2,6,3,1,7,4,8]=>[4,3,1]=>70
[4,2,6,3,1,7,8,5]=>[4,3,1]=>70
[3,5,7,2,8,6,4,1]=>[4,2,1,1]=>90
[2,4,7,1,3,6,5,8]=>[4,3,1]=>70
[2,6,1,3,7,5,4,8]=>[4,3,1]=>70
[5,1,6,2,7,4,3,8]=>[4,3,1]=>70
[5,2,1,6,4,3,7,8]=>[4,2,2]=>56
[5,4,2,1,6,3,7,8]=>[4,2,1,1]=>90
[5,4,1,6,2,7,3,8]=>[4,3,1]=>70
[5,1,6,4,2,7,3,8]=>[4,3,1]=>70
[2,6,1,5,4,3,7,8]=>[4,2,1,1]=>90
[3,1,6,2,5,4,7,8]=>[5,2,1]=>64
[5,1,6,4,3,2,7,8]=>[4,2,1,1]=>90
[5,4,1,6,3,2,7,8]=>[4,2,1,1]=>90
[5,4,3,1,6,2,7,8]=>[4,2,1,1]=>90
[3,8,2,6,5,4,1,7]=>[3,2,1,1,1]=>64
[7,3,2,1,5,4,6,8]=>[4,2,1,1]=>90
[5,2,7,6,8,4,1,3]=>[3,2,2,1]=>70
[3,8,7,2,5,4,1,6]=>[3,2,1,1,1]=>64
[3,2,9,8,7,6,5,4,1,10]=>[3,2,1,1,1,1,1]=>160
[7,4,2,1,5,6,3,8]=>[4,2,1,1]=>90
[7,2,8,6,5,1,3,4]=>[3,2,2,1]=>70
[4,3,7,2,5,6,1,8]=>[4,2,1,1]=>90
[6,7,1,4,3,2,5,8]=>[4,2,1,1]=>90
[3,4,2,6,7,1,5,8]=>[5,2,1]=>64
[3,7,1,6,5,2,4,8]=>[4,2,1,1]=>90
[3,5,6,2,4,7,1,8]=>[5,2,1]=>64
[3,5,8,7,2,4,6,1]=>[3,3,1,1]=>56
[1,7,8,2,5,4,3,6]=>[4,2,1,1]=>90
[8,7,2,5,4,3,6,1]=>[3,1,1,1,1,1]=>21
[2,5,6,4,7,1,3,8]=>[5,2,1]=>64
[4,7,1,6,3,5,2,8]=>[4,2,1,1]=>90
[4,5,3,8,7,2,6,1]=>[3,2,2,1]=>70
[1,4,5,3,7,8,2,6]=>[5,2,1]=>64
[1,4,8,2,7,6,3,5]=>[4,2,1,1]=>90
[4,7,3,5,1,8,6,2]=>[3,3,2]=>42
[8,7,3,6,1,5,4,2]=>[2,2,1,1,1,1]=>20
[2,5,8,7,4,6,1,3]=>[3,2,2,1]=>70
[5,4,2,1,7,8,3,6]=>[3,3,1,1]=>56
[4,7,8,3,5,2,1,6]=>[3,3,1,1]=>56
[4,7,6,2,1,8,3,5]=>[3,3,1,1]=>56
[1,4,6,7,3,5,8,2]=>[5,2,1]=>64
[8,3,6,2,1,7,5,4]=>[3,2,2,1]=>70
[8,3,7,6,4,2,1,5]=>[3,1,1,1,1,1]=>21
[2,3,1,8,4,7,6,5]=>[4,2,1,1]=>90
[2,7,4,8,6,5,1,3]=>[3,2,2,1]=>70
[8,6,5,1,4,7,3,2]=>[3,1,1,1,1,1]=>21
[8,5,4,1,7,3,6,2]=>[3,2,1,1,1]=>64
[6,3,7,2,8,5,4,1]=>[3,2,2,1]=>70
[1,6,3,8,2,7,5,4]=>[3,2,2,1]=>70
[1,7,5,3,8,2,6,4]=>[3,2,2,1]=>70
[6,2,7,4,1,8,5,3]=>[3,3,2]=>42
[8,6,3,2,7,5,1,4]=>[2,2,2,1,1]=>28
[2,7,5,1,3,8,6,4]=>[3,3,2]=>42
[1,7,6,4,3,8,2,5]=>[3,2,1,1,1]=>64
[3,7,2,4,8,6,5,1]=>[3,3,1,1]=>56
[3,4,2,8,7,6,1,5]=>[3,2,2,1]=>70
[5,1,4,3,2,7,8,6]=>[4,2,1,1]=>90
[3,7,8,5,2,4,1,6]=>[3,3,1,1]=>56
[3,7,6,2,4,1,8,5]=>[3,3,1,1]=>56
[1,6,8,2,5,7,4,3]=>[4,2,1,1]=>90
[6,7,2,5,8,4,3,1]=>[3,2,1,1,1]=>64
[5,2,7,8,4,3,1,6]=>[3,3,1,1]=>56
[5,3,1,7,8,4,2,6]=>[3,3,2]=>42
[2,7,6,4,1,3,8,5]=>[3,3,1,1]=>56
[4,1,7,6,3,2,8,5]=>[3,3,1,1]=>56
[8,4,2,7,6,3,1,5]=>[3,2,1,1,1]=>64
[6,3,1,7,5,2,8,4]=>[3,3,2]=>42
[6,2,7,5,3,1,8,4]=>[3,3,1,1]=>56
[1,5,8,2,7,4,6,3]=>[4,2,1,1]=>90
[5,7,2,8,4,6,3,1]=>[3,3,1,1]=>56
[5,7,3,1,8,4,6,2]=>[3,3,2]=>42
[8,4,7,3,1,6,5,2]=>[2,2,2,1,1]=>28
[2,6,8,5,7,4,1,3]=>[3,2,2,1]=>70
[6,5,2,1,7,4,8,3]=>[3,2,2,1]=>70
[5,7,4,6,2,1,8,3]=>[3,2,2,1]=>70
[5,6,4,8,3,7,2,1]=>[3,2,1,1,1]=>64
[6,7,1,8,3,4,2,5]=>[4,3,1]=>70
[5,6,2,7,1,8,3,4]=>[4,3,1]=>70
[1,8,2,7,4,5,3,6]=>[5,1,1,1]=>35
[2,3,1,8,5,6,4,7]=>[5,2,1]=>64
[4,6,2,7,1,5,3,8]=>[4,2,2]=>56
[4,7,1,6,2,5,3,8]=>[4,2,1,1]=>90
[4,7,1,5,3,6,2,8]=>[4,2,1,1]=>90
[1,8,5,6,3,4,2,7]=>[4,2,1,1]=>90
[4,6,5,8,1,7,2,3]=>[3,3,2]=>42
[3,5,4,6,2,8,1,7]=>[4,2,1,1]=>90
[4,7,2,3,1,8,5,6]=>[4,3,1]=>70
[2,4,3,8,1,7,5,6]=>[4,2,2]=>56
[4,5,7,8,2,6,3,1]=>[4,2,1,1]=>90
[5,2,6,8,3,7,4,1]=>[3,3,1,1]=>56
[3,1,6,8,7,4,5,2]=>[3,3,1,1]=>56
[6,1,4,8,7,2,5,3]=>[3,2,2,1]=>70
[6,1,8,4,7,3,5,2]=>[3,2,2,1]=>70
[4,6,7,8,2,5,3,1]=>[4,2,1,1]=>90
[7,4,5,2,8,6,3,1]=>[3,2,2,1]=>70
[6,8,2,5,3,7,4,1]=>[3,2,2,1]=>70
[3,4,7,5,8,6,2,1]=>[4,2,1,1]=>90
[2,7,5,3,8,6,4,1]=>[3,2,2,1]=>70
[5,6,2,8,3,7,4,1]=>[3,3,1,1]=>56
[1,5,8,2,7,3,6,4]=>[4,2,1,1]=>90
[6,8,5,3,7,2,4,1]=>[2,2,2,1,1]=>28
[6,8,5,2,3,7,4,1]=>[3,2,2,1]=>70
[7,5,3,8,2,6,4,1]=>[2,2,2,1,1]=>28
[7,5,2,3,8,6,4,1]=>[3,2,2,1]=>70
[6,7,3,4,8,5,2,1]=>[3,3,1,1]=>56
[7,4,2,5,8,6,3,1]=>[3,2,2,1]=>70
[7,4,5,8,1,6,3,2]=>[3,2,2,1]=>70
[6,3,4,7,8,5,2,1]=>[4,2,1,1]=>90
[6,1,2,7,4,5,8,3]=>[5,2,1]=>64
[2,5,8,3,4,1,6,7]=>[5,2,1]=>64
[11,1,2,3,4,5,6,7,8,9,12,10]=>[10,2]=>54
[5,6,2,7,4,3,8,1]=>[4,2,1,1]=>90
[4,6,7,3,2,5,8,1]=>[4,2,1,1]=>90
[2,6,7,3,8,5,4,1]=>[4,2,1,1]=>90
[2,5,7,8,4,3,6,1]=>[4,2,1,1]=>90
[2,12,1,3,4,5,6,7,8,9,10,11]=>[10,2]=>54
[3,4,5,7,8,6,1,2]=>[5,2,1]=>64
[3,4,5,7,6,8,1,2]=>[5,2,1]=>64
[3,6,7,4,8,5,1,2]=>[4,2,2]=>56
[3,4,5,6,8,7,1,2]=>[5,2,1]=>64
[1,2,5,8,3,6,4,7]=>[5,2,1]=>64
[1,2,5,8,3,4,7,6]=>[5,2,1]=>64
[7,8,1,2,3,5,4,6]=>[5,2,1]=>64
[1,2,5,7,3,6,8,4]=>[5,2,1]=>64
[1,6,8,2,3,7,4,5]=>[5,2,1]=>64
[1,4,5,7,6,2,8,3]=>[5,2,1]=>64
[7,8,1,2,3,4,6,5]=>[5,2,1]=>64
[7,8,1,2,3,6,4,5]=>[5,2,1]=>64
[4,2,1,6,5,3,8,7]=>[3,3,2]=>42
[6,8,2,1,4,3,7,5]=>[3,3,2]=>42
[8,6,2,4,3,1,5,7]=>[4,1,1,1,1]=>35
[4,6,5,2,8,3,7,1]=>[3,3,1,1]=>56
[8,4,2,6,3,5,1,7]=>[4,2,1,1]=>90
[4,2,6,3,5,8,7,1]=>[4,3,1]=>70
[6,2,4,3,8,5,7,1]=>[4,2,1,1]=>90
[8,2,4,3,6,5,1,7]=>[4,2,1,1]=>90
[6,4,8,5,2,1,7,3]=>[3,2,2,1]=>70
[4,6,8,7,5,2,1,3]=>[3,2,1,1,1]=>64
[2,6,8,7,4,5,1,3]=>[3,2,2,1]=>70
[4,2,8,6,5,7,1,3]=>[3,2,2,1]=>70
[8,2,6,4,5,1,3,7]=>[4,2,1,1]=>90
[2,8,5,3,1,4,6,7]=>[5,1,1,1]=>35
[2,7,4,8,3,5,1,6]=>[4,2,1,1]=>90
[2,7,4,8,3,5,6,1]=>[4,2,1,1]=>90
[7,2,8,4,3,5,1,6]=>[4,2,1,1]=>90
[8,4,2,1,5,3,6,7]=>[4,2,1,1]=>90
[8,5,1,4,2,3,6,7]=>[5,1,1,1]=>35
[8,4,1,5,3,2,6,7]=>[4,2,1,1]=>90
[6,7,3,8,4,2,5,1]=>[3,3,1,1]=>56
[6,7,3,8,4,2,1,5]=>[3,3,1,1]=>56
[7,1,8,4,3,5,2,6]=>[4,2,1,1]=>90
[1,7,8,4,3,5,2,6]=>[4,2,1,1]=>90
[7,1,4,8,3,5,2,6]=>[4,2,1,1]=>90
[7,4,8,1,5,6,2,3]=>[3,3,2]=>42
[7,1,8,4,3,5,6,2]=>[4,2,1,1]=>90
[6,7,3,1,8,4,5,2]=>[3,3,2]=>42
[6,7,3,8,4,5,2,1]=>[3,3,1,1]=>56
[6,7,1,4,8,3,5,2]=>[3,3,1,1]=>56
[6,7,4,1,3,8,2,5]=>[3,3,1,1]=>56
[1,6,7,8,4,3,2,5]=>[4,2,1,1]=>90
[7,2,1,8,4,5,3,6]=>[4,2,2]=>56
[6,2,7,1,8,4,3,5]=>[3,3,2]=>42
[6,2,7,8,4,3,1,5]=>[3,3,1,1]=>56
[6,2,7,8,4,3,5,1]=>[3,3,1,1]=>56
[2,6,7,4,8,3,5,1]=>[4,2,1,1]=>90
[2,6,7,4,8,3,1,5]=>[4,2,1,1]=>90
[7,8,1,3,6,2,4,5]=>[4,2,2]=>56
[1,2,7,8,6,3,4,5]=>[5,2,1]=>64
[2,6,7,1,8,5,3,4]=>[4,3,1]=>70
[2,6,7,8,5,3,1,4]=>[4,2,1,1]=>90
[2,6,7,8,5,3,4,1]=>[4,2,1,1]=>90
[6,2,7,8,4,5,3,1]=>[3,3,1,1]=>56
[7,2,1,8,4,5,6,3]=>[4,2,2]=>56
[1,7,2,8,4,5,6,3]=>[5,2,1]=>64
[3,7,8,1,5,6,2,4]=>[3,3,2]=>42
[6,3,7,8,1,5,2,4]=>[3,3,2]=>42
[6,7,1,2,8,5,3,4]=>[4,3,1]=>70
[1,6,7,8,4,2,5,3]=>[4,2,2]=>56
[3,1,2,7,6,5,8,4]=>[4,2,1,1]=>90
[6,1,2,4,7,3,8,5]=>[5,2,1]=>64
[1,7,5,3,6,4,8,2]=>[4,2,1,1]=>90
[5,1,2,6,7,4,8,3]=>[5,2,1]=>64
[4,1,5,7,3,2,6,8]=>[4,3,1]=>70
[4,6,1,7,3,2,5,8]=>[4,3,1]=>70
[4,6,1,8,3,2,5,7]=>[4,3,1]=>70
[4,7,1,8,3,5,2,6]=>[4,3,1]=>70
[4,1,7,8,6,2,3,5]=>[4,3,1]=>70
[1,6,5,7,8,3,4,2]=>[4,2,1,1]=>90
[1,6,5,8,7,3,4,2]=>[3,2,2,1]=>70
[4,1,8,7,6,2,3,5]=>[4,2,1,1]=>90
[4,8,1,7,3,5,2,6]=>[4,2,1,1]=>90
[4,8,1,6,3,2,5,7]=>[4,2,1,1]=>90
[4,7,1,6,3,2,5,8]=>[4,2,1,1]=>90
[6,1,2,3,7,5,4,8]=>[5,2,1]=>64
[6,8,1,5,3,7,2,4]=>[3,2,2,1]=>70
[8,7,5,2,4,1,6,3]=>[3,2,1,1,1]=>64
[1,5,7,3,4,8,6,2]=>[4,3,1]=>70
[1,5,8,3,4,7,6,2]=>[4,2,1,1]=>90
[7,8,5,2,4,1,6,3]=>[3,2,2,1]=>70
[7,1,2,3,5,6,4,8]=>[6,1,1]=>21
[8,1,2,3,5,6,4,7]=>[6,1,1]=>21
[8,1,2,3,5,4,7,6]=>[5,2,1]=>64
[7,1,8,4,6,3,2,5]=>[3,2,2,1]=>70
[6,8,2,4,3,1,5,7]=>[4,2,1,1]=>90
[6,7,2,4,3,1,5,8]=>[4,2,1,1]=>90
[3,8,1,2,4,5,7,6]=>[5,2,1]=>64
[3,7,1,8,6,4,2,5]=>[3,3,1,1]=>56
[1,6,4,3,7,5,8,2]=>[4,2,1,1]=>90
[3,1,2,6,7,5,8,4]=>[5,2,1]=>64
[3,8,1,7,6,4,2,5]=>[3,2,1,1,1]=>64
[7,6,2,4,3,1,5,8]=>[4,1,1,1,1]=>35
[8,7,2,4,3,5,1,6]=>[4,1,1,1,1]=>35
[8,1,7,4,6,3,2,5]=>[3,2,1,1,1]=>64
[8,1,7,6,5,3,2,4]=>[3,1,1,1,1,1]=>21
[1,5,7,3,4,6,8,2]=>[5,2,1]=>64
[8,7,2,5,3,6,1,4]=>[3,2,1,1,1]=>64
[7,1,2,3,5,4,8,6]=>[5,2,1]=>64
[6,1,2,3,5,8,4,7]=>[5,2,1]=>64
[6,1,2,3,5,7,4,8]=>[6,1,1]=>21
[5,1,2,3,7,6,4,8]=>[5,2,1]=>64
[5,1,2,3,8,6,4,7]=>[5,2,1]=>64
[1,5,6,3,4,7,8,2]=>[5,2,1]=>64
[8,6,5,2,4,7,1,3]=>[3,2,1,1,1]=>64
[7,6,2,5,3,1,8,4]=>[3,2,1,1,1]=>64
[7,4,5,2,3,8,6,1]=>[3,3,1,1]=>56
[8,2,3,7,4,5,1,6]=>[5,1,1,1]=>35
[8,4,7,3,2,5,1,6]=>[3,2,1,1,1]=>64
[5,4,6,3,1,2,8,7]=>[3,3,1,1]=>56
[4,6,2,3,1,5,8,7]=>[4,3,1]=>70
[7,2,3,4,5,8,6,1]=>[5,2,1]=>64
[8,2,3,4,5,7,1,6]=>[5,2,1]=>64
[7,3,4,6,8,5,1,2]=>[4,2,1,1]=>90
[4,7,3,2,8,6,1,5]=>[3,2,2,1]=>70
[3,7,4,5,1,8,6,2]=>[4,2,2]=>56
[3,8,2,6,7,4,5,1]=>[3,3,1,1]=>56
[4,8,1,5,6,7,3,2]=>[4,2,1,1]=>90
[5,8,2,4,6,7,1,3]=>[4,2,2]=>56
[6,8,1,3,4,2,7,5]=>[4,2,2]=>56
[5,8,2,4,3,1,7,6]=>[3,2,2,1]=>70
[2,1,7,6,8,5,3,4]=>[3,3,1,1]=>56
[3,7,6,1,8,5,2,4]=>[3,3,1,1]=>56
[4,7,2,3,8,5,1,6]=>[4,3,1]=>70
[7,1,3,6,4,8,5,2]=>[4,2,1,1]=>90
[7,6,1,4,8,5,2,3]=>[3,2,2,1]=>70
[6,2,3,7,8,5,4,1]=>[4,2,1,1]=>90
[6,2,3,8,4,5,1,7]=>[5,2,1]=>64
[7,2,3,6,8,4,1,5]=>[4,2,1,1]=>90
[8,2,3,5,7,1,4,6]=>[4,3,1]=>70
[6,4,8,3,5,1,7,2]=>[3,2,2,1]=>70
[5,4,8,3,6,7,1,2]=>[3,2,2,1]=>70
[3,5,1,8,4,6,7,2]=>[4,3,1]=>70
[3,6,1,8,4,5,2,7]=>[4,3,1]=>70
[4,6,8,3,5,2,7,1]=>[3,3,1,1]=>56
[5,7,8,3,2,4,1,6]=>[3,3,1,1]=>56
[4,8,2,3,5,6,1,7]=>[5,2,1]=>64
[6,8,2,3,1,4,5,7]=>[5,2,1]=>64
[5,2,7,4,8,3,1,6]=>[3,3,1,1]=>56
[3,7,8,2,1,4,6,5]=>[3,3,2]=>42
[3,7,5,2,8,4,1,6]=>[3,3,1,1]=>56
[6,3,2,4,1,8,7,5]=>[3,2,2,1]=>70
[7,2,3,4,8,5,1,6]=>[5,2,1]=>64
[5,7,3,1,4,2,6,8]=>[4,2,2]=>56
[3,7,4,1,8,2,5,6]=>[4,3,1]=>70
[6,3,7,4,8,1,2,5]=>[3,3,2]=>42
[8,3,7,4,2,6,1,5]=>[3,2,1,1,1]=>64
[3,7,4,1,5,6,2,8]=>[5,2,1]=>64
[1,8,3,2,4,5,7,6]=>[5,2,1]=>64
[8,4,1,6,3,7,5,2]=>[3,3,1,1]=>56
[8,7,4,2,1,6,3,5]=>[3,2,1,1,1]=>64
[8,3,5,2,7,4,1,6]=>[3,3,1,1]=>56
[1,5,3,8,7,6,4,2]=>[3,2,1,1,1]=>64
[7,2,4,8,1,3,6,5]=>[3,3,2]=>42
[1,2,8,7,5,6,3,4]=>[4,2,1,1]=>90
[3,1,8,6,7,5,2,4]=>[3,3,1,1]=>56
[1,4,8,6,5,7,2,3]=>[4,2,1,1]=>90
[1,6,5,4,8,2,3,7]=>[4,2,1,1]=>90
[5,1,6,8,3,4,2,7]=>[4,3,1]=>70
[6,2,5,1,7,4,3,8]=>[4,2,1,1]=>90
[5,2,1,8,7,4,3,6]=>[3,2,2,1]=>70
[5,2,6,3,8,1,4,7]=>[4,3,1]=>70
[5,2,8,3,4,6,1,7]=>[5,2,1]=>64
[6,2,8,4,3,1,7,5]=>[3,2,2,1]=>70
[7,2,8,1,3,6,5,4]=>[3,2,2,1]=>70
[7,3,8,1,4,6,2,5]=>[3,3,2]=>42
[1,7,8,5,4,6,3,2]=>[3,2,1,1,1]=>64
[1,5,8,4,6,3,7,2]=>[4,2,1,1]=>90
[5,3,8,4,1,2,7,6]=>[3,3,2]=>42
[5,8,4,3,6,2,1,7]=>[3,2,1,1,1]=>64
[1,8,3,6,5,2,7,4]=>[4,2,1,1]=>90
[1,8,2,4,7,6,5,3]=>[4,1,1,1,1]=>35
[3,8,1,4,6,7,5,2]=>[4,2,1,1]=>90
[3,8,2,5,1,7,6,4]=>[3,2,2,1]=>70
[4,3,8,2,5,1,6,7]=>[4,2,1,1]=>90
[8,2,4,3,5,1,7,6]=>[4,2,1,1]=>90
[8,2,1,4,6,5,7,3]=>[4,2,1,1]=>90
[8,1,3,4,5,7,6,2]=>[5,1,1,1]=>35
[6,1,5,2,4,7,8,3]=>[5,1,1,1]=>35
[4,1,8,5,2,7,6,3]=>[3,3,1,1]=>56
[4,1,8,2,3,7,5,6]=>[5,2,1]=>64
[5,3,8,7,2,1,4,6]=>[3,2,2,1]=>70
[6,7,3,5,1,4,8,2]=>[3,2,2,1]=>70
[6,4,7,5,8,2,3,1]=>[3,2,2,1]=>70
[5,7,8,4,2,6,3,1]=>[3,2,2,1]=>70
[5,7,4,1,6,8,3,2]=>[3,2,2,1]=>70
[5,8,4,6,1,7,3,2]=>[3,2,2,1]=>70
[5,6,1,4,7,8,3,2]=>[4,2,1,1]=>90
[5,3,6,7,4,8,2,1]=>[4,2,1,1]=>90
[7,4,8,5,6,2,1,3]=>[3,2,2,1]=>70
[5,6,3,8,4,7,2,1]=>[3,3,1,1]=>56
[5,6,3,8,2,7,4,1]=>[3,2,2,1]=>70
[6,7,3,8,5,2,4,1]=>[3,2,2,1]=>70
[6,2,7,5,1,4,8,3]=>[3,2,2,1]=>70
[3,5,7,8,4,6,2,1]=>[4,2,1,1]=>90
[5,3,7,8,4,6,2,1]=>[3,3,1,1]=>56
[2,5,8,4,3,7,6,1]=>[3,2,2,1]=>70
[3,7,4,8,6,2,1,5]=>[3,2,2,1]=>70
[3,6,4,8,7,2,5,1]=>[3,2,2,1]=>70
[4,5,7,3,8,6,2,1]=>[4,2,1,1]=>90
[3,5,6,8,4,7,2,1]=>[4,2,1,1]=>90
[6,3,1,8,7,5,4,2]=>[2,2,2,1,1]=>28
[5,4,8,1,7,6,3,2]=>[2,2,2,1,1]=>28
[8,5,4,1,7,6,3,2]=>[2,2,2,1,1]=>28
[1,8,2,5,6,3,4,7]=>[5,2,1]=>64
[7,2,8,4,5,1,3,6]=>[4,2,2]=>56
[1,3,7,5,6,2,4,8]=>[5,2,1]=>64
[1,6,7,4,3,5,2,8]=>[4,2,1,1]=>90
[1,8,5,2,3,7,4,6]=>[5,2,1]=>64
[1,8,2,5,3,6,7,4]=>[5,2,1]=>64
[2,6,8,4,3,5,7,1]=>[4,2,1,1]=>90
[7,5,8,3,2,1,6,4]=>[2,2,2,1,1]=>28
[7,2,8,4,1,5,6,3]=>[4,2,2]=>56
[7,5,8,1,2,6,3,4]=>[4,2,2]=>56
[1,6,7,4,3,2,8,5]=>[4,2,1,1]=>90
[1,5,2,6,4,7,8,3]=>[5,2,1]=>64
[1,5,4,6,2,3,7,8]=>[5,2,1]=>64
[6,2,5,7,1,4,8,3]=>[4,2,1,1]=>90
[6,5,4,3,8,1,7,2]=>[2,2,2,1,1]=>28
[7,3,6,8,5,2,4,1]=>[3,2,1,1,1]=>64
[2,7,8,3,6,5,1,4]=>[3,2,2,1]=>70
[2,7,8,5,4,6,3,1]=>[3,2,1,1,1]=>64
[2,6,5,8,3,4,1,7]=>[4,2,1,1]=>90
[2,6,5,7,3,4,1,8]=>[4,2,1,1]=>90
[6,2,5,7,4,1,3,8]=>[4,2,1,1]=>90
[6,2,5,8,4,1,3,7]=>[3,3,1,1]=>56
[2,7,8,4,6,1,3,5]=>[3,3,2]=>42
[6,1,2,8,3,7,4,5]=>[5,2,1]=>64
[6,1,2,8,5,4,7,3]=>[4,2,1,1]=>90
[6,2,5,7,8,1,3,4]=>[4,3,1]=>70
[1,5,4,2,6,7,3,8]=>[5,2,1]=>64
[2,6,5,7,3,8,1,4]=>[4,2,1,1]=>90
[1,6,2,7,5,8,4,3]=>[4,2,1,1]=>90
[1,3,2,7,8,5,6,4]=>[4,3,1]=>70
[1,6,2,4,8,7,3,5]=>[4,2,2]=>56
[6,5,2,1,8,7,3,4]=>[3,2,2,1]=>70
[2,6,5,3,7,8,4,1]=>[4,2,1,1]=>90
[6,2,5,3,8,4,7,1]=>[4,2,1,1]=>90
[6,5,2,3,8,7,1,4]=>[3,2,2,1]=>70
[5,4,1,2,3,8,6,7]=>[5,2,1]=>64
[5,1,4,2,3,7,8,6]=>[5,2,1]=>64
[1,5,4,2,6,3,8,7]=>[4,3,1]=>70
[5,1,6,3,8,2,7,4]=>[3,3,2]=>42
[9,8,7,6,5,4,3,1,2,10]=>[3,1,1,1,1,1,1,1]=>36
[8,7,6,5,4,2,1,3,9]=>[3,1,1,1,1,1,1]=>28
[1,8,7,6,2,5,4,3]=>[3,1,1,1,1,1]=>21
[2,1,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1]=>27
[1,2,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1]=>28
[3,2,1,9,8,7,6,5,4]=>[2,2,2,1,1,1]=>48
[1,2,3,9,8,7,6,5,4]=>[4,1,1,1,1,1]=>56
[4,3,2,1,9,8,7,6,5]=>[2,2,2,2,1]=>42
[1,2,3,4,9,8,7,6,5]=>[5,1,1,1,1]=>70
[1,2,3,4,5,9,8,7,6]=>[6,1,1,1]=>56
[1,2,3,5,4,7,6,9,8]=>[6,3]=>48
[1,2,3,4,5,7,6,9,8]=>[7,2]=>27
[1,2,10,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1,1]=>36
[3,2,1,10,9,8,7,6,5,4]=>[2,2,2,1,1,1,1]=>75
[1,2,3,10,9,8,7,6,5,4]=>[4,1,1,1,1,1,1]=>84
[1,2,3,4,10,9,8,7,6,5]=>[5,1,1,1,1,1]=>126
[1,2,3,4,5,6,10,9,8,7]=>[7,1,1,1]=>84
[1,2,3,4,5,6,7,10,9,8]=>[8,1,1]=>36
[5,2,7,4,1,6,3,8]=>[4,2,2]=>56
[4,7,3,1,5,6,2,8]=>[4,2,2]=>56
[5,8,3,4,1,6,7,2]=>[4,2,2]=>56
[1,7,8,4,5,6,2,3]=>[4,2,2]=>56
[1,5,8,4,2,6,7,3]=>[4,2,2]=>56
[1,6,3,8,5,2,7,4]=>[4,2,2]=>56
[1,7,3,4,8,6,2,5]=>[4,2,2]=>56
[8,7,3,2,1,6,5,4]=>[2,2,2,1,1]=>28
[8,7,6,3,1,5,2,4]=>[3,2,1,1,1]=>64
[8,5,1,7,2,3,4,6]=>[5,2,1]=>64
[7,1,9,2,3,4,5,6,8]=>[7,2]=>27
[2,4,8,5,3,7,1,6]=>[4,2,1,1]=>90
[2,4,1,8,5,3,7,6]=>[4,3,1]=>70
[2,4,8,6,3,1,7,5]=>[4,2,1,1]=>90
[3,4,6,8,2,1,7,5]=>[4,2,2]=>56
[3,4,1,5,8,2,7,6]=>[4,3,1]=>70
[8,1,4,5,3,2,7,6]=>[4,2,1,1]=>90
[3,4,1,5,2,8,7,6]=>[4,3,1]=>70
[3,4,6,2,1,8,7,5]=>[4,2,2]=>56
[3,5,6,2,1,7,8,4]=>[5,2,1]=>64
[3,4,6,2,7,8,1,5]=>[5,2,1]=>64
[8,1,4,6,3,7,2,5]=>[4,2,1,1]=>90
[8,1,4,6,3,7,5,2]=>[4,2,1,1]=>90
[3,5,6,2,1,7,4,8]=>[5,2,1]=>64
[8,1,5,6,7,3,4,2]=>[4,2,1,1]=>90
[8,1,5,6,7,3,2,4]=>[4,2,1,1]=>90
[3,4,1,6,8,7,2,5]=>[4,3,1]=>70
[3,5,6,1,8,7,2,4]=>[4,3,1]=>70
[2,1,3,8,6,7,4,5]=>[4,3,1]=>70
[8,1,3,2,6,7,5,4]=>[4,2,1,1]=>90
[2,3,8,6,7,1,5,4]=>[4,2,1,1]=>90
[2,4,1,8,6,7,5,3]=>[4,2,1,1]=>90
[2,5,8,6,1,7,4,3]=>[4,2,1,1]=>90
[3,5,6,1,8,7,4,2]=>[4,2,1,1]=>90
[3,4,1,6,8,7,5,2]=>[4,2,1,1]=>90
[3,4,6,8,7,1,5,2]=>[4,2,1,1]=>90
[8,1,4,6,2,7,5,3]=>[4,2,1,1]=>90
[3,5,1,6,7,8,4,2]=>[5,2,1]=>64
[4,5,6,1,7,8,3,2]=>[5,2,1]=>64
[4,5,6,1,7,3,8,2]=>[5,2,1]=>64
[3,5,1,6,7,4,8,2]=>[5,2,1]=>64
[8,1,5,6,7,4,2,3]=>[4,2,1,1]=>90
[8,1,5,6,7,4,3,2]=>[4,1,1,1,1]=>35
[3,5,1,6,7,4,2,8]=>[5,2,1]=>64
[4,5,6,1,7,3,2,8]=>[5,2,1]=>64
[6,5,8,7,4,3,1,2]=>[2,2,2,1,1]=>28
[6,4,2,7,8,5,1,3]=>[3,2,2,1]=>70
[6,1,4,8,7,5,2,3]=>[3,2,2,1]=>70
[1,6,4,8,7,5,2,3]=>[3,2,2,1]=>70
[1,8,6,2,4,7,3,5]=>[4,2,1,1]=>90
[8,1,6,2,4,7,3,5]=>[4,2,1,1]=>90
[7,6,2,1,4,8,3,5]=>[3,3,1,1]=>56
[6,4,1,7,8,5,2,3]=>[3,3,2]=>42
[7,6,1,2,4,8,3,5]=>[4,2,1,1]=>90
[7,6,1,3,4,8,2,5]=>[4,2,1,1]=>90
[8,1,6,3,4,7,2,5]=>[4,2,1,1]=>90
[1,8,6,3,4,7,2,5]=>[4,2,1,1]=>90
[1,7,2,5,4,8,3,6]=>[4,2,1,1]=>90
[7,1,2,5,4,8,3,6]=>[4,2,1,1]=>90
[2,7,1,5,4,8,3,6]=>[3,3,1,1]=>56
[2,8,6,3,4,7,1,5]=>[4,2,1,1]=>90
[2,8,6,1,4,7,3,5]=>[3,3,1,1]=>56
[7,2,1,5,4,8,3,6]=>[3,3,1,1]=>56
[1,2,7,5,4,8,3,6]=>[4,2,1,1]=>90
[3,2,7,5,4,8,1,6]=>[3,3,1,1]=>56
[2,5,8,4,7,3,1,6]=>[3,2,2,1]=>70
[2,3,7,5,4,8,1,6]=>[4,2,1,1]=>90
[6,8,3,2,4,7,1,5]=>[3,2,2,1]=>70
[3,7,2,5,4,8,1,6]=>[3,3,1,1]=>56
[3,1,7,5,4,8,2,6]=>[3,3,1,1]=>56
[1,3,7,5,4,8,2,6]=>[4,2,1,1]=>90
[1,5,8,4,7,3,2,6]=>[3,2,2,1]=>70
[5,1,8,4,7,3,2,6]=>[3,2,2,1]=>70
[5,8,2,4,7,3,1,6]=>[3,2,2,1]=>70
[6,8,4,3,7,5,1,2]=>[2,2,2,2]=>14
[8,7,5,6,2,1,4,3]=>[2,2,2,1,1]=>28
[8,5,2,4,7,3,1,6]=>[3,2,1,1,1]=>64
[8,1,5,4,7,3,2,6]=>[3,2,1,1,1]=>64
[1,8,5,4,7,3,2,6]=>[3,2,1,1,1]=>64
[1,7,3,5,4,8,2,6]=>[4,2,1,1]=>90
[8,6,3,1,4,7,2,5]=>[3,3,1,1]=>56
[8,6,4,2,7,5,1,3]=>[2,2,2,1,1]=>28
[8,6,4,1,7,2,5,3]=>[3,2,2,1]=>70
[5,3,7,4,6,8,2,1]=>[4,2,1,1]=>90
[4,1,3,2,7,8,5,6]=>[4,3,1]=>70
[1,4,3,2,7,8,5,6]=>[4,3,1]=>70
[2,4,3,1,7,8,5,6]=>[4,3,1]=>70
[2,7,3,5,4,8,1,6]=>[4,2,1,1]=>90
[2,8,5,4,7,3,1,6]=>[3,2,1,1,1]=>64
[5,7,3,4,6,8,2,1]=>[4,2,1,1]=>90
[8,2,5,4,7,3,1,6]=>[3,2,1,1,1]=>64
[7,2,3,5,4,8,1,6]=>[4,2,1,1]=>90
[3,2,1,4,7,8,5,6]=>[4,3,1]=>70
[8,1,7,6,4,3,5,2]=>[3,1,1,1,1,1]=>21
[8,6,4,5,2,7,1,3]=>[3,2,1,1,1]=>64
[7,1,8,6,4,3,5,2]=>[3,2,1,1,1]=>64
[7,4,2,5,1,6,3,8]=>[4,2,1,1]=>90
[7,3,6,5,2,1,4,8]=>[3,2,1,1,1]=>64
[8,3,6,5,2,1,7,4]=>[3,2,1,1,1]=>64
[7,3,6,5,2,1,8,4]=>[3,2,1,1,1]=>64
[7,5,8,6,4,2,1,3]=>[2,2,2,1,1]=>28
[5,4,2,8,1,3,7,6]=>[3,2,2,1]=>70
[5,8,2,6,4,1,3,7]=>[3,2,2,1]=>70
[6,4,2,5,1,8,3,7]=>[3,3,1,1]=>56
[6,3,5,2,1,4,7,8]=>[4,2,1,1]=>90
[2,5,8,6,3,1,4,7]=>[4,2,1,1]=>90
[2,3,5,8,1,4,7,6]=>[4,3,1]=>70
[2,3,6,8,1,5,7,4]=>[4,3,1]=>70
[6,3,8,5,2,7,1,4]=>[3,2,2,1]=>70
[6,3,7,5,2,1,4,8]=>[3,2,2,1]=>70
[2,5,7,6,3,1,4,8]=>[4,2,1,1]=>90
[2,8,7,6,3,1,5,4]=>[3,2,1,1,1]=>64
[2,5,8,7,6,3,1,4]=>[3,2,1,1,1]=>64
[2,4,8,1,6,5,7,3]=>[4,2,1,1]=>90
[2,8,7,3,6,1,4,5]=>[4,2,1,1]=>90
[7,3,5,2,1,4,6,8]=>[4,2,1,1]=>90
[8,4,2,5,1,3,7,6]=>[3,3,1,1]=>56
[2,3,6,8,1,4,7,5]=>[4,3,1]=>70
[2,7,8,6,3,1,4,5]=>[4,2,1,1]=>90
[7,3,8,5,2,1,4,6]=>[3,2,2,1]=>70
[2,3,6,1,8,4,7,5]=>[4,3,1]=>70
[2,8,6,3,1,4,5,7]=>[5,1,1,1]=>35
[8,3,5,2,1,4,6,7]=>[4,2,1,1]=>90
[2,4,8,1,3,7,5,6]=>[4,3,1]=>70
[3,8,6,1,4,7,5,2]=>[3,3,1,1]=>56
[2,7,1,5,8,3,4,6]=>[4,3,1]=>70
[3,7,5,8,1,2,6,4]=>[3,3,2]=>42
[7,3,6,1,2,8,4,5]=>[4,3,1]=>70
[7,4,8,1,6,5,2,3]=>[3,2,2,1]=>70
[7,4,5,8,6,1,2,3]=>[3,3,2]=>42
[5,1,8,7,6,2,3,4]=>[4,2,1,1]=>90
[4,6,1,8,7,5,2,3]=>[3,3,1,1]=>56
[4,5,1,8,7,2,3,6]=>[4,3,1]=>70
[3,4,8,7,1,2,5,6]=>[4,3,1]=>70
[6,4,8,7,1,2,5,3]=>[3,2,2,1]=>70
[6,5,1,2,7,3,8,4]=>[4,3,1]=>70
[6,5,1,8,2,7,3,4]=>[4,2,2]=>56
[6,5,1,8,7,2,3,4]=>[4,2,2]=>56
[6,5,1,7,2,8,3,4]=>[4,3,1]=>70
[6,5,1,7,2,3,8,4]=>[4,3,1]=>70
[5,6,8,7,4,1,2,3]=>[3,3,1,1]=>56
[6,8,5,7,4,1,2,3]=>[3,2,2,1]=>70
[7,3,8,1,5,2,4,6]=>[4,2,2]=>56
[4,1,7,5,3,6,2,8]=>[4,2,1,1]=>90
[1,8,4,2,3,6,7,5]=>[5,2,1]=>64
[2,5,8,3,4,6,7,1]=>[5,2,1]=>64
[4,1,7,2,3,6,8,5]=>[5,2,1]=>64
[4,6,2,1,5,7,8,3]=>[4,2,2]=>56
[4,5,2,3,1,7,8,6]=>[4,3,1]=>70
[3,2,6,7,4,1,8,5]=>[4,3,1]=>70
[5,6,2,7,1,4,8,3]=>[4,2,2]=>56
[6,2,3,8,1,7,4,5]=>[4,2,2]=>56
[2,6,8,3,4,7,1,5]=>[4,2,2]=>56
[4,6,2,7,5,1,3,8]=>[4,2,2]=>56
[2,6,3,1,8,4,5,7]=>[5,2,1]=>64
[2,4,3,7,8,1,5,6]=>[4,3,1]=>70
[5,3,2,7,4,8,1,6]=>[3,3,1,1]=>56
[5,1,2,7,6,8,4,3]=>[4,2,1,1]=>90
[2,6,3,1,8,7,4,5]=>[4,2,2]=>56
[3,5,6,4,7,8,1,2]=>[5,2,1]=>64
[5,3,6,4,2,8,7,1]=>[3,3,1,1]=>56
[5,4,2,3,7,8,6,1]=>[4,2,1,1]=>90
[4,1,8,2,5,7,3,6]=>[4,3,1]=>70
[6,2,3,8,4,1,7,5]=>[4,2,2]=>56
[2,6,4,1,5,3,8,7]=>[4,3,1]=>70
[6,2,1,4,7,8,3,5]=>[4,3,1]=>70
[4,2,3,7,8,1,6,5]=>[4,2,2]=>56
[5,8,3,1,7,2,4,6]=>[4,2,2]=>56
[5,1,7,4,2,6,3,8]=>[4,2,2]=>56
[6,8,3,2,5,1,7,4]=>[3,2,2,1]=>70
[6,8,4,3,1,5,7,2]=>[3,2,2,1]=>70
[6,8,4,2,1,5,7,3]=>[3,2,2,1]=>70
[5,1,7,3,2,4,6,8]=>[5,2,1]=>64
[5,2,1,8,3,6,7,4]=>[4,2,2]=>56
[4,3,8,1,6,2,7,5]=>[3,3,2]=>42
[4,2,1,8,5,7,3,6]=>[3,3,2]=>42
[6,3,2,1,7,4,5,8]=>[4,2,1,1]=>90
[6,4,2,1,7,5,3,8]=>[3,2,2,1]=>70
[7,5,2,1,8,6,3,4]=>[3,2,2,1]=>70
[5,3,2,7,6,1,4,8]=>[3,2,2,1]=>70
[5,3,2,8,6,1,4,7]=>[3,2,2,1]=>70
[6,3,2,8,7,1,4,5]=>[3,2,2,1]=>70
[4,2,8,1,7,3,5,6]=>[4,2,2]=>56
[4,3,8,7,2,1,5,6]=>[3,2,2,1]=>70
[2,1,5,8,4,7,3,6]=>[3,3,2]=>42
[5,4,1,7,2,8,6,3]=>[3,3,2]=>42
[6,5,3,1,7,8,4,2]=>[3,2,2,1]=>70
[6,4,2,1,7,8,5,3]=>[3,2,2,1]=>70
[5,3,2,1,6,7,8,4]=>[4,2,1,1]=>90
[8,6,1,4,5,7,2,3]=>[4,2,1,1]=>90
[5,2,8,3,7,4,6,1]=>[4,2,1,1]=>90
[6,2,8,5,4,7,3,1]=>[3,2,1,1,1]=>64
[1,8,6,3,7,4,2,5]=>[4,2,1,1]=>90
[6,5,3,8,4,7,2,1]=>[3,2,1,1,1]=>64
[6,2,8,3,7,4,1,5]=>[4,2,1,1]=>90
[6,4,3,7,1,2,8,5]=>[3,3,1,1]=>56
[6,4,3,8,1,2,7,5]=>[3,2,2,1]=>70
[7,6,3,8,4,2,1,5]=>[3,2,1,1,1]=>64
[7,5,3,8,4,2,6,1]=>[3,2,1,1,1]=>64
[6,4,2,7,3,1,5,8]=>[4,2,1,1]=>90
[5,4,1,6,3,8,7,2]=>[3,3,1,1]=>56
[6,5,1,7,8,2,3,4]=>[4,3,1]=>70
[6,3,1,7,8,4,2,5]=>[3,3,2]=>42
[6,1,5,4,3,2,8,7]=>[3,2,1,1,1]=>64
[8,7,6,1,3,5,2,4]=>[3,2,1,1,1]=>64
[8,1,6,5,7,3,4,2]=>[3,2,1,1,1]=>64
[8,4,1,5,7,6,2,3]=>[3,3,1,1]=>56
[7,8,6,2,5,3,1,4]=>[3,2,1,1,1]=>64
[6,1,3,5,2,8,4,7]=>[4,3,1]=>70
[8,1,3,7,4,2,5,6]=>[5,1,1,1]=>35
[4,3,8,7,5,2,1,6]=>[3,2,1,1,1]=>64
[6,7,1,8,5,3,4,2]=>[3,3,1,1]=>56
[2,7,6,4,8,3,5,1]=>[3,2,1,1,1]=>64
[6,5,2,7,1,4,8,3]=>[3,2,2,1]=>70
[7,4,6,1,3,2,8,5]=>[3,3,1,1]=>56
[7,5,2,1,3,8,4,6]=>[4,2,1,1]=>90
[8,4,7,6,3,1,5,2]=>[2,2,2,1,1]=>28
[7,4,1,5,6,3,8,2]=>[4,2,1,1]=>90
[3,4,7,5,6,1,8,2]=>[5,2,1]=>64
[2,4,7,5,6,3,8,1]=>[5,1,1,1]=>35
[5,4,1,7,6,2,8,3]=>[3,3,2]=>42
[3,5,6,7,1,4,8,2]=>[5,2,1]=>64
[2,7,6,1,3,4,8,5]=>[4,3,1]=>70
[5,7,2,1,6,3,8,4]=>[3,3,2]=>42
[4,7,2,5,6,3,8,1]=>[4,2,1,1]=>90
[8,6,2,5,7,1,4,3]=>[3,2,1,1,1]=>64
[2,7,4,5,3,8,1,6]=>[4,2,1,1]=>90
[6,8,7,1,3,2,5,4]=>[3,2,2,1]=>70
[2,8,6,5,7,1,4,3]=>[3,2,1,1,1]=>64
[5,8,4,3,2,6,7,1]=>[3,2,1,1,1]=>64
[1,8,5,6,2,4,7,3]=>[4,2,1,1]=>90
[8,1,5,6,2,4,7,3]=>[4,2,1,1]=>90
[6,4,8,1,3,2,7,5]=>[3,2,2,1]=>70
[1,4,5,2,8,6,7,3]=>[5,2,1]=>64
[2,3,1,7,8,6,4,5]=>[4,3,1]=>70
[3,5,7,6,2,8,1,4]=>[4,2,1,1]=>90
[4,5,6,1,2,8,7,3]=>[4,3,1]=>70
[5,4,1,2,8,6,7,3]=>[4,2,2]=>56
[8,4,5,2,1,6,7,3]=>[4,2,1,1]=>90
[3,1,2,6,8,4,7,5]=>[4,3,1]=>70
[5,1,3,2,7,8,4,6]=>[4,3,1]=>70
[1,5,4,2,7,8,3,6]=>[4,3,1]=>70
[4,6,7,8,3,1,5,2]=>[4,2,2]=>56
[7,6,2,8,4,3,1,5]=>[3,2,1,1,1]=>64
[5,2,8,6,3,4,7,1]=>[4,2,1,1]=>90
[5,6,8,4,3,2,7,1]=>[3,2,1,1,1]=>64
[5,3,8,1,7,2,4,6]=>[4,2,2]=>56
[3,6,7,8,4,2,1,5]=>[4,2,1,1]=>90
[6,5,1,8,4,3,7,2]=>[3,2,1,1,1]=>64
[6,3,8,4,2,1,7,5]=>[3,2,2,1]=>70
[2,5,8,3,1,6,7,4]=>[4,2,2]=>56
[3,5,8,1,2,6,7,4]=>[4,3,1]=>70
[3,2,8,1,5,6,7,4]=>[4,2,2]=>56
[1,5,8,3,2,6,7,4]=>[4,2,2]=>56
[1,3,8,6,2,4,7,5]=>[4,3,1]=>70
[3,2,7,8,4,6,1,5]=>[3,3,2]=>42
[5,1,8,3,4,6,7,2]=>[5,2,1]=>64
[4,8,7,2,1,6,3,5]=>[3,2,2,1]=>70
[2,8,1,6,3,4,7,5]=>[4,3,1]=>70
[8,3,4,2,1,6,5,7]=>[4,2,1,1]=>90
[6,4,7,2,5,8,1,3]=>[3,2,2,1]=>70
[8,4,5,2,6,3,1,7]=>[4,2,1,1]=>90
[2,4,5,8,3,6,1,7]=>[5,2,1]=>64
[3,5,8,1,2,6,4,7]=>[4,3,1]=>70
[8,6,1,3,5,2,4,7]=>[4,2,1,1]=>90
[8,5,1,2,6,4,3,7]=>[4,2,1,1]=>90
[5,8,6,1,3,4,2,7]=>[4,2,1,1]=>90
[5,8,4,6,1,3,2,7]=>[3,2,2,1]=>70
[7,3,4,5,2,8,1,6]=>[4,2,1,1]=>90
[5,7,4,3,6,1,8,2]=>[3,2,2,1]=>70
[2,6,4,3,7,8,5,1]=>[4,2,1,1]=>90
[7,4,1,8,3,2,5,6]=>[4,2,1,1]=>90
[6,2,1,7,8,4,5,3]=>[3,3,2]=>42
[7,6,3,1,5,4,8,2]=>[3,2,1,1,1]=>64
[2,4,6,5,1,7,8,3]=>[5,2,1]=>64
[1,4,7,5,6,8,2,3]=>[5,2,1]=>64
[1,4,7,6,5,8,2,3]=>[4,2,1,1]=>90
[3,7,5,2,4,6,8,1]=>[4,2,1,1]=>90
[5,6,1,7,4,2,8,3]=>[4,3,1]=>70
[3,7,4,8,1,2,6,5]=>[3,3,2]=>42
[6,3,5,7,8,1,4,2]=>[4,2,1,1]=>90
[3,6,5,7,1,8,4,2]=>[4,2,1,1]=>90
[6,4,7,8,2,1,3,5]=>[3,3,1,1]=>56
[6,7,3,8,4,1,2,5]=>[3,3,2]=>42
[2,7,8,3,4,6,1,5]=>[4,2,2]=>56
[7,5,8,4,1,3,2,6]=>[3,2,1,1,1]=>64
[4,7,5,8,3,1,2,6]=>[3,3,1,1]=>56
[3,6,7,4,8,1,2,5]=>[4,3,1]=>70
[5,7,3,1,6,8,4,2]=>[3,2,2,1]=>70
[2,7,3,1,8,6,4,5]=>[4,2,2]=>56
[2,8,4,3,1,5,7,6]=>[4,2,1,1]=>90
[4,8,1,2,3,5,7,6]=>[5,2,1]=>64
[7,6,8,1,2,4,3,5]=>[4,2,1,1]=>90
[7,6,8,5,1,3,2,4]=>[3,2,1,1,1]=>64
[2,8,5,4,6,1,7,3]=>[4,2,1,1]=>90
[8,4,5,2,7,6,1,3]=>[3,2,2,1]=>70
[8,7,6,4,1,2,5,3]=>[3,2,1,1,1]=>64
[6,7,1,3,5,2,8,4]=>[4,2,2]=>56
[5,7,2,3,6,8,1,4]=>[4,2,2]=>56
[8,5,3,2,7,6,1,4]=>[2,2,2,1,1]=>28
[3,4,6,7,5,8,1,2]=>[5,2,1]=>64
[3,4,5,7,6,1,8,2]=>[5,2,1]=>64
[2,6,4,5,7,8,3,1]=>[5,1,1,1]=>35
[3,8,5,1,6,2,7,4]=>[4,3,1]=>70
[2,5,1,3,6,8,7,4]=>[4,3,1]=>70
[5,4,6,1,3,7,8,2]=>[4,2,1,1]=>90
[6,3,5,7,1,4,8,2]=>[4,2,1,1]=>90
[7,3,4,6,8,1,5,2]=>[4,2,1,1]=>90
[3,7,8,4,1,5,6,2]=>[4,2,2]=>56
[6,7,2,5,1,8,4,3]=>[3,2,2,1]=>70
[3,6,1,2,5,8,4,7]=>[4,3,1]=>70
[1,4,5,8,2,3,7,6]=>[4,3,1]=>70
[1,2,6,4,5,8,3,7]=>[5,2,1]=>64
[1,5,2,4,6,8,3,7]=>[5,2,1]=>64
[3,6,1,5,8,2,4,7]=>[4,3,1]=>70
[2,6,5,1,4,8,3,7]=>[3,3,1,1]=>56
[5,2,6,1,4,8,3,7]=>[3,3,2]=>42
[2,5,1,8,4,7,3,6]=>[3,3,2]=>42
[2,7,1,4,3,6,8,5]=>[4,3,1]=>70
[1,3,7,5,8,2,4,6]=>[4,3,1]=>70
[8,2,1,5,7,3,4,6]=>[4,3,1]=>70
[2,5,4,8,1,3,7,6]=>[3,3,2]=>42
[2,4,1,3,8,6,7,5]=>[4,3,1]=>70
[8,4,3,7,1,2,6,5]=>[3,2,2,1]=>70
[1,7,3,5,8,2,6,4]=>[4,2,2]=>56
[1,8,4,2,6,7,3,5]=>[4,3,1]=>70
[3,1,6,8,7,2,4,5]=>[4,3,1]=>70
[7,2,1,6,8,3,4,5]=>[4,3,1]=>70
[3,1,7,6,8,2,4,5]=>[4,3,1]=>70
[4,1,7,2,6,8,3,5]=>[4,3,1]=>70
[5,1,7,2,3,6,8,4]=>[5,2,1]=>64
[7,2,1,6,3,5,8,4]=>[4,2,1,1]=>90
[2,6,1,7,3,5,8,4]=>[4,3,1]=>70
[7,1,2,5,3,6,8,4]=>[5,2,1]=>64
[5,4,1,2,7,8,3,6]=>[4,3,1]=>70
[8,1,3,2,4,6,7,5]=>[5,2,1]=>64
[7,3,1,2,4,6,8,5]=>[5,2,1]=>64
[1,8,3,4,7,2,5,6]=>[5,2,1]=>64
[3,5,8,1,2,7,4,6]=>[4,3,1]=>70
[3,6,8,1,2,4,7,5]=>[4,3,1]=>70
[4,1,3,8,7,2,6,5]=>[3,2,2,1]=>70
[1,3,7,4,8,2,6,5]=>[4,2,2]=>56
[1,4,6,8,2,3,7,5]=>[4,3,1]=>70
[3,5,8,1,7,2,4,6]=>[4,3,1]=>70
[2,6,8,1,7,3,4,5]=>[4,3,1]=>70
[6,1,5,8,2,3,7,4]=>[4,2,2]=>56
[1,8,3,2,7,5,6,4]=>[4,2,1,1]=>90
[3,1,7,2,8,5,6,4]=>[4,3,1]=>70
[2,6,7,3,8,1,5,4]=>[4,2,2]=>56
[8,4,1,7,3,6,2,5]=>[3,2,2,1]=>70
[3,7,2,8,6,1,5,4]=>[3,2,2,1]=>70
[6,2,3,8,7,1,5,4]=>[3,2,2,1]=>70
[5,1,7,8,4,2,6,3]=>[3,3,2]=>42
[5,1,8,7,4,2,6,3]=>[3,2,2,1]=>70
[4,7,2,8,3,6,5,1]=>[3,3,1,1]=>56
[4,1,7,8,5,3,6,2]=>[3,3,1,1]=>56
[5,1,7,4,8,3,6,2]=>[3,3,1,1]=>56
[4,1,8,7,5,3,6,2]=>[3,2,1,1,1]=>64
[4,8,2,7,3,6,5,1]=>[3,2,1,1,1]=>64
[4,7,2,6,3,5,8,1]=>[4,2,1,1]=>90
[6,8,2,4,3,7,5,1]=>[3,2,2,1]=>70
[6,7,2,4,3,8,5,1]=>[3,3,1,1]=>56
[6,8,2,7,3,5,4,1]=>[3,2,1,1,1]=>64
[3,8,7,2,4,1,5,6]=>[4,2,1,1]=>90
[3,7,8,2,4,1,5,6]=>[4,3,1]=>70
[3,6,8,2,4,5,7,1]=>[4,3,1]=>70
[3,6,7,2,4,5,8,1]=>[4,3,1]=>70
[6,5,1,4,2,3,8,7]=>[4,2,1,1]=>90
[8,6,1,7,2,5,4,3]=>[3,2,1,1,1]=>64
[8,7,6,1,2,3,5,4]=>[4,1,1,1,1]=>35
[5,4,3,1,6,2,8,7]=>[3,3,1,1]=>56
[8,3,4,7,1,6,2,5]=>[3,3,1,1]=>56
[6,3,4,1,8,5,2,7]=>[4,2,2]=>56
[3,8,5,2,7,1,6,4]=>[3,2,2,1]=>70
[2,8,6,7,5,3,4,1]=>[3,2,1,1,1]=>64
[2,1,8,7,3,6,4,5]=>[4,2,1,1]=>90
[3,6,5,8,2,4,7,1]=>[3,3,1,1]=>56
[5,2,1,8,7,3,4,6]=>[4,2,2]=>56
[6,5,2,7,4,3,8,1]=>[3,2,1,1,1]=>64
[4,6,5,2,7,3,8,1]=>[4,2,1,1]=>90
[6,2,7,1,8,3,5,4]=>[3,3,2]=>42
[2,7,5,4,8,3,6,1]=>[3,2,1,1,1]=>64
[8,7,5,1,2,6,4,3]=>[3,2,1,1,1]=>64
[8,4,3,2,7,1,6,5]=>[2,2,2,1,1]=>28
[7,1,6,2,3,8,5,4]=>[4,2,1,1]=>90
[4,8,1,3,2,7,5,6]=>[4,2,2]=>56
[3,8,1,4,7,5,2,6]=>[4,2,1,1]=>90
[6,3,8,7,4,5,1,2]=>[3,2,2,1]=>70
[6,1,4,8,5,2,3,7]=>[4,2,2]=>56
[8,5,7,4,6,2,1,3]=>[2,2,2,1,1]=>28
[4,6,7,8,2,3,5,1]=>[4,3,1]=>70
[8,7,4,6,2,1,5,3]=>[2,2,2,1,1]=>28
[7,6,1,3,5,2,8,4]=>[4,2,1,1]=>90
[5,8,3,2,4,6,1,7]=>[4,2,1,1]=>90
[8,2,6,5,3,1,7,4]=>[3,2,1,1,1]=>64
[4,8,7,6,5,2,3,1]=>[2,2,1,1,1,1]=>20
[2,1,8,6,4,3,7,5]=>[3,3,1,1]=>56
[2,1,7,6,5,3,8,4]=>[3,3,1,1]=>56
[2,7,6,1,3,5,8,4]=>[4,2,1,1]=>90
[7,2,5,4,6,1,8,3]=>[4,2,1,1]=>90
[4,7,6,1,2,5,8,3]=>[4,2,1,1]=>90
[2,4,1,7,6,8,5,3]=>[4,2,1,1]=>90
[3,4,1,7,8,5,6,2]=>[4,3,1]=>70
[7,5,4,3,1,8,6,2]=>[2,2,2,1,1]=>28
[8,5,6,2,7,3,1,4]=>[3,3,1,1]=>56
[8,4,2,5,6,1,7,3]=>[4,2,1,1]=>90
[6,3,5,4,1,7,8,2]=>[4,2,1,1]=>90
[4,1,3,6,7,5,8,2]=>[5,2,1]=>64
[1,7,2,4,5,8,3,6]=>[5,2,1]=>64
[1,7,4,5,8,3,2,6]=>[4,2,1,1]=>90
[2,6,4,7,8,3,5,1]=>[4,2,1,1]=>90
[1,2,6,4,7,8,3,5]=>[5,2,1]=>64
[6,1,4,7,8,3,5,2]=>[4,2,1,1]=>90
[3,6,4,7,8,1,5,2]=>[4,2,2]=>56
[4,3,6,7,1,8,2,5]=>[4,3,1]=>70
[3,6,4,7,8,1,2,5]=>[4,3,1]=>70
[1,3,6,4,7,2,8,5]=>[5,2,1]=>64
[3,6,4,7,2,8,5,1]=>[4,2,1,1]=>90
[5,1,3,4,2,7,8,6]=>[5,2,1]=>64
[5,4,2,1,3,7,8,6]=>[4,2,1,1]=>90
[1,6,7,3,8,2,5,4]=>[4,2,2]=>56
[6,1,4,7,8,5,2,3]=>[4,2,2]=>56
[6,3,2,1,7,8,5,4]=>[3,2,2,1]=>70
[8,6,5,1,3,2,4,7]=>[4,1,1,1,1]=>35
[6,4,7,8,3,2,5,1]=>[3,2,1,1,1]=>64
[3,8,4,7,1,2,5,6]=>[4,3,1]=>70
[8,6,1,2,5,4,3,7]=>[4,1,1,1,1]=>35
[4,8,6,1,5,3,2,7]=>[3,2,1,1,1]=>64
[5,8,6,4,1,3,2,7]=>[3,2,1,1,1]=>64
[8,3,6,4,5,2,1,7]=>[4,1,1,1,1]=>35
[6,8,5,7,4,2,3,1]=>[2,2,2,1,1]=>28
[2,3,8,7,1,6,4,5]=>[4,2,1,1]=>90
[4,3,7,8,1,6,2,5]=>[3,3,2]=>42
[3,5,8,7,4,1,2,6]=>[3,3,1,1]=>56
[7,3,8,4,1,2,5,6]=>[4,2,2]=>56
[4,8,1,2,7,3,5,6]=>[5,2,1]=>64
[6,8,1,2,7,4,5,3]=>[4,2,1,1]=>90
[5,6,8,4,1,3,7,2]=>[3,3,1,1]=>56
[8,5,4,7,1,6,3,2]=>[2,2,2,1,1]=>28
[2,5,8,7,3,6,4,1]=>[3,2,1,1,1]=>64
[2,4,8,7,5,6,1,3]=>[4,2,1,1]=>90
[3,7,4,8,5,6,2,1]=>[4,2,1,1]=>90
[6,4,8,7,5,1,2,3]=>[3,2,2,1]=>70
[3,8,5,2,4,6,7,1]=>[4,2,1,1]=>90
[5,7,1,8,4,6,2,3]=>[3,3,2]=>42
[6,3,8,7,2,1,4,5]=>[3,2,2,1]=>70
[2,3,7,8,5,6,1,4]=>[4,2,2]=>56
[3,7,6,8,5,1,2,4]=>[3,3,1,1]=>56
[2,6,7,8,5,1,3,4]=>[4,3,1]=>70
[2,4,7,8,1,6,3,5]=>[4,3,1]=>70
[5,4,7,8,2,6,3,1]=>[3,2,2,1]=>70
[2,8,3,4,1,5,7,6]=>[5,2,1]=>64
[6,8,3,4,1,2,7,5]=>[3,3,2]=>42
[6,8,7,1,5,2,3,4]=>[4,2,1,1]=>90
[5,8,3,2,7,6,1,4]=>[2,2,2,2]=>14
[2,5,3,1,8,6,7,4]=>[4,2,2]=>56
[4,5,3,2,8,6,7,1]=>[4,2,1,1]=>90
[3,5,8,6,1,4,7,2]=>[4,2,1,1]=>90
[2,8,5,6,1,4,7,3]=>[4,2,1,1]=>90
[4,8,6,1,5,2,7,3]=>[3,3,1,1]=>56
[5,8,2,3,7,6,1,4]=>[3,2,2,1]=>70
[4,6,8,5,3,2,7,1]=>[3,2,1,1,1]=>64
[2,6,4,8,5,1,7,3]=>[4,2,2]=>56
[7,6,4,8,5,2,1,3]=>[2,2,2,1,1]=>28
[3,4,8,6,5,2,7,1]=>[4,1,1,1,1]=>35
[3,4,8,7,5,6,2,1]=>[4,1,1,1,1]=>35
[7,5,3,2,8,6,1,4]=>[2,2,2,1,1]=>28
[2,5,1,3,8,6,7,4]=>[4,3,1]=>70
[4,5,1,2,8,6,7,3]=>[4,3,1]=>70
[5,4,8,1,3,6,7,2]=>[4,2,1,1]=>90
[8,3,5,4,1,6,7,2]=>[4,2,1,1]=>90
[7,3,4,8,5,6,1,2]=>[4,2,2]=>56
[6,1,5,7,2,4,8,3]=>[4,2,1,1]=>90
[7,4,5,1,2,3,8,6]=>[4,3,1]=>70
[7,4,3,1,2,8,5,6]=>[4,2,1,1]=>90
[8,4,7,6,2,1,5,3]=>[2,2,2,1,1]=>28
[8,4,6,5,7,1,3,2]=>[3,2,1,1,1]=>64
[7,2,1,4,5,8,3,6]=>[4,3,1]=>70
[7,4,1,6,3,5,8,2]=>[4,2,1,1]=>90
[3,5,7,6,4,1,8,2]=>[4,2,1,1]=>90
[4,7,5,2,1,3,8,6]=>[3,3,1,1]=>56
[5,7,2,3,6,4,8,1]=>[4,2,1,1]=>90
[8,6,2,3,7,1,4,5]=>[4,2,1,1]=>90
[5,7,2,4,8,3,6,1]=>[3,3,1,1]=>56
[1,7,2,4,8,6,3,5]=>[4,2,2]=>56
[7,6,1,5,4,8,3,2]=>[3,1,1,1,1,1]=>21
[4,7,3,2,1,8,5,6]=>[3,3,1,1]=>56
[3,1,7,2,5,8,4,6]=>[4,3,1]=>70
[4,8,7,6,1,2,5,3]=>[3,2,1,1,1]=>64
[7,8,6,1,3,2,5,4]=>[3,2,2,1]=>70
[2,8,6,7,4,1,3,5]=>[3,3,1,1]=>56
[5,8,6,4,2,3,1,7]=>[3,2,1,1,1]=>64
[2,8,3,1,6,5,4,7]=>[4,2,1,1]=>90
[3,8,1,2,5,7,4,6]=>[4,3,1]=>70
[6,8,5,4,2,7,3,1]=>[2,2,2,1,1]=>28
[6,8,3,1,2,4,5,7]=>[5,2,1]=>64
[4,6,8,7,3,1,5,2]=>[3,2,2,1]=>70
[6,5,3,7,8,4,1,2]=>[3,2,2,1]=>70
[4,1,3,8,7,5,6,2]=>[4,2,1,1]=>90
[6,2,7,4,8,1,3,5]=>[3,3,2]=>42
[8,4,5,2,1,6,3,7]=>[4,2,1,1]=>90
[4,3,2,6,8,1,7,5]=>[3,2,2,1]=>70
[7,1,5,6,3,8,2,4]=>[4,2,1,1]=>90
[5,1,2,4,7,8,3,6]=>[5,2,1]=>64
[3,5,4,2,8,1,6,7]=>[4,2,1,1]=>90
[5,1,3,8,4,2,7,6]=>[4,2,2]=>56
[6,2,8,7,3,5,4,1]=>[3,2,1,1,1]=>64
[7,1,8,4,3,6,5,2]=>[3,2,2,1]=>70
[3,6,8,7,4,1,2,5]=>[3,3,1,1]=>56
[5,6,8,1,7,3,2,4]=>[3,3,1,1]=>56
[3,1,6,8,7,4,2,5]=>[3,3,1,1]=>56
[7,4,6,8,2,1,5,3]=>[3,2,2,1]=>70
[6,5,8,4,3,1,2,7]=>[3,2,1,1,1]=>64
[2,5,8,3,6,7,4,1]=>[4,2,1,1]=>90
[8,5,1,3,7,4,6,2]=>[4,2,1,1]=>90
[1,5,8,3,7,4,2,6]=>[4,2,1,1]=>90
[3,8,2,7,1,5,6,4]=>[3,2,2,1]=>70
[5,8,2,3,6,4,1,7]=>[4,2,1,1]=>90
[6,8,2,3,4,7,5,1]=>[4,2,1,1]=>90
[7,5,1,8,4,2,6,3]=>[3,2,2,1]=>70
[3,6,8,5,2,7,4,1]=>[3,2,2,1]=>70
[2,1,6,5,4,8,3,7]=>[3,3,1,1]=>56
[2,1,7,8,4,6,5,3]=>[3,3,1,1]=>56
[2,1,7,4,3,5,8,6]=>[4,3,1]=>70
[7,5,2,8,4,6,3,1]=>[3,2,1,1,1]=>64
[7,6,3,8,1,5,4,2]=>[2,2,2,1,1]=>28
[8,4,3,1,7,5,2,6]=>[3,2,2,1]=>70
[7,3,1,4,6,8,5,2]=>[4,2,1,1]=>90
[4,3,8,7,1,6,5,2]=>[2,2,2,1,1]=>28
[5,2,4,3,6,8,1,7]=>[4,2,1,1]=>90
[4,7,5,6,3,8,2,1]=>[4,1,1,1,1]=>35
[5,8,2,7,3,4,6,1]=>[4,2,1,1]=>90
[6,3,2,1,4,8,5,7]=>[4,2,1,1]=>90
[6,2,3,1,4,7,8,5]=>[5,2,1]=>64
[5,2,1,3,6,4,8,7]=>[4,3,1]=>70
[7,1,8,3,5,4,6,2]=>[4,2,1,1]=>90
[7,1,2,4,8,5,6,3]=>[5,2,1]=>64
[7,2,1,3,4,5,8,6]=>[5,2,1]=>64
[8,7,3,5,4,2,1,6]=>[3,1,1,1,1,1]=>21
[5,1,6,4,3,2,8,7]=>[3,3,1,1]=>56
[8,3,7,1,4,6,5,2]=>[3,2,1,1,1]=>64
[2,8,3,6,4,7,5,1]=>[4,2,1,1]=>90
[6,2,1,7,5,8,3,4]=>[3,3,2]=>42
[6,3,8,7,5,2,1,4]=>[2,2,2,1,1]=>28
[6,7,2,1,5,8,4,3]=>[3,2,2,1]=>70
[9,1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]=>8
[7,6,8,1,5,4,3,2]=>[2,2,1,1,1,1]=>20
[3,1,9,8,7,6,5,4,2]=>[2,2,1,1,1,1,1]=>27
[10,1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]=>9
[7,6,1,8,5,4,3,2]=>[2,2,1,1,1,1]=>20
[6,5,8,1,7,4,3,2]=>[2,2,2,1,1]=>28
[6,5,8,7,4,1,3,2]=>[2,2,2,1,1]=>28
[3,1,10,9,8,7,6,5,4,2]=>[2,2,1,1,1,1,1,1]=>35
[1,6,4,8,3,2,5,7]=>[4,2,1,1]=>90
[1,8,3,5,6,2,4,7]=>[5,2,1]=>64
[1,4,8,5,6,2,3,7]=>[5,2,1]=>64
[1,2,8,5,3,7,4,6]=>[5,2,1]=>64
[6,1,4,8,2,3,5,7]=>[5,2,1]=>64
[8,7,2,5,6,1,4,3]=>[3,2,1,1,1]=>64
[1,8,2,5,4,7,3,6]=>[4,2,1,1]=>90
[5,7,4,1,2,3,8,6]=>[4,3,1]=>70
[1,7,4,2,5,3,8,6]=>[4,3,1]=>70
[6,7,4,2,1,3,8,5]=>[3,3,1,1]=>56
[6,4,3,8,5,7,1,2]=>[3,2,2,1]=>70
[7,4,3,6,2,1,5,8]=>[3,2,1,1,1]=>64
[7,2,5,3,4,1,6,8]=>[5,1,1,1]=>35
[8,3,7,4,5,6,1,2]=>[4,2,1,1]=>90
[2,7,4,3,1,5,6,8]=>[5,1,1,1]=>35
[6,8,4,2,3,1,5,7]=>[4,2,1,1]=>90
[3,7,5,2,4,1,6,8]=>[4,2,1,1]=>90
[7,1,3,2,8,4,5,6]=>[5,2,1]=>64
[2,1,7,4,8,3,5,6]=>[4,3,1]=>70
[5,2,8,6,1,3,4,7]=>[4,2,2]=>56
[2,8,3,1,4,5,6,7]=>[6,1,1]=>21
[7,4,8,2,3,1,5,6]=>[4,2,1,1]=>90
[4,2,7,3,1,5,6,8]=>[5,2,1]=>64
[8,3,7,2,1,4,5,6]=>[4,2,1,1]=>90
[6,5,2,4,7,1,3,8]=>[4,2,1,1]=>90
[6,5,7,4,1,8,2,3]=>[3,3,1,1]=>56
[7,6,4,5,1,8,2,3]=>[3,3,1,1]=>56
[8,6,4,1,3,7,2,5]=>[3,2,1,1,1]=>64
[6,4,3,1,8,2,5,7]=>[4,2,1,1]=>90
[7,4,1,2,8,3,5,6]=>[5,2,1]=>64
[4,8,1,3,5,7,2,6]=>[4,2,2]=>56
[7,8,4,1,3,6,2,5]=>[3,2,2,1]=>70
[6,5,8,1,3,7,2,4]=>[3,2,2,1]=>70
[5,3,6,1,8,2,4,7]=>[4,3,1]=>70
[4,7,3,1,8,2,5,6]=>[4,3,1]=>70
[8,3,1,7,2,4,5,6]=>[5,2,1]=>64
[2,8,1,4,7,3,5,6]=>[4,3,1]=>70
[3,1,8,5,4,7,6,2]=>[3,3,1,1]=>56
[4,1,5,8,3,7,6,2]=>[3,3,1,1]=>56
[4,1,5,3,8,7,6,2]=>[3,3,1,1]=>56
[4,5,1,8,2,7,6,3]=>[3,3,1,1]=>56
[4,8,5,3,1,7,6,2]=>[3,2,2,1]=>70
[4,5,2,8,1,7,6,3]=>[3,2,2,1]=>70
[4,5,2,1,8,7,6,3]=>[3,2,2,1]=>70
[5,6,2,7,8,1,4,3]=>[4,2,2]=>56
[4,6,2,8,7,1,5,3]=>[3,2,2,1]=>70
[4,8,6,3,7,1,5,2]=>[3,2,2,1]=>70
[4,8,6,3,7,5,1,2]=>[3,2,2,1]=>70
[4,6,8,2,7,5,1,3]=>[3,2,2,1]=>70
[4,6,2,8,7,5,1,3]=>[3,2,2,1]=>70
[5,6,2,7,4,1,8,3]=>[4,2,2]=>56
[5,6,7,2,3,1,8,4]=>[4,3,1]=>70
[5,6,7,2,8,3,1,4]=>[4,3,1]=>70
[5,6,7,2,1,8,3,4]=>[4,3,1]=>70
[5,6,7,2,1,3,8,4]=>[4,3,1]=>70
[5,6,1,7,8,2,4,3]=>[4,3,1]=>70
[5,6,1,7,2,4,8,3]=>[4,3,1]=>70
[5,1,6,7,8,3,4,2]=>[4,3,1]=>70
[4,1,6,8,7,3,5,2]=>[3,3,1,1]=>56
[3,1,8,6,7,5,4,2]=>[3,2,1,1,1]=>64
[4,1,6,8,7,5,3,2]=>[3,2,1,1,1]=>64
[5,1,6,7,4,8,3,2]=>[4,2,1,1]=>90
[5,6,1,7,8,4,2,3]=>[4,3,1]=>70
[4,6,8,1,7,5,2,3]=>[3,3,1,1]=>56
[4,8,6,1,7,5,3,2]=>[3,2,1,1,1]=>64
[5,6,7,1,8,3,2,4]=>[4,3,1]=>70
[5,6,7,1,3,8,2,4]=>[4,3,1]=>70
[5,6,7,1,3,2,8,4]=>[4,3,1]=>70
[5,6,7,3,1,2,8,4]=>[4,3,1]=>70
[5,6,7,3,8,1,2,4]=>[4,3,1]=>70
[5,6,8,7,4,2,1,3]=>[3,2,1,1,1]=>64
[5,6,7,3,8,2,1,4]=>[4,2,1,1]=>90
[7,4,6,2,3,5,1,8]=>[4,2,1,1]=>90
[1,4,8,6,3,2,5,7]=>[4,2,1,1]=>90
[7,4,1,6,3,8,5,2]=>[3,3,1,1]=>56
[7,6,3,1,5,8,4,2]=>[3,2,1,1,1]=>64
[6,4,2,5,7,3,1,8]=>[4,2,1,1]=>90
[4,2,5,7,6,3,1,8]=>[4,2,1,1]=>90
[7,4,5,6,1,8,3,2]=>[4,2,1,1]=>90
[4,1,5,8,6,3,2,7]=>[4,2,1,1]=>90
[3,2,7,6,1,8,5,4]=>[3,2,2,1]=>70
[4,7,5,1,6,8,2,3]=>[4,3,1]=>70
[8,6,5,1,2,7,4,3]=>[3,2,1,1,1]=>64
[3,2,5,1,4,8,7,6]=>[3,3,2]=>42
[8,5,4,1,3,2,7,6]=>[3,2,1,1,1]=>64
[1,4,2,3,6,8,7,5]=>[5,2,1]=>64
[5,4,8,3,7,1,6,2]=>[2,2,2,2]=>14
[4,7,1,8,2,5,3,6]=>[4,3,1]=>70
[6,4,1,8,5,3,7,2]=>[3,2,2,1]=>70
[8,4,6,1,3,5,2,7]=>[4,2,1,1]=>90
[3,2,5,4,7,8,1,6]=>[4,3,1]=>70
[5,2,4,3,7,8,1,6]=>[4,2,1,1]=>90
[8,1,6,7,2,5,3,4]=>[4,2,1,1]=>90
[3,1,7,6,5,8,2,4]=>[3,3,1,1]=>56
[1,2,7,5,6,8,3,4]=>[5,2,1]=>64
[6,1,4,7,2,8,3,5]=>[4,3,1]=>70
[3,2,1,7,6,8,4,5]=>[3,3,2]=>42
[3,2,8,6,4,7,1,5]=>[3,3,1,1]=>56
[7,8,4,6,3,2,1,5]=>[2,2,2,1,1]=>28
[1,8,6,5,3,7,2,4]=>[3,2,1,1,1]=>64
[8,2,5,3,6,7,1,4]=>[4,2,1,1]=>90
[3,8,5,2,7,6,1,4]=>[3,2,2,1]=>70
[4,7,5,3,1,8,6,2]=>[3,2,2,1]=>70
[4,5,3,6,8,1,7,2]=>[4,2,2]=>56
[3,5,2,6,1,8,7,4]=>[4,2,2]=>56
[1,6,3,5,7,2,8,4]=>[5,2,1]=>64
[1,5,4,6,7,8,2,3]=>[5,2,1]=>64
[8,4,6,5,7,2,1,3]=>[3,2,1,1,1]=>64
[7,4,5,2,6,8,1,3]=>[4,2,1,1]=>90
[5,4,2,6,8,7,1,3]=>[3,2,2,1]=>70
[6,5,1,4,3,2,8,7]=>[3,2,1,1,1]=>64
[3,6,4,5,2,1,8,7]=>[4,2,1,1]=>90
[7,5,4,2,3,8,1,6]=>[3,2,1,1,1]=>64
[7,8,1,3,5,6,2,4]=>[4,2,2]=>56
[1,7,8,3,5,6,2,4]=>[4,2,2]=>56
[3,1,7,8,5,2,6,4]=>[3,3,2]=>42
[1,3,7,5,8,2,6,4]=>[4,2,2]=>56
[3,5,7,1,8,4,6,2]=>[4,3,1]=>70
[3,5,7,8,1,4,6,2]=>[4,3,1]=>70
[5,3,7,1,8,4,6,2]=>[3,3,2]=>42
[3,6,2,1,4,5,8,7]=>[4,3,1]=>70
[4,6,2,5,1,3,8,7]=>[3,3,2]=>42
[6,4,2,5,1,3,8,7]=>[3,3,1,1]=>56
[8,6,1,7,3,2,4,5]=>[4,2,1,1]=>90
[2,5,8,1,7,3,4,6]=>[4,3,1]=>70
[6,8,2,7,3,1,4,5]=>[4,2,1,1]=>90
[6,8,2,3,7,1,4,5]=>[4,2,2]=>56
[8,6,2,7,4,5,1,3]=>[3,2,2,1]=>70
[5,2,8,1,7,3,4,6]=>[4,2,2]=>56
[4,2,3,8,1,5,6,7]=>[5,2,1]=>64
[5,2,8,3,7,1,4,6]=>[4,2,2]=>56
[5,2,8,4,6,1,3,7]=>[4,2,2]=>56
[2,1,5,8,4,3,6,7]=>[4,3,1]=>70
[5,8,3,2,7,1,4,6]=>[3,2,2,1]=>70
[4,1,3,8,2,5,6,7]=>[5,2,1]=>64
[3,5,8,2,7,1,4,6]=>[3,3,2]=>42
[4,5,8,2,6,1,3,7]=>[4,2,2]=>56
[2,6,8,3,7,1,4,5]=>[4,2,2]=>56
[5,1,8,3,7,2,4,6]=>[4,2,2]=>56
[5,1,8,4,6,2,3,7]=>[4,2,2]=>56
[5,8,4,1,6,2,3,7]=>[4,2,2]=>56
[4,5,8,1,6,2,3,7]=>[4,3,1]=>70
[5,4,8,1,6,2,3,7]=>[4,2,2]=>56
[4,8,5,1,6,2,3,7]=>[4,3,1]=>70
[2,1,5,4,8,3,6,7]=>[4,3,1]=>70
[2,4,3,8,1,5,6,7]=>[5,2,1]=>64
[3,1,8,4,2,5,6,7]=>[5,2,1]=>64
[3,8,4,2,1,5,6,7]=>[5,1,1,1]=>35
[2,3,8,4,1,5,6,7]=>[6,1,1]=>21
[3,4,2,8,1,5,6,7]=>[5,2,1]=>64
[3,8,5,2,7,1,4,6]=>[3,3,1,1]=>56
[4,8,5,2,6,1,3,7]=>[4,2,1,1]=>90
[2,1,4,8,5,3,6,7]=>[5,2,1]=>64
[3,2,8,4,1,5,6,7]=>[5,2,1]=>64
[2,8,4,3,1,5,6,7]=>[5,1,1,1]=>35
[5,7,4,3,8,2,6,1]=>[3,2,1,1,1]=>64
[6,1,7,5,2,8,4,3]=>[3,3,1,1]=>56
[6,7,4,8,2,5,3,1]=>[3,2,2,1]=>70
[2,1,6,7,5,3,8,4]=>[4,3,1]=>70
[3,8,4,2,1,6,7,5]=>[4,2,1,1]=>90
[6,7,5,8,1,2,4,3]=>[3,3,1,1]=>56
[3,4,8,1,2,5,7,6]=>[4,3,1]=>70
[6,1,3,4,8,2,5,7]=>[5,2,1]=>64
[6,2,3,4,8,1,5,7]=>[5,2,1]=>64
[6,7,4,8,2,3,5,1]=>[3,3,1,1]=>56
[2,6,7,5,1,3,8,4]=>[4,3,1]=>70
[6,7,4,8,1,3,2,5]=>[3,3,1,1]=>56
[6,7,5,8,4,1,3,2]=>[3,2,1,1,1]=>64
[6,7,4,8,2,1,3,5]=>[3,3,1,1]=>56
[1,4,3,6,5,8,2,7]=>[4,3,1]=>70
[6,7,8,2,3,5,4,1]=>[3,3,1,1]=>56
[5,8,6,2,3,7,4,1]=>[3,3,1,1]=>56
[1,8,3,4,7,6,2,5]=>[4,2,1,1]=>90
[8,7,2,3,6,5,4,1]=>[3,1,1,1,1,1]=>21
[3,8,1,7,5,2,6,4]=>[3,3,1,1]=>56
[4,8,1,6,7,2,5,3]=>[3,3,1,1]=>56
[2,1,3,8,4,6,5,7]=>[5,2,1]=>64
[1,3,2,8,5,4,6,7]=>[5,2,1]=>64
[1,5,6,8,7,4,2,3]=>[4,2,1,1]=>90
[2,4,8,5,7,3,6,1]=>[4,2,1,1]=>90
[4,3,8,6,5,7,2,1]=>[3,2,1,1,1]=>64
[4,2,8,6,7,3,5,1]=>[3,3,1,1]=>56
[3,1,8,7,5,6,2,4]=>[3,3,1,1]=>56
[5,1,7,8,6,4,2,3]=>[3,3,1,1]=>56
[7,8,3,2,6,1,4,5]=>[3,2,2,1]=>70
[7,8,1,4,5,6,3,2]=>[4,2,1,1]=>90
[7,8,4,5,1,6,3,2]=>[3,2,2,1]=>70
[6,2,4,8,1,5,3,7]=>[4,2,2]=>56
[3,4,8,5,1,6,7,2]=>[5,2,1]=>64
[1,4,8,2,6,3,7,5]=>[4,3,1]=>70
[5,3,8,1,4,6,7,2]=>[4,2,2]=>56
[7,4,2,8,1,5,3,6]=>[3,2,2,1]=>70
[6,1,7,5,8,4,3,2]=>[3,2,1,1,1]=>64
[6,2,1,8,4,5,3,7]=>[4,2,2]=>56
[1,2,7,8,5,3,4,6]=>[5,2,1]=>64
[3,1,8,4,5,6,7,2]=>[5,2,1]=>64
[2,1,4,8,6,5,3,7]=>[4,2,1,1]=>90
[3,2,7,8,5,1,4,6]=>[3,3,2]=>42
[2,3,7,8,5,1,4,6]=>[4,3,1]=>70
[4,1,2,8,7,5,3,6]=>[4,2,1,1]=>90
[1,4,2,8,7,5,3,6]=>[4,2,1,1]=>90
[7,2,1,8,5,3,4,6]=>[4,2,2]=>56
[7,1,6,5,8,4,3,2]=>[3,1,1,1,1,1]=>21
[6,5,7,1,8,4,3,2]=>[3,2,1,1,1]=>64
[5,7,6,1,8,4,3,2]=>[3,2,1,1,1]=>64
[6,7,3,8,5,4,1,2]=>[3,2,2,1]=>70
[7,1,2,8,4,5,3,6]=>[5,2,1]=>64
[7,6,1,5,8,4,3,2]=>[3,1,1,1,1,1]=>21
[7,1,6,5,3,2,4,8]=>[4,1,1,1,1]=>35
[1,8,7,5,3,2,4,6]=>[4,1,1,1,1]=>35
[1,8,7,4,2,5,3,6]=>[4,2,1,1]=>90
[8,7,4,2,5,3,6,1]=>[3,2,1,1,1]=>64
[7,1,6,4,2,5,3,8]=>[4,2,1,1]=>90
[2,6,5,4,7,1,3,8]=>[4,2,1,1]=>90
[7,1,5,3,6,4,2,8]=>[4,2,1,1]=>90
[5,3,7,1,6,4,2,8]=>[3,2,2,1]=>70
[5,3,6,4,2,7,1,8]=>[4,2,1,1]=>90
[1,5,3,8,7,4,2,6]=>[4,2,1,1]=>90
[7,4,2,8,6,3,5,1]=>[3,2,2,1]=>70
[5,3,6,1,8,7,4,2]=>[3,2,2,1]=>70
[6,1,5,3,8,7,4,2]=>[3,2,2,1]=>70
[2,8,7,5,4,6,1,3]=>[3,2,1,1,1]=>64
[2,3,1,8,7,5,4,6]=>[4,2,1,1]=>90
[5,3,8,7,4,2,1,6]=>[3,2,1,1,1]=>64
[7,4,2,1,8,6,3,5]=>[3,2,2,1]=>70
[8,6,3,5,7,4,2,1]=>[3,1,1,1,1,1]=>21
[1,8,6,3,5,7,4,2]=>[4,1,1,1,1]=>35
[6,3,8,5,2,1,7,4]=>[3,2,2,1]=>70
[8,6,3,7,4,2,1,5]=>[3,2,1,1,1]=>64
[2,8,6,4,7,5,1,3]=>[3,2,2,1]=>70
[5,1,8,6,3,7,4,2]=>[3,3,1,1]=>56
[6,3,7,4,1,8,5,2]=>[3,3,2]=>42
[8,5,2,6,3,7,4,1]=>[3,3,1,1]=>56
[6,1,8,7,4,2,5,3]=>[3,2,2,1]=>70
[8,6,3,7,4,2,5,1]=>[3,2,1,1,1]=>64
[1,8,6,3,2,4,7,5]=>[4,2,1,1]=>90
[8,6,3,2,4,7,5,1]=>[3,2,1,1,1]=>64
[7,5,1,8,6,3,2,4]=>[3,2,2,1]=>70
[6,1,8,7,5,3,2,4]=>[3,2,1,1,1]=>64
[4,3,2,8,7,6,1,5]=>[2,2,2,2]=>14
[2,4,5,1,3,8,7,6]=>[4,3,1]=>70
[7,5,8,6,3,2,4,1]=>[2,2,2,1,1]=>28
[1,7,5,8,6,3,2,4]=>[3,2,2,1]=>70
[1,7,4,2,5,8,6,3]=>[4,2,2]=>56
[8,6,3,1,7,4,2,5]=>[3,2,2,1]=>70
[8,7,4,2,5,3,1,6]=>[3,2,1,1,1]=>64
[5,3,1,8,7,4,2,6]=>[3,2,2,1]=>70
[4,1,8,7,5,3,2,6]=>[3,2,1,1,1]=>64
[2,8,6,4,1,3,7,5]=>[3,3,1,1]=>56
[4,1,8,6,3,2,7,5]=>[3,3,1,1]=>56
[7,4,2,8,6,3,1,5]=>[3,2,2,1]=>70
[6,3,1,8,5,2,7,4]=>[3,3,2]=>42
[8,5,2,6,3,1,7,4]=>[3,3,1,1]=>56
[7,4,8,5,2,6,3,1]=>[3,2,2,1]=>70
[1,8,5,2,7,4,6,3]=>[4,2,1,1]=>90
[8,5,2,7,4,6,3,1]=>[3,2,1,1,1]=>64
[7,4,6,3,1,8,5,2]=>[3,2,2,1]=>70
[6,3,1,7,4,8,5,2]=>[3,3,2]=>42
[8,6,3,1,5,7,4,2]=>[3,2,1,1,1]=>64
[4,1,7,5,8,6,3,2]=>[3,3,1,1]=>56
[2,3,1,7,5,8,6,4]=>[4,3,1]=>70
[7,4,8,5,2,1,6,3]=>[3,2,2,1]=>70
[8,5,2,1,7,4,6,3]=>[3,2,2,1]=>70
[1,7,4,6,3,8,5,2]=>[4,2,1,1]=>90
[4,1,8,5,7,3,2,6]=>[3,3,1,1]=>56
[5,1,7,4,8,3,2,6]=>[3,3,1,1]=>56
[4,6,2,7,3,1,8,5]=>[4,3,1]=>70
[6,2,8,4,1,7,3,5]=>[3,3,2]=>42
[6,3,4,8,1,7,2,5]=>[3,3,2]=>42
[1,8,5,4,2,3,7,6]=>[4,2,1,1]=>90
[3,5,4,8,1,2,7,6]=>[3,3,2]=>42
[5,6,3,8,7,1,2,4]=>[3,3,2]=>42
[2,6,8,4,1,7,3,5]=>[3,3,2]=>42
[1,8,7,4,2,6,3,5]=>[4,2,1,1]=>90
[5,2,8,6,7,1,3,4]=>[3,3,2]=>42
[6,2,8,7,5,1,3,4]=>[3,2,2,1]=>70
[1,8,5,7,6,2,3,4]=>[4,2,1,1]=>90
[3,6,7,8,5,1,2,4]=>[4,3,1]=>70
[1,8,6,7,5,2,3,4]=>[4,2,1,1]=>90
[6,3,8,7,5,1,2,4]=>[3,2,2,1]=>70
[2,8,7,4,1,3,5,6]=>[4,2,1,1]=>90
[5,4,8,7,1,3,2,6]=>[3,2,2,1]=>70
[4,8,6,1,3,2,5,7]=>[4,2,1,1]=>90
[5,4,2,7,6,8,1,3]=>[3,2,2,1]=>70
[2,8,7,1,4,5,3,6]=>[4,2,1,1]=>90
[4,2,1,8,7,3,5,6]=>[4,2,2]=>56
[5,1,6,3,2,8,7,4]=>[3,3,2]=>42
[4,6,1,8,7,3,2,5]=>[3,3,1,1]=>56
[8,7,2,3,5,4,1,6]=>[4,1,1,1,1]=>35
[5,3,1,4,8,7,2,6]=>[3,3,2]=>42
[4,3,5,2,8,7,1,6]=>[3,2,2,1]=>70
[3,4,2,8,6,1,5,7]=>[4,2,2]=>56
[3,7,6,8,1,5,2,4]=>[3,3,1,1]=>56
[8,1,4,2,3,6,7,5]=>[5,2,1]=>64
[3,7,2,1,8,6,4,5]=>[3,3,2]=>42
[2,8,6,1,7,3,5,4]=>[3,3,1,1]=>56
[1,7,6,3,5,8,2,4]=>[4,2,1,1]=>90
[3,7,5,1,6,8,2,4]=>[4,3,1]=>70
[3,6,5,8,1,4,7,2]=>[3,3,1,1]=>56
[8,1,5,6,4,7,2,3]=>[4,2,1,1]=>90
[3,6,7,4,1,8,2,5]=>[4,3,1]=>70
[1,7,4,6,8,2,5,3]=>[4,2,1,1]=>90
[7,5,8,2,6,3,1,4]=>[3,2,2,1]=>70
[2,7,1,6,5,4,8,3]=>[3,2,1,1,1]=>64
[7,3,2,6,1,8,5,4]=>[3,2,2,1]=>70
[6,4,7,2,3,1,8,5]=>[3,3,1,1]=>56
[5,3,1,8,4,6,2,7]=>[4,2,2]=>56
[3,8,1,6,7,4,2,5]=>[3,3,1,1]=>56
[2,7,4,3,6,8,1,5]=>[4,2,1,1]=>90
[2,8,4,6,1,5,3,7]=>[4,2,1,1]=>90
[8,4,1,6,3,2,5,7]=>[4,2,1,1]=>90
[4,7,3,8,5,2,1,6]=>[3,3,1,1]=>56
[3,1,7,4,8,5,2,6]=>[4,3,1]=>70
[7,4,1,6,3,2,8,5]=>[3,3,1,1]=>56
[3,8,6,2,7,4,1,5]=>[3,3,1,1]=>56
[7,3,1,4,5,2,8,6]=>[4,3,1]=>70
[6,1,4,8,5,3,2,7]=>[4,2,1,1]=>90
[8,1,2,4,6,7,5,3]=>[5,1,1,1]=>35
[8,1,3,6,7,5,4,2]=>[4,1,1,1,1]=>35
[7,5,2,3,8,6,1,4]=>[3,2,2,1]=>70
[8,6,2,4,1,3,7,5]=>[3,3,1,1]=>56
[4,7,5,1,8,6,3,2]=>[3,2,2,1]=>70
[4,7,3,2,8,5,6,1]=>[3,3,1,1]=>56
[8,4,5,7,6,1,3,2]=>[3,2,1,1,1]=>64
[7,5,8,4,2,3,6,1]=>[3,2,1,1,1]=>64
[3,8,4,6,1,7,5,2]=>[4,2,1,1]=>90
[3,7,4,6,5,2,8,1]=>[4,1,1,1,1]=>35
[4,2,7,6,1,5,8,3]=>[3,2,2,1]=>70
[8,3,1,4,5,7,6,2]=>[4,2,1,1]=>90
[3,5,1,6,8,4,7,2]=>[4,3,1]=>70
[6,1,5,7,3,8,4,2]=>[4,2,1,1]=>90
[5,8,4,7,3,2,6,1]=>[2,2,2,1,1]=>28
[7,2,6,5,8,4,1,3]=>[3,2,1,1,1]=>64
[8,3,2,5,1,6,7,4]=>[4,2,1,1]=>90
[2,6,8,3,7,4,1,5]=>[4,2,1,1]=>90
[8,1,5,6,4,7,3,2]=>[4,1,1,1,1]=>35
[2,5,8,1,6,4,7,3]=>[4,2,1,1]=>90
[7,4,1,8,3,2,6,5]=>[3,2,2,1]=>70
[8,3,7,4,2,1,6,5]=>[3,2,1,1,1]=>64
[5,2,6,8,3,1,7,4]=>[3,3,2]=>42
[3,6,5,8,4,1,7,2]=>[3,2,2,1]=>70
[7,3,6,1,8,4,5,2]=>[3,3,1,1]=>56
[8,2,7,3,4,6,5,1]=>[4,1,1,1,1]=>35
[7,3,8,2,5,6,4,1]=>[3,2,2,1]=>70
[5,7,3,1,6,4,8,2]=>[3,2,2,1]=>70
[6,1,3,2,4,8,7,5]=>[4,2,2]=>56
[8,7,4,2,3,6,1,5]=>[3,2,1,1,1]=>64
[8,7,1,5,4,2,3,6]=>[4,1,1,1,1]=>35
[3,7,1,5,2,8,6,4]=>[3,3,2]=>42
[8,7,2,5,4,1,3,6]=>[3,2,1,1,1]=>64
[8,7,2,5,3,1,4,6]=>[4,1,1,1,1]=>35
[5,2,8,7,1,4,3,6]=>[3,2,2,1]=>70
[7,1,8,6,2,4,3,5]=>[4,2,1,1]=>90
[8,1,6,2,7,5,3,4]=>[4,2,1,1]=>90
[7,1,6,2,8,5,3,4]=>[4,2,1,1]=>90
[6,3,4,1,7,2,8,5]=>[4,3,1]=>70
[7,2,4,3,5,1,8,6]=>[4,2,1,1]=>90
[5,1,7,2,3,8,6,4]=>[4,3,1]=>70
[8,2,3,5,1,7,6,4]=>[4,2,1,1]=>90
[7,6,3,1,4,8,2,5]=>[3,3,1,1]=>56
[6,1,8,2,7,5,3,4]=>[4,2,1,1]=>90
[7,2,8,1,6,5,3,4]=>[3,2,2,1]=>70
[7,2,6,4,3,8,1,5]=>[3,2,1,1,1]=>64
[5,1,7,4,3,8,2,6]=>[3,3,1,1]=>56
[5,3,1,7,4,8,2,6]=>[3,3,2]=>42
[7,4,8,2,1,5,3,6]=>[3,2,2,1]=>70
[8,2,4,1,6,3,7,5]=>[4,3,1]=>70
[8,2,7,5,1,6,4,3]=>[3,2,1,1,1]=>64
[6,1,7,3,2,8,5,4]=>[3,3,2]=>42
[4,7,2,1,6,3,8,5]=>[3,3,2]=>42
[6,2,1,5,3,8,4,7]=>[4,3,1]=>70
[5,3,1,6,2,8,4,7]=>[4,3,1]=>70
[6,1,5,2,8,4,3,7]=>[4,2,1,1]=>90
[7,4,3,8,1,5,2,6]=>[3,2,2,1]=>70
[7,4,8,1,5,3,2,6]=>[3,2,2,1]=>70
[6,1,5,3,2,8,4,7]=>[4,2,1,1]=>90
[6,3,2,8,4,1,5,7]=>[4,2,1,1]=>90
[7,3,4,2,8,5,1,6]=>[4,2,1,1]=>90
[7,1,6,3,4,2,8,5]=>[4,2,1,1]=>90
[8,5,1,3,7,4,2,6]=>[4,2,1,1]=>90
[3,8,6,1,5,2,7,4]=>[3,3,1,1]=>56
[8,6,1,3,7,5,2,4]=>[3,2,2,1]=>70
[4,8,5,6,1,7,3,2]=>[4,2,1,1]=>90
[6,7,1,3,8,5,2,4]=>[3,3,2]=>42
[3,6,7,1,5,2,8,4]=>[4,3,1]=>70
[7,1,3,8,4,2,6,5]=>[4,2,2]=>56
[5,6,2,7,1,3,8,4]=>[4,3,1]=>70
[5,6,2,8,1,3,7,4]=>[3,3,2]=>42
[6,1,8,3,7,5,2,4]=>[3,2,2,1]=>70
[7,4,2,1,5,8,3,6]=>[3,3,1,1]=>56
[7,4,1,5,8,3,2,6]=>[3,3,1,1]=>56
[7,3,2,6,4,8,1,5]=>[3,3,1,1]=>56
[6,4,2,7,3,8,1,5]=>[3,3,1,1]=>56
[5,1,8,3,7,4,2,6]=>[4,2,1,1]=>90
[7,4,8,3,1,5,2,6]=>[3,2,2,1]=>70
[5,2,1,7,4,8,3,6]=>[3,3,2]=>42
[6,1,8,4,5,2,7,3]=>[4,2,2]=>56
[7,1,6,4,5,2,8,3]=>[4,2,1,1]=>90
[3,5,2,7,1,6,8,4]=>[4,2,2]=>56
[4,5,7,3,1,6,8,2]=>[4,2,2]=>56
[4,5,7,2,8,6,1,3]=>[4,2,2]=>56
[3,5,1,7,2,6,8,4]=>[4,3,1]=>70
[4,5,7,2,8,1,3,6]=>[4,3,1]=>70
[4,6,7,2,1,5,8,3]=>[4,2,2]=>56
[4,6,7,1,3,8,5,2]=>[4,3,1]=>70
[3,6,1,5,7,8,4,2]=>[4,2,1,1]=>90
[4,6,7,1,5,8,3,2]=>[4,2,1,1]=>90
[6,1,3,7,4,8,5,2]=>[4,3,1]=>70
[3,2,1,7,4,8,5,6]=>[4,3,1]=>70
[4,1,5,2,7,6,3,8]=>[4,3,1]=>70
[2,5,1,3,7,6,4,8]=>[4,3,1]=>70
[2,5,1,4,3,8,6,7]=>[4,3,1]=>70
[3,7,2,1,5,8,6,4]=>[3,3,2]=>42
[6,2,7,1,4,8,5,3]=>[3,3,2]=>42
[3,7,4,2,1,8,5,6]=>[4,2,1,1]=>90
[7,2,5,3,1,8,6,4]=>[3,2,2,1]=>70
[7,5,1,4,2,8,6,3]=>[3,2,2,1]=>70
[7,5,4,1,3,8,6,2]=>[3,2,1,1,1]=>64
[5,3,2,1,7,6,4,8]=>[3,2,2,1]=>70
[6,3,2,8,1,5,7,4]=>[3,2,2,1]=>70
[7,4,3,2,8,1,6,5]=>[2,2,2,1,1]=>28
[7,6,2,4,8,3,5,1]=>[3,2,1,1,1]=>64
[7,3,6,4,8,1,5,2]=>[3,2,2,1]=>70
[2,7,5,3,8,1,4,6]=>[4,2,1,1]=>90
[1,8,5,3,6,4,2,7]=>[4,2,1,1]=>90
[8,6,2,3,7,5,4,1]=>[3,2,1,1,1]=>64
[8,6,3,2,7,5,4,1]=>[2,2,2,1,1]=>28
[8,3,2,7,1,6,4,5]=>[3,2,2,1]=>70
[7,2,6,1,5,4,3,8]=>[3,2,1,1,1]=>64
[8,5,7,4,3,6,2,1]=>[2,2,1,1,1,1]=>20
[8,5,7,2,4,6,3,1]=>[3,2,1,1,1]=>64
[8,4,6,7,1,3,2,5]=>[3,3,1,1]=>56
[2,8,5,6,1,4,3,7]=>[4,2,1,1]=>90
[7,2,6,8,4,1,5,3]=>[3,2,2,1]=>70
[7,6,4,8,3,2,5,1]=>[2,2,1,1,1,1]=>20
[6,5,8,1,4,2,7,3]=>[3,2,2,1]=>70
[6,5,8,4,1,3,7,2]=>[3,2,1,1,1]=>64
[5,4,8,3,2,1,7,6]=>[2,2,2,1,1]=>28
[4,3,7,2,1,6,5,8]=>[3,2,2,1]=>70
[2,5,8,1,4,3,7,6]=>[3,3,2]=>42
[3,6,8,2,1,5,7,4]=>[3,3,2]=>42
[5,7,4,8,1,3,6,2]=>[3,3,1,1]=>56
[5,7,1,4,8,2,6,3]=>[3,3,2]=>42
[2,7,4,1,8,3,6,5]=>[3,3,2]=>42
[3,5,1,8,4,2,7,6]=>[3,3,2]=>42
[4,1,5,7,3,6,2,8]=>[4,3,1]=>70
[4,2,5,8,3,1,7,6]=>[3,3,2]=>42
[6,1,2,7,8,3,5,4]=>[4,3,1]=>70
[5,3,1,8,6,4,2,7]=>[3,2,2,1]=>70
[3,1,8,4,7,5,2,6]=>[4,2,1,1]=>90
[4,2,8,7,3,5,1,6]=>[4,2,1,1]=>90
[4,8,1,7,6,2,3,5]=>[4,2,1,1]=>90
[6,8,1,4,7,5,2,3]=>[3,2,2,1]=>70
[7,3,8,1,6,4,2,5]=>[3,2,2,1]=>70
[4,7,8,1,5,3,2,6]=>[3,3,1,1]=>56
[7,1,8,6,2,5,3,4]=>[4,2,1,1]=>90
[5,8,7,1,3,6,4,2]=>[3,2,1,1,1]=>64
[3,8,7,2,1,6,4,5]=>[3,2,2,1]=>70
[2,8,7,1,6,3,5,4]=>[3,2,1,1,1]=>64
[3,7,6,1,5,4,2,8]=>[3,2,1,1,1]=>64
[4,8,7,6,1,3,5,2]=>[3,2,1,1,1]=>64
[5,8,7,2,6,1,4,3]=>[2,2,2,1,1]=>28
[6,8,1,7,5,2,4,3]=>[3,2,1,1,1]=>64
[7,3,8,6,5,1,2,4]=>[3,2,2,1]=>70
[5,7,8,4,3,1,2,6]=>[3,3,1,1]=>56
[5,8,6,4,3,2,1,7]=>[3,1,1,1,1,1]=>21
[8,7,3,6,4,2,1,5]=>[3,1,1,1,1,1]=>21
[5,2,6,3,4,7,1,8]=>[5,2,1]=>64
[3,4,7,5,8,6,1,2]=>[4,2,2]=>56
[2,4,7,1,5,3,8,6]=>[4,3,1]=>70
[4,7,6,5,2,1,8,3]=>[3,2,1,1,1]=>64
[5,3,6,2,4,1,7,8]=>[4,2,1,1]=>90
[5,3,6,1,4,2,7,8]=>[4,2,2]=>56
[1,7,4,2,6,3,8,5]=>[4,3,1]=>70
[4,7,6,3,8,5,1,2]=>[3,2,2,1]=>70
[2,7,1,6,8,3,5,4]=>[3,3,1,1]=>56
[9,1,2,3,4,5,6,8,7]=>[7,1,1]=>28
[10,1,2,3,4,5,6,7,9,8]=>[8,1,1]=>36
[9,1,2,3,4,5,7,8,6]=>[7,1,1]=>28
[2,3,4,5,6,9,7,8,1]=>[7,1,1]=>28
[2,3,4,5,6,7,8,10,9,1]=>[8,1,1]=>36
[5,2,8,7,6,4,3,1]=>[2,2,1,1,1,1]=>20
[8,2,7,6,1,5,4,3]=>[2,2,1,1,1,1]=>20
[8,4,1,7,6,5,3,2]=>[2,2,1,1,1,1]=>20
[4,5,6,2,3,8,1,7]=>[4,3,1]=>70
[4,5,3,2,7,8,1,6]=>[4,2,1,1]=>90
[6,5,7,3,8,4,2,1]=>[3,2,1,1,1]=>64
[6,8,7,2,4,3,5,1]=>[3,2,1,1,1]=>64
[3,2,7,4,5,8,1,6]=>[4,3,1]=>70
[6,8,1,5,2,4,3,7]=>[4,2,1,1]=>90
[8,3,4,6,1,5,2,7]=>[4,2,1,1]=>90
[2,3,4,7,5,8,1,6]=>[5,2,1]=>64
[6,3,4,7,8,2,5,1]=>[4,2,1,1]=>90
[5,3,7,4,8,6,1,2]=>[3,3,2]=>42
[8,3,6,4,1,7,2,5]=>[3,3,1,1]=>56
[1,3,7,4,8,6,2,5]=>[4,2,2]=>56
[3,7,8,5,4,1,2,6]=>[3,3,1,1]=>56
[5,4,3,1,7,8,2,6]=>[3,3,1,1]=>56
[5,7,6,2,8,4,1,3]=>[3,2,2,1]=>70
[6,1,7,5,8,3,4,2]=>[3,3,1,1]=>56
[7,5,6,4,1,3,8,2]=>[3,2,1,1,1]=>64
[1,5,6,8,4,7,3,2]=>[4,2,1,1]=>90
[4,1,3,7,6,5,8,2]=>[4,2,1,1]=>90
[3,4,1,7,5,8,6,2]=>[4,3,1]=>70
[8,5,7,4,3,1,6,2]=>[2,2,2,1,1]=>28
[6,8,5,1,7,2,4,3]=>[3,2,2,1]=>70
[8,2,4,1,3,7,6,5]=>[3,3,1,1]=>56
[7,8,3,6,2,1,4,5]=>[3,2,2,1]=>70
[8,1,7,4,2,3,6,5]=>[4,2,1,1]=>90
[1,8,7,2,3,5,6,4]=>[5,1,1,1]=>35
[2,8,3,1,6,7,5,4]=>[4,2,1,1]=>90
[8,2,3,1,5,7,6,4]=>[4,2,1,1]=>90
[3,8,4,1,2,7,6,5]=>[3,3,1,1]=>56
[5,4,7,2,3,6,8,1]=>[4,2,1,1]=>90
[6,3,2,1,8,4,7,5]=>[3,2,2,1]=>70
[2,3,7,4,1,8,5,6]=>[5,2,1]=>64
[6,4,1,3,2,7,8,5]=>[4,2,1,1]=>90
[2,7,8,5,1,3,6,4]=>[3,3,2]=>42
[8,2,5,6,7,1,3,4]=>[4,3,1]=>70
[2,8,5,4,7,6,1,3]=>[3,2,2,1]=>70
[6,7,1,5,8,2,4,3]=>[3,3,1,1]=>56
[4,8,7,6,2,3,5,1]=>[3,2,1,1,1]=>64
[7,8,1,5,3,2,6,4]=>[3,2,2,1]=>70
[6,5,7,3,8,2,1,4]=>[3,2,1,1,1]=>64
[8,1,4,7,2,5,6,3]=>[4,2,1,1]=>90
[7,3,4,6,1,5,8,2]=>[4,2,1,1]=>90
[8,3,4,5,7,1,6,2]=>[4,2,1,1]=>90
[4,2,6,8,3,1,5,7]=>[4,3,1]=>70
[3,7,6,2,4,5,1,8]=>[4,2,1,1]=>90
[2,3,6,5,8,1,4,7]=>[4,3,1]=>70
[2,3,5,8,6,1,4,7]=>[5,2,1]=>64
[4,2,3,8,6,1,5,7]=>[4,2,2]=>56
[6,4,1,2,8,3,5,7]=>[5,2,1]=>64
[1,2,3,7,4,6,8,5]=>[6,1,1]=>21
[3,2,7,1,4,5,8,6]=>[4,3,1]=>70
[2,1,5,3,8,7,4,6]=>[4,3,1]=>70
[5,8,3,2,4,1,6,7]=>[4,2,1,1]=>90
[4,2,7,1,8,3,5,6]=>[4,3,1]=>70
[4,1,8,2,7,3,5,6]=>[5,2,1]=>64
[1,2,7,5,3,8,4,6]=>[5,2,1]=>64
[3,2,7,1,4,8,5,6]=>[4,3,1]=>70
[1,2,3,7,6,8,4,5]=>[5,2,1]=>64
[1,2,3,6,8,7,4,5]=>[5,2,1]=>64
[1,2,3,7,8,4,6,5]=>[5,2,1]=>64
[1,2,3,6,8,4,7,5]=>[5,2,1]=>64
[1,2,3,7,8,6,4,5]=>[5,2,1]=>64
[6,2,8,3,7,5,1,4]=>[3,2,2,1]=>70
[4,2,8,3,7,5,6,1]=>[4,2,1,1]=>90
[7,3,4,8,6,5,1,2]=>[3,2,2,1]=>70
[5,3,4,8,7,2,6,1]=>[3,2,2,1]=>70
[4,3,5,8,7,2,6,1]=>[3,2,2,1]=>70
[4,6,3,8,5,7,2,1]=>[3,3,1,1]=>56
[7,5,3,8,6,2,4,1]=>[2,2,2,1,1]=>28
[2,6,8,3,7,4,5,1]=>[4,2,1,1]=>90
[1,8,4,3,7,5,6,2]=>[4,2,1,1]=>90
[2,5,8,3,7,4,6,1]=>[4,2,1,1]=>90
[7,4,3,8,6,2,5,1]=>[2,2,2,1,1]=>28
[3,5,4,8,7,2,6,1]=>[3,2,2,1]=>70
[4,5,3,8,6,7,2,1]=>[4,2,1,1]=>90
[3,6,7,8,4,5,2,1]=>[4,2,1,1]=>90
[2,6,8,5,4,7,3,1]=>[3,2,1,1,1]=>64
[1,8,5,6,4,7,3,2]=>[4,1,1,1,1]=>35
[2,5,8,6,4,7,3,1]=>[4,1,1,1,1]=>35
[7,4,6,5,8,3,2,1]=>[3,1,1,1,1,1]=>21
[6,3,7,8,4,5,2,1]=>[3,3,1,1]=>56
[4,3,7,8,5,6,2,1]=>[3,3,1,1]=>56
[5,2,8,6,4,7,3,1]=>[3,2,1,1,1]=>64
[4,2,8,6,5,7,3,1]=>[3,2,1,1,1]=>64
[3,2,8,6,7,4,5,1]=>[3,3,1,1]=>56
[2,3,8,7,5,4,6,1]=>[4,1,1,1,1]=>35
[1,8,2,7,4,5,6,3]=>[5,1,1,1]=>35
[7,2,8,6,3,4,5,1]=>[4,2,1,1]=>90
[6,2,8,4,5,7,3,1]=>[4,2,1,1]=>90
[5,2,8,4,6,7,3,1]=>[4,2,1,1]=>90
[4,2,8,5,6,7,3,1]=>[4,2,1,1]=>90
[4,3,6,8,5,7,2,1]=>[3,3,1,1]=>56
[3,4,6,8,7,2,5,1]=>[4,2,1,1]=>90
[7,3,5,8,6,2,4,1]=>[3,2,2,1]=>70
[1,8,3,5,7,4,6,2]=>[4,2,1,1]=>90
[2,7,8,4,5,6,3,1]=>[4,2,1,1]=>90
[3,7,5,8,4,6,2,1]=>[3,2,1,1,1]=>64
[5,7,4,6,8,3,2,1]=>[3,2,1,1,1]=>64
[3,6,5,8,4,7,2,1]=>[3,2,1,1,1]=>64
[2,6,8,4,5,7,3,1]=>[4,2,1,1]=>90
[4,2,7,1,3,8,5,6]=>[4,3,1]=>70
[4,2,5,1,3,8,6,7]=>[4,3,1]=>70
[5,3,6,1,7,2,4,8]=>[4,3,1]=>70
[3,7,1,2,5,8,6,4]=>[4,3,1]=>70
[3,7,4,1,2,8,5,6]=>[4,3,1]=>70
[7,5,1,3,4,8,6,2]=>[4,2,1,1]=>90
[7,5,1,2,4,8,6,3]=>[4,2,1,1]=>90
[6,4,2,3,7,1,5,8]=>[4,2,1,1]=>90
[7,6,3,8,1,2,5,4]=>[3,2,2,1]=>70
[7,4,2,3,8,1,6,5]=>[3,2,2,1]=>70
[4,7,5,2,8,1,3,6]=>[3,3,1,1]=>56
[8,2,6,3,7,1,4,5]=>[4,2,1,1]=>90
[8,6,1,2,7,4,5,3]=>[4,2,1,1]=>90
[8,4,7,1,2,3,6,5]=>[4,2,1,1]=>90
[8,5,7,1,2,4,6,3]=>[4,2,1,1]=>90
[8,5,7,1,3,4,6,2]=>[4,2,1,1]=>90
[8,6,2,7,1,3,5,4]=>[3,2,2,1]=>70
[3,8,5,6,1,2,4,7]=>[4,3,1]=>70
[3,7,5,8,1,2,4,6]=>[4,3,1]=>70
[7,6,4,8,1,3,5,2]=>[3,2,1,1,1]=>64
[6,5,8,1,2,4,7,3]=>[4,2,1,1]=>90
[3,6,8,1,2,5,7,4]=>[4,3,1]=>70
[3,7,2,4,8,1,6,5]=>[3,3,2]=>42
[4,6,3,8,1,2,5,7]=>[4,3,1]=>70
[4,6,3,7,1,2,5,8]=>[4,3,1]=>70
[4,1,7,8,2,3,6,5]=>[4,3,1]=>70
[5,1,2,8,6,3,4,7]=>[5,2,1]=>64
[5,3,8,1,6,2,4,7]=>[4,2,2]=>56
[6,1,8,5,2,3,4,7]=>[5,2,1]=>64
[6,1,7,5,2,3,4,8]=>[5,2,1]=>64
[6,8,1,3,7,4,5,2]=>[4,2,1,1]=>90
[7,2,8,1,6,3,4,5]=>[4,2,2]=>56
[4,7,8,2,5,1,3,6]=>[3,3,2]=>42
[6,8,2,7,1,4,5,3]=>[3,2,2,1]=>70
[4,8,7,1,3,5,6,2]=>[4,2,1,1]=>90
[3,8,7,1,2,4,6,5]=>[4,2,1,1]=>90
[4,8,7,1,2,3,6,5]=>[4,2,1,1]=>90
[5,8,7,1,2,4,6,3]=>[4,2,1,1]=>90
[5,8,7,1,3,4,6,2]=>[4,2,1,1]=>90
[7,1,8,6,2,3,5,4]=>[4,2,1,1]=>90
[5,8,6,4,1,2,3,7]=>[4,2,1,1]=>90
[7,8,4,1,2,5,3,6]=>[4,2,2]=>56
[7,8,1,2,6,5,3,4]=>[4,2,1,1]=>90
[1,4,8,2,7,5,3,6]=>[4,2,1,1]=>90
[1,2,8,7,5,4,3,6]=>[4,1,1,1,1]=>35
[5,1,7,3,6,4,8,2]=>[4,2,1,1]=>90
[6,2,1,5,7,4,3,8]=>[4,2,1,1]=>90
[3,4,8,7,5,6,1,2]=>[4,2,1,1]=>90
[1,8,3,7,6,4,5,2]=>[4,1,1,1,1]=>35
[5,1,2,4,7,6,8,3]=>[5,2,1]=>64
[5,7,4,1,2,6,3,8]=>[4,2,2]=>56
[4,8,1,2,6,7,3,5]=>[4,3,1]=>70
[3,1,2,4,6,8,7,5]=>[5,2,1]=>64
[4,8,2,1,6,3,7,5]=>[3,3,2]=>42
[3,8,6,5,2,7,1,4]=>[3,2,1,1,1]=>64
[3,7,8,5,2,1,6,4]=>[3,2,2,1]=>70
[2,8,7,5,1,6,4,3]=>[3,2,1,1,1]=>64
[2,8,6,7,5,1,4,3]=>[3,2,1,1,1]=>64
[6,1,7,4,3,8,2,5]=>[3,3,1,1]=>56
[4,8,2,3,1,5,7,6]=>[4,2,2]=>56
[1,7,8,4,2,3,6,5]=>[4,2,2]=>56
[4,7,1,3,8,2,6,5]=>[3,3,2]=>42
[2,4,3,7,5,8,1,6]=>[4,3,1]=>70
[1,8,3,4,2,6,7,5]=>[5,2,1]=>64
[6,4,1,3,7,2,8,5]=>[4,2,1,1]=>90
[8,1,4,3,6,2,7,5]=>[4,2,1,1]=>90
[7,2,5,8,4,3,1,6]=>[3,2,1,1,1]=>64
[6,1,8,3,4,2,7,5]=>[4,2,2]=>56
[6,3,1,4,2,8,7,5]=>[3,3,2]=>42
[7,3,8,1,2,6,4,5]=>[4,2,2]=>56
[7,1,4,5,3,2,6,8]=>[5,1,1,1]=>35
[1,8,4,2,6,5,3,7]=>[4,2,1,1]=>90
[5,1,4,8,6,3,2,7]=>[4,2,1,1]=>90
[5,3,1,8,4,7,2,6]=>[3,3,2]=>42
[4,3,8,1,5,7,2,6]=>[3,3,2]=>42
[6,3,1,2,5,7,4,8]=>[5,2,1]=>64
[7,1,4,2,6,5,3,8]=>[4,2,1,1]=>90
[3,8,4,1,6,5,2,7]=>[4,2,1,1]=>90
[7,3,6,4,5,8,2,1]=>[4,1,1,1,1]=>35
[7,1,5,4,8,6,3,2]=>[3,2,1,1,1]=>64
[2,1,8,7,5,3,6,4]=>[3,3,1,1]=>56
[5,8,3,7,4,1,6,2]=>[3,2,2,1]=>70
[5,7,1,4,8,6,3,2]=>[3,3,1,1]=>56
[3,5,7,4,8,6,2,1]=>[4,2,1,1]=>90
[5,3,7,4,8,6,2,1]=>[3,3,1,1]=>56
[7,5,8,4,1,6,3,2]=>[2,2,2,1,1]=>28
[5,7,3,8,4,1,6,2]=>[3,3,2]=>42
[5,6,3,8,1,4,7,2]=>[3,3,2]=>42
[3,7,8,4,1,6,5,2]=>[3,2,2,1]=>70
[8,7,3,1,5,4,2,6]=>[3,2,1,1,1]=>64
[3,6,2,1,5,4,8,7]=>[3,3,2]=>42
[5,4,2,6,1,3,8,7]=>[3,3,1,1]=>56
[3,2,6,5,1,4,8,7]=>[3,3,2]=>42
[2,5,8,1,7,4,3,6]=>[3,3,1,1]=>56
[6,8,2,7,4,3,1,5]=>[3,2,1,1,1]=>64
[6,8,2,3,7,5,1,4]=>[3,2,2,1]=>70
[7,6,2,5,4,8,1,3]=>[3,2,1,1,1]=>64
[2,6,5,1,8,4,3,7]=>[3,3,1,1]=>56
[4,2,7,3,1,8,5,6]=>[4,3,1]=>70
[4,2,3,7,1,5,8,6]=>[4,3,1]=>70
[5,2,7,3,8,6,1,4]=>[3,3,2]=>42
[2,1,5,8,4,3,7,6]=>[3,3,2]=>42
[5,8,4,2,6,7,1,3]=>[3,2,2,1]=>70
[3,2,4,8,1,5,7,6]=>[4,2,2]=>56
[2,4,8,3,1,7,5,6]=>[4,2,2]=>56
[4,8,3,2,1,7,6,5]=>[2,2,2,2]=>14
[4,1,3,7,2,6,8,5]=>[4,2,2]=>56
[3,4,8,2,1,6,5,7]=>[4,2,2]=>56
[6,8,3,7,2,1,5,4]=>[2,2,2,2]=>14
[3,5,8,1,7,2,6,4]=>[3,3,1,1]=>56
[5,1,7,4,6,8,3,2]=>[4,2,1,1]=>90
[7,6,4,8,1,5,3,2]=>[2,2,2,1,1]=>28
[5,3,7,1,8,2,6,4]=>[3,3,2]=>42
[2,7,6,3,8,1,4,5]=>[4,2,1,1]=>90
[2,1,7,6,4,8,3,5]=>[3,3,1,1]=>56
[2,1,5,4,8,7,3,6]=>[3,3,2]=>42
[5,4,8,7,2,6,1,3]=>[2,2,2,2]=>14
[2,4,3,8,7,1,5,6]=>[4,2,2]=>56
[3,4,1,8,6,2,7,5]=>[4,3,1]=>70
[3,8,5,4,2,1,7,6]=>[3,2,1,1,1]=>64
[4,8,6,5,2,7,1,3]=>[3,2,1,1,1]=>64
[3,2,8,7,5,4,1,6]=>[3,2,1,1,1]=>64
[2,8,6,5,4,3,1,7]=>[3,1,1,1,1,1]=>21
[7,3,6,5,2,8,4,1]=>[3,2,1,1,1]=>64
[8,7,5,3,1,4,2,6]=>[3,2,1,1,1]=>64
[7,1,5,3,8,4,6,2]=>[4,2,1,1]=>90
[2,1,8,7,4,3,5,6]=>[4,2,1,1]=>90
[3,8,7,4,2,1,5,6]=>[4,1,1,1,1]=>35
[8,5,2,6,1,7,3,4]=>[3,3,1,1]=>56
[5,4,2,6,8,3,7,1]=>[3,3,1,1]=>56
[6,5,2,8,1,4,3,7]=>[3,2,2,1]=>70
[3,4,8,1,5,2,7,6]=>[4,3,1]=>70
[4,8,1,2,5,3,6,7]=>[5,2,1]=>64
[2,3,4,6,5,7,8,9,10,1]=>[8,1,1]=>36
[4,8,7,6,3,5,2,1]=>[2,2,1,1,1,1]=>20
[3,8,7,6,5,2,4,1]=>[2,2,1,1,1,1]=>20
[5,8,4,7,6,3,2,1]=>[2,2,1,1,1,1]=>20
[6,8,5,4,7,3,2,1]=>[2,2,1,1,1,1]=>20
[4,8,7,6,3,2,5,1]=>[2,2,1,1,1,1]=>20
[3,8,7,6,5,2,1,4]=>[2,2,1,1,1,1]=>20
[9,7,10,5,8,3,6,2,4,1]=>[2,2,2,2,1,1]=>90
[3,5,2,4,7,6,1,8]=>[4,3,1]=>70
[3,5,4,7,2,6,1,8]=>[4,2,1,1]=>90
[3,5,4,7,6,1,2,8]=>[4,2,2]=>56
[3,5,4,7,6,1,8,2]=>[4,2,2]=>56
[3,5,7,4,6,1,8,2]=>[4,2,2]=>56
[3,5,7,4,6,1,2,8]=>[4,2,2]=>56
[3,5,7,4,6,2,1,8]=>[4,2,1,1]=>90
[3,2,5,7,4,6,1,8]=>[4,3,1]=>70
[3,5,2,7,6,4,1,8]=>[4,2,1,1]=>90
[3,5,7,2,6,4,1,8]=>[4,2,1,1]=>90
[5,3,7,6,2,4,1,8]=>[3,2,2,1]=>70
[5,3,7,6,1,2,8,4]=>[3,3,2]=>42
[5,3,7,6,1,4,2,8]=>[3,2,2,1]=>70
[5,3,7,6,4,1,2,8]=>[3,2,2,1]=>70
[3,5,7,2,6,1,4,8]=>[4,2,2]=>56
[3,5,2,7,6,1,4,8]=>[4,2,2]=>56
[5,3,7,6,4,1,8,2]=>[3,2,2,1]=>70
[3,7,5,4,1,8,2,6]=>[3,3,1,1]=>56
[3,7,5,4,1,8,6,2]=>[3,2,2,1]=>70
[3,7,5,1,4,8,6,2]=>[3,3,1,1]=>56
[3,7,5,1,4,8,2,6]=>[3,3,1,1]=>56
[3,5,7,1,2,6,8,4]=>[4,3,1]=>70
[3,5,7,2,1,6,8,4]=>[4,2,2]=>56
[3,5,2,7,1,6,4,8]=>[4,2,2]=>56
[3,5,7,2,1,6,4,8]=>[4,2,2]=>56
[5,3,7,1,6,2,4,8]=>[4,2,2]=>56
[3,5,7,1,4,6,8,2]=>[4,3,1]=>70
[3,5,7,1,4,6,2,8]=>[4,3,1]=>70
[3,5,7,1,4,2,6,8]=>[4,3,1]=>70
[3,5,7,2,1,4,6,8]=>[4,3,1]=>70
[3,5,2,7,1,4,6,8]=>[4,3,1]=>70
[3,2,5,7,4,1,6,8]=>[4,3,1]=>70
[3,5,2,7,4,1,6,8]=>[4,3,1]=>70
[3,5,7,4,2,1,6,8]=>[4,2,1,1]=>90
[3,5,7,4,1,2,6,8]=>[4,3,1]=>70
[3,5,4,7,1,6,8,2]=>[4,2,2]=>56
[3,5,4,7,1,2,6,8]=>[4,3,1]=>70
[3,5,4,7,2,1,6,8]=>[4,2,1,1]=>90
[3,5,4,2,7,1,6,8]=>[4,2,1,1]=>90
[3,2,5,4,7,1,6,8]=>[4,3,1]=>70
[3,5,4,7,2,1,8,6]=>[4,2,1,1]=>90
[3,5,4,7,1,2,8,6]=>[4,3,1]=>70
[5,7,6,3,1,8,4,2]=>[3,2,2,1]=>70
[5,7,6,3,1,8,2,4]=>[3,3,1,1]=>56
[3,5,7,4,1,2,8,6]=>[4,3,1]=>70
[3,5,7,4,2,1,8,6]=>[4,2,1,1]=>90
[3,2,5,7,4,1,8,6]=>[4,3,1]=>70
[3,2,5,7,1,4,8,6]=>[4,3,1]=>70
[3,5,2,7,1,4,8,6]=>[4,3,1]=>70
[3,5,7,2,1,4,8,6]=>[4,3,1]=>70
[3,5,7,1,4,2,8,6]=>[4,3,1]=>70
[3,7,5,2,1,8,6,4]=>[3,2,2,1]=>70
[3,7,2,5,1,8,6,4]=>[3,3,2]=>42
[3,2,7,5,1,8,6,4]=>[3,3,2]=>42
[3,2,7,5,1,8,4,6]=>[3,3,2]=>42
[3,7,2,5,1,8,4,6]=>[3,3,2]=>42
[3,7,5,2,1,8,4,6]=>[3,3,1,1]=>56
[2,1,7,5,8,4,6,3]=>[3,3,1,1]=>56
[1,3,4,5,6,7,9,2,8]=>[7,2]=>27
[2,3,4,5,6,7,1,9,8]=>[7,2]=>27
[2,1,4,5,6,7,8,9,3]=>[7,2]=>27
[3,1,4,5,6,7,8,2,9]=>[7,2]=>27
[5,8,3,4,1,7,6,2]=>[3,2,2,1]=>70
[5,8,7,2,4,1,6,3]=>[3,2,2,1]=>70
[3,8,6,4,1,7,5,2]=>[3,2,2,1]=>70
[4,3,5,6,8,1,7,2]=>[4,2,2]=>56
[3,7,6,4,1,8,5,2]=>[3,2,2,1]=>70
[3,7,4,1,8,6,5,2]=>[3,2,2,1]=>70
[3,8,4,1,7,6,5,2]=>[3,2,1,1,1]=>64
[3,2,7,6,1,5,4,8]=>[3,2,2,1]=>70
[3,2,8,7,6,1,5,4]=>[2,2,2,1,1]=>28
[5,7,8,2,4,1,6,3]=>[3,3,2]=>42
[4,2,5,8,1,6,7,3]=>[4,2,2]=>56
[4,2,5,8,1,7,3,6]=>[3,3,2]=>42
[5,8,2,4,1,6,3,7]=>[4,2,2]=>56
[8,4,2,6,5,1,3,7]=>[3,2,2,1]=>70
[3,2,6,8,1,5,4,7]=>[3,3,2]=>42
[8,3,2,5,6,1,4,7]=>[4,2,1,1]=>90
[3,2,8,6,7,1,5,4]=>[3,2,2,1]=>70
[3,2,6,8,7,1,5,4]=>[3,2,2,1]=>70
[3,2,6,7,1,5,4,8]=>[4,2,2]=>56
[8,7,3,2,5,6,1,4]=>[3,2,1,1,1]=>64
[7,2,8,1,5,3,6,4]=>[3,3,2]=>42
[8,4,2,7,5,1,3,6]=>[3,2,2,1]=>70
[7,4,2,8,5,1,3,6]=>[3,2,2,1]=>70
[7,2,4,1,8,3,6,5]=>[3,3,2]=>42
[3,2,8,5,7,1,4,6]=>[3,3,2]=>42
[2,6,5,7,1,8,3,4]=>[4,3,1]=>70
[2,5,1,8,7,4,3,6]=>[3,3,1,1]=>56
[8,1,4,6,3,5,2,7]=>[4,2,1,1]=>90
[8,3,5,4,1,6,2,7]=>[4,2,1,1]=>90
[8,6,3,4,1,5,2,7]=>[4,2,1,1]=>90
[5,4,7,6,8,2,3,1]=>[3,2,2,1]=>70
[4,1,8,2,3,7,6,5]=>[4,2,1,1]=>90
[2,1,8,5,3,4,7,6]=>[4,3,1]=>70
[5,2,4,6,8,7,3,1]=>[4,2,1,1]=>90
[1,6,8,3,4,5,7,2]=>[5,2,1]=>64
[5,7,4,8,6,1,3,2]=>[3,2,2,1]=>70
[5,4,2,6,7,8,1,3]=>[4,2,1,1]=>90
[6,4,2,7,3,5,8,1]=>[4,2,1,1]=>90
[7,4,1,8,3,5,6,2]=>[4,2,1,1]=>90
[6,5,4,8,7,3,1,2]=>[2,2,2,1,1]=>28
[8,7,4,2,1,3,6,5]=>[3,2,1,1,1]=>64
[8,7,1,3,2,5,6,4]=>[4,2,1,1]=>90
[6,8,2,3,1,7,5,4]=>[3,2,2,1]=>70
[7,4,3,2,6,8,5,1]=>[3,2,1,1,1]=>64
[2,7,4,3,8,5,6,1]=>[4,2,1,1]=>90
[8,3,7,2,1,5,6,4]=>[3,2,2,1]=>70
[5,7,8,2,4,3,1,6]=>[3,3,1,1]=>56
[8,4,7,3,2,6,1,5]=>[2,2,2,1,1]=>28
[8,3,1,6,7,4,2,5]=>[3,3,1,1]=>56
[3,2,5,7,4,8,1,6]=>[4,3,1]=>70
[8,2,7,3,4,1,5,6]=>[5,1,1,1]=>35
[7,1,6,3,5,8,2,4]=>[4,2,1,1]=>90
[2,8,5,6,7,1,4,3]=>[4,2,1,1]=>90
[1,5,2,7,8,6,4,3]=>[4,2,1,1]=>90
[2,6,8,5,1,4,7,3]=>[3,3,1,1]=>56
[1,4,2,8,6,5,7,3]=>[4,2,1,1]=>90
[3,5,1,6,8,7,2,4]=>[4,3,1]=>70
[5,7,6,2,1,3,8,4]=>[3,3,1,1]=>56
[2,5,8,7,4,1,6,3]=>[3,2,2,1]=>70
[4,1,7,5,2,6,8,3]=>[4,3,1]=>70
[7,6,2,4,5,1,8,3]=>[4,2,1,1]=>90
[7,3,4,2,5,8,6,1]=>[4,2,1,1]=>90
[8,7,4,2,5,1,6,3]=>[3,2,1,1,1]=>64
[8,1,4,5,2,6,7,3]=>[5,2,1]=>64
[5,2,4,8,6,7,1,3]=>[4,2,2]=>56
[8,5,6,2,1,3,7,4]=>[3,3,1,1]=>56
[4,2,1,5,6,7,8,3]=>[5,2,1]=>64
[3,4,6,5,1,7,8,2]=>[5,2,1]=>64
[7,3,5,2,4,6,1,8]=>[4,2,1,1]=>90
[5,3,7,2,4,6,1,8]=>[4,2,1,1]=>90
[3,7,5,2,4,6,1,8]=>[4,2,1,1]=>90
[5,7,3,2,4,6,1,8]=>[4,2,1,1]=>90
[1,5,3,2,4,7,6,8]=>[5,2,1]=>64
[1,5,3,2,7,4,6,8]=>[5,2,1]=>64
[5,7,3,2,1,4,6,8]=>[4,2,1,1]=>90
[5,7,3,2,4,1,6,8]=>[4,2,1,1]=>90
[3,7,2,5,4,1,6,8]=>[4,2,1,1]=>90
[5,1,3,2,4,7,6,8]=>[5,2,1]=>64
[5,1,3,2,7,4,6,8]=>[5,2,1]=>64
[7,1,3,2,5,4,6,8]=>[5,2,1]=>64
[1,7,3,2,5,4,6,8]=>[5,2,1]=>64
[7,1,3,5,2,4,6,8]=>[5,2,1]=>64
[5,1,3,7,2,4,6,8]=>[5,2,1]=>64
[3,2,7,5,1,4,6,8]=>[4,2,2]=>56
[3,7,5,1,2,4,6,8]=>[5,2,1]=>64
[5,7,3,1,2,4,6,8]=>[5,2,1]=>64
[1,5,3,7,2,4,6,8]=>[5,2,1]=>64
[5,3,2,7,4,1,6,8]=>[4,2,1,1]=>90
[5,3,2,4,7,1,6,8]=>[4,2,1,1]=>90
[5,3,2,1,4,7,6,8]=>[4,2,1,1]=>90
[5,3,2,1,7,4,6,8]=>[4,2,1,1]=>90
[1,3,2,7,5,4,6,8]=>[5,2,1]=>64
[1,3,7,2,5,4,6,8]=>[5,2,1]=>64
[7,3,1,2,5,4,6,8]=>[5,2,1]=>64
[5,3,1,2,7,4,6,8]=>[5,2,1]=>64
[5,3,1,2,4,7,6,8]=>[5,2,1]=>64
[3,2,5,1,4,7,6,8]=>[4,3,1]=>70
[7,3,1,5,2,4,6,8]=>[5,2,1]=>64
[1,3,7,5,2,4,6,8]=>[5,2,1]=>64
[7,5,1,3,2,4,6,8]=>[5,1,1,1]=>35
[5,7,1,3,2,4,6,8]=>[5,2,1]=>64
[3,7,1,5,2,4,6,8]=>[5,2,1]=>64
[3,7,1,2,5,4,6,8]=>[5,2,1]=>64
[3,7,2,1,5,4,6,8]=>[4,2,2]=>56
[3,2,1,7,5,4,6,8]=>[4,2,2]=>56
[3,1,2,7,5,4,6,8]=>[5,2,1]=>64
[3,1,7,2,5,4,6,8]=>[5,2,1]=>64
[3,1,7,5,2,4,6,8]=>[5,2,1]=>64
[7,1,5,3,2,4,6,8]=>[5,1,1,1]=>35
[1,7,5,3,2,4,6,8]=>[5,1,1,1]=>35
[1,2,3,4,5,7,9,6,8]=>[7,2]=>27
[1,2,3,4,6,9,5,7,8]=>[7,2]=>27
[1,2,3,5,9,4,6,7,8]=>[7,2]=>27
[1,2,4,9,3,5,6,7,8]=>[7,2]=>27
[1,3,9,2,4,5,6,7,8]=>[7,2]=>27
[7,5,3,4,2,8,1,6]=>[3,2,1,1,1]=>64
[8,5,6,2,7,4,3,1]=>[3,2,1,1,1]=>64
[3,5,1,4,8,2,7,6]=>[3,3,2]=>42
[1,7,5,4,8,6,3,2]=>[3,2,1,1,1]=>64
[2,5,1,4,8,7,3,6]=>[3,3,2]=>42
[1,5,6,4,8,7,2,3]=>[4,2,2]=>56
[3,6,4,1,8,7,2,5]=>[3,3,2]=>42
[1,6,4,3,8,5,2,7]=>[4,2,1,1]=>90
[7,6,1,4,5,3,8,2]=>[4,1,1,1,1]=>35
[1,6,4,2,8,5,3,7]=>[4,2,2]=>56
[7,6,5,8,3,1,4,2]=>[2,2,2,1,1]=>28
[2,6,4,3,8,5,7,1]=>[4,2,1,1]=>90
[7,2,3,1,5,8,6,4]=>[4,2,2]=>56
[7,1,5,6,3,8,4,2]=>[4,2,1,1]=>90
[7,2,6,5,3,8,1,4]=>[3,2,1,1,1]=>64
[1,5,6,4,8,3,7,2]=>[4,2,1,1]=>90
[7,6,1,3,4,5,8,2]=>[5,1,1,1]=>35
[7,1,3,2,4,8,5,6]=>[5,2,1]=>64
[7,6,1,5,4,3,8,2]=>[3,1,1,1,1,1]=>21
[3,5,6,8,2,1,7,4]=>[4,2,2]=>56
[4,2,1,5,3,7,8,6]=>[4,3,1]=>70
[3,5,6,8,1,7,2,4]=>[4,3,1]=>70
[4,5,3,1,7,2,8,6]=>[4,3,1]=>70
[5,1,3,4,2,6,7,8]=>[6,1,1]=>21
[5,3,1,4,2,6,7,8]=>[5,2,1]=>64
[4,6,2,7,1,3,5,8]=>[4,3,1]=>70
[5,1,4,2,3,6,7,8]=>[6,1,1]=>21
[3,6,1,7,2,5,8,4]=>[4,3,1]=>70
[5,1,4,3,2,6,7,8]=>[5,1,1,1]=>35
[6,2,4,5,1,8,3,7]=>[4,3,1]=>70
[2,1,4,8,6,3,7,5]=>[4,3,1]=>70
[8,6,2,4,7,5,1,3]=>[3,2,2,1]=>70
[2,6,8,1,4,5,7,3]=>[4,3,1]=>70
[8,4,2,6,7,3,1,5]=>[3,3,1,1]=>56
[1,6,7,5,8,2,3,4]=>[4,3,1]=>70
[6,2,3,8,7,4,1,5]=>[4,2,1,1]=>90
[5,8,1,4,3,6,2,7]=>[4,2,1,1]=>90
[5,8,4,1,3,7,6,2]=>[3,2,2,1]=>70
[6,4,5,3,8,1,7,2]=>[3,2,2,1]=>70
[4,3,5,7,2,1,6,8]=>[4,2,1,1]=>90
[3,4,6,2,5,8,7,1]=>[4,3,1]=>70
[4,2,8,3,5,7,1,6]=>[4,2,2]=>56
[1,3,7,2,6,5,8,4]=>[4,2,1,1]=>90
[1,3,6,4,2,5,8,7]=>[5,2,1]=>64
[1,5,4,7,3,6,8,2]=>[4,2,1,1]=>90
[1,6,3,7,8,2,4,5]=>[4,3,1]=>70
[3,2,6,7,8,1,4,5]=>[4,3,1]=>70
[5,1,8,3,6,4,7,2]=>[4,2,1,1]=>90
[3,8,5,6,1,7,2,4]=>[4,3,1]=>70
[3,4,8,1,7,6,2,5]=>[3,3,1,1]=>56
[4,7,6,8,5,1,3,2]=>[3,2,1,1,1]=>64
[6,7,4,8,5,1,3,2]=>[3,2,2,1]=>70
[6,4,8,3,1,7,5,2]=>[2,2,2,2]=>14
[3,6,5,8,7,1,4,2]=>[3,2,2,1]=>70
[5,7,4,8,2,6,3,1]=>[3,2,2,1]=>70
[5,6,4,8,2,7,3,1]=>[3,2,2,1]=>70
[6,5,3,8,2,7,4,1]=>[2,2,2,1,1]=>28
[6,4,8,1,3,7,5,2]=>[3,2,2,1]=>70
[7,6,3,1,4,2,5,8]=>[4,2,1,1]=>90
[1,5,4,3,7,8,2,6]=>[4,2,1,1]=>90
[7,8,4,2,5,3,1,6]=>[3,2,2,1]=>70
[4,2,7,8,5,3,1,6]=>[3,3,1,1]=>56
[4,2,5,3,1,7,8,6]=>[4,3,1]=>70
[4,2,8,7,6,3,1,5]=>[3,2,1,1,1]=>64
[4,2,7,6,3,1,5,8]=>[4,2,1,1]=>90
[6,3,1,7,5,2,4,8]=>[4,2,2]=>56
[6,3,1,8,7,5,2,4]=>[3,2,2,1]=>70
[8,6,3,1,7,5,2,4]=>[3,2,2,1]=>70
[4,2,7,6,3,1,8,5]=>[3,3,1,1]=>56
[7,6,3,1,8,4,2,5]=>[3,2,2,1]=>70
[7,6,4,2,1,8,3,5]=>[3,2,1,1,1]=>64
[1,8,2,7,6,4,3,5]=>[4,1,1,1,1]=>35
[8,3,5,7,6,4,2,1]=>[3,1,1,1,1,1]=>21
[8,4,2,5,7,6,3,1]=>[3,2,1,1,1]=>64
[7,5,2,4,8,6,3,1]=>[3,2,1,1,1]=>64
[8,7,5,2,4,6,3,1]=>[3,1,1,1,1,1]=>21
[7,5,2,4,6,3,1,8]=>[4,1,1,1,1]=>35
[5,2,8,6,3,7,4,1]=>[3,3,1,1]=>56
[8,4,7,5,2,6,3,1]=>[3,2,1,1,1]=>64
[8,3,6,4,7,5,2,1]=>[3,2,1,1,1]=>64
[1,8,2,7,5,3,6,4]=>[4,2,1,1]=>90
[7,5,2,1,8,3,6,4]=>[3,2,2,1]=>70
[7,5,2,6,3,1,8,4]=>[3,3,1,1]=>56
[5,2,7,4,1,8,6,3]=>[3,3,2]=>42
[5,2,8,7,4,1,6,3]=>[3,2,2,1]=>70
[8,7,4,1,5,2,6,3]=>[3,3,1,1]=>56
[7,4,1,5,2,8,6,3]=>[3,3,2]=>42
[7,6,3,1,4,2,8,5]=>[3,3,1,1]=>56
[7,5,2,8,6,3,1,4]=>[3,2,2,1]=>70
[8,7,5,2,6,3,1,4]=>[3,2,1,1,1]=>64
[7,5,2,1,3,6,4,8]=>[4,2,1,1]=>90
[8,7,5,2,1,3,6,4]=>[3,2,1,1,1]=>64
[7,5,2,1,3,8,6,4]=>[3,2,2,1]=>70
[1,3,7,6,5,8,2,4]=>[4,2,1,1]=>90
[8,6,4,7,5,2,1,3]=>[2,2,2,1,1]=>28
[6,4,8,7,5,2,1,3]=>[2,2,2,1,1]=>28
[6,4,7,5,2,1,3,8]=>[3,2,2,1]=>70
[6,3,1,4,7,5,2,8]=>[4,2,2]=>56
[6,3,1,4,8,7,5,2]=>[3,2,2,1]=>70
[8,6,3,1,4,7,5,2]=>[3,2,2,1]=>70
[8,5,7,6,3,1,4,2]=>[2,2,2,1,1]=>28
[1,8,2,5,7,6,4,3]=>[4,1,1,1,1]=>35
[1,8,2,6,4,7,5,3]=>[4,2,1,1]=>90
[7,5,2,1,6,4,8,3]=>[3,2,2,1]=>70
[6,3,8,7,4,1,5,2]=>[3,2,2,1]=>70
[6,3,7,4,1,5,2,8]=>[4,2,2]=>56
[7,4,1,6,3,5,2,8]=>[4,2,1,1]=>90
[7,4,1,8,6,3,5,2]=>[3,2,2,1]=>70
[8,4,6,3,1,7,5,2]=>[3,2,2,1]=>70
[6,4,7,5,2,1,8,3]=>[3,2,2,1]=>70
[1,6,4,7,5,3,8,2]=>[4,2,1,1]=>90
[8,6,3,5,2,7,4,1]=>[3,2,1,1,1]=>64
[6,3,5,2,8,7,4,1]=>[3,2,2,1]=>70
[6,3,5,2,7,4,1,8]=>[4,2,1,1]=>90
[1,4,7,3,5,2,6,8]=>[5,2,1]=>64
[5,7,4,2,6,3,1,8]=>[3,2,2,1]=>70
[4,2,6,3,5,7,1,8]=>[5,2,1]=>64
[2,4,5,8,1,6,7,3]=>[5,2,1]=>64
[6,1,3,7,4,2,5,8]=>[5,2,1]=>64
[3,2,6,8,1,5,7,4]=>[3,3,2]=>42
[8,6,2,7,1,5,4,3]=>[2,2,2,1,1]=>28
[7,6,8,3,1,5,4,2]=>[2,2,2,1,1]=>28
[6,3,7,2,8,1,5,4]=>[3,2,2,1]=>70
[7,5,2,8,6,1,4,3]=>[2,2,2,2]=>14
[2,7,3,8,1,5,6,4]=>[4,2,2]=>56
[1,6,8,5,2,4,3,7]=>[4,2,1,1]=>90
[4,5,7,2,8,1,6,3]=>[4,2,2]=>56
[8,4,6,5,3,1,7,2]=>[3,2,1,1,1]=>64
[4,5,3,1,7,2,6,8]=>[4,3,1]=>70
[7,8,1,2,4,3,6,5]=>[4,2,2]=>56
[8,4,1,6,2,3,7,5]=>[4,3,1]=>70
[6,1,3,4,2,8,5,7]=>[5,2,1]=>64
[8,1,4,3,5,7,6,2]=>[4,2,1,1]=>90
[5,2,4,1,3,7,8,6]=>[4,3,1]=>70
[1,7,4,3,6,8,2,5]=>[4,2,1,1]=>90
[8,7,1,3,6,5,4,2]=>[3,1,1,1,1,1]=>21
[1,8,5,7,4,2,6,3]=>[3,2,2,1]=>70
[4,7,5,3,8,2,1,6]=>[3,2,1,1,1]=>64
[6,3,5,8,7,4,1,2]=>[3,2,2,1]=>70
[8,1,7,6,3,5,4,2]=>[3,1,1,1,1,1]=>21
[3,6,8,5,7,4,1,2]=>[3,2,2,1]=>70
[4,7,6,8,5,3,1,2]=>[3,2,1,1,1]=>64
[3,8,7,5,6,4,2,1]=>[3,1,1,1,1,1]=>21
[2,8,7,6,4,5,3,1]=>[3,1,1,1,1,1]=>21
[1,8,7,6,5,3,4,2]=>[3,1,1,1,1,1]=>21
[4,6,7,2,5,3,1,8]=>[4,2,1,1]=>90
[2,4,7,8,1,6,5,3]=>[4,2,1,1]=>90
[4,2,6,8,7,1,5,3]=>[3,2,2,1]=>70
[5,1,8,4,2,7,6,3]=>[3,2,2,1]=>70
[2,7,3,8,1,6,5,4]=>[3,2,2,1]=>70
[2,6,8,4,1,7,5,3]=>[3,2,2,1]=>70
[4,6,7,1,2,8,5,3]=>[4,3,1]=>70
[3,6,1,8,2,7,5,4]=>[3,3,1,1]=>56
[5,7,4,1,2,8,6,3]=>[3,3,2]=>42
[6,3,7,1,2,8,5,4]=>[3,3,2]=>42
[1,7,8,5,4,3,2,6]=>[3,2,1,1,1]=>64
[1,2,6,7,8,4,3,5]=>[5,2,1]=>64
[8,1,4,6,7,3,5,2]=>[4,2,1,1]=>90
[4,7,1,3,6,8,2,5]=>[4,2,2]=>56
[3,7,6,4,8,1,2,5]=>[3,3,1,1]=>56
[1,3,6,7,4,2,8,5]=>[5,2,1]=>64
[3,6,4,8,2,7,5,1]=>[3,2,2,1]=>70
[8,1,6,7,5,3,2,4]=>[3,2,1,1,1]=>64
[8,7,2,4,6,5,3,1]=>[3,1,1,1,1,1]=>21
[8,7,2,5,4,6,1,3]=>[3,2,1,1,1]=>64
[8,7,3,2,1,5,6,4]=>[3,2,1,1,1]=>64
[3,7,8,2,1,6,5,4]=>[3,2,2,1]=>70
[8,7,6,1,4,5,3,2]=>[3,1,1,1,1,1]=>21
[1,8,5,4,6,2,3,7]=>[4,2,1,1]=>90
[2,5,8,4,7,3,6,1]=>[3,2,2,1]=>70
[3,6,4,2,7,8,5,1]=>[4,2,1,1]=>90
[4,5,8,1,7,6,2,3]=>[3,3,1,1]=>56
[1,5,8,4,7,3,6,2]=>[3,2,2,1]=>70
[3,6,4,1,7,8,5,2]=>[4,2,2]=>56
[1,6,4,3,7,8,5,2]=>[4,2,1,1]=>90
[7,1,3,4,8,6,5,2]=>[4,2,1,1]=>90
[2,6,4,3,7,1,8,5]=>[4,2,1,1]=>90
[2,6,4,1,7,8,3,5]=>[4,3,1]=>70
[7,2,3,4,8,6,5,1]=>[4,2,1,1]=>90
[7,2,3,1,8,6,4,5]=>[4,2,2]=>56
[7,2,3,8,1,6,5,4]=>[3,2,2,1]=>70
[1,5,8,4,7,6,2,3]=>[3,2,2,1]=>70
[7,1,3,2,5,6,8,4]=>[5,2,1]=>64
[7,6,1,8,5,4,2,3]=>[3,2,1,1,1]=>64
[3,2,6,5,8,4,7,1]=>[3,3,1,1]=>56
[4,3,7,1,6,5,8,2]=>[3,2,2,1]=>70
[5,3,7,4,8,1,6,2]=>[3,3,2]=>42
[4,3,7,1,5,2,8,6]=>[3,3,2]=>42
[5,4,8,2,6,3,7,1]=>[3,2,2,1]=>70
[5,4,8,1,6,3,7,2]=>[3,2,2,1]=>70
[4,1,7,5,2,3,6,8]=>[5,2,1]=>64
[4,1,7,8,6,3,2,5]=>[3,3,1,1]=>56
[6,8,3,2,1,4,7,5]=>[3,2,2,1]=>70
[7,2,4,1,6,5,8,3]=>[4,2,1,1]=>90
[7,5,8,4,3,1,6,2]=>[2,2,2,1,1]=>28
[6,8,2,4,1,3,7,5]=>[3,3,2]=>42
[2,8,4,7,6,3,5,1]=>[3,2,1,1,1]=>64
[4,2,7,3,8,5,6,1]=>[4,3,1]=>70
[4,5,2,6,8,3,7,1]=>[4,3,1]=>70
[6,8,5,3,4,7,2,1]=>[3,2,1,1,1]=>64
[6,8,4,1,5,3,7,2]=>[3,2,2,1]=>70
[6,8,3,5,1,4,7,2]=>[3,2,2,1]=>70
[6,8,5,4,2,3,7,1]=>[3,2,1,1,1]=>64
[8,1,3,4,2,6,5,7]=>[5,2,1]=>64
[8,1,3,2,5,6,4,7]=>[5,2,1]=>64
[8,1,2,4,5,3,7,6]=>[5,2,1]=>64
[10,1,3,2,5,4,7,6,9,8]=>[5,4,1]=>288
[10,1,2,3,4,6,7,8,9,5]=>[8,1,1]=>36
[12,1,3,2,5,4,7,6,9,8,11,10]=>[6,5,1]=>1155
[12,1,2,3,4,5,7,8,9,10,11,6]=>[10,1,1]=>55
[6,5,3,8,4,2,7,1]=>[3,2,1,1,1]=>64
[7,4,5,1,6,2,8,3]=>[4,3,1]=>70
[4,7,3,5,6,2,8,1]=>[4,2,1,1]=>90
[6,7,8,4,1,3,5,2]=>[3,3,1,1]=>56
[3,1,6,8,4,7,5,2]=>[3,3,1,1]=>56
[8,3,6,1,5,7,4,2]=>[3,2,1,1,1]=>64
[3,2,7,5,8,6,1,4]=>[3,3,2]=>42
[2,5,4,7,8,1,6,3]=>[4,2,2]=>56
[2,4,6,7,8,1,5,3]=>[5,2,1]=>64
[2,4,6,8,1,7,5,3]=>[4,2,1,1]=>90
[7,4,3,8,6,2,1,5]=>[2,2,2,1,1]=>28
[2,4,7,8,3,5,6,1]=>[4,3,1]=>70
[3,2,7,6,1,8,4,5]=>[3,3,2]=>42
[3,2,6,8,1,7,4,5]=>[3,3,2]=>42
[4,3,6,2,1,8,5,7]=>[3,3,1,1]=>56
[4,6,2,3,7,5,8,1]=>[4,3,1]=>70
[5,8,4,2,3,6,7,1]=>[4,2,1,1]=>90
[8,4,5,3,2,1,7,6]=>[3,2,1,1,1]=>64
[5,8,3,4,2,1,7,6]=>[3,2,2,1]=>70
[6,4,8,3,2,7,1,5]=>[2,2,2,1,1]=>28
[5,8,3,7,2,1,6,4]=>[2,2,2,2]=>14
[2,5,6,4,7,1,8,3]=>[5,2,1]=>64
[6,4,7,3,8,2,1,5]=>[3,2,1,1,1]=>64
[6,7,4,3,2,1,8,5]=>[3,2,1,1,1]=>64
[8,4,3,7,2,1,5,6]=>[3,2,1,1,1]=>64
[1,5,2,8,4,6,7,3]=>[5,2,1]=>64
[1,5,2,7,4,6,8,3]=>[5,2,1]=>64
[5,1,2,7,3,6,8,4]=>[5,2,1]=>64
[5,1,2,8,3,6,7,4]=>[5,2,1]=>64
[5,6,3,4,8,7,2,1]=>[3,3,1,1]=>56
[6,5,3,4,8,7,2,1]=>[3,2,1,1,1]=>64
[4,1,2,8,3,6,7,5]=>[5,2,1]=>64
[4,1,2,7,3,6,8,5]=>[5,2,1]=>64
[7,5,3,8,4,6,2,1]=>[3,2,1,1,1]=>64
[8,5,3,7,4,6,2,1]=>[3,2,1,1,1]=>64
[5,8,1,2,3,4,7,6]=>[5,2,1]=>64
[7,1,2,8,3,6,4,5]=>[5,2,1]=>64
[6,1,8,2,3,5,7,4]=>[5,2,1]=>64
[6,1,7,2,3,5,8,4]=>[5,2,1]=>64
[1,6,8,2,4,5,7,3]=>[5,2,1]=>64
[4,3,8,7,5,6,2,1]=>[3,2,1,1,1]=>64
[1,8,2,7,4,6,5,3]=>[4,1,1,1,1]=>35
[7,1,6,2,3,5,8,4]=>[5,1,1,1]=>35
[8,1,6,2,3,5,7,4]=>[5,1,1,1]=>35
[8,1,7,2,3,5,6,4]=>[5,1,1,1]=>35
[5,8,3,7,4,6,2,1]=>[3,2,1,1,1]=>64
[6,8,7,3,4,5,2,1]=>[3,2,1,1,1]=>64
[1,8,7,2,4,5,3,6]=>[5,1,1,1]=>35
[8,7,1,2,3,4,6,5]=>[5,1,1,1]=>35
[8,6,1,2,3,4,7,5]=>[5,2,1]=>64
[8,1,6,2,3,5,4,7]=>[5,1,1,1]=>35
[1,7,6,2,4,5,3,8]=>[5,1,1,1]=>35
[1,8,7,4,6,3,5,2]=>[3,2,1,1,1]=>64
[1,8,3,5,7,2,6,4]=>[4,2,1,1]=>90
[2,3,4,6,8,5,7,1]=>[5,2,1]=>64
[2,3,5,7,4,8,6,1]=>[5,2,1]=>64
[2,4,6,3,7,8,5,1]=>[5,2,1]=>64
[2,5,7,1,8,6,3,4]=>[4,3,1]=>70
[2,6,7,1,8,4,5,3]=>[4,3,1]=>70
[5,8,3,1,4,2,6,7]=>[4,2,2]=>56
[3,8,4,2,6,7,1,5]=>[4,2,1,1]=>90
[2,4,1,8,5,6,3,7]=>[5,2,1]=>64
[3,5,2,6,7,8,4,1]=>[5,2,1]=>64
[4,5,1,6,7,3,8,2]=>[5,2,1]=>64
[2,8,4,1,7,5,3,6]=>[4,2,1,1]=>90
[8,5,3,1,7,4,2,6]=>[3,2,2,1]=>70
[4,2,8,7,1,5,3,6]=>[3,2,2,1]=>70
[5,2,6,8,1,7,4,3]=>[3,2,2,1]=>70
[5,7,3,2,6,8,1,4]=>[3,2,2,1]=>70
[6,7,1,2,3,5,8,4]=>[5,2,1]=>64
[3,1,6,7,8,4,2,5]=>[4,3,1]=>70
[3,1,4,8,5,6,2,7]=>[5,2,1]=>64
[8,3,1,4,5,7,2,6]=>[4,3,1]=>70
[1,6,7,8,9,2,3,4,5]=>[5,4]=>42
[6,7,8,9,1,2,3,4,5,10]=>[6,4]=>90
[6,7,8,1,2,3,4,5,9]=>[6,3]=>48
[1,7,8,9,2,3,4,5,6]=>[6,3]=>48
[1,7,8,9,10,2,3,4,5,6]=>[6,4]=>90
[6,7,8,9,10,1,2,3,4,5,11]=>[6,5]=>132
[5,6,7,8,9,1,2,3,4,10]=>[6,4]=>90
[5,6,7,1,8,2,3,4,9]=>[5,4]=>42
[4,6,7,8,1,2,3,5,9]=>[5,4]=>42
[1,6,7,8,2,9,3,4,5]=>[5,4]=>42
[1,5,7,8,9,2,3,4,6]=>[5,4]=>42
[1,6,7,8,9,10,2,3,4,5]=>[6,4]=>90
[1,7,8,9,10,11,2,3,4,5,6]=>[6,5]=>132
[8,6,2,3,5,1,4,7]=>[4,2,1,1]=>90
[8,2,4,5,7,3,1,6]=>[4,2,1,1]=>90
[2,6,3,8,7,5,4,1]=>[3,2,1,1,1]=>64
[8,2,3,7,5,4,1,6]=>[4,1,1,1,1]=>35
[8,2,6,3,5,4,1,7]=>[4,1,1,1,1]=>35
[8,6,1,5,2,4,3,7]=>[4,1,1,1,1]=>35
[8,6,2,4,1,5,3,7]=>[4,2,1,1]=>90
[8,4,1,6,5,3,2,7]=>[3,2,1,1,1]=>64
[8,3,6,1,5,4,2,7]=>[3,2,1,1,1]=>64
[8,3,2,6,5,4,1,7]=>[3,2,1,1,1]=>64
[8,3,2,5,7,4,1,6]=>[3,3,1,1]=>56
[8,3,1,7,5,4,2,6]=>[3,2,1,1,1]=>64
[8,2,7,4,1,5,3,6]=>[4,2,1,1]=>90
[6,1,3,8,7,5,4,2]=>[3,2,1,1,1]=>64
[3,6,1,8,7,5,4,2]=>[3,2,1,1,1]=>64
[3,8,1,5,7,6,4,2]=>[3,2,1,1,1]=>64
[3,5,2,8,7,6,4,1]=>[3,2,1,1,1]=>64
[3,4,8,2,7,6,5,1]=>[3,2,1,1,1]=>64
[3,4,8,7,1,6,5,2]=>[3,2,1,1,1]=>64
[8,1,3,5,7,6,4,2]=>[4,1,1,1,1]=>35
[4,1,8,5,7,6,3,2]=>[3,2,1,1,1]=>64
[8,2,7,1,4,5,6,3]=>[4,2,1,1]=>90
[8,1,7,3,4,6,2,5]=>[4,2,1,1]=>90
[8,3,1,7,2,6,5,4]=>[3,2,1,1,1]=>64
[3,8,2,4,7,6,5,1]=>[3,2,1,1,1]=>64
[2,8,3,7,4,6,5,1]=>[4,1,1,1,1]=>35
[8,2,3,7,1,6,5,4]=>[3,2,1,1,1]=>64
[8,2,7,1,3,6,5,4]=>[3,2,1,1,1]=>64
[8,1,7,2,6,4,3,5]=>[4,1,1,1,1]=>35
[8,1,7,5,2,4,3,6]=>[4,1,1,1,1]=>35
[8,2,3,7,4,6,1,5]=>[4,2,1,1]=>90
[2,4,8,5,7,6,3,1]=>[4,1,1,1,1]=>35
[8,2,4,3,7,6,1,5]=>[3,2,2,1]=>70
[8,2,7,3,5,1,4,6]=>[4,2,1,1]=>90
[8,2,7,4,3,1,5,6]=>[4,1,1,1,1]=>35
[8,2,7,3,1,5,6,4]=>[4,2,1,1]=>90
[8,2,1,5,7,6,4,3]=>[3,2,1,1,1]=>64
[6,2,1,8,7,5,4,3]=>[2,2,2,1,1]=>28
[6,1,8,2,7,5,4,3]=>[3,2,1,1,1]=>64
[8,1,7,3,5,2,6,4]=>[4,2,1,1]=>90
[8,1,5,2,7,6,4,3]=>[3,2,1,1,1]=>64
[8,1,7,2,4,6,5,3]=>[4,1,1,1,1]=>35
[8,2,4,1,7,6,5,3]=>[3,2,1,1,1]=>64
[4,2,8,3,7,6,5,1]=>[3,2,1,1,1]=>64
[4,8,2,1,7,6,5,3]=>[2,2,2,1,1]=>28
[5,1,8,7,2,6,4,3]=>[3,2,1,1,1]=>64
[5,8,1,3,7,6,2,4]=>[3,2,2,1]=>70
[8,2,5,4,1,7,6,3]=>[3,2,2,1]=>70
[5,1,4,8,7,6,3,2]=>[3,2,1,1,1]=>64
[8,1,4,3,7,6,5,2]=>[3,2,1,1,1]=>64
[4,8,1,3,7,6,5,2]=>[3,2,1,1,1]=>64
[4,3,8,1,7,6,5,2]=>[2,2,2,1,1]=>28
[5,8,6,3,2,1,7,4]=>[3,2,1,1,1]=>64
[5,7,6,3,2,4,1,8]=>[3,2,1,1,1]=>64
[6,5,7,2,4,3,1,8]=>[3,2,1,1,1]=>64
[5,7,1,3,2,8,6,4]=>[3,3,2]=>42
[5,8,1,3,2,7,4,6]=>[4,2,2]=>56
[8,5,1,3,2,4,6,7]=>[5,1,1,1]=>35
[7,5,8,2,1,4,3,6]=>[3,2,2,1]=>70
[6,7,1,2,5,4,8,3]=>[4,2,1,1]=>90
[6,8,1,2,5,7,4,3]=>[4,2,1,1]=>90
[8,1,6,4,2,3,5,7]=>[5,1,1,1]=>35
[1,5,4,8,2,3,7,6]=>[4,2,2]=>56
[1,7,8,2,3,5,6,4]=>[5,2,1]=>64
[7,5,8,2,3,1,4,6]=>[4,2,1,1]=>90
[7,4,1,2,6,8,3,5]=>[4,3,1]=>70
[6,2,8,1,5,7,3,4]=>[3,3,2]=>42
[7,3,5,4,2,1,8,6]=>[3,2,1,1,1]=>64
[7,3,2,8,5,6,1,4]=>[3,2,2,1]=>70
[1,7,4,3,6,8,5,2]=>[4,2,1,1]=>90
[4,7,6,5,2,3,8,1]=>[3,2,1,1,1]=>64
[6,7,4,2,1,8,5,3]=>[3,2,2,1]=>70
[6,5,8,1,7,3,4,2]=>[3,2,2,1]=>70
[6,5,8,2,3,7,4,1]=>[3,2,2,1]=>70
[4,1,2,8,5,3,6,7]=>[5,2,1]=>64
[3,5,8,2,6,1,7,4]=>[4,2,2]=>56
[3,7,6,1,5,2,8,4]=>[3,3,1,1]=>56
[1,7,6,2,5,8,4,3]=>[4,1,1,1,1]=>35
[1,7,6,5,8,4,2,3]=>[3,2,1,1,1]=>64
[3,7,6,2,8,4,5,1]=>[3,3,1,1]=>56
[2,7,6,1,8,4,3,5]=>[3,3,1,1]=>56
[7,1,2,6,3,5,4,8]=>[5,1,1,1]=>35
[7,2,6,3,4,5,1,8]=>[5,1,1,1]=>35
[6,1,2,5,7,8,4,3]=>[5,1,1,1]=>35
[4,1,2,7,8,5,3,6]=>[4,3,1]=>70
[4,7,3,1,2,6,8,5]=>[4,2,2]=>56
[3,7,6,1,5,8,2,4]=>[3,3,1,1]=>56
[3,8,5,6,4,2,7,1]=>[4,1,1,1,1]=>35
[3,2,6,4,7,8,5,1]=>[4,3,1]=>70
[4,2,7,5,8,3,1,6]=>[3,3,1,1]=>56
[5,2,1,4,7,8,3,6]=>[4,3,1]=>70
[5,6,2,7,3,4,8,1]=>[4,3,1]=>70
[6,1,3,8,5,4,7,2]=>[4,2,1,1]=>90
[2,7,6,8,5,1,3,4]=>[3,3,1,1]=>56
[2,7,6,8,5,3,1,4]=>[3,2,1,1,1]=>64
[1,5,8,6,4,2,3,7]=>[4,2,1,1]=>90
[2,5,8,6,4,1,7,3]=>[4,2,1,1]=>90
[1,6,2,3,5,8,7,4]=>[5,2,1]=>64
[4,7,2,3,1,6,8,5]=>[4,2,2]=>56
[6,7,3,1,5,4,8,2]=>[3,2,2,1]=>70
[7,4,6,2,8,3,5,1]=>[3,3,1,1]=>56
[7,3,5,1,4,8,2,6]=>[3,3,1,1]=>56
[3,4,6,5,1,2,7,8]=>[5,2,1]=>64
[4,3,8,2,6,7,5,1]=>[3,2,2,1]=>70
[5,1,8,6,4,7,2,3]=>[3,3,1,1]=>56
[4,2,6,1,5,3,8,7]=>[3,3,2]=>42
[6,7,2,3,1,5,8,4]=>[4,2,2]=>56
[7,5,2,3,8,1,6,4]=>[3,2,2,1]=>70
[7,5,2,3,8,4,1,6]=>[4,2,1,1]=>90
[4,5,1,7,6,3,8,2]=>[4,2,1,1]=>90
[8,1,7,5,2,3,4,6]=>[5,1,1,1]=>35
[8,6,3,1,4,2,5,7]=>[4,2,1,1]=>90
[4,5,1,6,2,8,7,3]=>[4,3,1]=>70
[6,2,7,8,3,4,5,1]=>[4,3,1]=>70
[9,2,3,4,5,6,7,8,1]=>[7,1,1]=>28
[8,2,3,4,5,6,7,1,9]=>[7,1,1]=>28
[7,2,3,4,5,6,1,8,9]=>[7,1,1]=>28
[1,2,4,3,5,6,7,8,9]=>[8,1]=>8
[1,2,4,6,8,9,7,5,3]=>[6,1,1,1]=>56
[1,2,4,5,3,6,7,8,9]=>[8,1]=>8
[1,2,4,3,5,6,7,8,9,10]=>[9,1]=>9
[1,2,4,6,8,10,9,7,5,3]=>[6,1,1,1,1]=>126
[1,2,4,6,8,5,7,3]=>[5,2,1]=>64
[2,1,7,5,8,6,3,4]=>[3,3,2]=>42
[4,7,3,8,6,5,2,1]=>[3,2,1,1,1]=>64
[3,8,7,4,6,5,1,2]=>[3,2,1,1,1]=>64
[7,3,8,4,6,5,1,2]=>[3,2,2,1]=>70
[7,4,3,6,5,8,1,2]=>[3,2,2,1]=>70
[4,5,8,7,2,6,1,3]=>[3,2,2,1]=>70
[3,8,6,7,5,1,4,2]=>[3,2,1,1,1]=>64
[4,2,7,6,5,8,3,1]=>[3,2,1,1,1]=>64
[4,6,7,8,5,2,3,1]=>[4,2,1,1]=>90
[4,5,3,8,2,7,6,1]=>[3,2,2,1]=>70
[3,8,5,4,1,7,6,2]=>[3,2,2,1]=>70
[6,4,7,2,5,8,3,1]=>[3,2,2,1]=>70
[6,3,8,7,5,1,4,2]=>[2,2,2,1,1]=>28
[5,3,6,4,1,2,8,7]=>[3,3,2]=>42
[6,8,4,3,5,7,1,2]=>[3,2,2,1]=>70
[5,2,4,8,7,6,1,3]=>[3,2,2,1]=>70
[4,2,5,1,7,8,3,6]=>[4,3,1]=>70
[2,5,4,1,3,8,6,7]=>[4,3,1]=>70
[1,4,5,3,8,2,6,7]=>[5,2,1]=>64
[5,1,8,2,4,3,6,7]=>[5,2,1]=>64
[1,5,4,8,2,3,6,7]=>[5,2,1]=>64
[4,8,3,1,6,7,2,5]=>[3,3,2]=>42
[3,4,8,2,6,5,7,1]=>[4,2,1,1]=>90
[3,6,2,4,8,7,1,5]=>[3,3,2]=>42
[4,7,3,2,6,8,1,5]=>[3,2,2,1]=>70
[7,3,4,6,8,1,2,5]=>[4,3,1]=>70
[3,6,7,2,5,8,1,4]=>[4,2,2]=>56
[1,5,6,8,3,7,2,4]=>[4,2,2]=>56
[6,1,5,8,3,4,7,2]=>[4,2,1,1]=>90
[5,6,8,1,3,4,7,2]=>[4,3,1]=>70
[2,8,5,6,3,4,7,1]=>[4,2,1,1]=>90
[6,8,1,3,5,4,7,2]=>[4,2,1,1]=>90
[8,1,6,3,5,4,7,2]=>[4,1,1,1,1]=>35
[7,1,2,5,8,4,6,3]=>[4,2,1,1]=>90
[6,2,4,8,1,7,3,5]=>[3,3,2]=>42
[3,1,7,8,5,4,6,2]=>[3,3,1,1]=>56
[1,6,2,7,4,8,5,3]=>[4,3,1]=>70
[2,7,1,8,4,3,5,6]=>[4,3,1]=>70
[6,7,1,8,3,2,4,5]=>[4,3,1]=>70
[2,7,6,3,5,8,1,4]=>[4,2,1,1]=>90
[2,7,5,6,8,1,3,4]=>[4,3,1]=>70
[6,7,2,8,1,3,4,5]=>[4,3,1]=>70
[5,1,6,8,7,2,3,4]=>[4,3,1]=>70
[1,5,7,6,8,2,3,4]=>[4,3,1]=>70
[7,4,6,8,5,3,1,2]=>[3,2,1,1,1]=>64
[3,8,6,7,5,1,2,4]=>[3,3,1,1]=>56
[1,6,8,3,2,5,4,7]=>[4,2,2]=>56
[2,6,8,1,5,4,7,3]=>[3,3,1,1]=>56
[1,5,4,7,6,2,8,3]=>[4,2,2]=>56
[6,1,5,8,3,2,7,4]=>[3,2,2,1]=>70
[3,1,2,4,8,5,7,6]=>[5,2,1]=>64
[7,1,5,4,8,3,2,6]=>[3,2,1,1,1]=>64
[6,4,1,7,5,3,2,8]=>[3,2,2,1]=>70
[2,7,6,4,8,1,5,3]=>[3,2,2,1]=>70
[7,2,5,4,8,1,6,3]=>[3,2,2,1]=>70
[1,7,2,5,3,8,6,4]=>[4,2,2]=>56
[2,4,1,3,6,8,5,7,9]=>[5,4]=>42
[7,2,3,8,6,1,5,4]=>[3,2,2,1]=>70
[5,3,8,4,1,2,6,7]=>[4,2,2]=>56
[2,4,8,3,7,1,5,6]=>[4,2,2]=>56
[5,2,8,4,1,6,3,7]=>[4,2,2]=>56
[7,6,5,2,1,8,4,3]=>[2,2,2,1,1]=>28
[2,7,5,1,8,3,6,4]=>[3,3,2]=>42
[5,1,8,7,4,3,6,2]=>[3,2,1,1,1]=>64
[3,8,7,2,4,6,1,5]=>[3,2,2,1]=>70
[5,7,1,3,2,4,8,6]=>[4,3,1]=>70
[4,2,7,6,3,5,8,1]=>[4,2,1,1]=>90
[8,4,7,6,3,5,1,2]=>[2,2,2,1,1]=>28
[8,1,7,4,2,3,5,6]=>[5,1,1,1]=>35
[6,5,1,3,8,7,4,2]=>[3,2,2,1]=>70
[4,7,8,3,2,5,1,6]=>[3,3,1,1]=>56
[6,1,8,5,3,7,2,4]=>[3,2,2,1]=>70
[5,1,6,8,3,7,4,2]=>[3,3,1,1]=>56
[8,6,5,1,7,4,3,2]=>[2,2,1,1,1,1]=>20
[7,6,4,1,3,5,8,2]=>[4,1,1,1,1]=>35
[8,2,3,7,1,4,5,6]=>[5,2,1]=>64
[2,8,3,7,1,4,5,6]=>[5,2,1]=>64
[5,6,2,7,4,3,1,8]=>[4,2,1,1]=>90
[8,6,2,7,4,1,3,5]=>[3,2,2,1]=>70
[3,7,8,5,2,1,4,6]=>[3,3,1,1]=>56
[6,8,4,7,3,1,5,2]=>[2,2,2,2]=>14
[4,8,6,5,1,2,7,3]=>[3,3,1,1]=>56
[4,8,6,5,1,2,3,7]=>[4,2,1,1]=>90
[3,4,5,1,7,6,8,2]=>[5,2,1]=>64
[3,8,7,6,5,1,2,4]=>[3,2,1,1,1]=>64
[8,4,6,7,1,2,5,3]=>[3,3,1,1]=>56
[5,7,2,6,1,8,4,3]=>[3,2,2,1]=>70
[5,7,2,6,1,3,8,4]=>[3,3,2]=>42
[5,8,2,6,1,4,7,3]=>[3,2,2,1]=>70
[3,8,7,5,6,1,4,2]=>[3,2,1,1,1]=>64
[6,8,4,7,2,1,5,3]=>[2,2,2,2]=>14
[1,7,3,4,5,2,8,6]=>[5,2,1]=>64
[1,7,2,5,4,3,8,6]=>[4,2,1,1]=>90
[2,1,5,7,4,3,8,6]=>[4,3,1]=>70
[6,4,1,3,8,7,5,2]=>[3,2,2,1]=>70
[2,1,7,4,6,8,3,5]=>[4,3,1]=>70
[8,6,4,2,7,3,5,1]=>[3,2,1,1,1]=>64
[2,1,8,3,5,7,6,4]=>[4,2,1,1]=>90
[7,2,4,8,6,1,5,3]=>[3,2,2,1]=>70
[2,4,1,5,6,7,8,9,10,3]=>[8,2]=>35
[2,3,4,5,6,7,9,1,10,8]=>[8,2]=>35
[2,3,5,1,6,7,8,9,10,4]=>[8,2]=>35
[2,3,4,5,6,8,1,9,10,7]=>[8,2]=>35
[2,3,4,6,1,7,8,9,10,5]=>[8,2]=>35
[2,3,4,5,7,1,8,9,10,6]=>[8,2]=>35
[4,1,2,5,6,7,8,9,10,3]=>[8,2]=>35
[4,3,1,5,6,7,8,10,2,9]=>[6,3,1]=>315
[2,4,1,5,6,7,8,9,10,11,3]=>[9,2]=>44
[2,6,1,5,3,7,8,9,10,4]=>[6,3,1]=>315
[2,3,4,5,6,7,8,10,1,11,9]=>[9,2]=>44
[5,3,4,1,6,7,9,2,10,8]=>[6,3,1]=>315
[2,3,5,1,6,7,8,9,10,11,4]=>[9,2]=>44
[2,3,8,1,6,7,4,9,10,5]=>[6,3,1]=>315
[2,3,4,5,6,7,9,1,10,11,8]=>[9,2]=>44
[6,3,4,5,1,8,2,9,10,7]=>[6,3,1]=>315
[2,3,4,6,1,7,8,9,10,11,5]=>[9,2]=>44
[2,3,4,10,1,7,8,9,5,6]=>[6,3,1]=>315
[2,3,4,5,6,8,1,9,10,11,7]=>[9,2]=>44
[2,3,4,5,7,1,8,9,10,11,6]=>[9,2]=>44
[3,2,4,5,6,7,8,1,9]=>[7,1,1]=>28
[6,4,3,2,8,1,7,5]=>[2,2,2,1,1]=>28
[6,2,4,3,8,1,7,5]=>[3,2,2,1]=>70
[5,8,4,3,1,6,7,2]=>[3,2,2,1]=>70
[8,7,2,4,6,10,1,3,5,9]=>[4,4,1,1]=>300
[2,10,7,9,4,6,8,1,3,5]=>[4,3,2,1]=>768
[6,5,2,4,8,10,1,3,7,9]=>[4,4,1,1]=>300
[2,8,5,7,4,6,10,1,3,9]=>[4,3,2,1]=>768
[10,5,2,4,7,9,6,8,1,3]=>[4,3,2,1]=>768
[10,9,2,8,5,7,4,6,1,3]=>[3,2,2,1,1,1]=>315
[8,7,6,5,2,4,10,1,3,9]=>[3,3,1,1,1,1]=>225
[10,7,2,6,5,9,4,8,1,3]=>[3,2,2,1,1,1]=>315
[6,10,5,9,8,7,2,4,1,3]=>[2,2,2,2,1,1]=>90
[4,10,3,9,2,6,8,1,5,7]=>[3,3,2,2]=>252
[4,3,10,7,9,2,6,8,1,5]=>[3,3,2,2]=>252
[3,6,2,5,4,8,10,1,7,9]=>[4,4,1,1]=>300
[3,6,10,2,5,9,4,8,1,7]=>[3,3,2,2]=>252
[3,5,8,2,4,7,6,10,1,9]=>[4,4,1,1]=>300
[3,5,7,10,2,4,6,9,8,1]=>[4,4,1,1]=>300
[10,9,3,5,8,2,4,7,6,1]=>[3,3,1,1,1,1]=>225
[8,7,3,6,2,5,4,10,1,9]=>[3,3,1,1,1,1]=>225
[7,6,3,5,10,2,4,9,8,1]=>[3,3,2,1,1]=>450
[3,6,10,9,8,2,5,7,4,1]=>[3,3,1,1,1,1]=>225
[10,9,8,7,3,6,2,5,4,1]=>[2,2,1,1,1,1,1,1]=>35
[5,4,3,8,2,7,6,10,1,9]=>[3,3,2,1,1]=>450
[5,4,3,7,10,2,6,9,8,1]=>[3,3,2,1,1]=>450
[5,10,4,9,3,8,2,7,6,1]=>[2,2,2,2,1,1]=>90
[4,8,3,7,6,5,2,10,1,9]=>[3,3,1,1,1,1]=>225
[4,7,3,6,5,10,2,9,8,1]=>[3,3,2,1,1]=>450
[4,6,10,3,5,9,8,7,2,1]=>[3,3,1,1,1,1]=>225
[10,9,4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1,1,1]=>35
[7,6,5,4,3,10,2,9,8,1]=>[2,2,2,1,1,1,1]=>75
[6,5,4,10,3,9,8,7,2,1]=>[2,2,2,2,1,1]=>90
[5,10,4,9,8,7,6,3,2,1]=>[2,2,1,1,1,1,1,1]=>35
[12,11,2,4,6,8,10,1,3,5,7,9]=>[5,5,1,1]=>1485
[10,9,2,4,6,8,12,1,3,5,7,11]=>[5,5,1,1]=>1485
[2,12,9,11,4,6,8,10,1,3,5,7]=>[5,4,2,1]=>5775
[12,11,10,9,2,4,6,8,1,3,5,7]=>[4,4,1,1,1,1]=>1925
[8,7,2,4,6,10,12,1,3,5,9,11]=>[5,5,1,1]=>1485
[8,12,7,11,2,4,6,10,1,3,5,9]=>[4,4,2,2]=>2640
[2,10,7,9,4,6,8,12,1,3,5,11]=>[5,4,2,1]=>5775
[2,4,12,7,9,11,6,8,10,1,3,5]=>[5,3,3,1]=>4158
[12,11,2,10,7,9,4,6,8,1,3,5]=>[4,3,2,1,1,1]=>5632
[10,9,8,7,2,4,6,12,1,3,5,11]=>[4,4,1,1,1,1]=>1925
[12,9,2,8,7,11,4,6,10,1,3,5]=>[4,3,2,1,1,1]=>5632
[8,12,7,11,10,9,2,4,6,1,3,5]=>[3,3,2,2,1,1]=>2673
[12,11,10,9,8,7,2,4,6,1,3,5]=>[3,3,1,1,1,1,1,1]=>616
[6,5,2,4,8,10,12,1,3,7,9,11]=>[5,5,1,1]=>1485
[6,12,5,11,2,4,8,10,1,3,7,9]=>[4,4,2,2]=>2640
[6,10,5,9,2,4,8,12,1,3,7,11]=>[4,4,2,2]=>2640
[6,5,12,9,11,2,4,8,10,1,3,7]=>[4,3,3,2]=>2970
[12,11,6,10,5,9,2,4,8,1,3,7]=>[3,3,2,2,1,1]=>2673
[2,8,5,7,4,6,10,12,1,3,9,11]=>[5,4,2,1]=>5775
[2,8,12,5,7,11,4,6,10,1,3,9]=>[4,3,3,2]=>2970
[10,5,2,4,7,9,6,8,12,1,3,11]=>[5,4,2,1]=>5775
[12,5,7,2,4,6,9,11,8,10,1,3]=>[5,4,2,1]=>5775
[12,5,11,10,2,4,7,9,6,8,1,3]=>[4,3,2,1,1,1]=>5632
[10,9,2,8,5,7,4,6,12,1,3,11]=>[4,3,2,1,1,1]=>5632
[12,5,9,8,2,4,7,11,6,10,1,3]=>[4,3,2,1,1,1]=>5632
[2,12,5,11,8,10,7,9,4,6,1,3]=>[4,2,2,2,1,1]=>3080
[12,11,10,9,2,8,5,7,4,6,1,3]=>[3,2,2,1,1,1,1,1]=>891
[8,7,6,5,2,4,10,12,1,3,9,11]=>[4,4,1,1,1,1]=>1925
[8,7,6,12,5,11,2,4,10,1,3,9]=>[3,3,2,2,1,1]=>2673
[10,7,2,6,5,9,4,8,12,1,3,11]=>[4,3,2,1,1,1]=>5632
[7,6,12,5,2,4,9,11,8,10,1,3]=>[4,3,2,2,1]=>5775
[2,12,7,11,6,10,5,9,4,8,1,3]=>[3,2,2,2,2,1]=>1155
[6,10,5,9,8,7,2,4,12,1,3,11]=>[3,3,2,2,1,1]=>2673
[2,12,6,9,5,8,7,11,4,10,1,3]=>[4,3,2,1,1,1]=>5632
[6,8,12,5,7,11,10,9,2,4,1,3]=>[3,3,2,2,1,1]=>2673
[12,11,6,10,5,9,8,7,2,4,1,3]=>[2,2,2,2,1,1,1,1]=>275
[10,9,8,7,6,5,2,4,12,1,3,11]=>[3,3,1,1,1,1,1,1]=>616
[12,9,8,7,2,6,5,11,4,10,1,3]=>[3,2,2,1,1,1,1,1]=>891
[8,7,6,12,5,11,10,9,2,4,1,3]=>[2,2,2,2,2,2]=>132
[7,12,6,11,10,9,8,5,2,4,1,3]=>[2,2,2,2,1,1,1,1]=>275
[12,11,10,9,8,7,6,5,2,4,1,3]=>[2,2,1,1,1,1,1,1,1,1]=>54
[4,3,2,6,8,10,12,1,5,7,9,11]=>[5,5,1,1]=>1485
[4,12,3,11,2,6,8,10,1,5,7,9]=>[4,4,2,2]=>2640
[4,10,3,9,2,6,8,12,1,5,7,11]=>[4,4,2,2]=>2640
[4,3,12,9,11,2,6,8,10,1,5,7]=>[4,3,3,2]=>2970
[12,11,4,10,3,9,2,6,8,1,5,7]=>[3,3,2,2,1,1]=>2673
[4,8,3,7,2,6,10,12,1,5,9,11]=>[4,4,2,2]=>2640
[4,8,12,3,7,11,2,6,10,1,5,9]=>[3,3,3,3]=>462
[4,3,10,7,9,2,6,8,12,1,5,11]=>[4,4,2,2]=>2640
[4,3,7,9,12,11,2,6,8,10,1,5]=>[4,4,2,2]=>2640
[12,4,11,3,10,7,9,2,6,8,1,5]=>[3,3,2,2,1,1]=>2673
[10,9,4,8,3,7,2,6,12,1,5,11]=>[3,3,2,2,1,1]=>2673
[12,4,9,3,8,7,11,2,6,10,1,5]=>[3,3,2,2,1,1]=>2673
[4,8,12,11,10,3,7,9,2,6,1,5]=>[3,3,2,2,1,1]=>2673
[12,11,10,9,4,8,3,7,2,6,1,5]=>[2,2,2,2,1,1,1,1]=>275
[3,6,2,5,4,8,10,12,1,7,9,11]=>[5,5,1,1]=>1485
[3,6,12,2,5,11,4,8,10,1,7,9]=>[4,4,2,2]=>2640
[3,6,10,2,5,9,4,8,12,1,7,11]=>[4,4,2,2]=>2640
[3,12,6,2,5,9,11,4,8,10,1,7]=>[4,4,2,1,1]=>4455
[12,11,3,6,10,2,5,9,4,8,1,7]=>[3,3,2,2,1,1]=>2673
[3,5,8,2,4,7,6,10,12,1,9,11]=>[5,5,1,1]=>1485
[3,5,8,12,2,4,7,11,6,10,1,9]=>[4,4,2,2]=>2640
[3,5,7,10,2,4,6,9,8,12,1,11]=>[5,5,1,1]=>1485
[3,5,7,9,12,2,4,6,8,11,10,1]=>[5,5,1,1]=>1485
[12,11,3,5,7,10,2,4,6,9,8,1]=>[4,4,1,1,1,1]=>1925
[10,9,3,5,8,2,4,7,6,12,1,11]=>[4,4,1,1,1,1]=>1925
[9,8,3,5,7,12,2,4,6,11,10,1]=>[4,4,2,1,1]=>4455
[3,5,12,11,8,10,2,4,7,9,6,1]=>[4,4,1,1,1,1]=>1925
[12,11,10,9,3,5,8,2,4,7,6,1]=>[3,3,1,1,1,1,1,1]=>616
[8,7,3,6,2,5,4,10,12,1,9,11]=>[4,4,1,1,1,1]=>1925
[8,7,3,6,12,2,5,11,4,10,1,9]=>[3,3,2,2,1,1]=>2673
[7,6,3,5,10,2,4,9,8,12,1,11]=>[4,4,2,1,1]=>4455
[7,6,3,5,9,12,2,4,8,11,10,1]=>[4,4,2,1,1]=>4455
[7,12,6,11,3,5,10,2,4,9,8,1]=>[3,3,2,2,1,1]=>2673
[3,6,10,9,8,2,5,7,4,12,1,11]=>[4,4,1,1,1,1]=>1925
[3,9,6,8,5,7,12,2,4,11,10,1]=>[4,3,3,1,1]=>4158
[3,2,12,6,8,11,10,5,7,9,4,1]=>[4,4,1,1,1,1]=>1925
[12,11,3,6,10,9,8,2,5,7,4,1]=>[3,3,1,1,1,1,1,1]=>616
[10,9,8,7,3,6,2,5,4,12,1,11]=>[3,3,1,1,1,1,1,1]=>616
[9,8,7,6,3,5,12,2,4,11,10,1]=>[3,3,2,1,1,1,1]=>1925
[8,7,3,6,12,11,10,2,5,9,4,1]=>[3,3,2,2,1,1]=>2673
[3,12,7,11,10,9,6,8,2,5,4,1]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,9,8,7,3,6,2,5,4,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[6,5,4,3,2,8,10,12,1,7,9,11]=>[4,4,1,1,1,1]=>1925
[6,5,4,12,3,11,2,8,10,1,7,9]=>[3,3,2,2,1,1]=>2673
[6,5,4,10,3,9,2,8,12,1,7,11]=>[3,3,2,2,1,1]=>2673
[6,12,5,4,3,9,11,2,8,10,1,7]=>[3,3,2,2,1,1]=>2673
[5,4,3,8,2,7,6,10,12,1,9,11]=>[4,4,2,1,1]=>4455
[5,4,3,8,12,2,7,11,6,10,1,9]=>[3,3,3,2,1]=>2112
[5,4,3,7,10,2,6,9,8,12,1,11]=>[4,4,2,1,1]=>4455
[5,4,3,7,9,12,2,6,8,11,10,1]=>[4,4,2,1,1]=>4455
[5,12,4,11,3,7,10,2,6,9,8,1]=>[3,3,2,2,1,1]=>2673
[5,10,4,9,3,8,2,7,6,12,1,11]=>[3,3,2,2,1,1]=>2673
[5,9,4,8,3,7,12,2,6,11,10,1]=>[3,3,3,2,1]=>2112
[12,11,5,4,3,8,10,2,7,9,6,1]=>[3,3,2,1,1,1,1]=>1925
[12,11,5,10,4,9,3,8,2,7,6,1]=>[2,2,2,2,1,1,1,1]=>275
[4,8,3,7,6,5,2,10,12,1,9,11]=>[4,4,1,1,1,1]=>1925
[4,8,3,7,6,12,5,11,2,10,1,9]=>[3,3,2,2,1,1]=>2673
[4,7,3,6,5,10,2,9,8,12,1,11]=>[4,4,2,1,1]=>4455
[4,7,3,6,5,9,12,2,8,11,10,1]=>[4,4,2,1,1]=>4455
[4,7,12,3,6,11,5,10,2,9,8,1]=>[3,3,2,2,1,1]=>2673
[4,6,10,3,5,9,8,7,2,12,1,11]=>[4,4,1,1,1,1]=>1925
[4,6,9,3,5,8,7,12,2,11,10,1]=>[4,4,2,1,1]=>4455
[4,6,8,12,3,5,7,11,10,9,2,1]=>[4,4,1,1,1,1]=>1925
[12,11,4,6,10,3,5,9,8,7,2,1]=>[3,3,1,1,1,1,1,1]=>616
[10,9,4,8,3,7,6,5,2,12,1,11]=>[3,3,1,1,1,1,1,1]=>616
[9,8,4,7,3,6,5,12,2,11,10,1]=>[3,3,2,1,1,1,1]=>1925
[8,7,4,6,12,3,5,11,10,9,2,1]=>[3,3,2,2,1,1]=>2673
[4,7,12,11,10,3,6,9,8,5,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,10,9,4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[8,7,6,5,4,3,2,10,12,1,9,11]=>[3,3,1,1,1,1,1,1]=>616
[8,7,6,5,4,12,3,11,2,10,1,9]=>[2,2,2,2,1,1,1,1]=>275
[7,6,5,4,3,10,2,9,8,12,1,11]=>[3,3,2,1,1,1,1]=>1925
[7,6,5,4,3,9,12,2,8,11,10,1]=>[3,3,2,1,1,1,1]=>1925
[7,6,5,12,4,11,3,10,2,9,8,1]=>[2,2,2,2,2,1,1]=>297
[6,5,4,10,3,9,8,7,2,12,1,11]=>[3,3,2,2,1,1]=>2673
[6,5,4,9,3,8,7,12,2,11,10,1]=>[3,3,3,1,1,1]=>1650
[6,5,4,8,12,3,7,11,10,9,2,1]=>[3,3,2,2,1,1]=>2673
[6,12,5,11,4,10,3,9,8,7,2,1]=>[2,2,2,2,1,1,1,1]=>275
[5,10,4,9,8,7,6,3,2,12,1,11]=>[3,3,1,1,1,1,1,1]=>616
[5,9,4,8,7,6,3,12,2,11,10,1]=>[3,3,2,1,1,1,1]=>1925
[5,8,4,7,6,12,3,11,10,9,2,1]=>[3,3,2,2,1,1]=>2673
[5,7,12,4,6,11,10,9,8,3,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,5,10,4,9,8,7,6,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[10,9,8,7,6,5,4,3,2,12,1,11]=>[2,2,1,1,1,1,1,1,1,1]=>54
[9,8,7,6,5,4,3,12,2,11,10,1]=>[2,2,2,1,1,1,1,1,1]=>154
[8,7,6,5,4,12,3,11,10,9,2,1]=>[2,2,2,2,1,1,1,1]=>275
[7,6,5,12,4,11,10,9,8,3,2,1]=>[2,2,2,2,1,1,1,1]=>275
[6,12,5,11,10,9,8,7,4,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[4,2,8,1,5,7,6,3]=>[3,2,2,1]=>70
[6,3,7,2,5,4,8,1]=>[3,2,2,1]=>70
[5,4,7,3,2,6,8,1]=>[3,2,1,1,1]=>64
[5,7,2,6,3,4,8,1]=>[4,2,1,1]=>90
[3,7,5,4,6,2,8,1]=>[4,1,1,1,1]=>35
[6,8,3,2,1,7,4,5]=>[3,2,2,1]=>70
[4,8,1,7,5,3,2,6]=>[3,2,1,1,1]=>64
[5,4,3,7,2,8,6,1]=>[3,2,1,1,1]=>64
[3,6,5,7,2,8,4,1]=>[4,2,1,1]=>90
[4,6,5,3,8,2,1,7]=>[3,2,1,1,1]=>64
[2,6,5,8,7,3,1,4]=>[3,2,2,1]=>70
[6,3,8,4,1,7,2,5]=>[3,3,2]=>42
[7,2,8,1,6,4,3,5]=>[3,2,2,1]=>70
[8,2,6,4,3,5,1,7]=>[4,1,1,1,1]=>35
[5,4,2,8,6,3,7,1]=>[3,2,2,1]=>70
[2,8,7,5,3,1,4,6]=>[4,1,1,1,1]=>35
[2,5,6,3,1,4,8,7]=>[4,3,1]=>70
[2,4,7,8,5,3,1,6]=>[4,2,1,1]=>90
[6,5,3,2,4,1,8,7]=>[3,2,1,1,1]=>64
[2,1,4,7,8,5,3,6]=>[4,3,1]=>70
[8,5,6,7,3,1,4,2]=>[3,2,2,1]=>70
[8,7,5,3,2,6,4,1]=>[2,2,1,1,1,1]=>20
[8,5,3,1,4,6,7,2]=>[4,2,1,1]=>90
[8,5,1,6,4,3,7,2]=>[3,2,1,1,1]=>64
[6,1,4,3,7,8,2,5]=>[4,2,1,1]=>90
[6,1,2,7,5,8,3,4]=>[4,3,1]=>70
[2,7,3,1,4,6,8,5]=>[5,2,1]=>64
[2,8,3,1,6,5,7,4]=>[4,2,1,1]=>90
[3,8,5,6,7,1,2,4]=>[4,3,1]=>70
[2,5,8,1,4,6,7,3]=>[4,3,1]=>70
[2,1,8,7,5,4,6,3]=>[3,2,1,1,1]=>64
[7,8,3,4,1,6,5,2]=>[3,2,2,1]=>70
[8,7,3,4,2,6,5,1]=>[3,2,1,1,1]=>64
[8,4,5,2,3,7,1,6]=>[3,3,1,1]=>56
[4,7,2,8,6,3,1,5]=>[3,3,1,1]=>56
[4,7,5,2,3,8,1,6]=>[3,3,1,1]=>56
[6,4,7,5,2,8,3,1]=>[3,2,2,1]=>70
[7,5,1,3,6,4,8,2]=>[4,2,1,1]=>90
[6,5,2,3,7,8,4,1]=>[4,2,1,1]=>90
[7,2,6,3,1,5,8,4]=>[4,2,1,1]=>90
[1,8,4,2,5,7,6,3]=>[4,2,1,1]=>90
[1,8,5,2,4,7,6,3]=>[4,2,1,1]=>90
[1,4,6,2,8,7,5,3]=>[4,2,1,1]=>90
[2,1,6,8,7,5,3,4]=>[3,3,1,1]=>56
[1,2,8,3,5,7,6,4]=>[5,1,1,1]=>35
[2,3,8,1,5,7,6,4]=>[4,2,1,1]=>90
[2,6,1,8,7,5,3,4]=>[3,3,1,1]=>56
[2,6,3,8,7,5,1,4]=>[3,2,2,1]=>70
[3,2,8,1,5,7,6,4]=>[3,2,2,1]=>70
[2,8,1,4,5,7,6,3]=>[4,2,1,1]=>90
[2,3,6,8,7,5,1,4]=>[4,2,1,1]=>90
[3,8,4,5,1,6,2,7]=>[5,2,1]=>64
[6,1,4,5,7,2,3,8]=>[5,2,1]=>64
[8,1,4,7,6,3,2,5]=>[3,2,1,1,1]=>64
[8,3,1,6,4,7,2,5]=>[3,3,1,1]=>56
[5,3,8,6,2,7,1,4]=>[3,2,2,1]=>70
[8,3,6,1,5,7,2,4]=>[3,3,1,1]=>56
[8,4,6,3,1,2,5,7]=>[4,2,1,1]=>90
[6,8,1,4,5,2,3,7]=>[4,2,2]=>56
[1,5,8,4,6,2,3,7]=>[4,2,2]=>56
[2,1,6,5,3,8,4,7]=>[4,3,1]=>70
[5,6,8,1,4,2,3,7]=>[4,3,1]=>70
[5,7,4,8,1,2,3,6]=>[4,3,1]=>70
[8,2,1,5,3,7,4,6]=>[4,3,1]=>70
[4,7,8,1,2,6,3,5]=>[4,3,1]=>70
[8,7,1,5,6,2,3,4]=>[4,2,1,1]=>90
[1,6,5,8,7,2,3,4]=>[4,2,2]=>56
[5,1,2,7,6,8,3,4]=>[4,3,1]=>70
[6,1,7,2,5,8,3,4]=>[4,3,1]=>70
[1,7,6,5,8,2,3,4]=>[4,2,1,1]=>90
[1,6,8,5,7,2,3,4]=>[4,2,2]=>56
[7,5,1,2,6,8,3,4]=>[4,3,1]=>70
[6,1,5,2,7,8,3,4]=>[4,3,1]=>70
[1,7,3,2,4,6,8,5]=>[5,2,1]=>64
[8,3,1,4,2,5,7,6]=>[4,3,1]=>70
[3,1,2,7,8,4,6,5]=>[4,3,1]=>70
[5,1,2,6,8,7,3,4]=>[4,3,1]=>70
[1,8,6,2,5,7,3,4]=>[4,2,1,1]=>90
[5,7,8,1,2,6,3,4]=>[4,3,1]=>70
[8,1,5,7,6,2,3,4]=>[4,2,1,1]=>90
[7,1,6,8,5,2,3,4]=>[4,2,1,1]=>90
[8,3,1,2,7,6,4,5]=>[4,2,1,1]=>90
[1,5,8,7,6,2,3,4]=>[4,2,1,1]=>90
[7,8,6,1,5,2,3,4]=>[4,2,1,1]=>90
[1,9,3,4,5,6,7,8,2]=>[7,1,1]=>28
[9,2,3,4,5,6,7,8,1,10]=>[8,1,1]=>36
[1,9,8,4,5,6,7,3,2]=>[5,1,1,1,1]=>70
[1,10,3,4,5,6,7,8,9,2]=>[8,1,1]=>36
[1,10,9,4,5,6,7,8,3,2]=>[6,1,1,1,1]=>126
[7,8,6,3,1,5,2,4]=>[3,2,2,1]=>70
[7,8,1,3,4,5,2,6]=>[5,2,1]=>64
[1,7,4,8,2,5,3,6]=>[4,2,2]=>56
[3,8,6,1,4,2,7,5]=>[3,3,1,1]=>56
[7,1,8,2,4,6,3,5]=>[4,2,2]=>56
[7,6,8,4,1,5,3,2]=>[2,2,2,1,1]=>28
[7,3,2,8,1,5,4,6]=>[3,2,2,1]=>70
[3,5,4,1,7,2,6,8]=>[4,3,1]=>70
[6,4,7,3,2,5,1,8]=>[3,2,1,1,1]=>64
[7,6,5,3,8,4,1,2]=>[2,2,2,1,1]=>28
[6,4,5,7,8,1,3,2]=>[4,2,1,1]=>90
[3,7,4,1,6,8,5,2]=>[4,2,1,1]=>90
[3,1,2,7,6,8,5,4]=>[4,2,1,1]=>90
[6,3,2,8,4,5,1,7]=>[4,2,1,1]=>90
[6,1,8,3,5,4,2,7]=>[4,2,1,1]=>90
[3,8,5,2,4,6,1,7]=>[4,2,1,1]=>90
[1,6,4,8,3,5,2,7]=>[4,2,1,1]=>90
[1,5,4,8,6,3,7,2]=>[4,2,1,1]=>90
[4,8,2,5,3,7,1,6]=>[3,3,1,1]=>56
[3,8,4,5,2,6,7,1]=>[5,1,1,1]=>35
[4,1,8,6,5,3,7,2]=>[3,2,1,1,1]=>64
[5,7,8,4,6,3,2,1]=>[3,2,1,1,1]=>64
[5,3,2,8,6,4,7,1]=>[3,2,2,1]=>70
[6,8,1,2,7,4,3,5]=>[4,2,1,1]=>90
[5,8,7,3,6,2,4,1]=>[2,2,2,1,1]=>28
[7,5,2,3,4,8,6,1]=>[4,2,1,1]=>90
[7,3,5,4,2,8,6,1]=>[3,2,1,1,1]=>64
[5,6,1,3,2,4,7,8]=>[5,2,1]=>64
[2,5,1,3,7,8,6,4]=>[4,3,1]=>70
[4,3,7,2,1,8,6,5]=>[3,2,2,1]=>70
[4,6,7,2,1,3,5,8]=>[4,3,1]=>70
[4,6,2,3,1,5,7,8]=>[5,2,1]=>64
[3,6,4,2,5,1,7,8]=>[5,1,1,1]=>35
[3,1,6,4,7,5,2,8]=>[4,3,1]=>70
[3,6,2,7,5,4,1,8]=>[4,2,1,1]=>90
[2,4,7,5,3,6,1,8]=>[5,1,1,1]=>35
[2,5,7,3,4,1,6,8]=>[5,2,1]=>64
[2,3,5,8,6,4,7,1]=>[5,1,1,1]=>35
[2,4,7,3,8,6,5,1]=>[4,2,1,1]=>90
[3,4,2,7,5,8,6,1]=>[4,3,1]=>70
[3,1,5,4,7,8,6,2]=>[4,3,1]=>70
[4,5,7,2,3,1,8,6]=>[4,3,1]=>70
[3,7,8,1,4,6,5,2]=>[3,3,1,1]=>56
[2,5,8,7,4,1,3,6]=>[3,3,1,1]=>56
[2,6,4,7,5,3,8,1]=>[4,2,1,1]=>90
[6,2,4,7,1,3,8,5]=>[4,3,1]=>70
[7,3,5,1,4,2,8,6]=>[3,3,1,1]=>56
[5,4,7,1,3,2,8,6]=>[3,3,1,1]=>56
[6,1,4,7,5,3,8,2]=>[4,2,1,1]=>90
[8,7,4,3,1,5,6,2]=>[3,2,1,1,1]=>64
[8,7,1,4,3,5,6,2]=>[4,1,1,1,1]=>35
[6,1,8,4,7,3,2,5]=>[3,2,2,1]=>70
[4,7,3,6,1,2,8,5]=>[3,3,2]=>42
[5,2,1,7,4,3,8,6]=>[3,3,2]=>42
[4,7,6,2,3,1,8,5]=>[3,3,1,1]=>56
[7,6,8,2,5,3,4,1]=>[3,2,1,1,1]=>64
[2,3,6,1,8,7,5,4]=>[4,2,1,1]=>90
[2,6,8,7,5,3,1,4]=>[3,2,1,1,1]=>64
[6,4,1,7,5,2,8,3]=>[3,3,2]=>42
[5,7,8,2,3,6,1,4]=>[3,3,2]=>42
[4,8,7,1,2,5,6,3]=>[4,2,1,1]=>90
[2,8,7,4,1,5,6,3]=>[4,2,1,1]=>90
[8,6,2,1,5,7,4,3]=>[3,2,1,1,1]=>64
[3,8,6,7,5,2,1,4]=>[3,2,1,1,1]=>64
[6,1,3,7,5,8,2,4]=>[4,2,2]=>56
[4,7,3,1,8,5,6,2]=>[3,3,2]=>42
[2,6,7,5,3,4,8,1]=>[4,2,1,1]=>90
[2,6,4,5,7,3,8,1]=>[5,1,1,1]=>35
[6,1,4,5,8,3,7,2]=>[4,2,1,1]=>90
[6,1,8,5,3,4,7,2]=>[4,2,1,1]=>90
[4,1,5,6,8,3,7,2]=>[4,3,1]=>70
[6,4,1,8,7,2,5,3]=>[3,2,2,1]=>70
[8,1,2,3,4,5,6,7,10,9]=>[8,2]=>35
[1,7,2,3,4,5,6,9,8]=>[7,2]=>27
[6,9,1,2,3,4,5,7,8]=>[7,2]=>27
[1,3,8,5,2,7,4,6]=>[4,3,1]=>70
[1,3,8,6,7,2,4,5]=>[4,3,1]=>70
[2,8,3,7,6,1,4,5]=>[4,2,1,1]=>90
[4,2,7,8,6,1,3,5]=>[3,3,2]=>42
[1,3,8,7,6,2,4,5]=>[4,2,1,1]=>90
[7,4,6,8,5,2,3,1]=>[3,2,1,1,1]=>64
[5,2,6,7,8,1,3,4]=>[4,3,1]=>70
[4,5,6,8,1,2,7,3]=>[4,3,1]=>70
[3,5,8,6,1,2,7,4]=>[4,3,1]=>70
[4,2,6,8,7,1,3,5]=>[3,3,2]=>42
[1,4,6,8,7,2,3,5]=>[4,3,1]=>70
[4,5,3,8,1,7,2,6]=>[3,3,2]=>42
[3,5,8,4,1,7,2,6]=>[3,3,2]=>42
[1,6,5,7,8,2,3,4]=>[4,3,1]=>70
[6,5,4,8,1,3,7,2]=>[3,2,1,1,1]=>64
[7,6,4,8,5,1,3,2]=>[2,2,2,1,1]=>28
[6,3,7,5,2,4,8,1]=>[3,2,2,1]=>70
[8,1,2,7,4,5,3,6]=>[5,1,1,1]=>35
[2,5,7,4,6,1,3,8]=>[4,2,2]=>56
[6,1,7,4,5,3,8,2]=>[4,2,1,1]=>90
[8,2,7,3,1,5,4,6]=>[4,2,1,1]=>90
[8,1,3,7,5,6,4,2]=>[4,1,1,1,1]=>35
[1,2,5,3,8,6,7,4]=>[5,2,1]=>64
[4,1,6,5,7,8,2,3]=>[4,3,1]=>70
[6,1,3,7,4,2,8,5]=>[4,3,1]=>70
[6,7,2,4,1,3,8,5]=>[3,3,2]=>42
[8,5,3,4,2,7,1,6]=>[3,2,1,1,1]=>64
[1,3,8,2,5,6,7,4]=>[5,2,1]=>64
[1,8,6,7,2,5,4,3]=>[3,2,1,1,1]=>64
[8,7,2,4,6,1,5,3]=>[3,2,1,1,1]=>64
[7,8,6,5,2,4,3,1]=>[2,2,1,1,1,1]=>20
[3,6,7,5,2,8,4,1]=>[4,2,1,1]=>90
[5,4,6,7,8,1,3,2]=>[4,2,1,1]=>90
[5,3,6,7,8,1,4,2]=>[4,2,2]=>56
[5,3,7,6,8,4,1,2]=>[3,2,2,1]=>70
[7,5,3,2,8,6,4,1]=>[2,2,2,1,1]=>28
[5,4,8,6,7,2,3,1]=>[3,2,2,1]=>70
[5,4,8,6,3,1,2,7]=>[3,2,2,1]=>70
[4,5,7,3,6,2,8,1]=>[4,2,1,1]=>90
[4,5,6,3,8,2,7,1]=>[4,2,1,1]=>90
[5,4,8,7,2,1,3,6]=>[3,2,2,1]=>70
[2,5,4,7,8,1,3,6]=>[4,3,1]=>70
[5,3,6,4,8,2,7,1]=>[3,3,1,1]=>56
[5,3,7,4,6,2,8,1]=>[4,2,1,1]=>90
[8,2,4,7,3,5,6,1]=>[4,2,1,1]=>90
[4,5,6,2,7,3,8,1]=>[5,2,1]=>64
[5,4,6,2,8,3,7,1]=>[3,3,1,1]=>56
[8,4,6,1,7,2,5,3]=>[3,3,1,1]=>56
[5,2,1,6,3,8,7,4]=>[3,3,2]=>42
[4,5,6,3,7,1,8,2]=>[5,2,1]=>64
[6,3,2,8,5,4,1,7]=>[3,2,2,1]=>70
[4,3,1,5,2,8,6,7]=>[4,3,1]=>70
[8,5,4,1,3,2,6,7]=>[4,1,1,1,1]=>35
[3,8,4,1,5,2,6,7]=>[5,2,1]=>64
[2,5,4,3,8,1,6,7]=>[4,2,1,1]=>90
[2,5,7,4,3,1,6,8]=>[4,2,1,1]=>90
[5,3,4,2,7,1,6,8]=>[4,2,1,1]=>90
[3,7,5,4,1,2,6,8]=>[4,2,1,1]=>90
[4,2,5,1,3,8,7,6]=>[3,3,2]=>42
[4,3,5,1,2,7,6,8]=>[4,3,1]=>70
[4,1,6,3,5,2,7,8]=>[5,2,1]=>64
[4,2,1,8,6,3,7,5]=>[3,3,2]=>42
[3,1,7,2,5,6,4,8]=>[5,2,1]=>64
[3,7,2,4,1,6,5,8]=>[4,2,2]=>56
[7,3,2,1,6,4,5,8]=>[4,2,1,1]=>90
[2,8,6,1,7,4,3,5]=>[3,3,1,1]=>56
[2,5,4,6,1,3,7,8]=>[5,2,1]=>64
[2,5,6,4,1,3,7,8]=>[5,2,1]=>64
[8,5,2,6,1,3,7,4]=>[3,3,1,1]=>56
[7,1,5,6,3,2,4,8]=>[4,2,1,1]=>90
[7,1,2,5,4,6,3,8]=>[5,1,1,1]=>35
[2,4,1,6,5,3,7,8]=>[5,2,1]=>64
[4,1,2,7,5,6,3,8]=>[5,2,1]=>64
[7,1,2,6,5,4,3,8]=>[4,1,1,1,1]=>35
[8,2,1,5,6,3,7,4]=>[4,3,1]=>70
[6,1,4,5,3,2,7,8]=>[5,1,1,1]=>35
[3,1,6,5,4,2,7,8]=>[4,2,1,1]=>90
[3,1,4,6,5,2,7,8]=>[5,2,1]=>64
[5,8,3,1,7,6,4,2]=>[2,2,2,1,1]=>28
[7,6,3,2,8,5,1,4]=>[2,2,2,1,1]=>28
[5,6,3,8,7,4,1,2]=>[3,2,2,1]=>70
[5,2,6,8,7,4,1,3]=>[3,2,2,1]=>70
[6,3,8,5,4,1,2,7]=>[3,2,2,1]=>70
[6,3,8,4,5,1,2,7]=>[4,2,2]=>56
[5,2,3,1,4,8,6,7]=>[5,2,1]=>64
[5,4,1,3,2,8,6,7]=>[4,2,1,1]=>90
[5,1,3,4,2,8,6,7]=>[5,2,1]=>64
[4,2,7,3,8,5,1,6]=>[4,3,1]=>70
[4,3,7,2,8,5,6,1]=>[3,3,1,1]=>56
[5,3,1,2,4,8,6,7]=>[5,2,1]=>64
[5,4,3,1,2,8,6,7]=>[4,2,1,1]=>90
[5,2,3,4,1,8,6,7]=>[5,2,1]=>64
[5,1,7,3,4,6,8,2]=>[5,2,1]=>64
[5,8,7,4,3,1,6,2]=>[2,2,2,1,1]=>28
[6,8,1,3,4,5,7,2]=>[5,2,1]=>64
[3,1,7,8,2,5,4,6]=>[4,3,1]=>70
[6,3,7,4,1,2,5,8]=>[4,2,2]=>56
[3,7,2,8,6,5,1,4]=>[3,2,2,1]=>70
[3,6,7,5,1,2,4,8]=>[4,3,1]=>70
[7,4,5,1,8,2,3,6]=>[4,3,1]=>70
[7,2,3,1,8,4,5,6]=>[5,2,1]=>64
[2,1,4,8,3,7,5,6]=>[4,3,1]=>70
[1,2,7,8,4,3,6,5]=>[4,2,2]=>56
[4,8,1,3,5,6,2,7]=>[5,2,1]=>64
[5,3,7,8,4,2,6,1]=>[3,3,1,1]=>56
[6,3,7,8,2,4,5,1]=>[3,3,1,1]=>56
[8,5,2,4,3,1,7,6]=>[3,2,1,1,1]=>64
[7,5,4,2,3,1,8,6]=>[3,2,1,1,1]=>64
[3,5,4,6,7,1,8,2]=>[5,2,1]=>64
[1,4,2,6,5,8,7,3]=>[4,3,1]=>70
[1,3,2,6,4,8,7,5]=>[4,3,1]=>70
[1,4,2,5,3,8,7,6]=>[4,3,1]=>70
[1,5,2,6,4,8,7,3]=>[4,3,1]=>70
[1,6,2,5,3,8,7,4]=>[4,2,2]=>56
[2,5,1,4,3,8,7,6]=>[3,3,2]=>42
[1,7,3,5,4,8,6,2]=>[4,2,1,1]=>90
[1,8,3,6,4,7,5,2]=>[4,2,1,1]=>90
[1,7,2,6,4,8,5,3]=>[4,2,1,1]=>90
[1,5,2,7,4,8,6,3]=>[4,3,1]=>70
[1,4,2,8,5,7,6,3]=>[4,2,1,1]=>90
[4,8,1,3,2,6,5,7]=>[4,2,2]=>56
[1,8,4,7,3,6,5,2]=>[3,2,1,1,1]=>64
[2,6,3,8,1,5,4,7]=>[4,2,2]=>56
[8,3,1,4,2,6,5,7]=>[4,3,1]=>70
[4,8,7,3,5,2,1,6]=>[3,2,1,1,1]=>64
[6,8,7,3,5,2,4,1]=>[2,2,2,1,1]=>28
[8,3,5,1,2,6,4,7]=>[4,3,1]=>70
[8,6,3,1,5,4,2,7]=>[3,2,1,1,1]=>64
[8,6,4,1,5,3,2,7]=>[3,2,1,1,1]=>64
[8,6,5,4,1,3,2,7]=>[3,1,1,1,1,1]=>21
[5,3,8,7,4,6,2,1]=>[3,2,1,1,1]=>64
[2,3,8,7,4,6,1,5]=>[4,2,1,1]=>90
[8,3,5,7,4,1,2,6]=>[3,3,1,1]=>56
[4,8,5,3,1,2,7,6]=>[3,3,1,1]=>56
[6,8,7,3,1,5,4,2]=>[2,2,2,1,1]=>28
[6,8,5,4,1,3,7,2]=>[3,2,1,1,1]=>64
[2,5,8,7,4,6,3,1]=>[3,2,1,1,1]=>64
[4,8,7,6,5,1,3,2]=>[2,2,1,1,1,1]=>20
[3,8,7,5,1,6,2,4]=>[3,3,1,1]=>56
[2,3,8,7,5,6,1,4]=>[4,2,1,1]=>90
[2,8,7,1,3,6,4,5]=>[4,2,1,1]=>90
[8,5,4,7,2,1,3,6]=>[3,2,1,1,1]=>64
[6,8,7,3,5,2,1,4]=>[2,2,2,1,1]=>28
[3,5,8,6,4,2,7,1]=>[4,1,1,1,1]=>35
[6,8,4,1,5,2,7,3]=>[3,3,2]=>42
[6,8,2,1,7,5,3,4]=>[3,2,2,1]=>70
[5,8,4,6,1,2,7,3]=>[3,3,2]=>42
[2,4,8,6,5,1,7,3]=>[4,2,1,1]=>90
[4,8,7,6,5,2,1,3]=>[2,2,1,1,1,1]=>20
[4,8,7,5,1,6,2,3]=>[3,3,1,1]=>56
[4,5,2,1,8,6,7,3]=>[4,2,2]=>56
[4,5,8,3,1,6,7,2]=>[4,2,2]=>56
[5,7,2,8,4,6,1,3]=>[3,3,2]=>42
[7,2,8,6,4,5,1,3]=>[3,2,2,1]=>70
[8,7,2,6,5,1,3,4]=>[3,2,1,1,1]=>64
[5,1,6,3,4,8,2,7]=>[4,3,1]=>70
[3,5,2,6,4,8,1,7]=>[4,3,1]=>70
[6,3,8,2,4,1,7,5]=>[3,2,2,1]=>70
[6,3,8,7,5,4,2,1]=>[2,2,1,1,1,1]=>20
[6,8,4,2,1,7,5,3]=>[2,2,2,2]=>14
[5,2,6,4,3,8,1,7]=>[3,3,1,1]=>56
[6,5,3,1,4,8,2,7]=>[3,3,1,1]=>56
[3,8,1,7,6,2,5,4]=>[3,2,1,1,1]=>64
[8,1,7,6,4,2,5,3]=>[3,2,1,1,1]=>64
[7,2,6,3,8,5,4,1]=>[3,2,1,1,1]=>64
[7,3,8,6,4,1,5,2]=>[3,2,2,1]=>70
[1,7,5,8,2,4,3,6]=>[4,2,1,1]=>90
[6,1,5,2,4,8,3,7]=>[4,2,1,1]=>90
[2,6,7,4,3,8,5,1]=>[4,2,1,1]=>90
[5,2,4,7,3,8,6,1]=>[4,2,1,1]=>90
[8,3,7,2,5,1,6,4]=>[3,2,2,1]=>70
[7,2,8,1,4,3,6,5]=>[3,3,2]=>42
[1,7,5,4,8,3,2,6]=>[3,2,1,1,1]=>64
[6,1,5,4,3,8,2,7]=>[3,2,1,1,1]=>64
[1,7,4,5,6,8,2,3]=>[5,2,1]=>64
[1,3,4,5,6,7,9,8,2]=>[7,1,1]=>28
[2,3,4,5,6,7,9,8,1,10]=>[8,1,1]=>36
[7,3,4,5,6,8,1,2,9]=>[6,2,1]=>105
[2,3,4,5,7,6,8,1,9]=>[7,1,1]=>28
[1,8,4,5,6,7,9,2,3]=>[6,2,1]=>105
[1,3,4,5,6,8,7,9,2]=>[7,1,1]=>28
[1,3,4,5,6,7,8,10,9,2]=>[8,1,1]=>36
[1,6,4,2,3,5,7,8]=>[6,1,1]=>21
[1,8,7,2,3,4,5,6]=>[6,1,1]=>21
[1,5,8,6,2,3,4,7]=>[5,2,1]=>64
[1,6,5,7,2,3,4,8]=>[5,2,1]=>64
[1,7,5,6,2,3,4,8]=>[5,2,1]=>64
[1,3,2,7,6,4,5,8]=>[5,2,1]=>64
[1,2,3,7,6,4,5,8]=>[6,1,1]=>21
[1,5,4,2,3,7,6,8]=>[5,2,1]=>64
[1,5,4,2,3,8,6,7]=>[5,2,1]=>64
[1,3,2,8,6,4,5,7]=>[5,2,1]=>64
[1,7,5,8,2,3,4,6]=>[5,2,1]=>64
[1,8,7,5,2,3,4,6]=>[5,1,1,1]=>35
[2,1,5,8,6,3,7,4]=>[4,3,1]=>70
[2,5,8,4,6,1,7,3]=>[4,2,2]=>56
[2,5,3,8,6,1,7,4]=>[4,2,2]=>56
[2,6,3,5,8,1,7,4]=>[4,2,2]=>56
[6,3,2,5,8,1,7,4]=>[3,2,2,1]=>70
[5,3,2,8,6,1,7,4]=>[3,2,2,1]=>70
[5,8,4,6,1,3,7,2]=>[3,2,2,1]=>70
[5,3,8,6,1,4,7,2]=>[3,2,2,1]=>70
[2,6,5,4,8,1,7,3]=>[3,2,2,1]=>70
[8,3,5,7,2,6,4,1]=>[3,2,1,1,1]=>64
[2,4,6,8,5,3,7,1]=>[4,2,1,1]=>90
[2,4,8,1,7,6,5,3]=>[3,2,1,1,1]=>64
[4,3,8,1,5,7,6,2]=>[3,2,2,1]=>70
[3,8,4,1,5,7,6,2]=>[4,2,1,1]=>90
[4,3,6,8,5,2,7,1]=>[3,3,1,1]=>56
[8,5,4,7,2,6,3,1]=>[2,2,2,1,1]=>28
[3,6,8,5,4,2,7,1]=>[3,2,1,1,1]=>64
[3,6,4,8,5,2,7,1]=>[4,2,1,1]=>90
[3,6,4,1,8,2,7,5]=>[3,3,2]=>42
[3,6,4,1,5,2,8,7]=>[4,3,1]=>70
[4,8,6,5,1,3,7,2]=>[3,2,1,1,1]=>64
[2,8,3,5,6,7,1,4]=>[5,2,1]=>64
[5,6,2,4,7,1,8,3]=>[4,2,2]=>56
[2,7,5,4,6,1,8,3]=>[4,2,1,1]=>90
[2,3,7,4,6,1,8,5]=>[5,2,1]=>64
[2,6,7,4,1,3,8,5]=>[4,3,1]=>70
[6,5,7,4,1,3,8,2]=>[3,2,1,1,1]=>64
[2,4,6,3,5,7,8,1]=>[5,2,1]=>64
[4,1,6,3,5,7,8,2]=>[5,2,1]=>64
[3,6,4,2,5,7,8,1]=>[5,1,1,1]=>35
[2,3,6,1,5,7,8,4]=>[5,2,1]=>64
[4,3,6,2,5,7,8,1]=>[4,2,1,1]=>90
[4,6,1,2,5,7,8,3]=>[5,2,1]=>64
[2,6,4,1,5,7,8,3]=>[5,2,1]=>64
[2,4,1,6,5,7,8,3]=>[5,2,1]=>64
[7,5,4,2,6,1,8,3]=>[3,2,1,1,1]=>64
[4,7,3,1,8,6,5,2]=>[3,2,2,1]=>70
[5,6,4,2,7,1,8,3]=>[4,2,1,1]=>90
[5,3,6,4,8,2,1,7]=>[3,3,1,1]=>56
[7,3,2,5,4,1,8,6]=>[3,3,1,1]=>56
[7,3,2,5,1,8,6,4]=>[3,2,2,1]=>70
[4,7,6,3,8,2,1,5]=>[3,2,1,1,1]=>64
[5,7,3,2,6,1,8,4]=>[3,2,2,1]=>70
[5,7,3,2,6,4,1,8]=>[3,2,2,1]=>70
[2,7,5,3,1,8,6,4]=>[3,2,2,1]=>70
[7,3,2,4,1,8,6,5]=>[3,2,2,1]=>70
[4,3,7,5,8,2,1,6]=>[3,3,1,1]=>56
[8,4,5,3,7,2,1,6]=>[3,2,1,1,1]=>64
[4,3,5,2,8,6,1,7]=>[4,2,1,1]=>90
[1,2,3,4,5,9,7,8,6]=>[7,1,1]=>28
[1,2,3,4,9,6,7,8,5]=>[7,1,1]=>28
[1,2,3,9,5,6,7,8,4]=>[7,1,1]=>28
[1,2,9,4,5,6,7,8,3]=>[7,1,1]=>28
[1,2,3,4,5,6,10,8,9,7]=>[8,1,1]=>36
[1,2,3,4,9,7,6,8,5]=>[6,1,1,1]=>56
[1,2,3,4,5,10,7,8,9,6]=>[8,1,1]=>36
[1,2,8,6,4,5,7,3]=>[5,1,1,1]=>35
[1,2,3,9,6,5,7,8,4]=>[6,1,1,1]=>56
[1,2,3,4,10,6,7,8,9,5]=>[8,1,1]=>36
[1,8,5,3,4,6,7,2]=>[5,1,1,1]=>35
[1,2,9,5,4,6,7,8,3]=>[6,1,1,1]=>56
[1,2,3,10,5,6,7,8,9,4]=>[8,1,1]=>36
[1,9,4,3,5,6,7,8,2]=>[6,1,1,1]=>56
[1,2,10,4,5,6,7,8,9,3]=>[8,1,1]=>36
[9,3,2,4,5,6,7,8,1]=>[6,1,1,1]=>56
[10,2,3,4,5,6,7,8,9,1]=>[8,1,1]=>36
[3,5,6,7,8,9,4,2,1]=>[6,1,1,1]=>56
[7,8,4,1,6,3,5,2]=>[3,2,2,1]=>70
[8,7,5,6,1,3,4,2]=>[3,2,1,1,1]=>64
[1,2,3,5,7,4,6,9,8]=>[6,3]=>48
[1,2,3,6,4,7,5,9,8]=>[6,3]=>48
[1,2,3,4,6,8,5,7,10,9]=>[7,3]=>75
[1,2,3,4,6,8,5,7,9]=>[7,2]=>27
[1,2,3,4,7,5,8,6,9]=>[7,2]=>27
[1,2,3,4,7,5,8,6,10,9]=>[7,3]=>75
[1,2,3,4,6,8,5,7,10,9,11]=>[8,3]=>110
[1,2,3,5,7,4,6,9,8,10]=>[7,3]=>75
[1,2,5,7,3,4,6,9,8]=>[6,3]=>48
[1,2,4,5,7,3,6,9,8]=>[6,3]=>48
[1,2,6,3,4,7,5,9,8]=>[6,3]=>48
[1,2,5,6,3,7,4,9,8]=>[6,3]=>48
[1,2,3,6,4,7,5,9,8,10]=>[7,3]=>75
[1,2,3,4,7,5,8,6,10,9,11]=>[8,3]=>110
[3,2,6,4,1,8,5,7]=>[4,3,1]=>70
[2,8,6,5,3,1,4,7]=>[4,1,1,1,1]=>35
[5,4,8,6,2,3,1,7]=>[3,2,2,1]=>70
[4,8,7,5,2,3,1,6]=>[3,2,1,1,1]=>64
[5,2,4,7,6,8,3,1]=>[4,2,1,1]=>90
[3,4,2,8,7,5,1,6]=>[4,2,1,1]=>90
[8,5,7,6,3,2,4,1]=>[2,2,1,1,1,1]=>20
[6,4,1,8,7,3,2,5]=>[3,2,2,1]=>70
[1,8,5,4,2,7,3,6]=>[4,2,1,1]=>90
[8,3,2,7,4,6,5,1]=>[3,2,1,1,1]=>64
[7,5,8,4,1,3,6,2]=>[3,2,1,1,1]=>64
[7,1,6,2,3,8,4,5]=>[5,2,1]=>64
[6,4,7,1,3,2,8,5]=>[3,3,1,1]=>56
[5,1,3,8,7,2,6,4]=>[3,2,2,1]=>70
[8,7,1,6,2,5,3,4]=>[4,1,1,1,1]=>35
[3,8,5,2,4,7,6,1]=>[3,3,1,1]=>56
[7,1,5,2,4,8,3,6]=>[4,2,1,1]=>90
[3,8,5,1,4,7,2,6]=>[3,3,1,1]=>56
[7,2,5,4,1,3,8,6]=>[3,3,1,1]=>56
[7,5,8,1,6,3,2,4]=>[3,2,2,1]=>70
[2,3,1,9,4,5,6,7,8]=>[7,2]=>27
[4,9,1,2,3,5,6,7,8]=>[7,2]=>27
[3,9,1,2,4,5,6,7,8]=>[7,2]=>27
[6,8,1,9,2,3,4,5,7]=>[6,3]=>48
[7,10,1,2,3,4,5,6,8,9]=>[8,2]=>35
[6,10,1,2,3,4,5,7,8,9]=>[8,2]=>35
[4,8,1,2,3,9,5,6,7]=>[6,3]=>48
[3,8,1,2,4,5,9,6,7]=>[6,3]=>48
[4,10,1,2,3,5,6,7,8,9]=>[8,2]=>35
[3,10,1,2,4,5,6,7,8,9]=>[8,2]=>35
[1,8,2,3,4,5,6,7,9]=>[8,1]=>8
[7,4,6,1,3,2,5,8]=>[4,2,1,1]=>90
[1,4,5,8,6,3,2,7]=>[5,1,1,1]=>35
[8,4,5,7,2,6,1,3]=>[3,2,2,1]=>70
[4,5,2,6,7,3,1,8]=>[5,2,1]=>64
[8,1,7,5,3,6,2,4]=>[3,2,1,1,1]=>64
[5,2,8,3,6,1,4,7]=>[4,2,2]=>56
[5,2,6,3,1,7,8,4]=>[4,3,1]=>70
[4,3,5,1,6,7,8,2]=>[5,2,1]=>64
[5,7,6,1,2,3,8,4]=>[4,3,1]=>70
[3,6,7,5,1,2,8,4]=>[4,3,1]=>70
[1,7,6,8,5,2,4,3]=>[3,2,1,1,1]=>64
[5,7,6,8,1,2,4,3]=>[3,3,1,1]=>56
[5,6,3,7,1,4,8,2]=>[4,2,2]=>56
[5,3,2,1,8,6,4,7]=>[3,2,2,1]=>70
[9,8,7,5,6,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[2,1,9,8,6,7,5,4,3]=>[3,2,1,1,1,1]=>105
[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[10,9,8,7,5,6,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,7,5,4,6,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[9,8,7,4,6,5,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[2,1,9,8,6,5,7,4,3]=>[3,2,1,1,1,1]=>105
[2,1,9,8,5,7,6,4,3]=>[3,2,1,1,1,1]=>105
[2,1,10,9,8,6,7,5,4,3]=>[3,2,1,1,1,1,1]=>160
[2,1,11,10,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1,1,1]=>44
[1,8,7,6,5,4,3,2,9]=>[3,1,1,1,1,1,1]=>28
[1,9,8,7,6,5,4,3,2,10]=>[3,1,1,1,1,1,1,1]=>36
[2,1,8,7,6,5,4,3,9]=>[3,2,1,1,1,1]=>105
[6,5,8,3,7,2,1,4]=>[2,2,2,1,1]=>28
[7,8,5,3,6,2,1,4]=>[2,2,2,1,1]=>28
[7,8,5,3,6,2,4,1]=>[2,2,2,1,1]=>28
[1,8,4,3,2,6,7,5]=>[4,2,1,1]=>90
[5,4,3,8,2,1,7,6]=>[2,2,2,1,1]=>28
[6,4,8,3,2,1,7,5]=>[2,2,2,1,1]=>28
[1,8,4,3,2,7,6,5]=>[3,2,2,1]=>70
[1,8,6,7,3,2,4,5]=>[4,2,1,1]=>90
[5,4,3,8,2,1,6,7]=>[3,2,1,1,1]=>64
[1,8,4,3,2,5,7,6]=>[4,2,1,1]=>90
[4,5,6,7,8,1,2,9,3]=>[6,3]=>48
[4,5,6,7,1,2,8,9,3]=>[6,3]=>48
[4,5,6,1,2,7,8,9,3]=>[6,3]=>48
[4,5,1,2,6,7,8,9,3]=>[6,3]=>48
[6,4,2,3,5,1,8,7]=>[4,2,1,1]=>90
[5,2,3,6,1,4,8,7]=>[4,3,1]=>70
[5,2,3,8,6,4,7,1]=>[4,2,1,1]=>90
[5,2,3,7,4,8,1,6]=>[4,3,1]=>70
[8,6,3,2,5,4,7,1]=>[3,2,1,1,1]=>64
[7,2,3,4,5,8,1,6]=>[5,2,1]=>64
[7,2,8,1,5,3,4,6]=>[4,2,2]=>56
[3,8,6,4,7,2,5,1]=>[3,2,1,1,1]=>64
[2,1,8,6,4,5,7,3]=>[4,2,1,1]=>90
[4,8,2,5,7,3,1,6]=>[3,3,1,1]=>56
[5,8,2,3,4,7,1,6]=>[4,2,2]=>56
[6,3,4,7,8,2,1,5]=>[4,2,1,1]=>90
[3,8,5,1,4,7,6,2]=>[3,3,1,1]=>56
[4,8,5,1,3,6,7,2]=>[4,2,1,1]=>90
[4,6,8,5,2,7,3,1]=>[3,2,2,1]=>70
[3,7,8,5,2,6,4,1]=>[3,2,2,1]=>70
[3,8,6,2,7,4,5,1]=>[3,3,1,1]=>56
[8,5,4,7,1,3,6,2]=>[3,2,1,1,1]=>64
[7,3,6,2,8,1,5,4]=>[3,2,2,1]=>70
[8,1,5,2,3,7,6,4]=>[4,2,1,1]=>90
[6,4,2,3,7,8,5,1]=>[4,2,1,1]=>90
[8,4,2,3,6,7,1,5]=>[4,2,1,1]=>90
[4,5,8,3,7,2,1,6]=>[3,2,2,1]=>70
[3,7,2,8,4,5,1,6]=>[4,3,1]=>70
[3,5,1,8,4,6,2,7]=>[4,3,1]=>70
[4,2,1,5,6,8,3,7]=>[4,3,1]=>70
[4,1,2,6,5,8,3,7]=>[4,3,1]=>70
[4,1,8,3,2,6,7,5]=>[4,2,2]=>56
[4,2,7,5,8,1,3,6]=>[3,3,2]=>42
[4,6,2,7,8,3,1,5]=>[4,3,1]=>70
[4,6,1,3,8,2,5,7]=>[4,3,1]=>70
[4,3,6,2,1,8,7,5]=>[3,2,2,1]=>70
[3,7,4,5,1,6,2,8]=>[5,2,1]=>64
[3,6,4,5,8,2,1,7]=>[4,2,1,1]=>90
[6,1,4,5,2,8,7,3]=>[4,2,2]=>56
[7,2,4,5,1,6,3,8]=>[5,2,1]=>64
[7,5,4,1,6,3,2,8]=>[3,2,1,1,1]=>64
[1,5,4,8,6,3,2,7]=>[4,2,1,1]=>90
[7,5,4,8,6,3,1,2]=>[2,2,2,1,1]=>28
[1,8,7,5,3,6,4,2]=>[3,2,1,1,1]=>64
[8,3,7,4,1,6,2,5]=>[3,3,1,1]=>56
[8,5,4,1,6,3,2,7]=>[3,2,1,1,1]=>64
[1,7,4,2,6,5,3,8]=>[4,2,1,1]=>90
[8,2,1,5,6,7,3,4]=>[4,3,1]=>70
[6,3,1,8,4,7,2,5]=>[3,3,2]=>42
[7,1,4,8,6,3,2,5]=>[3,2,2,1]=>70
[4,1,8,5,6,7,2,3]=>[4,3,1]=>70
[5,7,4,8,6,2,1,3]=>[3,2,2,1]=>70
[5,3,6,8,2,7,1,4]=>[3,2,2,1]=>70
[6,3,7,4,8,2,1,5]=>[3,3,1,1]=>56
[5,3,6,1,4,7,2,8]=>[4,2,2]=>56
[4,3,6,8,2,7,1,5]=>[3,2,2,1]=>70
[5,3,7,4,8,2,1,6]=>[3,3,1,1]=>56
[5,3,8,4,1,6,2,7]=>[4,2,2]=>56
[5,3,8,1,4,7,2,6]=>[3,3,2]=>42
[5,8,4,1,6,3,2,7]=>[3,2,2,1]=>70
[7,3,8,4,1,6,2,5]=>[3,3,2]=>42
[1,5,8,3,6,7,4,2]=>[4,2,1,1]=>90
[1,8,2,5,6,7,3,4]=>[5,2,1]=>64
[7,8,4,1,6,5,2,3]=>[3,2,2,1]=>70
[6,3,8,1,5,7,2,4]=>[3,3,2]=>42
[8,3,1,2,5,7,4,6]=>[4,3,1]=>70
[8,1,4,2,6,5,3,7]=>[4,2,1,1]=>90
[7,8,1,2,3,4,5,9,6]=>[6,3]=>48
[2,8,9,1,3,4,5,6,7]=>[6,3]=>48
[2,8,9,10,1,3,4,5,6,7]=>[6,4]=>90
[7,1,8,2,9,3,4,5,6]=>[6,3]=>48
[6,1,7,2,8,3,9,4,5]=>[5,4]=>42
[5,1,6,2,7,3,8,4,9]=>[5,4]=>42
[8,1,9,2,10,3,4,5,6,7]=>[7,3]=>75
[7,1,8,2,3,9,4,5,6]=>[6,3]=>48
[7,1,8,2,9,3,10,4,5,6]=>[6,4]=>90
[6,1,7,2,8,3,4,9,5]=>[5,4]=>42
[5,1,6,2,7,3,9,4,8]=>[5,4]=>42
[5,1,6,2,7,3,8,4,10,9]=>[5,5]=>42
[4,1,5,2,7,3,8,6,9]=>[5,4]=>42
[4,1,5,2,6,3,8,7,10,9]=>[5,5]=>42
[5,1,3,7,4,8,2,6]=>[4,3,1]=>70
[5,1,3,4,7,8,2,6]=>[5,2,1]=>64
[2,5,8,7,4,3,6,1]=>[3,2,1,1,1]=>64
[5,1,7,8,3,4,2,6]=>[4,3,1]=>70
[2,5,4,8,3,7,6,1]=>[3,2,2,1]=>70
[5,6,8,2,3,4,1,7]=>[4,3,1]=>70
[2,3,5,7,4,6,8,1]=>[5,2,1]=>64
[3,7,4,5,8,1,2,6]=>[4,3,1]=>70
[3,7,8,1,4,5,2,6]=>[4,3,1]=>70
[5,8,2,1,6,3,4,7]=>[4,2,2]=>56
[4,8,1,3,7,5,2,6]=>[4,2,1,1]=>90
[2,4,7,8,5,3,6,1]=>[4,2,1,1]=>90
[5,3,1,4,7,2,8,6]=>[4,3,1]=>70
[2,4,7,5,8,3,6,1]=>[4,2,1,1]=>90
[4,8,5,7,3,1,2,6]=>[3,3,1,1]=>56
[4,8,7,5,1,3,2,6]=>[3,2,1,1,1]=>64
[3,7,8,4,1,5,2,6]=>[4,2,2]=>56
[1,8,5,7,2,4,3,6]=>[4,2,1,1]=>90
[1,8,5,4,2,3,6,7]=>[5,1,1,1]=>35
[1,3,6,8,5,4,2,7]=>[4,2,1,1]=>90
[1,3,6,8,2,7,5,4]=>[4,2,1,1]=>90
[1,6,5,4,3,8,2,7]=>[3,2,1,1,1]=>64
[1,8,3,4,5,6,2,7]=>[6,1,1]=>21
[1,8,3,6,2,4,5,7]=>[5,2,1]=>64
[1,4,5,8,3,6,2,7]=>[5,2,1]=>64
[1,2,7,8,4,5,3,6]=>[5,2,1]=>64
[7,2,8,5,6,3,4,1]=>[3,2,2,1]=>70
[7,6,3,8,5,4,2,1]=>[2,2,1,1,1,1]=>20
[6,2,8,7,5,4,1,3]=>[2,2,2,1,1]=>28
[6,2,8,4,3,7,1,5]=>[3,2,2,1]=>70
[5,2,8,4,3,1,7,6]=>[3,2,2,1]=>70
[1,4,3,6,8,7,2,5]=>[4,2,2]=>56
[3,2,5,7,6,8,1,4]=>[4,2,2]=>56
[5,3,2,6,8,4,7,1]=>[3,3,1,1]=>56
[3,1,8,6,4,7,2,5]=>[3,3,1,1]=>56
[5,3,2,8,7,6,4,1]=>[2,2,2,1,1]=>28
[5,3,8,2,7,6,1,4]=>[2,2,2,2]=>14
[6,5,4,8,3,7,2,1]=>[2,2,1,1,1,1]=>20
[4,8,5,1,3,7,2,6]=>[3,3,1,1]=>56
[4,3,8,7,2,6,5,1]=>[2,2,2,1,1]=>28
[2,7,5,1,8,4,6,3]=>[3,3,1,1]=>56
[7,8,5,2,1,6,4,3]=>[2,2,2,2]=>14
[7,6,4,8,1,2,5,3]=>[3,2,2,1]=>70
[3,8,5,6,2,7,1,4]=>[4,2,1,1]=>90
[2,4,5,8,7,3,1,6]=>[4,2,1,1]=>90
[2,4,5,8,6,7,1,3]=>[5,2,1]=>64
[4,3,1,5,6,2,8,7]=>[4,3,1]=>70
[4,1,5,8,6,7,2,3]=>[4,3,1]=>70
[4,3,7,6,1,2,8,5]=>[3,3,2]=>42
[4,7,5,6,1,2,8,3]=>[4,3,1]=>70
[4,3,7,5,6,2,8,1]=>[4,2,1,1]=>90
[4,5,1,8,6,7,3,2]=>[4,2,1,1]=>90
[3,4,5,8,6,7,2,1]=>[5,1,1,1]=>35
[2,1,5,8,6,7,4,3]=>[4,2,1,1]=>90
[3,4,5,8,7,1,2,6]=>[4,3,1]=>70
[4,7,1,5,6,2,8,3]=>[4,3,1]=>70
[2,6,4,7,1,3,8,5]=>[4,3,1]=>70
[5,3,8,6,4,7,2,1]=>[3,2,1,1,1]=>64
[6,4,1,5,7,8,3,2]=>[4,2,1,1]=>90
[3,6,4,7,2,1,8,5]=>[4,2,1,1]=>90
[3,8,4,6,1,7,2,5]=>[4,3,1]=>70
[3,8,5,6,4,7,2,1]=>[4,1,1,1,1]=>35
[3,8,4,5,6,7,2,1]=>[5,1,1,1]=>35
[3,8,6,5,2,7,4,1]=>[3,2,1,1,1]=>64
[3,8,7,5,2,1,4,6]=>[3,2,1,1,1]=>64
[3,8,6,5,1,7,2,4]=>[3,3,1,1]=>56
[6,4,1,7,3,2,8,5]=>[3,3,1,1]=>56
[5,1,4,6,7,2,8,3]=>[5,2,1]=>64
[6,5,4,7,1,3,8,2]=>[3,2,1,1,1]=>64
[2,1,6,5,3,7,8,4]=>[4,3,1]=>70
[6,1,4,7,2,3,8,5]=>[4,3,1]=>70
[2,1,3,4,5,6,8,9,7]=>[7,2]=>27
[2,1,3,4,5,6,7,9,8]=>[7,2]=>27
[1,2,3,4,5,6,7,8,10,11,9]=>[10,1]=>10
[2,1,3,4,5,6,7,9,10,8]=>[8,2]=>35
[2,3,1,4,5,6,8,9,7]=>[7,2]=>27
[1,3,2,4,5,6,8,9,7]=>[7,2]=>27
[2,3,1,4,5,6,7,9,8]=>[7,2]=>27
[1,3,2,4,5,6,7,9,8]=>[7,2]=>27
[2,1,3,4,5,6,7,8,10,9]=>[8,2]=>35
[1,6,2,5,4,8,3,7]=>[4,2,1,1]=>90
[6,1,3,5,8,2,4,7]=>[4,3,1]=>70
[6,7,3,2,1,8,4,5]=>[3,3,1,1]=>56
[2,5,7,3,1,4,8,6]=>[4,3,1]=>70
[1,2,6,7,4,3,8,5]=>[5,2,1]=>64
[2,7,5,8,1,6,3,4]=>[3,3,2]=>42
[8,2,5,7,1,4,6,3]=>[3,3,1,1]=>56
[8,7,3,6,2,1,5,4]=>[2,2,2,1,1]=>28
[8,4,3,7,6,5,1,2]=>[2,2,2,1,1]=>28
[8,4,2,7,5,1,6,3]=>[3,2,2,1]=>70
[8,3,4,2,7,5,6,1]=>[4,2,1,1]=>90
[8,4,7,6,5,1,2,3]=>[3,2,1,1,1]=>64
[8,6,2,4,7,3,1,5]=>[3,2,1,1,1]=>64
[8,5,2,3,7,4,1,6]=>[4,2,1,1]=>90
[8,6,1,5,4,3,2,7]=>[3,1,1,1,1,1]=>21
[2,4,5,8,3,1,6,7]=>[5,2,1]=>64
[2,7,4,6,1,5,8,3]=>[4,2,1,1]=>90
[2,4,3,8,5,1,6,7]=>[5,2,1]=>64
[7,8,3,2,5,4,6,1]=>[3,2,2,1]=>70
[1,5,6,7,3,8,2,4]=>[5,2,1]=>64
[1,6,5,4,8,3,2,7]=>[3,2,1,1,1]=>64
[1,7,3,5,8,4,6,2]=>[4,2,1,1]=>90
[7,2,1,6,4,8,5,3]=>[3,3,1,1]=>56
[3,8,7,2,4,6,5,1]=>[3,2,1,1,1]=>64
[3,1,8,7,6,4,2,5]=>[3,2,1,1,1]=>64
[3,1,8,7,5,4,2,6]=>[3,2,1,1,1]=>64
[3,1,7,6,5,4,2,8]=>[3,2,1,1,1]=>64
[4,7,1,6,5,3,2,8]=>[3,2,1,1,1]=>64
[4,8,1,6,5,3,2,7]=>[3,2,1,1,1]=>64
[8,4,1,7,6,3,2,5]=>[3,2,1,1,1]=>64
[5,4,1,8,6,3,2,7]=>[3,2,2,1]=>70
[5,4,1,7,6,3,2,8]=>[3,2,2,1]=>70
[6,4,1,8,5,3,2,7]=>[3,2,2,1]=>70
[8,4,1,7,5,3,2,6]=>[3,2,1,1,1]=>64
[7,4,1,6,5,3,2,8]=>[3,2,1,1,1]=>64
[7,5,6,1,4,3,2,8]=>[3,2,1,1,1]=>64
[8,5,6,1,4,3,2,7]=>[3,2,1,1,1]=>64
[8,5,7,1,4,3,2,6]=>[3,2,1,1,1]=>64
[5,7,6,1,4,3,2,8]=>[3,2,1,1,1]=>64
[5,8,6,1,4,3,2,7]=>[3,2,1,1,1]=>64
[6,7,5,1,4,3,2,8]=>[3,2,1,1,1]=>64
[8,7,5,1,4,3,2,6]=>[3,1,1,1,1,1]=>21
[8,6,5,1,4,3,2,7]=>[3,1,1,1,1,1]=>21
[1,8,6,3,4,2,5,7]=>[5,1,1,1]=>35
[3,1,6,4,5,8,2,7]=>[4,3,1]=>70
[7,6,3,8,4,5,2,1]=>[3,2,1,1,1]=>64
[8,2,7,6,1,4,3,5]=>[3,2,1,1,1]=>64
[5,6,3,8,4,1,2,7]=>[3,3,2]=>42
[8,2,7,6,1,4,5,3]=>[3,2,1,1,1]=>64
[5,2,3,4,7,1,6,8]=>[5,2,1]=>64
[5,2,3,7,1,6,8,4]=>[4,2,2]=>56
[8,7,5,3,1,6,4,2]=>[2,2,2,1,1]=>28
[1,4,7,8,5,2,3,6]=>[4,3,1]=>70
[5,8,3,7,6,4,1,2]=>[2,2,2,1,1]=>28
[6,5,1,7,2,4,8,3]=>[4,2,1,1]=>90
[3,6,7,1,4,2,5,8]=>[4,3,1]=>70
[8,1,2,7,5,4,3,6]=>[4,1,1,1,1]=>35
[6,5,1,8,3,7,2,4]=>[3,2,2,1]=>70
[1,8,7,5,3,2,6,4]=>[3,2,1,1,1]=>64
[7,8,1,5,4,2,3,6]=>[4,2,1,1]=>90
[6,8,1,7,5,4,2,3]=>[3,2,1,1,1]=>64
[7,6,3,1,2,8,5,4]=>[3,2,2,1]=>70
[1,7,5,2,6,4,8,3]=>[4,2,1,1]=>90
[7,1,3,6,8,2,4,5]=>[4,3,1]=>70
[1,2,5,7,8,4,6,3]=>[5,2,1]=>64
[3,1,2,7,5,4,8,6]=>[4,3,1]=>70
[6,7,4,1,3,2,8,5]=>[3,3,1,1]=>56
[1,7,2,8,4,3,5,6]=>[5,2,1]=>64
[1,6,3,5,7,8,2,4]=>[5,2,1]=>64
[8,6,1,7,5,2,4,3]=>[3,2,1,1,1]=>64
[7,6,4,1,8,3,2,5]=>[3,2,1,1,1]=>64
[8,4,1,6,5,2,7,3]=>[3,3,1,1]=>56
[1,5,3,4,7,8,2,6]=>[5,2,1]=>64
[4,2,1,5,7,8,3,6]=>[4,3,1]=>70
[5,4,1,6,7,8,2,3]=>[4,3,1]=>70
[5,1,4,6,7,8,2,3]=>[5,2,1]=>64
[4,1,5,3,7,8,2,6]=>[4,3,1]=>70
[8,1,4,6,5,2,7,3]=>[4,2,1,1]=>90
[7,1,5,4,6,3,2,8]=>[4,1,1,1,1]=>35
[8,2,1,6,7,5,4,3]=>[3,2,1,1,1]=>64
[1,2,4,7,6,3,8,5]=>[5,2,1]=>64
[6,7,4,1,8,5,2,3]=>[3,3,2]=>42
[8,6,4,1,5,7,3,2]=>[3,2,1,1,1]=>64
[5,2,4,3,7,1,6,8]=>[4,2,1,1]=>90
[6,1,5,4,8,3,2,7]=>[3,2,1,1,1]=>64
[1,2,8,7,4,3,6,5]=>[4,2,1,1]=>90
[3,2,1,7,5,8,4,6]=>[3,3,2]=>42
[1,3,6,4,7,8,2,5]=>[5,2,1]=>64
[4,5,1,3,7,8,2,6]=>[4,3,1]=>70
[5,2,3,1,7,8,4,6]=>[4,3,1]=>70
[1,6,4,3,7,8,2,5]=>[4,2,1,1]=>90
[7,6,4,3,1,5,2,8]=>[3,2,1,1,1]=>64
[7,5,4,6,1,3,2,8]=>[3,2,1,1,1]=>64
[8,4,6,5,1,2,7,3]=>[3,3,1,1]=>56
[1,5,6,3,7,8,2,4]=>[5,2,1]=>64
[7,1,2,3,4,5,8,9,10,6]=>[8,2]=>35
[6,7,1,2,3,4,8,9,5]=>[6,3]=>48
[6,1,2,3,4,7,8,9,10,5]=>[8,2]=>35
[5,1,2,3,6,7,8,9,10,4]=>[8,2]=>35
[1,5,2,4,3,8,7,6]=>[4,2,2]=>56
[8,6,5,7,2,1,4,3]=>[2,2,2,1,1]=>28
[1,6,3,8,4,5,7,2]=>[5,2,1]=>64
[7,5,4,2,6,3,8,1]=>[3,2,1,1,1]=>64
[9,7,6,5,4,3,1,2,8]=>[3,1,1,1,1,1,1]=>28
[2,4,3,5,6,7,8,9,1]=>[7,1,1]=>28
[2,3,8,4,7,5,6,1]=>[5,1,1,1]=>35
[3,7,2,8,6,4,5,1]=>[3,3,1,1]=>56
[4,3,7,8,6,2,5,1]=>[3,2,2,1]=>70
[3,8,1,7,5,2,4,6]=>[4,2,1,1]=>90
[2,4,7,8,6,1,5,3]=>[4,2,1,1]=>90
[2,4,8,5,1,7,3,6]=>[4,3,1]=>70
[2,8,3,5,1,6,4,7]=>[5,2,1]=>64
[8,2,4,6,3,7,5,1]=>[4,2,1,1]=>90
[4,5,6,7,8,9,2,1,3]=>[6,2,1]=>105
[5,6,7,8,9,2,1,3,4]=>[5,3,1]=>162
[1,4,6,2,7,5,3,8]=>[5,2,1]=>64
[8,2,1,4,5,6,7,3]=>[5,2,1]=>64
[7,3,1,2,5,6,4,8]=>[5,2,1]=>64
[7,8,2,1,5,4,6,3]=>[3,2,2,1]=>70
[1,4,8,5,2,6,3,7]=>[5,2,1]=>64
[5,2,3,7,8,1,6,4]=>[4,2,2]=>56
[1,2,8,4,3,6,7,5]=>[5,2,1]=>64
[1,2,7,5,3,4,6,8]=>[6,1,1]=>21
[1,7,3,2,6,8,4,5]=>[4,3,1]=>70
[3,5,8,6,1,4,2,7]=>[4,2,1,1]=>90
[1,8,4,2,7,6,3,5]=>[4,2,1,1]=>90
[7,3,8,1,6,5,4,2]=>[2,2,2,1,1]=>28
[7,3,8,2,6,5,4,1]=>[2,2,2,1,1]=>28
[7,1,3,8,6,5,4,2]=>[3,2,1,1,1]=>64
[8,1,3,7,6,5,4,2]=>[3,1,1,1,1,1]=>21
[2,4,1,8,7,3,6,5]=>[3,3,1,1]=>56
[7,3,8,6,1,5,4,2]=>[2,2,2,1,1]=>28
[3,5,1,7,8,2,6,4]=>[4,3,1]=>70
[5,4,7,8,2,1,6,3]=>[3,2,2,1]=>70
[6,3,8,7,1,5,4,2]=>[2,2,2,1,1]=>28
[8,6,4,7,1,5,3,2]=>[2,2,2,1,1]=>28
[3,4,6,2,1,8,5,7]=>[4,3,1]=>70
[5,6,4,8,3,2,1,7]=>[3,2,1,1,1]=>64
[5,7,4,8,2,1,6,3]=>[3,2,2,1]=>70
[4,7,5,8,2,1,6,3]=>[3,2,2,1]=>70
[5,7,4,2,6,3,8,1]=>[3,2,2,1]=>70
[5,7,4,1,6,2,8,3]=>[3,3,2]=>42
[8,5,6,1,7,3,2,4]=>[3,3,1,1]=>56
[4,5,1,6,7,8,3,2]=>[5,2,1]=>64
[4,5,2,6,1,3,8,7]=>[4,3,1]=>70
[8,4,6,7,2,5,1,3]=>[3,2,2,1]=>70
[7,1,4,6,8,3,5,2]=>[4,2,1,1]=>90
[6,7,1,2,4,8,5,3]=>[4,3,1]=>70
[2,3,6,4,7,5,8,1]=>[5,2,1]=>64
[7,8,1,3,4,5,6,2]=>[5,2,1]=>64
[1,8,2,6,7,3,4,5]=>[5,2,1]=>64
[4,7,3,2,8,1,5,6]=>[3,3,1,1]=>56
[4,7,8,3,1,6,2,5]=>[3,3,2]=>42
[7,4,3,1,6,2,8,5]=>[3,3,1,1]=>56
[7,4,3,1,8,6,2,5]=>[3,2,2,1]=>70
[3,7,6,2,4,8,1,5]=>[3,3,1,1]=>56
[4,3,7,2,8,6,1,5]=>[3,2,2,1]=>70
[6,1,2,7,4,3,8,5]=>[4,3,1]=>70
[5,1,2,6,3,8,7,4]=>[4,3,1]=>70
[5,1,2,7,3,8,6,4]=>[4,3,1]=>70
[6,1,2,7,3,5,8,4]=>[5,2,1]=>64
[7,5,3,2,1,8,6,4]=>[2,2,2,1,1]=>28
[4,2,1,5,3,6,7,8]=>[5,2,1]=>64
[8,6,4,3,2,1,9,7,5]=>[2,2,2,1,1,1]=>48
[7,5,3,1,8,6,4,2,9]=>[3,2,2,2]=>84
[7,4,1,8,5,2,9,6,3]=>[3,3,3]=>42
[5,3,1,6,4,2,7,8,9]=>[5,2,2]=>120
[4,1,5,2,6,3,7,8,9]=>[6,3]=>48
[3,1,4,2,5,6,7,8,9]=>[7,2]=>27
[9,7,5,4,3,2,1,10,8,6]=>[2,2,2,1,1,1,1]=>75
[7,5,3,1,8,6,4,2,9,10]=>[4,2,2,2]=>300
[7,4,1,8,5,2,9,6,3,10]=>[4,3,3]=>210
[5,3,1,6,4,2,7,8,9,10]=>[6,2,2]=>225
[5,1,6,2,7,3,8,4,9,10]=>[6,4]=>90
[4,1,5,2,6,3,7,8,9,10]=>[7,3]=>75
[3,1,4,2,5,6,7,8,9,10]=>[8,2]=>35
[6,2,5,4,1,8,7,3]=>[3,2,2,1]=>70
[4,6,3,2,1,8,7,5]=>[3,2,2,1]=>70
[6,5,3,2,1,8,7,4]=>[2,2,2,1,1]=>28
[8,4,3,2,7,6,1,5]=>[2,2,2,1,1]=>28
[1,5,8,4,7,6,3,2]=>[3,2,1,1,1]=>64
[3,2,7,4,8,6,1,5]=>[3,3,2]=>42
[7,4,3,2,8,6,1,5]=>[2,2,2,1,1]=>28
[6,8,3,7,5,2,1,4]=>[2,2,2,1,1]=>28
[5,7,8,4,3,2,1,6]=>[3,2,1,1,1]=>64
[6,4,3,8,5,2,1,7]=>[3,2,1,1,1]=>64
[8,2,5,4,7,6,1,3]=>[3,2,2,1]=>70
[7,2,5,4,8,6,1,3]=>[3,2,2,1]=>70
[4,5,3,2,8,6,1,7]=>[4,2,1,1]=>90
[3,2,5,4,8,6,1,7]=>[4,3,1]=>70
[3,2,8,6,5,4,1,7]=>[3,2,1,1,1]=>64
[8,4,3,6,5,2,1,7]=>[3,2,1,1,1]=>64
[8,4,3,7,5,2,1,6]=>[3,2,1,1,1]=>64
[3,2,7,8,5,4,1,6]=>[3,3,1,1]=>56
[6,8,7,4,3,2,1,5]=>[2,2,1,1,1,1]=>20
[3,6,1,4,8,7,2,5]=>[3,3,2]=>42
[5,8,1,3,7,2,6,4]=>[3,2,2,1]=>70
[6,3,2,1,8,7,4,5]=>[3,2,2,1]=>70
[6,2,3,1,8,7,4,5]=>[4,2,2]=>56
[7,2,5,1,8,3,6,4]=>[3,3,2]=>42
[7,2,1,5,8,4,6,3]=>[3,3,1,1]=>56
[4,2,8,1,7,5,6,3]=>[3,2,2,1]=>70
[7,3,1,5,2,8,6,4]=>[3,3,2]=>42
[7,1,6,4,2,8,5,3]=>[3,2,2,1]=>70
[3,7,4,1,5,8,6,2]=>[4,2,2]=>56
[5,8,6,1,2,7,4,3]=>[3,3,1,1]=>56
[6,8,1,4,3,7,5,2]=>[3,2,2,1]=>70
[6,7,1,4,3,8,5,2]=>[3,3,1,1]=>56
[4,7,1,5,3,8,6,2]=>[3,3,1,1]=>56
[6,8,1,2,4,7,5,3]=>[4,2,1,1]=>90
[7,1,6,4,8,3,5,2]=>[3,2,1,1,1]=>64
[8,6,4,1,3,7,5,2]=>[3,2,1,1,1]=>64
[8,5,3,6,1,7,4,2]=>[3,2,2,1]=>70
[7,2,1,4,5,8,6,3]=>[4,2,2]=>56
[8,5,6,1,2,7,4,3]=>[3,3,1,1]=>56
[8,6,2,5,4,7,3,1]=>[3,1,1,1,1,1]=>21
[8,5,2,1,4,3,6,7]=>[4,2,1,1]=>90
[8,1,2,4,5,6,7,3]=>[6,1,1]=>21
[6,1,4,3,2,7,8,5]=>[4,2,1,1]=>90
[1,8,3,6,7,2,4,5]=>[4,3,1]=>70
[1,2,8,3,7,4,6,5]=>[5,1,1,1]=>35
[1,9,2,3,4,5,6,7,8,10]=>[9,1]=>9
[1,7,2,3,4,5,6,8,9]=>[8,1]=>8
[2,4,1,3,6,5,8,7,10,9,11]=>[6,5]=>132
[8,2,6,5,4,3,1,7]=>[3,1,1,1,1,1]=>21
[8,2,7,6,4,5,3,1]=>[3,1,1,1,1,1]=>21
[8,7,3,5,4,2,6,1]=>[3,1,1,1,1,1]=>21
[12,10,9,8,7,6,5,4,3,2,1,11]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[4,6,7,2,1,8,3,5]=>[4,3,1]=>70
[3,7,1,8,2,5,4,6]=>[4,3,1]=>70
[4,5,8,6,1,3,7,2]=>[4,2,1,1]=>90
[4,5,8,6,2,7,3,1]=>[4,2,1,1]=>90
[4,6,7,1,5,3,8,2]=>[4,2,1,1]=>90
[4,6,7,2,1,8,5,3]=>[4,2,2]=>56
[4,2,5,6,7,8,3,1]=>[5,2,1]=>64
[4,1,3,5,6,7,8,2]=>[6,1,1]=>21
[3,7,8,4,5,1,6,2]=>[4,2,2]=>56
[4,6,8,3,2,7,1,5]=>[3,2,2,1]=>70
[4,6,8,2,3,7,1,5]=>[3,3,2]=>42
[3,8,1,7,4,5,2,6]=>[4,2,1,1]=>90
[4,5,8,3,7,1,2,6]=>[3,3,2]=>42
[3,7,8,4,6,2,5,1]=>[3,2,2,1]=>70
[3,6,1,5,7,8,2,4]=>[4,3,1]=>70
[3,8,2,5,4,7,1,6]=>[3,3,1,1]=>56
[3,8,6,2,5,1,7,4]=>[3,2,2,1]=>70
[4,5,8,6,2,1,7,3]=>[4,2,1,1]=>90
[4,5,8,6,1,2,7,3]=>[4,3,1]=>70
[4,6,8,5,2,7,1,3]=>[3,2,2,1]=>70
[3,7,8,5,2,6,1,4]=>[3,2,2,1]=>70
[3,7,8,5,4,1,6,2]=>[3,2,2,1]=>70
[4,6,8,5,3,1,7,2]=>[3,2,2,1]=>70
[7,8,2,3,5,4,1,6]=>[4,2,1,1]=>90
[4,6,5,2,7,8,1,3]=>[4,2,1,1]=>90
[4,6,5,1,7,3,8,2]=>[4,2,1,1]=>90
[5,7,3,1,2,4,8,6]=>[4,3,1]=>70
[6,3,2,5,1,7,4,8]=>[4,2,1,1]=>90
[6,1,2,4,8,5,3,7]=>[5,2,1]=>64
[6,3,1,7,2,5,8,4]=>[4,2,2]=>56
[3,6,5,8,1,7,2,4]=>[3,3,2]=>42
[1,2,3,4,5,6,8,7,9]=>[8,1]=>8
[1,2,3,4,5,6,7,9,8,10]=>[9,1]=>9
[1,2,3,4,5,7,6,8,9]=>[8,1]=>8
[9,2,3,4,5,6,7,1,8]=>[7,1,1]=>28
[5,2,7,3,4,6,1,8]=>[5,2,1]=>64
[1,3,5,8,6,4,7,2]=>[5,1,1,1]=>35
[1,3,5,8,6,7,2,4]=>[5,2,1]=>64
[6,1,7,4,8,5,3,2]=>[3,3,1,1]=>56
[5,7,4,1,3,6,8,2]=>[4,2,1,1]=>90
[7,8,1,4,6,5,3,2]=>[3,2,1,1,1]=>64
[6,2,7,3,8,5,4,1]=>[3,3,1,1]=>56
[1,2,7,5,3,4,8,6]=>[5,2,1]=>64
[7,2,8,3,6,4,5,1]=>[4,2,1,1]=>90
[6,2,7,8,3,1,4,5]=>[4,3,1]=>70
[1,7,8,2,5,3,4,6]=>[5,2,1]=>64
[1,2,8,7,3,4,6,5]=>[5,1,1,1]=>35
[3,8,1,5,7,2,6,4]=>[3,3,1,1]=>56
[7,5,4,8,6,1,2,3]=>[3,2,2,1]=>70
[7,1,8,6,4,5,2,3]=>[3,2,2,1]=>70
[8,7,5,1,4,3,6,2]=>[3,1,1,1,1,1]=>21
[8,4,1,3,7,5,6,2]=>[4,2,1,1]=>90
[4,8,1,3,7,5,6,2]=>[4,2,1,1]=>90
[1,2,6,8,5,3,4,7]=>[5,2,1]=>64
[5,6,8,7,3,1,2,4]=>[3,3,1,1]=>56
[6,7,5,3,8,1,2,4]=>[3,3,1,1]=>56
[6,8,5,7,3,1,2,4]=>[3,2,2,1]=>70
[5,1,4,2,6,8,7,3]=>[4,2,2]=>56
[6,3,2,4,7,1,8,5]=>[4,2,1,1]=>90
[1,5,8,6,2,4,3,7]=>[4,2,1,1]=>90
[5,1,8,6,2,4,3,7]=>[4,2,1,1]=>90
[5,8,6,3,7,1,2,4]=>[3,3,1,1]=>56
[5,7,6,3,8,1,2,4]=>[3,3,1,1]=>56
[6,8,7,5,3,1,2,4]=>[3,2,1,1,1]=>64
[1,2,5,3,6,8,7,4]=>[5,2,1]=>64
[6,8,7,2,1,5,3,4]=>[3,2,2,1]=>70
[7,3,6,1,4,8,2,5]=>[3,3,1,1]=>56
[8,7,3,2,1,4,6,5]=>[3,2,1,1,1]=>64
[8,3,5,1,7,4,2,6]=>[3,3,1,1]=>56
[5,8,2,6,4,3,7,1]=>[3,2,1,1,1]=>64
[2,8,6,3,4,1,7,5]=>[4,2,1,1]=>90
[1,7,2,3,5,8,6,4]=>[5,2,1]=>64
[2,8,3,7,5,1,6,4]=>[4,2,1,1]=>90
[6,4,8,7,2,1,5,3]=>[2,2,2,2]=>14
[1,8,2,3,7,5,6,4]=>[5,1,1,1]=>35
[2,8,4,3,6,7,1,5]=>[4,2,1,1]=>90
[7,3,2,5,6,1,8,4]=>[4,2,1,1]=>90
[1,6,7,8,2,4,3,5]=>[4,3,1]=>70
[4,1,2,8,5,3,7,6]=>[4,3,1]=>70
[3,8,4,2,5,1,7,6]=>[4,2,1,1]=>90
[2,8,3,5,6,4,1,7]=>[5,1,1,1]=>35
[7,6,8,3,2,5,1,4]=>[2,2,2,1,1]=>28
[2,7,1,4,5,3,8,6]=>[4,3,1]=>70
[1,5,2,7,4,3,6,8]=>[5,2,1]=>64
[1,3,6,5,2,7,4,8]=>[5,2,1]=>64
[1,7,2,5,6,8,3,4]=>[5,2,1]=>64
[1,7,2,4,8,3,5,6]=>[5,2,1]=>64
[1,6,2,4,5,3,7,8]=>[6,1,1]=>21
[1,3,2,8,4,5,7,6]=>[5,2,1]=>64
[1,6,8,2,4,3,5,7]=>[5,2,1]=>64
[1,6,7,2,5,3,4,8]=>[5,2,1]=>64
[1,2,8,3,6,7,4,5]=>[5,2,1]=>64
[1,7,2,5,3,4,8,6]=>[5,2,1]=>64
[10,3,4,5,6,7,8,9,1,2]=>[7,2,1]=>160
[9,3,4,5,6,7,8,1,10,2]=>[7,2,1]=>160
[8,3,4,5,6,7,1,9,10,2]=>[7,2,1]=>160
[7,3,4,5,6,1,8,9,10,2]=>[7,2,1]=>160
[6,3,4,5,1,7,8,9,10,2]=>[7,2,1]=>160
[5,3,4,1,6,7,8,9,10,2]=>[7,2,1]=>160
[4,3,1,5,6,7,8,9,10,2]=>[7,2,1]=>160
[11,3,4,5,6,7,8,9,10,1,2]=>[8,2,1]=>231
[10,9,4,5,6,7,8,1,2,3]=>[5,3,1,1]=>567
[10,3,4,5,6,7,8,9,1,11,2]=>[8,2,1]=>231
[10,3,8,5,6,7,1,9,2,4]=>[5,3,1,1]=>567
[9,3,4,5,6,7,8,1,10,11,2]=>[8,2,1]=>231
[10,3,4,7,6,1,8,9,2,5]=>[5,3,1,1]=>567
[8,3,4,5,6,7,1,9,10,11,2]=>[8,2,1]=>231
[10,3,4,5,1,7,8,9,2,6]=>[6,3,1]=>315
[7,3,4,5,6,1,8,9,10,11,2]=>[8,2,1]=>231
[5,3,4,1,6,10,8,9,2,7]=>[5,3,2]=>450
[6,3,4,5,1,7,8,9,10,11,2]=>[8,2,1]=>231
[4,3,1,5,6,7,10,9,2,8]=>[5,3,2]=>450
[5,3,4,1,6,7,8,9,10,11,2]=>[8,2,1]=>231
[3,1,4,5,6,7,8,10,2,9]=>[7,3]=>75
[4,3,1,5,6,7,8,9,10,11,2]=>[8,2,1]=>231
[7,1,5,6,2,3,8,4]=>[4,3,1]=>70
[8,2,1,4,6,7,3,5]=>[4,3,1]=>70
[7,2,6,1,3,4,8,5]=>[4,3,1]=>70
[4,1,3,7,2,5,8,6]=>[4,3,1]=>70
[6,2,7,5,1,3,8,4]=>[3,3,2]=>42
[1,7,5,6,2,3,8,4]=>[4,3,1]=>70
[3,7,6,1,2,4,8,5]=>[4,3,1]=>70
[8,6,1,3,5,7,2,4]=>[4,2,1,1]=>90
[1,7,4,3,8,2,5,6]=>[4,2,1,1]=>90
[6,1,5,3,4,8,2,7]=>[4,2,1,1]=>90
[3,6,7,5,2,8,1,4]=>[4,2,1,1]=>90
[7,8,4,1,5,6,2,3]=>[3,3,2]=>42
[5,8,1,3,6,7,2,4]=>[4,2,2]=>56
[2,8,4,3,7,1,5,6]=>[4,2,1,1]=>90
[3,8,4,6,7,1,2,5]=>[4,3,1]=>70
[6,3,8,4,7,1,2,5]=>[3,3,2]=>42
[1,2,5,4,8,3,6,7]=>[5,2,1]=>64
[7,1,3,8,2,4,5,6]=>[5,2,1]=>64
[8,1,3,7,2,4,5,6]=>[5,2,1]=>64
[3,5,4,7,8,1,2,6]=>[4,3,1]=>70
[8,3,1,4,7,2,5,6]=>[4,3,1]=>70
[1,6,4,7,8,2,3,5]=>[4,3,1]=>70
[5,2,3,6,7,8,1,4]=>[5,2,1]=>64
[6,2,7,3,8,5,1,4]=>[3,3,2]=>42
[1,3,7,8,5,6,2,4]=>[4,2,2]=>56
[8,2,6,7,5,1,3,4]=>[3,3,1,1]=>56
[8,1,7,4,6,2,3,5]=>[4,2,1,1]=>90
[2,5,8,4,7,1,3,6]=>[3,3,2]=>42
[4,5,8,7,1,2,3,6]=>[4,3,1]=>70
[4,1,8,5,7,2,3,6]=>[4,3,1]=>70
[1,8,7,4,6,2,3,5]=>[4,2,1,1]=>90
[2,6,5,4,1,8,3,7]=>[3,3,1,1]=>56
[6,2,5,1,4,8,3,7]=>[3,3,1,1]=>56
[6,5,4,1,3,8,2,7]=>[3,2,1,1,1]=>64
[6,3,5,4,2,8,1,7]=>[3,2,1,1,1]=>64
[1,3,8,7,4,2,6,5]=>[4,2,1,1]=>90
[8,7,4,3,1,5,2,6]=>[3,2,1,1,1]=>64
[8,2,5,1,4,6,7,3]=>[4,2,1,1]=>90
[3,8,4,5,1,6,7,2]=>[5,2,1]=>64
[8,5,4,1,3,6,7,2]=>[4,1,1,1,1]=>35
[8,3,1,7,5,6,4,2]=>[3,2,1,1,1]=>64
[8,4,7,6,5,3,1,2]=>[2,2,1,1,1,1]=>20
[8,1,4,5,7,6,3,2]=>[4,1,1,1,1]=>35
[2,4,1,8,5,7,6,3]=>[4,2,1,1]=>90
[8,2,1,4,7,6,3,5]=>[3,3,1,1]=>56
[8,3,1,7,4,2,6,5]=>[3,3,1,1]=>56
[8,2,7,3,1,6,5,4]=>[3,2,1,1,1]=>64
[1,8,4,2,3,7,6,5]=>[4,2,1,1]=>90
[3,1,2,8,7,4,6,5]=>[4,2,1,1]=>90
[8,5,1,2,4,3,7,6]=>[4,2,1,1]=>90
[2,8,3,7,4,1,6,5]=>[4,2,1,1]=>90
[8,4,5,7,6,2,3,1]=>[3,2,1,1,1]=>64
[2,3,1,8,7,6,4,5]=>[4,2,1,1]=>90
[4,2,8,7,3,1,5,6]=>[4,2,1,1]=>90
[1,3,4,8,7,2,5,6]=>[5,2,1]=>64
[8,1,3,4,6,7,2,5]=>[5,2,1]=>64
[3,4,8,2,6,7,1,5]=>[4,2,2]=>56
[3,6,8,2,5,1,7,4]=>[3,3,2]=>42
[3,8,2,5,7,4,6,1]=>[3,3,1,1]=>56
[8,4,2,1,7,5,6,3]=>[3,2,2,1]=>70
[8,2,7,5,6,4,1,3]=>[3,2,1,1,1]=>64
[6,2,8,5,4,1,7,3]=>[3,2,2,1]=>70
[6,8,5,4,1,7,2,3]=>[3,2,2,1]=>70
[2,8,1,5,7,6,3,4]=>[3,3,1,1]=>56
[3,1,8,2,7,5,6,4]=>[4,2,1,1]=>90
[8,5,7,1,6,4,2,3]=>[3,2,1,1,1]=>64
[2,8,4,7,3,6,5,1]=>[3,2,1,1,1]=>64
[8,4,7,2,1,6,5,3]=>[2,2,2,1,1]=>28
[1,8,4,7,6,5,2,3]=>[3,2,1,1,1]=>64
[3,5,8,1,7,4,6,2]=>[3,3,1,1]=>56
[8,4,7,1,3,6,5,2]=>[3,2,1,1,1]=>64
[8,2,3,4,5,6,9,1,7]=>[6,2,1]=>105
[8,2,3,9,5,6,7,1,4]=>[5,2,2]=>120
[8,2,9,4,5,6,7,1,3]=>[5,2,2]=>120
[8,9,3,4,5,6,7,1,2]=>[5,2,2]=>120
[9,2,3,4,5,6,7,10,1,8]=>[7,2,1]=>160
[4,2,3,1,9,8,7,6,5]=>[3,2,2,1,1]=>162
[3,2,1,9,8,6,7,5,4]=>[3,2,2,1,1]=>162
[9,2,10,4,5,6,7,8,1,3]=>[6,2,2]=>225
[2,3,4,7,6,8,1,5]=>[5,2,1]=>64
[3,8,1,2,5,6,4,7]=>[5,2,1]=>64
[8,5,2,1,4,6,7,3]=>[4,2,1,1]=>90
[4,8,1,6,5,2,7,3]=>[3,3,1,1]=>56
[4,2,6,3,8,5,7,1]=>[4,3,1]=>70
[4,5,2,6,7,1,8,3]=>[5,2,1]=>64
[8,3,5,4,2,7,1,6]=>[3,2,1,1,1]=>64
[2,8,6,4,7,3,1,5]=>[3,2,1,1,1]=>64
[3,1,8,6,5,2,7,4]=>[3,3,1,1]=>56
[8,3,1,5,2,6,7,4]=>[4,3,1]=>70
[6,5,3,2,4,8,1,7]=>[3,2,1,1,1]=>64
[5,2,4,6,1,3,8,7]=>[4,3,1]=>70
[7,2,3,4,6,8,1,5]=>[5,2,1]=>64
[8,3,4,6,7,5,1,2]=>[4,2,1,1]=>90
[6,8,3,4,7,5,2,1]=>[3,2,1,1,1]=>64
[5,8,6,1,3,4,7,2]=>[4,2,1,1]=>90
[4,8,1,5,7,6,3,2]=>[3,2,1,1,1]=>64
[3,7,4,6,8,2,5,1]=>[4,2,1,1]=>90
[4,7,1,6,8,3,2,5]=>[3,3,1,1]=>56
[4,5,2,8,1,7,3,6]=>[3,3,2]=>42
[3,7,5,2,8,6,1,4]=>[3,2,2,1]=>70
[4,8,5,2,6,7,1,3]=>[4,2,1,1]=>90
[5,4,8,6,1,2,7,3]=>[3,3,2]=>42
[8,4,6,5,2,7,3,1]=>[3,2,1,1,1]=>64
[8,1,6,4,7,5,2,3]=>[3,2,2,1]=>70
[5,2,7,6,4,8,1,3]=>[3,2,2,1]=>70
[8,6,2,3,5,1,7,4]=>[4,2,1,1]=>90
[8,2,5,7,4,1,3,6]=>[3,3,1,1]=>56
[7,2,4,5,6,8,1,3]=>[5,2,1]=>64
[7,1,3,5,6,2,8,4]=>[5,2,1]=>64
[7,1,5,8,4,6,3,2]=>[3,2,1,1,1]=>64
[6,3,8,4,7,1,5,2]=>[3,2,2,1]=>70
[7,1,4,3,2,8,5,6]=>[4,2,1,1]=>90
[5,3,6,1,4,2,8,7]=>[3,3,2]=>42
[5,7,2,1,4,3,8,6]=>[3,3,2]=>42
[7,1,8,3,5,2,4,6]=>[4,2,2]=>56
[7,2,4,8,1,5,6,3]=>[4,2,2]=>56
[7,1,8,4,2,5,6,3]=>[4,2,2]=>56
[6,4,2,5,8,1,7,3]=>[3,2,2,1]=>70
[2,1,7,5,8,3,6,4]=>[3,3,2]=>42
[7,3,8,5,6,2,1,4]=>[3,2,2,1]=>70
[2,7,4,8,1,5,6,3]=>[4,2,2]=>56
[7,4,8,3,1,5,6,2]=>[3,2,2,1]=>70
[6,1,5,8,3,7,4,2]=>[3,2,2,1]=>70
[2,6,3,5,8,7,4,1]=>[4,2,1,1]=>90
[8,6,5,3,7,2,1,4]=>[2,2,1,1,1,1]=>20
[4,8,5,3,7,2,1,6]=>[3,2,1,1,1]=>64
[7,4,8,6,5,3,2,1]=>[2,2,1,1,1,1]=>20
[7,4,8,5,6,3,1,2]=>[3,2,2,1]=>70
[7,8,4,1,3,5,6,2]=>[4,2,1,1]=>90
[7,8,3,4,1,5,6,2]=>[4,2,2]=>56
[7,3,1,8,2,5,6,4]=>[4,2,2]=>56
[7,2,3,8,1,5,6,4]=>[4,2,2]=>56
[6,4,8,7,3,2,1,5]=>[2,2,2,1,1]=>28
[2,7,4,8,6,3,1,5]=>[3,2,2,1]=>70
[6,4,8,2,3,1,7,5]=>[3,2,2,1]=>70
[7,2,1,8,3,5,6,4]=>[4,2,2]=>56
[5,1,6,3,8,2,4,7]=>[4,3,1]=>70
[7,3,6,2,8,4,1,5]=>[3,3,1,1]=>56
[7,5,4,8,1,6,2,3]=>[3,2,2,1]=>70
[3,5,6,8,1,4,2,7]=>[4,3,1]=>70
[4,3,5,8,2,1,6,7]=>[4,2,1,1]=>90
[6,4,7,2,3,1,5,8]=>[4,2,1,1]=>90
[6,8,1,5,4,2,7,3]=>[3,2,2,1]=>70
[7,8,6,3,5,1,2,4]=>[3,2,2,1]=>70
[6,1,8,4,7,2,3,5]=>[4,2,2]=>56
[5,6,4,3,7,1,8,2]=>[4,2,1,1]=>90
[6,5,3,7,2,4,8,1]=>[3,2,1,1,1]=>64
[5,6,2,8,4,3,7,1]=>[3,3,1,1]=>56
[7,1,3,6,5,8,4,2]=>[4,1,1,1,1]=>35
[4,6,2,7,8,3,5,1]=>[4,3,1]=>70
[5,1,2,4,6,7,8,3]=>[6,1,1]=>21
[4,6,3,5,2,8,7,1]=>[3,3,1,1]=>56
[5,6,3,4,8,2,7,1]=>[3,3,1,1]=>56
[5,2,6,4,1,7,8,3]=>[4,2,2]=>56
[5,8,4,6,3,2,7,1]=>[3,2,1,1,1]=>64
[5,4,3,8,6,2,7,1]=>[3,2,1,1,1]=>64
[5,7,8,2,4,3,6,1]=>[3,3,1,1]=>56
[5,6,2,4,8,3,7,1]=>[3,3,1,1]=>56
[6,4,7,8,2,3,5,1]=>[3,3,1,1]=>56
[3,7,5,2,4,8,1,6]=>[3,3,1,1]=>56
[4,7,5,2,3,8,6,1]=>[3,3,1,1]=>56
[6,4,7,3,2,5,8,1]=>[3,2,1,1,1]=>64
[5,7,3,2,8,4,6,1]=>[3,3,1,1]=>56
[5,3,7,2,8,4,6,1]=>[3,3,1,1]=>56
[4,3,7,2,5,8,6,1]=>[3,3,1,1]=>56
[4,7,3,2,5,8,6,1]=>[3,3,1,1]=>56
[4,7,3,2,6,8,5,1]=>[3,2,2,1]=>70
[7,5,3,2,6,4,8,1]=>[3,2,1,1,1]=>64
[8,5,2,6,7,3,4,1]=>[3,3,1,1]=>56
[8,4,2,6,3,7,5,1]=>[3,3,1,1]=>56
[7,4,6,2,3,8,5,1]=>[3,3,1,1]=>56
[7,5,6,2,8,3,4,1]=>[3,3,1,1]=>56
[5,7,6,2,8,3,4,1]=>[3,3,1,1]=>56
[4,7,6,2,3,8,5,1]=>[3,3,1,1]=>56
[7,6,3,2,5,8,1,4]=>[3,2,1,1,1]=>64
[7,6,4,2,5,8,3,1]=>[3,2,1,1,1]=>64
[2,10,4,5,6,7,8,9,1,3]=>[7,2,1]=>160
[9,8,4,5,6,7,1,2,10,3]=>[5,3,1,1]=>567
[2,10,9,5,6,7,8,1,3,4]=>[5,3,1,1]=>567
[2,11,4,5,6,7,8,9,10,1,3]=>[8,2,1]=>231
[11,3,4,5,6,7,8,9,10,1,12,2]=>[9,2,1]=>320
[10,9,4,5,6,7,8,1,2,11,3]=>[6,3,1,1]=>1232
[9,3,8,5,6,7,1,2,10,4]=>[5,3,1,1]=>567
[9,7,4,5,6,1,8,2,10,3]=>[5,3,1,1]=>567
[2,10,4,9,6,7,8,1,3,5]=>[5,3,1,1]=>567
[2,10,8,5,6,7,1,9,3,4]=>[5,3,1,1]=>567
[2,11,10,5,6,7,8,9,1,3,4]=>[6,3,1,1]=>1232
[2,12,4,5,6,7,8,9,10,11,1,3]=>[9,2,1]=>320
[6,3,8,5,4,7,2,1]=>[3,2,1,1,1]=>64
[1,3,2,4,5,6,7,8,9]=>[8,1]=>8
[1,4,2,3,5,6,7,8,9]=>[8,1]=>8
[1,3,2,4,5,6,7,8,9,10]=>[9,1]=>9
[2,4,6,3,8,7,5,1]=>[4,2,1,1]=>90
[2,4,3,6,8,7,1,5]=>[4,2,2]=>56
[2,4,6,3,8,7,1,5]=>[4,2,2]=>56
[2,4,6,5,8,7,1,3]=>[4,2,2]=>56
[2,4,6,8,5,7,3,1]=>[4,2,1,1]=>90
[2,4,6,8,5,7,1,3]=>[4,2,2]=>56
[2,4,6,8,3,7,1,5]=>[4,2,2]=>56
[2,4,6,8,1,7,3,5]=>[4,3,1]=>70
[2,4,6,5,8,3,7,1]=>[4,2,1,1]=>90
[2,4,6,5,8,1,7,3]=>[4,2,2]=>56
[2,4,6,8,5,1,7,3]=>[4,2,2]=>56
[2,4,6,8,7,3,5,1]=>[4,2,1,1]=>90
[2,4,6,8,7,1,5,3]=>[4,2,1,1]=>90
[2,4,6,8,7,1,3,5]=>[4,3,1]=>70
[2,4,6,8,5,1,3,7]=>[4,3,1]=>70
[2,4,6,5,1,8,3,7]=>[4,3,1]=>70
[2,4,6,5,3,8,1,7]=>[4,2,1,1]=>90
[2,4,6,5,8,3,1,7]=>[4,2,1,1]=>90
[2,4,6,8,5,3,1,7]=>[4,2,1,1]=>90
[2,4,6,8,7,3,1,5]=>[4,2,1,1]=>90
[2,4,6,8,7,5,1,3]=>[4,2,1,1]=>90
[4,8,7,5,2,1,3,6]=>[3,2,1,1,1]=>64
[6,1,4,7,5,8,2,3]=>[4,2,2]=>56
[1,8,6,5,3,2,7,4]=>[3,2,1,1,1]=>64
[1,6,3,5,8,2,4,7]=>[4,3,1]=>70
[4,6,1,7,8,5,3,2]=>[4,2,1,1]=>90
[6,1,2,7,8,4,5,3]=>[4,3,1]=>70
[6,1,3,2,7,8,5,4]=>[4,2,2]=>56
[5,6,3,1,7,4,8,2]=>[4,2,2]=>56
[4,8,3,7,1,6,5,2]=>[2,2,2,1,1]=>28
[8,7,2,6,5,1,4,3]=>[2,2,1,1,1,1]=>20
[5,8,3,2,1,7,6,4]=>[2,2,2,2]=>14
[5,4,3,8,1,7,6,2]=>[2,2,2,2]=>14
[6,5,3,8,7,1,4,2]=>[2,2,2,2]=>14
[4,3,8,2,7,6,5,1]=>[2,2,2,1,1]=>28
[4,8,2,7,6,5,3,1]=>[2,2,1,1,1,1]=>20
[7,8,2,6,5,4,1,3]=>[2,2,2,1,1]=>28
[3,8,7,6,2,5,1,4]=>[2,2,2,1,1]=>28
[4,8,3,7,2,1,6,5]=>[2,2,2,2]=>14
[8,6,3,1,7,5,4,2]=>[2,2,2,1,1]=>28
[8,6,3,7,1,5,4,2]=>[2,2,2,1,1]=>28
[4,8,3,7,6,2,5,1]=>[2,2,2,1,1]=>28
[5,8,2,7,6,4,1,3]=>[2,2,2,1,1]=>28
[8,4,2,1,7,6,5,3]=>[2,2,2,1,1]=>28
[1,6,4,2,5,3,7,8]=>[5,2,1]=>64
[1,8,6,2,7,3,4,5]=>[5,2,1]=>64
[1,6,3,2,4,5,7,8]=>[6,1,1]=>21
[1,5,2,6,4,3,7,8]=>[5,2,1]=>64
[1,5,2,4,6,3,7,8]=>[6,1,1]=>21
[1,8,6,2,3,7,4,5]=>[5,2,1]=>64
[1,5,2,8,6,3,4,7]=>[5,2,1]=>64
[1,3,6,8,2,7,4,5]=>[4,3,1]=>70
[1,4,3,8,2,5,6,7]=>[5,2,1]=>64
[1,7,2,3,8,5,4,6]=>[5,2,1]=>64
[1,3,8,4,2,5,6,7]=>[6,1,1]=>21
[1,6,2,8,5,4,3,7]=>[4,2,1,1]=>90
[1,7,2,3,8,6,4,5]=>[5,2,1]=>64
[1,5,3,8,2,7,4,6]=>[4,2,2]=>56
[1,4,8,2,5,6,3,7]=>[5,2,1]=>64
[1,5,7,3,2,8,4,6]=>[4,3,1]=>70
[1,2,7,3,6,8,4,5]=>[5,2,1]=>64
[1,7,2,3,6,8,4,5]=>[5,2,1]=>64
[1,4,8,3,2,5,6,7]=>[5,2,1]=>64
[1,7,2,5,8,3,4,6]=>[5,2,1]=>64
[8,2,3,4,5,6,7,9,1]=>[7,1,1]=>28
[7,2,3,4,5,6,9,8,1]=>[6,2,1]=>105
[6,2,3,4,5,9,7,8,1]=>[6,2,1]=>105
[5,2,3,4,9,6,7,8,1]=>[6,2,1]=>105
[4,2,3,9,5,6,7,8,1]=>[6,2,1]=>105
[3,2,9,4,5,6,7,8,1]=>[6,2,1]=>105
[2,9,3,4,5,6,7,8,1]=>[7,1,1]=>28
[9,2,3,4,5,6,7,8,10,1]=>[8,1,1]=>36
[6,2,3,4,5,1,8,9,7]=>[6,2,1]=>105
[8,2,3,4,5,6,7,10,9,1]=>[7,2,1]=>160
[5,2,3,4,1,7,9,8,6]=>[5,2,2]=>120
[7,2,3,4,5,6,10,8,9,1]=>[7,2,1]=>160
[6,2,3,5,8,1,7,4]=>[4,2,2]=>56
[4,2,3,1,6,9,7,8,5]=>[5,2,2]=>120
[6,2,3,4,5,10,7,8,9,1]=>[7,2,1]=>160
[5,2,4,8,1,6,7,3]=>[4,2,2]=>56
[3,2,1,5,9,6,7,8,4]=>[5,2,2]=>120
[5,2,3,4,10,6,7,8,9,1]=>[7,2,1]=>160
[2,1,4,9,5,6,7,8,3]=>[6,2,1]=>105
[4,2,3,10,5,6,7,8,9,1]=>[7,2,1]=>160
[1,3,9,4,5,6,7,8,2]=>[7,1,1]=>28
[3,2,10,4,5,6,7,8,9,1]=>[7,2,1]=>160
[2,10,3,4,5,6,7,8,9,1]=>[8,1,1]=>36
[2,3,5,6,4,7,8,1,9]=>[7,1,1]=>28
[1,3,4,6,7,5,8,9,2]=>[7,1,1]=>28
[2,3,4,6,7,5,8,9,1,10]=>[8,1,1]=>36
[2,3,6,5,7,4,8,1,9]=>[6,1,1,1]=>56
[2,3,5,6,7,1,8,4,9]=>[7,2]=>27
[2,6,4,5,7,3,1,8]=>[5,1,1,1]=>35
[2,5,6,3,4,7,1,8]=>[5,2,1]=>64
[1,3,7,5,6,8,4,2]=>[5,1,1,1]=>35
[1,3,6,7,4,5,8,2]=>[5,2,1]=>64
[1,3,4,7,6,8,5,9,2]=>[6,1,1,1]=>56
[1,3,4,6,7,8,2,9,5]=>[7,2]=>27
[1,3,4,5,7,8,6,9,10,2]=>[8,1,1]=>36
[1,5,6,3,4,2,7,8]=>[5,2,1]=>64
[1,5,3,6,4,2,7,8]=>[5,2,1]=>64
[1,5,3,7,4,6,2,8]=>[5,2,1]=>64
[1,5,7,3,6,4,8,2]=>[4,2,1,1]=>90
[6,7,3,1,8,5,2,4]=>[3,3,2]=>42
[4,6,3,5,8,2,1,7]=>[3,3,1,1]=>56
[7,4,5,2,1,8,6,3]=>[3,2,2,1]=>70
[4,7,5,2,1,8,6,3]=>[3,2,2,1]=>70
[8,5,3,6,2,1,7,4]=>[3,2,1,1,1]=>64
[4,5,7,3,1,2,8,6]=>[4,3,1]=>70
[4,5,1,8,3,2,7,6]=>[3,3,2]=>42
[5,7,4,6,3,2,1,8]=>[3,2,1,1,1]=>64
[3,6,1,2,4,8,7,5]=>[4,3,1]=>70
[7,5,2,3,1,8,6,4]=>[3,2,2,1]=>70
[6,3,1,2,4,8,7,5]=>[4,2,2]=>56
[7,2,6,5,3,4,1,8]=>[4,1,1,1,1]=>35
[8,2,6,5,4,1,3,7]=>[3,2,1,1,1]=>64
[2,3,1,7,8,5,6,4]=>[4,3,1]=>70
[3,7,8,5,1,4,2,6]=>[3,3,1,1]=>56
[3,7,2,1,8,4,6,5]=>[3,3,2]=>42
[8,7,1,6,5,2,3,4]=>[4,1,1,1,1]=>35
[3,5,7,8,2,4,6,1]=>[4,3,1]=>70
[7,8,2,5,4,3,6,1]=>[3,2,1,1,1]=>64
[4,5,3,7,8,2,6,1]=>[4,2,1,1]=>90
[1,5,4,7,3,6,2,8]=>[4,2,1,1]=>90
[1,7,3,6,8,4,5,2]=>[4,2,1,1]=>90
[4,6,8,2,7,3,5,1]=>[3,3,1,1]=>56
[4,7,6,3,5,1,8,2]=>[3,2,2,1]=>70
[7,8,3,6,1,5,4,2]=>[2,2,2,1,1]=>28
[2,5,7,8,4,6,1,3]=>[4,2,2]=>56
[3,7,5,6,2,1,4,8]=>[4,2,1,1]=>90
[6,2,1,7,4,5,3,8]=>[4,2,2]=>56
[1,2,6,4,7,5,3,8]=>[5,2,1]=>64
[7,5,6,3,8,4,2,1]=>[3,2,1,1,1]=>64
[8,5,4,2,1,6,7,3]=>[3,2,1,1,1]=>64
[2,6,8,4,7,5,1,3]=>[3,2,2,1]=>70
[6,7,5,1,4,8,3,2]=>[3,2,1,1,1]=>64
[7,4,1,6,5,3,8,2]=>[3,2,1,1,1]=>64
[5,8,2,7,3,6,4,1]=>[3,2,1,1,1]=>64
[1,6,5,7,3,8,4,2]=>[4,2,1,1]=>90
[1,5,6,8,4,2,7,3]=>[4,2,2]=>56
[7,5,4,1,8,2,6,3]=>[3,2,2,1]=>70
[6,4,1,8,2,7,5,3]=>[3,2,2,1]=>70
[7,8,5,3,2,6,1,4]=>[2,2,2,1,1]=>28
[8,2,5,1,7,6,4,3]=>[3,2,1,1,1]=>64
[6,7,4,3,8,2,5,1]=>[3,2,1,1,1]=>64
[3,4,2,7,8,6,1,5]=>[4,2,2]=>56
[7,8,6,1,4,3,2,5]=>[3,2,1,1,1]=>64
[2,4,7,8,6,1,3,5]=>[4,3,1]=>70
[3,7,8,6,5,2,4,1]=>[3,2,1,1,1]=>64
[4,5,2,7,8,6,3,1]=>[4,2,1,1]=>90
[4,6,2,5,3,1,7,8]=>[4,2,1,1]=>90
[4,1,5,6,3,2,7,8]=>[5,2,1]=>64
[2,6,7,5,4,1,3,8]=>[4,2,1,1]=>90
[4,1,6,7,5,3,2,8]=>[4,2,1,1]=>90
[6,7,4,3,1,5,2,8]=>[3,2,2,1]=>70
[1,7,5,6,4,3,2,8]=>[4,1,1,1,1]=>35
[7,6,5,3,1,8,4,2]=>[2,2,2,1,1]=>28
[7,8,6,4,3,1,5,2]=>[2,2,2,1,1]=>28
[4,1,7,8,6,5,3,2]=>[3,2,1,1,1]=>64
[4,5,7,3,8,6,1,2]=>[4,2,2]=>56
[6,8,5,3,7,2,1,4]=>[2,2,2,1,1]=>28
[4,7,1,5,8,2,6,3]=>[3,3,2]=>42
[2,7,5,8,3,6,4,1]=>[3,2,2,1]=>70
[7,4,8,2,6,5,3,1]=>[2,2,2,1,1]=>28
[7,5,4,8,2,6,3,1]=>[2,2,2,1,1]=>28
[4,3,8,1,6,5,2,7]=>[3,2,2,1]=>70
[2,3,6,5,7,8,1,4]=>[5,2,1]=>64
[8,3,4,1,2,6,7,5]=>[4,3,1]=>70
[7,3,4,8,5,2,1,6]=>[4,2,1,1]=>90
[7,3,8,4,1,5,6,2]=>[4,2,2]=>56
[7,2,4,5,1,8,3,6]=>[4,3,1]=>70
[7,3,1,2,8,5,6,4]=>[4,2,2]=>56
[4,8,2,3,5,7,6,1]=>[4,2,1,1]=>90
[4,5,2,3,8,6,7,1]=>[4,3,1]=>70
[6,7,4,8,5,3,2,1]=>[3,2,1,1,1]=>64
[4,3,5,6,1,7,8,2]=>[5,2,1]=>64
[3,5,2,6,4,7,8,1]=>[5,2,1]=>64
[4,1,2,8,5,7,6,3]=>[4,2,1,1]=>90
[3,1,5,6,4,7,8,2]=>[5,2,1]=>64
[3,1,4,6,7,5,8,2]=>[5,2,1]=>64
[2,6,4,5,8,1,3,7]=>[4,3,1]=>70
[6,4,1,3,5,8,2,7]=>[4,2,1,1]=>90
[3,4,1,7,2,6,8,5]=>[4,3,1]=>70
[2,4,7,5,8,1,3,6]=>[4,3,1]=>70
[3,7,6,2,1,5,8,4]=>[3,2,2,1]=>70
[4,2,6,1,3,7,8,5]=>[4,3,1]=>70
[8,5,4,2,7,6,3,1]=>[2,2,2,1,1]=>28
[2,8,4,6,7,1,3,5]=>[4,3,1]=>70
[5,8,2,1,4,6,7,3]=>[4,2,2]=>56
[8,4,6,1,2,5,7,3]=>[4,2,1,1]=>90
[5,6,2,8,7,1,3,4]=>[3,3,2]=>42
[7,1,3,8,4,5,6,2]=>[5,2,1]=>64
[7,8,1,4,3,5,6,2]=>[4,2,1,1]=>90
[3,6,7,2,8,1,5,4]=>[4,2,2]=>56
[2,6,7,1,3,5,8,4]=>[4,3,1]=>70
[3,6,7,1,8,2,5,4]=>[4,3,1]=>70
[3,4,1,8,7,2,6,5]=>[3,3,1,1]=>56
[3,1,5,7,2,8,6,4]=>[4,3,1]=>70
[4,8,1,3,2,7,6,5]=>[3,2,2,1]=>70
[4,1,8,3,2,7,6,5]=>[3,2,2,1]=>70
[3,2,4,8,7,1,6,5]=>[3,2,2,1]=>70
[3,2,5,7,1,8,6,4]=>[4,2,2]=>56
[4,2,8,3,1,7,6,5]=>[3,2,2,1]=>70
[4,8,2,1,3,7,6,5]=>[3,2,2,1]=>70
[4,2,8,1,3,7,6,5]=>[3,2,2,1]=>70
[2,3,4,6,8,7,1,5]=>[5,2,1]=>64
[5,6,4,7,1,2,8,3]=>[4,3,1]=>70
[4,5,7,1,6,8,3,2]=>[4,2,1,1]=>90
[3,2,7,6,8,1,4,5]=>[3,3,2]=>42
[4,5,1,7,6,8,2,3]=>[4,3,1]=>70
[6,7,2,8,3,1,4,5]=>[4,3,1]=>70
[7,6,3,1,2,8,4,5]=>[4,2,1,1]=>90
[6,2,7,8,4,1,3,5]=>[3,3,2]=>42
[7,8,5,2,4,1,3,6]=>[3,2,2,1]=>70
[7,6,2,3,1,8,4,5]=>[4,2,1,1]=>90
[4,2,5,1,3,7,8,6]=>[4,3,1]=>70
[3,4,1,7,8,5,2,6]=>[4,3,1]=>70
[4,1,3,7,8,5,2,6]=>[4,3,1]=>70
[4,3,1,8,5,2,7,6]=>[3,3,2]=>42
[7,6,3,5,8,4,2,1]=>[3,1,1,1,1,1]=>21
[4,5,1,3,2,7,8,6]=>[4,3,1]=>70
[5,1,3,2,4,7,8,6]=>[5,2,1]=>64
[8,3,5,6,1,7,2,4]=>[4,3,1]=>70
[4,5,8,1,2,6,7,3]=>[4,3,1]=>70
[5,3,6,7,8,2,1,4]=>[4,2,1,1]=>90
[1,3,4,8,6,2,7,5]=>[5,2,1]=>64
[7,2,4,1,3,8,5,6]=>[4,3,1]=>70
[4,6,8,2,3,7,5,1]=>[3,3,1,1]=>56
[6,7,2,3,4,8,1,5]=>[4,3,1]=>70
[3,5,2,4,6,7,8,1]=>[5,2,1]=>64
[4,2,6,3,5,7,8,1]=>[5,2,1]=>64
[2,3,4,5,6,1,8,7,9]=>[7,2]=>27
[2,3,4,5,1,7,6,8,9]=>[7,2]=>27
[2,3,4,1,6,5,7,8,9]=>[7,2]=>27
[2,3,1,5,4,6,7,8,9]=>[7,2]=>27
[1,4,8,5,6,2,7,3]=>[5,2,1]=>64
[1,3,8,5,2,6,7,4]=>[5,2,1]=>64
[7,2,8,4,5,1,6,3]=>[4,2,2]=>56
[8,6,2,4,1,5,7,3]=>[4,2,1,1]=>90
[1,6,4,3,2,7,8,5]=>[4,2,1,1]=>90
[8,5,3,2,1,6,7,4]=>[3,2,1,1,1]=>64
[1,7,5,2,3,6,8,4]=>[5,2,1]=>64
[7,1,5,2,3,6,8,4]=>[5,2,1]=>64
[8,1,2,5,3,6,7,4]=>[5,2,1]=>64
[8,4,1,6,3,7,2,5]=>[3,3,1,1]=>56
[6,7,5,3,8,2,1,4]=>[3,2,1,1,1]=>64
[5,2,6,8,3,7,1,4]=>[3,3,2]=>42
[4,2,5,8,6,7,1,3]=>[4,2,2]=>56
[5,8,6,3,4,1,7,2]=>[3,2,2,1]=>70
[2,4,7,8,5,1,3,6]=>[4,3,1]=>70
[2,5,3,8,4,1,6,7]=>[5,2,1]=>64
[2,4,8,3,5,7,1,6]=>[4,2,2]=>56
[8,1,7,2,4,3,5,6]=>[5,1,1,1]=>35
[1,3,8,2,4,7,5,6]=>[5,2,1]=>64
[1,3,7,2,4,6,5,8]=>[5,2,1]=>64
[1,7,3,2,4,6,5,8]=>[5,2,1]=>64
[1,8,3,7,4,2,5,6]=>[5,1,1,1]=>35
[8,7,3,1,4,2,5,6]=>[4,2,1,1]=>90
[2,8,4,3,5,7,1,6]=>[4,2,1,1]=>90
[3,2,8,7,4,1,5,6]=>[4,2,1,1]=>90
[3,2,1,7,4,6,5,8]=>[4,2,2]=>56
[3,2,6,5,1,7,8,4]=>[4,2,2]=>56
[5,3,2,6,7,1,8,4]=>[4,2,1,1]=>90
[3,2,8,6,7,4,1,5]=>[3,3,1,1]=>56
[8,4,6,2,7,3,1,5]=>[3,3,1,1]=>56
[4,3,8,6,7,2,1,5]=>[3,2,2,1]=>70
[4,3,6,2,8,7,1,5]=>[3,2,2,1]=>70
[3,8,4,7,6,5,1,2]=>[3,2,1,1,1]=>64
[7,8,4,2,6,3,5,1]=>[3,2,2,1]=>70
[3,2,7,8,6,4,5,1]=>[3,3,1,1]=>56
[3,2,7,5,6,8,4,1]=>[4,2,1,1]=>90
[5,7,8,6,3,2,4,1]=>[3,2,1,1,1]=>64
[6,5,4,2,1,7,8,3]=>[3,2,1,1,1]=>64
[5,4,2,1,7,6,3,8]=>[3,2,2,1]=>70
[4,1,6,5,2,7,8,3]=>[4,3,1]=>70
[5,4,1,6,7,2,8,3]=>[4,3,1]=>70
[6,8,5,3,1,7,2,4]=>[3,2,2,1]=>70
[5,2,6,3,8,7,1,4]=>[3,3,2]=>42
[8,6,1,7,3,4,2,5]=>[4,2,1,1]=>90
[1,8,3,6,7,4,2,5]=>[4,2,1,1]=>90
[1,6,3,5,2,7,8,4]=>[5,2,1]=>64
[1,5,7,3,2,6,4,8]=>[4,2,2]=>56
[5,1,3,7,2,6,4,8]=>[4,2,2]=>56
[8,1,6,7,2,4,3,5]=>[4,2,1,1]=>90
[6,1,4,8,2,7,3,5]=>[4,2,2]=>56
[6,2,4,8,3,7,1,5]=>[3,2,2,1]=>70
[8,7,2,6,3,5,1,4]=>[3,2,1,1,1]=>64
[8,1,7,6,5,2,3,4]=>[4,1,1,1,1]=>35
[7,1,5,6,8,2,4,3]=>[4,2,1,1]=>90
[6,7,1,5,2,4,8,3]=>[4,2,1,1]=>90
[7,6,1,5,2,4,3,8]=>[4,1,1,1,1]=>35
[7,1,6,3,5,4,2,8]=>[4,1,1,1,1]=>35
[1,6,7,3,5,4,8,2]=>[4,2,1,1]=>90
[1,7,3,5,6,8,4,2]=>[5,1,1,1]=>35
[1,7,8,3,6,4,5,2]=>[4,2,1,1]=>90
[1,8,7,6,4,5,2,3]=>[3,2,1,1,1]=>64
[8,2,7,4,6,5,1,3]=>[3,2,1,1,1]=>64
[2,8,5,7,6,4,1,3]=>[3,2,1,1,1]=>64
[7,4,5,1,6,8,3,2]=>[4,2,1,1]=>90
[4,1,7,5,6,8,3,2]=>[4,2,1,1]=>90
[5,6,7,4,3,1,8,2]=>[4,2,1,1]=>90
[6,7,8,5,3,1,4,2]=>[3,2,2,1]=>70
[1,4,6,2,5,3,7,8]=>[5,2,1]=>64
[1,6,3,2,5,4,7,8]=>[5,2,1]=>64
[1,6,8,2,5,4,7,3]=>[4,2,1,1]=>90
[1,5,4,2,6,3,7,8]=>[5,2,1]=>64
[1,2,6,4,3,5,7,8]=>[6,1,1]=>21
[1,6,8,2,7,5,4,3]=>[3,2,1,1,1]=>64
[1,7,4,3,2,6,8,5]=>[4,2,1,1]=>90
[1,5,4,7,2,6,8,3]=>[4,2,2]=>56
[1,3,7,6,2,8,5,4]=>[4,2,1,1]=>90
[1,7,6,2,8,4,3,5]=>[4,2,1,1]=>90
[1,5,2,8,4,3,7,6]=>[4,2,2]=>56
[1,2,8,4,3,6,5,7]=>[5,2,1]=>64
[1,2,8,5,6,3,4,7]=>[5,2,1]=>64
[1,7,3,5,2,8,6,4]=>[4,2,2]=>56
[1,6,7,2,5,8,4,3]=>[4,2,1,1]=>90
[1,5,8,3,2,7,4,6]=>[4,2,2]=>56
[1,4,5,8,2,6,3,7]=>[5,2,1]=>64
[1,7,6,4,8,2,5,3]=>[3,2,2,1]=>70
[1,4,8,6,5,2,7,3]=>[4,2,1,1]=>90
[1,3,8,2,6,5,4,7]=>[4,2,1,1]=>90
[1,7,6,3,8,2,4,5]=>[4,2,1,1]=>90
[1,5,2,7,6,4,8,3]=>[4,2,1,1]=>90
[1,2,4,3,8,7,5,6]=>[5,2,1]=>64
[1,4,3,8,7,2,5,6]=>[4,2,2]=>56
[1,3,8,6,2,4,5,7]=>[5,2,1]=>64
[1,3,8,5,4,2,6,7]=>[5,1,1,1]=>35
[1,7,2,4,8,6,5,3]=>[4,2,1,1]=>90
[1,6,5,3,2,8,7,4]=>[3,2,2,1]=>70
[1,3,2,8,7,5,4,6]=>[4,2,1,1]=>90
[1,2,8,6,5,4,3,7]=>[4,1,1,1,1]=>35
[8,1,3,4,6,5,2,7]=>[5,1,1,1]=>35
[8,3,1,4,6,5,2,7]=>[4,2,1,1]=>90
[5,8,3,1,2,6,4,7]=>[4,2,2]=>56
[4,8,1,7,5,2,3,6]=>[4,2,1,1]=>90
[4,8,1,7,5,2,6,3]=>[3,3,1,1]=>56
[8,5,1,4,2,6,3,7]=>[4,2,1,1]=>90
[8,4,1,3,5,6,2,7]=>[5,1,1,1]=>35
[8,5,3,2,1,6,4,7]=>[3,2,1,1,1]=>64
[8,1,5,4,2,6,3,7]=>[4,2,1,1]=>90
[8,5,2,4,1,6,3,7]=>[4,2,1,1]=>90
[4,8,7,1,5,2,6,3]=>[3,3,1,1]=>56
[4,8,7,1,5,2,3,6]=>[4,2,1,1]=>90
[7,6,8,4,1,3,2,5]=>[3,2,1,1,1]=>64
[7,6,8,4,1,3,5,2]=>[3,2,1,1,1]=>64
[3,8,7,5,4,1,2,6]=>[3,2,1,1,1]=>64
[4,8,2,7,5,1,3,6]=>[3,2,2,1]=>70
[7,6,8,4,1,5,2,3]=>[3,2,2,1]=>70
[8,7,6,1,5,2,3,4]=>[4,1,1,1,1]=>35
[7,1,4,8,6,3,5,2]=>[3,2,2,1]=>70
[8,1,6,5,3,4,7,2]=>[4,1,1,1,1]=>35
[8,6,2,5,3,4,7,1]=>[4,1,1,1,1]=>35
[8,6,5,1,3,4,7,2]=>[4,1,1,1,1]=>35
[8,7,5,1,3,6,2,4]=>[3,2,1,1,1]=>64
[8,7,1,5,3,6,2,4]=>[3,2,1,1,1]=>64
[8,6,1,3,5,4,7,2]=>[4,1,1,1,1]=>35
[7,1,4,8,3,6,5,2]=>[3,2,2,1]=>70
[7,8,5,2,4,3,6,1]=>[3,2,1,1,1]=>64
[7,3,8,2,5,4,6,1]=>[3,2,2,1]=>70
[8,4,2,5,3,7,6,1]=>[3,3,1,1]=>56
[4,8,1,5,3,7,6,2]=>[3,3,1,1]=>56
[7,4,8,2,6,3,5,1]=>[3,2,2,1]=>70
[7,4,8,2,6,3,1,5]=>[3,2,2,1]=>70
[8,7,3,1,6,4,2,5]=>[3,2,1,1,1]=>64
[8,7,3,1,6,4,5,2]=>[3,2,1,1,1]=>64
[8,7,3,1,4,6,5,2]=>[3,2,1,1,1]=>64
[8,4,3,2,7,5,6,1]=>[3,2,1,1,1]=>64
[6,4,1,7,8,5,3,2]=>[3,2,2,1]=>70
[7,6,3,4,1,8,5,2]=>[3,2,2,1]=>70
[8,7,3,1,6,2,5,4]=>[3,2,1,1,1]=>64
[7,8,6,4,2,5,1,3]=>[2,2,2,1,1]=>28
[7,8,2,4,6,5,1,3]=>[3,2,2,1]=>70
[8,1,7,3,5,6,2,4]=>[4,2,1,1]=>90
[8,7,5,2,4,6,1,3]=>[3,2,1,1,1]=>64
[8,1,7,5,4,6,2,3]=>[3,2,1,1,1]=>64
[8,7,3,2,6,1,5,4]=>[2,2,2,1,1]=>28
[5,3,1,7,6,4,2,8]=>[3,2,2,1]=>70
[1,8,6,4,2,9,7,5,3]=>[3,2,2,2]=>84
[9,7,5,3,1,8,6,4,2,10]=>[3,2,2,2,1]=>288
[8,6,4,2,1,7,5,3,9]=>[3,2,2,1,1]=>162
[8,7,5,3,1,6,4,2,9]=>[3,2,2,1,1]=>162
[7,5,3,2,1,6,4,8]=>[3,2,1,1,1]=>64
[7,6,5,3,1,4,2,8]=>[3,2,1,1,1]=>64
[1,8,6,4,3,2,7,5]=>[3,2,1,1,1]=>64
[1,9,7,5,3,2,8,6,4]=>[3,2,2,1,1]=>162
[1,8,7,6,4,2,5,3]=>[3,2,1,1,1]=>64
[1,9,8,6,4,2,7,5,3]=>[3,2,2,1,1]=>162
[1,10,8,6,4,2,9,7,5,3]=>[3,2,2,2,1]=>288
[8,4,6,7,5,3,2,1]=>[3,1,1,1,1,1]=>21
[1,4,8,6,7,5,3,2]=>[4,1,1,1,1]=>35
[7,6,2,5,8,4,3,1]=>[3,1,1,1,1,1]=>21
[1,7,3,6,8,5,4,2]=>[4,1,1,1,1]=>35
[8,6,2,5,7,4,3,1]=>[3,1,1,1,1,1]=>21
[7,1,3,6,8,5,4,2]=>[4,1,1,1,1]=>35
[1,8,3,6,7,5,4,2]=>[4,1,1,1,1]=>35
[8,1,7,6,4,5,3,2]=>[3,1,1,1,1,1]=>21
[7,1,8,6,4,5,3,2]=>[3,2,1,1,1]=>64
[1,6,2,7,4,5,3,8]=>[5,2,1]=>64
[1,8,2,6,4,3,5,7]=>[5,1,1,1]=>35
[1,7,2,6,4,3,5,8]=>[5,1,1,1]=>35
[1,7,2,5,4,6,3,8]=>[5,1,1,1]=>35
[6,5,7,2,8,3,4,1]=>[3,3,1,1]=>56
[6,2,7,5,8,1,4,3]=>[3,2,2,1]=>70
[6,7,2,5,8,1,4,3]=>[3,2,2,1]=>70
[6,5,7,3,8,1,4,2]=>[3,2,2,1]=>70
[6,3,7,4,8,2,5,1]=>[3,3,1,1]=>56
[6,3,7,4,8,1,5,2]=>[3,3,2]=>42
[6,7,5,1,4,3,8,2]=>[3,2,1,1,1]=>64
[7,8,5,1,4,3,6,2]=>[3,2,1,1,1]=>64
[7,2,1,5,3,8,6,4]=>[3,3,2]=>42
[5,8,2,7,6,1,3,4]=>[3,2,2,1]=>70
[5,1,8,7,3,4,2,6]=>[4,2,1,1]=>90
[8,2,3,6,7,1,4,5]=>[4,3,1]=>70
[4,2,3,1,5,8,6,7]=>[5,2,1]=>64
[8,6,5,4,3,2,1,7,9]=>[3,1,1,1,1,1,1]=>28
[3,1,2,4,5,6,7,8,9,10]=>[9,1]=>9
[9,7,6,5,4,3,2,1,8,10]=>[3,1,1,1,1,1,1,1]=>36
[2,4,8,7,5,3,1,6]=>[4,1,1,1,1]=>35
[2,6,8,7,5,3,4,1]=>[3,2,1,1,1]=>64
[2,6,5,1,4,3,8,7]=>[3,3,1,1]=>56
[6,5,1,2,4,3,8,7]=>[4,2,1,1]=>90
[4,6,5,3,1,2,8,7]=>[3,3,1,1]=>56
[4,8,7,5,3,1,2,6]=>[3,2,1,1,1]=>64
[4,6,8,7,5,3,1,2]=>[3,2,1,1,1]=>64
[6,8,7,5,3,1,4,2]=>[2,2,2,1,1]=>28
[8,7,5,6,3,1,4,2]=>[2,2,2,1,1]=>28
[8,7,3,4,6,5,1,2]=>[3,2,1,1,1]=>64
[2,1,4,8,7,3,6,5]=>[3,3,1,1]=>56
[4,8,7,3,1,2,6,5]=>[3,2,2,1]=>70
[8,7,3,4,1,2,6,5]=>[3,3,1,1]=>56
[8,7,3,1,6,5,2,4]=>[3,2,1,1,1]=>64
[8,7,3,2,6,5,1,4]=>[2,2,2,1,1]=>28
[2,8,7,3,4,6,5,1]=>[4,1,1,1,1]=>35
[2,8,7,3,6,5,1,4]=>[3,2,1,1,1]=>64
[2,8,7,1,6,5,3,4]=>[3,2,1,1,1]=>64
[8,7,1,2,6,5,3,4]=>[4,1,1,1,1]=>35
[8,7,1,2,4,3,6,5]=>[4,2,1,1]=>90
[2,1,8,7,3,4,6,5]=>[4,2,1,1]=>90
[8,7,5,1,2,4,3,6]=>[4,1,1,1,1]=>35
[2,8,7,1,4,3,6,5]=>[3,3,1,1]=>56
[2,8,7,3,4,1,6,5]=>[4,2,1,1]=>90
[2,8,7,5,6,3,4,1]=>[3,2,1,1,1]=>64
[2,4,8,7,3,1,6,5]=>[3,2,2,1]=>70
[2,8,7,3,1,4,6,5]=>[4,2,1,1]=>90
[2,4,3,1,8,7,5,6]=>[4,2,2]=>56
[4,3,1,2,6,8,7,5]=>[4,2,2]=>56
[2,8,7,5,6,3,1,4]=>[3,2,1,1,1]=>64
[2,8,7,5,3,1,6,4]=>[3,2,1,1,1]=>64
[2,8,7,5,3,6,4,1]=>[3,2,1,1,1]=>64
[2,8,7,5,6,1,4,3]=>[3,2,1,1,1]=>64
[2,6,8,7,5,1,4,3]=>[3,2,1,1,1]=>64
[6,8,7,5,1,2,4,3]=>[3,2,1,1,1]=>64
[8,7,5,6,1,2,4,3]=>[3,2,1,1,1]=>64
[8,7,1,2,4,6,5,3]=>[4,1,1,1,1]=>35
[2,4,8,7,3,6,5,1]=>[3,2,1,1,1]=>64
[8,7,2,4,3,6,5,1]=>[3,2,1,1,1]=>64
[4,8,7,1,2,6,5,3]=>[3,2,1,1,1]=>64
[8,7,5,3,1,2,6,4]=>[3,2,1,1,1]=>64
[8,7,5,3,6,4,1,2]=>[2,2,2,1,1]=>28
[8,7,1,4,3,6,5,2]=>[3,2,1,1,1]=>64
[8,7,3,4,1,6,5,2]=>[3,2,1,1,1]=>64
[11,2,3,4,5,6,7,8,9,10,1]=>[9,1,1]=>45
[10,3,2,4,5,6,7,8,9,1]=>[7,1,1,1]=>84
[9,4,3,2,5,6,7,8,1]=>[5,1,1,1,1]=>70
[8,1,2,3,4,5,7,6,9]=>[7,1,1]=>28
[7,1,2,3,5,4,6,8]=>[6,1,1]=>21
[1,9,2,3,4,5,6,8,7]=>[7,1,1]=>28
[9,1,2,3,4,5,6,8,7,10]=>[8,1,1]=>36
[8,1,2,3,4,7,6,5,9]=>[6,1,1,1]=>56
[8,1,2,3,4,6,5,7,9]=>[7,1,1]=>28
[7,1,2,6,4,5,3,8]=>[5,1,1,1]=>35
[7,1,2,4,3,5,6,8]=>[6,1,1]=>21
[1,9,2,3,4,5,8,7,6]=>[6,1,1,1]=>56
[1,9,2,3,4,5,7,6,8]=>[7,1,1]=>28
[1,10,2,3,4,5,6,7,9,8]=>[8,1,1]=>36
[4,7,3,6,5,1,2,8]=>[3,2,2,1]=>70
[7,5,4,2,8,3,1,6]=>[3,2,1,1,1]=>64
[5,7,2,1,8,4,6,3]=>[3,3,2]=>42
[7,2,8,6,4,3,1,5]=>[3,2,1,1,1]=>64
[6,3,8,7,4,2,1,5]=>[3,2,1,1,1]=>64
[7,6,3,2,8,4,1,5]=>[3,2,1,1,1]=>64
[8,6,1,3,2,4,5,7]=>[5,1,1,1]=>35
[5,8,3,7,4,2,1,6]=>[3,2,1,1,1]=>64
[8,4,7,3,5,2,1,6]=>[3,2,1,1,1]=>64
[5,4,8,1,3,2,6,7]=>[4,2,1,1]=>90
[4,5,8,2,1,3,6,7]=>[4,3,1]=>70
[8,1,3,5,2,4,6,7]=>[5,2,1]=>64
[1,8,3,5,7,2,4,6]=>[4,3,1]=>70
[8,1,4,2,7,6,3,5]=>[4,2,1,1]=>90
[1,3,4,5,6,7,8,2,9]=>[8,1]=>8
[1,3,4,5,6,7,8,10,2,9]=>[8,2]=>35
[2,1,4,5,6,7,9,3,8]=>[6,3]=>48
[2,1,4,5,6,7,8,3,9]=>[7,2]=>27
[1,3,4,5,6,7,8,9,2,10]=>[9,1]=>9
[1,5,7,3,6,8,2,4]=>[4,2,2]=>56
[1,3,4,7,6,8,2,5]=>[5,2,1]=>64
[1,2,4,7,8,5,3,6]=>[5,2,1]=>64
[5,1,7,3,6,8,2,4]=>[4,2,2]=>56
[5,8,6,1,7,3,2,4]=>[3,3,1,1]=>56
[1,3,2,8,6,5,4,7]=>[4,2,1,1]=>90
[2,5,7,1,8,4,3,6]=>[4,3,1]=>70
[3,5,7,1,6,8,2,4]=>[4,3,1]=>70
[5,4,7,6,8,3,1,2]=>[3,2,2,1]=>70
[8,4,6,7,5,2,1,3]=>[3,2,1,1,1]=>64
[8,1,7,6,4,3,2,5]=>[3,1,1,1,1,1]=>21
[1,3,9,8,7,6,5,4,2]=>[3,1,1,1,1,1,1]=>28
[1,5,8,4,3,7,6,2]=>[3,2,2,1]=>70
[8,1,3,5,2,7,6,4]=>[4,2,1,1]=>90
[8,1,4,5,6,3,7,2]=>[5,1,1,1]=>35
[7,3,4,1,6,8,2,5]=>[4,3,1]=>70
[7,2,1,6,3,4,8,5]=>[4,3,1]=>70
[2,3,5,1,4,8,7,6]=>[4,3,1]=>70
[2,7,1,3,8,4,6,5]=>[4,3,1]=>70
[3,8,7,1,6,2,5,4]=>[3,2,1,1,1]=>64
[8,3,7,2,4,1,5,6]=>[4,2,1,1]=>90
[8,6,7,2,1,4,3,5]=>[3,2,2,1]=>70
[8,3,7,5,1,2,6,4]=>[3,3,1,1]=>56
[3,4,7,6,1,2,8,5]=>[4,3,1]=>70
[8,7,3,5,6,1,4,2]=>[3,2,1,1,1]=>64
[8,5,2,7,6,1,3,4]=>[3,2,2,1]=>70
[8,4,2,5,1,6,7,3]=>[4,2,1,1]=>90
[8,5,3,1,6,4,7,2]=>[3,2,2,1]=>70
[8,7,3,1,4,5,6,2]=>[4,2,1,1]=>90
[8,5,3,7,1,6,4,2]=>[2,2,2,1,1]=>28
[7,4,8,2,6,1,5,3]=>[2,2,2,2]=>14
[8,5,3,1,6,4,2,7]=>[3,2,2,1]=>70
[8,7,5,1,2,6,3,4]=>[4,2,1,1]=>90
[8,6,4,1,2,7,5,3]=>[3,2,2,1]=>70
[8,7,4,1,2,5,3,6]=>[4,2,1,1]=>90
[6,5,3,7,4,2,1,8]=>[3,2,1,1,1]=>64
[1,6,3,8,4,2,5,7]=>[5,2,1]=>64
[4,7,2,5,3,6,1,8]=>[4,2,1,1]=>90
[1,8,3,4,5,2,6,7]=>[6,1,1]=>21
[1,8,6,4,2,5,3,7]=>[4,2,1,1]=>90
[8,2,6,4,1,5,7,3]=>[4,2,1,1]=>90
[7,8,3,4,6,1,5,2]=>[3,2,2,1]=>70
[4,8,7,5,3,1,6,2]=>[3,2,1,1,1]=>64
[6,1,4,8,3,2,5,7]=>[4,2,1,1]=>90
[4,1,8,5,3,2,6,7]=>[4,2,1,1]=>90
[8,1,6,4,2,7,3,5]=>[4,2,1,1]=>90
[3,1,7,4,2,5,8,6]=>[4,3,1]=>70
[1,2,7,4,3,5,6,8]=>[6,1,1]=>21
[6,1,8,5,2,4,3,7]=>[4,2,1,1]=>90
[6,8,2,5,1,4,7,3]=>[3,2,2,1]=>70
[4,5,2,1,6,8,7,3]=>[4,2,2]=>56
[7,2,8,6,5,1,4,3]=>[2,2,2,1,1]=>28
[7,4,8,6,1,5,3,2]=>[2,2,2,1,1]=>28
[8,7,2,6,1,4,5,3]=>[3,2,1,1,1]=>64
[1,7,8,6,2,4,3,5]=>[4,2,1,1]=>90
[7,6,3,1,2,5,4,8]=>[4,2,1,1]=>90
[8,5,3,1,2,4,7,6]=>[4,2,1,1]=>90
[8,2,1,6,5,3,4,7]=>[4,2,1,1]=>90
[3,8,1,5,6,2,4,7]=>[4,3,1]=>70
[6,8,4,1,5,2,3,7]=>[4,2,2]=>56
[3,2,8,1,6,4,5,7]=>[4,2,2]=>56
[5,2,1,3,7,6,4,8]=>[4,2,2]=>56
[5,4,1,2,8,3,7,6]=>[4,2,2]=>56
[5,8,4,1,2,3,7,6]=>[4,2,2]=>56
[7,1,2,5,3,4,6,8]=>[6,1,1]=>21
[1,6,7,3,2,8,4,5]=>[4,3,1]=>70
[1,8,6,3,2,7,4,5]=>[4,2,1,1]=>90
[1,5,3,7,2,8,4,6]=>[4,3,1]=>70
[1,4,6,2,8,5,3,7]=>[4,3,1]=>70
[1,5,6,2,8,4,3,7]=>[4,3,1]=>70
[1,2,5,7,4,6,8,3]=>[5,2,1]=>64
[3,5,8,6,1,7,2,4]=>[4,3,1]=>70
[2,3,7,1,8,6,4,5]=>[4,3,1]=>70
[2,6,1,7,8,5,3,4]=>[4,3,1]=>70
[4,8,3,1,6,5,7,2]=>[3,2,2,1]=>70
[1,6,8,5,4,2,7,3]=>[3,2,2,1]=>70
[6,5,8,4,2,1,7,3]=>[2,2,2,1,1]=>28
[1,7,8,6,5,4,2,3]=>[3,2,1,1,1]=>64
[6,8,7,4,5,1,3,2]=>[2,2,2,1,1]=>28
[3,6,4,2,5,1,8,7]=>[4,2,1,1]=>90
[2,1,5,8,6,4,7,3]=>[4,2,1,1]=>90
[4,2,8,5,6,3,7,1]=>[4,2,1,1]=>90
[5,7,2,3,4,6,8,1]=>[5,2,1]=>64
[1,8,7,3,2,5,6,4]=>[4,2,1,1]=>90
[5,7,1,2,3,8,6,4]=>[4,3,1]=>70
[7,8,6,2,4,1,5,3]=>[3,2,2,1]=>70
[7,2,8,4,6,1,5,3]=>[3,2,2,1]=>70
[7,4,6,2,8,1,5,3]=>[3,2,2,1]=>70
[7,1,5,8,2,3,6,4]=>[4,2,2]=>56
[7,6,4,8,2,1,5,3]=>[2,2,2,1,1]=>28
[6,1,8,4,2,3,5,7]=>[5,2,1]=>64
[7,3,6,2,1,8,5,4]=>[3,2,2,1]=>70
[1,8,6,4,2,5,7,3]=>[4,2,1,1]=>90
[5,6,2,1,8,4,7,3]=>[3,3,2]=>42
[5,1,6,4,3,8,7,2]=>[3,3,1,1]=>56
[5,4,6,8,1,3,7,2]=>[3,3,1,1]=>56
[3,7,1,6,4,5,8,2]=>[4,2,1,1]=>90
[3,5,2,1,4,6,7,8]=>[5,2,1]=>64
[1,3,8,7,5,4,6,2]=>[4,1,1,1,1]=>35
[9,3,4,2,5,6,7,8,1]=>[6,1,1,1]=>56
[1,2,3,4,5,7,9,8,6]=>[7,1,1]=>28
[1,2,3,4,6,7,9,8,5]=>[7,1,1]=>28
[1,2,3,4,6,8,9,7,5]=>[7,1,1]=>28
[1,2,3,4,6,9,8,7,5]=>[6,1,1,1]=>56
[1,2,3,5,6,7,9,8,4]=>[7,1,1]=>28
[1,2,3,5,6,8,9,7,4]=>[7,1,1]=>28
[1,2,3,5,6,9,8,7,4]=>[6,1,1,1]=>56
[1,2,3,5,7,9,8,6,4]=>[6,1,1,1]=>56
[1,2,3,5,9,8,7,6,4]=>[5,1,1,1,1]=>70
[1,2,4,5,7,8,9,6,3]=>[7,1,1]=>28
[1,2,4,5,7,9,8,6,3]=>[6,1,1,1]=>56
[1,2,4,5,9,8,7,6,3]=>[5,1,1,1,1]=>70
[1,2,4,6,9,8,7,5,3]=>[5,1,1,1,1]=>70
[1,2,4,9,8,7,6,5,3]=>[4,1,1,1,1,1]=>56
[1,3,5,7,9,8,6,4,2]=>[5,1,1,1,1]=>70
[1,3,5,9,8,7,6,4,2]=>[4,1,1,1,1,1]=>56
[1,2,3,4,5,6,8,10,9,7]=>[8,1,1]=>36
[1,2,3,4,5,7,8,10,9,6]=>[8,1,1]=>36
[1,2,3,4,5,7,9,10,8,6]=>[8,1,1]=>36
[1,2,3,4,5,7,10,9,8,6]=>[7,1,1,1]=>84
[1,2,3,4,6,7,8,10,9,5]=>[8,1,1]=>36
[1,2,3,4,6,7,9,10,8,5]=>[8,1,1]=>36
[1,2,3,4,6,7,10,9,8,5]=>[7,1,1,1]=>84
[1,2,3,4,6,8,10,9,7,5]=>[7,1,1,1]=>84
[1,2,3,4,6,10,9,8,7,5]=>[6,1,1,1,1]=>126
[1,2,3,5,6,7,9,10,8,4]=>[8,1,1]=>36
[1,2,3,5,6,7,10,9,8,4]=>[7,1,1,1]=>84
[1,2,3,5,6,8,9,10,7,4]=>[8,1,1]=>36
[1,2,3,5,6,8,10,9,7,4]=>[7,1,1,1]=>84
[1,2,3,5,6,10,9,8,7,4]=>[6,1,1,1,1]=>126
[1,2,3,5,7,9,10,8,6,4]=>[7,1,1,1]=>84
[1,2,3,5,7,10,9,8,6,4]=>[6,1,1,1,1]=>126
[1,2,3,5,10,9,8,7,6,4]=>[5,1,1,1,1,1]=>126
[1,2,4,5,7,8,10,9,6,3]=>[7,1,1,1]=>84
[1,2,4,5,7,9,10,8,6,3]=>[7,1,1,1]=>84
[1,2,4,5,7,10,9,8,6,3]=>[6,1,1,1,1]=>126
[1,2,4,5,10,9,8,7,6,3]=>[5,1,1,1,1,1]=>126
[1,2,4,6,10,9,8,7,5,3]=>[5,1,1,1,1,1]=>126
[1,2,4,10,9,8,7,6,5,3]=>[4,1,1,1,1,1,1]=>84
[1,3,5,7,9,10,8,6,4,2]=>[6,1,1,1,1]=>126
[1,3,5,7,10,9,8,6,4,2]=>[5,1,1,1,1,1]=>126
[1,3,5,10,9,8,7,6,4,2]=>[4,1,1,1,1,1,1]=>84
[1,3,10,9,8,7,6,5,4,2]=>[3,1,1,1,1,1,1,1]=>36
[6,7,3,4,8,5,1,2]=>[3,3,2]=>42
[7,4,1,8,2,5,6,3]=>[4,2,2]=>56
[3,1,7,2,5,6,8,4]=>[5,2,1]=>64
[4,1,5,7,3,2,8,6]=>[4,3,1]=>70
[6,4,1,7,2,8,5,3]=>[3,3,2]=>42
[7,3,1,6,2,8,5,4]=>[3,3,1,1]=>56
[4,8,2,5,3,1,6,7]=>[4,2,1,1]=>90
[5,1,3,4,8,2,6,7]=>[5,2,1]=>64
[6,1,4,5,7,8,2,3]=>[5,2,1]=>64
[6,3,4,7,1,8,5,2]=>[4,2,2]=>56
[7,1,3,4,5,6,8,2]=>[6,1,1]=>21
[8,5,2,7,6,3,1,4]=>[3,2,1,1,1]=>64
[1,8,3,5,6,2,7,4]=>[5,2,1]=>64
[8,3,2,5,6,1,7,4]=>[4,2,1,1]=>90
[4,2,5,1,6,8,7,3]=>[4,2,2]=>56
[5,4,2,7,8,6,1,3]=>[3,2,2,1]=>70
[6,8,7,2,1,3,4,5]=>[4,2,1,1]=>90
[3,7,6,8,5,2,4,1]=>[3,2,1,1,1]=>64
[1,7,8,5,2,6,3,4]=>[4,2,2]=>56
[7,6,1,2,5,3,8,4]=>[4,2,1,1]=>90
[7,6,2,4,8,1,5,3]=>[3,2,2,1]=>70
[1,5,7,3,8,6,2,4]=>[4,2,2]=>56
[6,7,5,1,8,2,3,4]=>[4,3,1]=>70
[7,6,1,2,4,3,8,5]=>[4,2,1,1]=>90
[6,7,2,1,5,3,8,4]=>[3,3,2]=>42
[4,3,2,8,7,1,6,5]=>[2,2,2,2]=>14
[4,8,3,1,7,6,5,2]=>[2,2,2,1,1]=>28
[5,3,8,7,1,6,4,2]=>[2,2,2,1,1]=>28
[5,8,7,3,1,6,4,2]=>[2,2,2,1,1]=>28
[5,3,8,2,1,7,6,4]=>[2,2,2,2]=>14
[3,8,7,2,6,5,1,4]=>[2,2,2,1,1]=>28
[7,4,1,8,6,5,3,2]=>[2,2,2,1,1]=>28
[5,4,2,8,1,7,6,3]=>[2,2,2,2]=>14
[5,8,4,2,1,7,6,3]=>[2,2,2,2]=>14
[5,8,4,7,1,6,3,2]=>[2,2,2,1,1]=>28
[5,4,8,3,1,7,6,2]=>[2,2,2,2]=>14
[8,5,6,1,4,7,2,3]=>[3,3,1,1]=>56
[6,7,4,1,2,5,8,3]=>[4,2,2]=>56
[1,6,7,4,2,5,8,3]=>[4,2,2]=>56
[3,6,7,5,8,1,2,4]=>[4,3,1]=>70
[1,6,7,5,8,3,2,4]=>[4,2,1,1]=>90
[3,8,6,5,7,4,1,2]=>[3,2,1,1,1]=>64
[5,2,1,6,8,4,7,3]=>[3,3,2]=>42
[6,8,5,7,4,2,1,3]=>[2,2,2,1,1]=>28
[4,7,5,3,6,1,2,8]=>[4,2,1,1]=>90
[2,7,5,3,6,4,8,1]=>[4,2,1,1]=>90
[2,7,5,6,3,8,4,1]=>[4,2,1,1]=>90
[8,7,5,3,1,4,6,2]=>[3,2,1,1,1]=>64
[2,7,5,3,1,4,8,6]=>[4,2,1,1]=>90
[5,1,6,3,2,4,8,7]=>[4,3,1]=>70
[5,7,6,1,8,3,2,4]=>[3,3,1,1]=>56
[3,8,7,2,1,5,4,6]=>[3,2,2,1]=>70
[6,1,7,2,8,4,3,5]=>[4,3,1]=>70
[3,7,6,2,8,5,1,4]=>[3,2,2,1]=>70
[6,1,7,3,8,5,2,4]=>[3,3,2]=>42
[7,1,8,3,2,5,4,6]=>[4,2,2]=>56
[5,8,6,2,7,4,1,3]=>[3,2,2,1]=>70
[2,4,6,7,8,5,1,3]=>[5,2,1]=>64
[2,4,6,7,8,3,1,5]=>[5,2,1]=>64
[4,7,6,2,8,5,1,3]=>[3,2,2,1]=>70
[5,8,7,3,2,4,1,6]=>[3,2,1,1,1]=>64
[4,6,5,8,7,3,1,2]=>[3,2,2,1]=>70
[8,3,1,7,2,6,4,5]=>[4,2,1,1]=>90
[4,5,1,2,8,7,3,6]=>[4,3,1]=>70
[5,6,1,2,8,3,7,4]=>[4,3,1]=>70
[5,8,7,1,6,2,4,3]=>[3,2,1,1,1]=>64
[6,3,1,4,8,2,7,5]=>[3,3,2]=>42
[8,5,6,1,7,2,4,3]=>[3,3,1,1]=>56
[7,5,6,1,3,8,4,2]=>[3,3,1,1]=>56
[5,7,6,1,3,8,4,2]=>[3,3,1,1]=>56
[6,7,1,4,2,8,5,3]=>[3,3,2]=>42
[2,1,6,4,8,3,7,5]=>[3,3,2]=>42
[1,5,7,8,4,2,3,6]=>[4,3,1]=>70
[1,3,6,4,2,5,7,8]=>[6,1,1]=>21
[1,4,5,7,8,3,6,2]=>[5,2,1]=>64
[1,5,7,8,3,6,2,4]=>[4,2,2]=>56
[1,5,7,8,2,4,3,6]=>[4,3,1]=>70
[6,8,4,7,3,2,1,5]=>[2,2,2,1,1]=>28
[6,8,5,4,2,7,1,3]=>[2,2,2,1,1]=>28
[1,8,4,6,3,2,7,5]=>[4,2,1,1]=>90
[6,4,8,5,3,2,1,7]=>[3,2,1,1,1]=>64
[3,5,6,1,4,2,7,8]=>[5,2,1]=>64
[1,6,3,8,4,2,7,5]=>[4,2,2]=>56
[7,1,3,2,4,6,8,5]=>[5,2,1]=>64
[2,6,5,7,8,3,1,4]=>[4,2,1,1]=>90
[4,1,8,2,6,7,5,3]=>[4,2,1,1]=>90
[3,6,7,8,2,1,4,5]=>[4,3,1]=>70
[4,2,8,3,6,5,1,7]=>[4,2,1,1]=>90
[6,3,8,7,2,4,5,1]=>[3,2,2,1]=>70
[7,6,1,8,2,4,5,3]=>[4,2,1,1]=>90
[2,5,6,3,4,8,1,7]=>[4,3,1]=>70
[5,2,4,7,8,6,1,3]=>[4,2,2]=>56
[7,2,1,3,4,8,5,6]=>[5,2,1]=>64
[8,1,6,2,3,4,7,5]=>[5,2,1]=>64
[6,1,4,2,5,7,8,3]=>[5,2,1]=>64
[6,5,1,2,3,7,8,9,4]=>[6,2,1]=>105
[1,8,3,4,5,2,7,6]=>[5,2,1]=>64
[1,8,3,6,4,7,2,5]=>[4,2,1,1]=>90
[1,4,7,2,5,6,3,8]=>[5,2,1]=>64
[7,3,5,8,2,6,1,4]=>[3,2,2,1]=>70
[3,4,8,2,5,1,7,6]=>[4,2,2]=>56
[1,4,6,7,8,3,5,2]=>[5,2,1]=>64
[4,1,5,3,6,8,7,2]=>[4,3,1]=>70
[5,8,7,4,6,2,3,1]=>[2,2,2,1,1]=>28
[1,6,8,3,5,2,7,4]=>[4,2,2]=>56
[2,4,7,8,5,6,1,3]=>[4,2,2]=>56
[2,6,3,8,5,1,7,4]=>[4,2,2]=>56
[4,3,6,5,1,8,2,7]=>[3,3,2]=>42
[1,5,6,8,7,3,2,4]=>[4,2,1,1]=>90
[1,4,8,3,6,5,2,7]=>[4,2,1,1]=>90
[1,3,8,6,4,7,2,5]=>[4,2,1,1]=>90
[4,1,7,6,8,3,2,5]=>[3,3,1,1]=>56
[1,8,4,7,6,2,3,5]=>[4,2,1,1]=>90
[7,2,3,8,4,5,6,1]=>[5,2,1]=>64
[5,8,4,3,7,2,1,6]=>[2,2,2,1,1]=>28
[6,1,2,8,7,3,4,5]=>[5,2,1]=>64
[4,5,1,7,6,2,8,3]=>[4,3,1]=>70
[6,5,1,8,7,4,3,2]=>[2,2,2,1,1]=>28
[7,5,1,8,6,4,3,2]=>[2,2,2,1,1]=>28
[8,5,1,7,6,4,3,2]=>[2,2,1,1,1,1]=>20
[8,5,3,7,6,1,4,2]=>[2,2,2,1,1]=>28
[3,8,7,6,1,5,4,2]=>[2,2,1,1,1,1]=>20
[10,9,1,2,3,4,5,6,7,11,8]=>[8,2,1]=>231
[9,1,8,2,3,4,5,6,10,7]=>[7,2,1]=>160
[9,7,1,2,3,4,5,6,10,8]=>[7,2,1]=>160
[2,10,1,9,3,4,5,6,7,8]=>[7,2,1]=>160
[2,10,8,1,3,4,5,6,7,9]=>[7,2,1]=>160
[2,11,10,1,3,4,5,6,7,8,9]=>[8,2,1]=>231
[8,3,7,5,4,1,6,2]=>[3,2,1,1,1]=>64
[4,5,3,1,8,7,2,6]=>[3,3,2]=>42
[3,4,8,1,5,2,6,7]=>[5,2,1]=>64
[8,6,5,7,1,3,2,4]=>[3,2,1,1,1]=>64
[1,5,8,6,2,7,4,3]=>[4,2,1,1]=>90
[3,1,8,5,7,2,6,4]=>[3,3,1,1]=>56
[6,8,5,3,4,2,1,7]=>[3,2,1,1,1]=>64
[8,5,2,6,4,3,1,7]=>[3,2,1,1,1]=>64
[8,5,2,6,1,4,7,3]=>[3,2,2,1]=>70
[2,7,5,8,1,4,6,3]=>[3,3,1,1]=>56
[3,2,6,7,1,8,5,4]=>[4,2,2]=>56
[3,4,6,7,8,2,1,5]=>[5,2,1]=>64
[3,2,6,7,8,4,1,5]=>[4,3,1]=>70
[6,2,7,4,8,5,1,3]=>[3,3,2]=>42
[6,7,1,3,8,5,4,2]=>[3,3,1,1]=>56
[6,7,1,8,5,2,4,3]=>[3,3,1,1]=>56
[1,6,7,4,8,3,2,5]=>[4,2,1,1]=>90
[1,4,6,7,8,3,2,5]=>[5,2,1]=>64
[10,3,4,5,6,7,9,1,2,8]=>[6,3,1]=>315
[8,7,2,1,5,4,6,3]=>[3,2,1,1,1]=>64
[2,7,4,8,6,5,3,1]=>[3,2,1,1,1]=>64
[7,6,5,2,4,1,8,3]=>[3,2,1,1,1]=>64
[7,6,4,3,1,5,8,2]=>[3,2,1,1,1]=>64
[6,1,8,7,2,3,5,4]=>[4,2,1,1]=>90
[8,6,1,2,7,3,4,5]=>[5,2,1]=>64
[3,6,8,2,7,1,5,4]=>[3,2,2,1]=>70
[2,8,6,1,4,5,7,3]=>[4,2,1,1]=>90
[6,8,7,2,5,4,1,3]=>[2,2,2,1,1]=>28
[3,5,7,9,1,2,4,6,8,10]=>[6,4]=>90
[4,1,2,3,5,6,7,8,9,10]=>[9,1]=>9
[5,1,2,3,4,6,7,8,9,10]=>[9,1]=>9
[8,1,2,3,4,5,6,7,9,10]=>[9,1]=>9
[7,1,2,3,4,5,6,8,9,10]=>[9,1]=>9
[6,1,2,3,4,5,7,8,9,10]=>[9,1]=>9
[3,1,2,4,5,6,7,8,9,10,11,12]=>[11,1]=>11
[4,7,1,8,6,5,3,2]=>[3,2,1,1,1]=>64
[4,1,8,3,5,2,7,6]=>[4,2,2]=>56
[3,8,1,5,2,4,7,6]=>[4,3,1]=>70
[7,5,6,4,1,3,2,8]=>[3,2,1,1,1]=>64
[7,8,6,4,1,3,2,5]=>[3,2,1,1,1]=>64
[7,1,4,2,5,6,3,8]=>[5,2,1]=>64
[7,3,2,1,4,6,5,8]=>[4,2,1,1]=>90
[7,6,1,4,3,2,5,8]=>[4,1,1,1,1]=>35
[7,4,1,3,5,6,2,8]=>[5,1,1,1]=>35
[2,7,1,3,5,6,8,4]=>[5,2,1]=>64
[3,6,2,1,5,8,7,4]=>[3,3,2]=>42
[2,3,6,1,5,8,7,4]=>[4,3,1]=>70
[3,4,7,1,5,6,8,2]=>[5,2,1]=>64
[3,6,7,4,1,2,8,5]=>[4,3,1]=>70
[4,3,2,7,1,6,8,5]=>[3,2,2,1]=>70
[7,3,2,8,1,6,4,5]=>[3,2,2,1]=>70
[7,4,8,1,5,6,3,2]=>[3,2,2,1]=>70
[2,6,8,1,5,3,7,4]=>[3,3,2]=>42
[6,8,2,1,5,3,7,4]=>[3,3,2]=>42
[4,8,2,5,3,6,7,1]=>[4,2,1,1]=>90
[4,5,8,2,3,6,7,1]=>[4,3,1]=>70
[2,4,8,5,3,6,7,1]=>[5,1,1,1]=>35
[5,3,2,6,4,8,7,1]=>[3,3,1,1]=>56
[2,4,5,3,8,6,7,1]=>[5,2,1]=>64
[4,3,5,2,8,6,7,1]=>[4,2,1,1]=>90
[4,8,5,3,2,6,7,1]=>[4,1,1,1,1]=>35
[3,5,4,2,8,6,7,1]=>[4,2,1,1]=>90
[4,1,2,7,5,6,8,3]=>[5,2,1]=>64
[5,6,7,4,2,8,3,1]=>[4,2,1,1]=>90
[2,5,7,4,6,8,3,1]=>[4,2,1,1]=>90
[7,5,2,4,3,8,6,1]=>[3,2,1,1,1]=>64
[6,8,1,2,5,4,7,3]=>[4,2,1,1]=>90
[6,4,1,8,5,2,7,3]=>[3,3,2]=>42
[2,6,1,8,5,4,7,3]=>[3,3,1,1]=>56
[7,1,2,8,5,6,4,3]=>[4,2,1,1]=>90
[4,3,2,6,8,5,7,1]=>[3,3,1,1]=>56
[3,7,6,4,8,5,2,1]=>[3,2,1,1,1]=>64
[3,1,6,8,5,4,7,2]=>[3,3,1,1]=>56
[2,3,5,8,4,6,7,1]=>[5,2,1]=>64
[3,5,2,8,4,6,7,1]=>[4,3,1]=>70
[3,4,5,8,2,6,7,1]=>[5,2,1]=>64
[5,4,2,8,3,6,7,1]=>[4,2,1,1]=>90
[5,3,4,8,2,6,7,1]=>[4,2,1,1]=>90
[2,5,4,8,3,6,7,1]=>[4,2,1,1]=>90
[6,3,2,5,8,4,7,1]=>[3,3,1,1]=>56
[6,1,8,3,5,4,7,2]=>[4,2,1,1]=>90
[5,4,8,3,2,6,7,1]=>[3,2,1,1,1]=>64
[5,8,2,3,4,6,7,1]=>[5,2,1]=>64
[6,2,1,7,8,5,4,3]=>[3,2,2,1]=>70
[7,4,6,8,3,2,5,1]=>[3,2,1,1,1]=>64
[3,4,5,2,7,1,6,8]=>[5,2,1]=>64
[7,5,6,1,2,3,8,4]=>[4,3,1]=>70
[1,5,7,6,3,2,8,4]=>[4,2,1,1]=>90
[8,4,6,7,3,2,5,1]=>[3,2,1,1,1]=>64
[8,4,6,2,3,1,5,7]=>[4,2,1,1]=>90
[7,5,2,1,4,3,8,6]=>[3,3,1,1]=>56
[3,1,7,8,5,4,2,6]=>[3,3,1,1]=>56
[7,6,4,8,3,1,2,5]=>[3,2,1,1,1]=>64
[7,4,8,5,6,1,2,3]=>[3,3,2]=>42
[6,2,8,5,1,3,4,7]=>[4,2,2]=>56
[3,2,7,8,6,1,4,5]=>[3,3,2]=>42
[6,8,2,5,1,3,7,4]=>[3,3,2]=>42
[6,7,4,2,1,5,3,8]=>[3,2,2,1]=>70
[5,7,4,1,3,6,2,8]=>[4,2,1,1]=>90
[4,2,7,5,1,8,3,6]=>[3,3,2]=>42
[4,1,6,5,3,8,2,7]=>[3,3,1,1]=>56
[1,5,4,6,3,8,2,7]=>[4,2,1,1]=>90
[1,8,6,4,7,3,2,5]=>[3,2,1,1,1]=>64
[4,7,1,8,6,3,5,2]=>[3,3,1,1]=>56
[5,4,8,1,7,3,6,2]=>[3,2,2,1]=>70
[4,3,8,6,2,1,7,5]=>[3,2,2,1]=>70
[8,3,6,2,4,1,7,5]=>[3,3,1,1]=>56
[7,8,3,2,4,6,5,1]=>[3,2,2,1]=>70
[7,2,8,5,3,1,6,4]=>[3,2,2,1]=>70
[2,5,4,8,7,3,6,1]=>[3,2,2,1]=>70
[6,4,2,8,7,3,1,5]=>[3,2,2,1]=>70
[3,6,8,1,7,4,2,5]=>[3,3,1,1]=>56
[7,8,6,3,1,4,5,2]=>[3,2,2,1]=>70
[3,8,6,1,7,5,2,4]=>[3,3,1,1]=>56
[2,7,5,4,8,3,1,6]=>[3,2,1,1,1]=>64
[6,8,7,5,2,1,3,4]=>[3,2,1,1,1]=>64
[7,6,2,8,5,1,3,4]=>[3,2,2,1]=>70
[1,5,7,6,2,8,4,3]=>[4,2,1,1]=>90
[1,6,5,2,7,8,4,3]=>[4,2,1,1]=>90
[4,7,8,5,6,2,3,1]=>[3,2,2,1]=>70
[4,7,8,1,2,5,6,3]=>[4,3,1]=>70
[8,6,4,1,2,5,7,3]=>[4,2,1,1]=>90
[6,1,4,7,2,5,8,3]=>[4,2,2]=>56
[5,6,3,2,7,4,1,8]=>[4,2,1,1]=>90
[2,6,4,3,7,5,8,1]=>[4,2,1,1]=>90
[7,2,3,6,1,8,4,5]=>[4,3,1]=>70
[3,4,6,5,7,1,2,8]=>[5,2,1]=>64
[8,5,2,4,3,6,1,7]=>[4,1,1,1,1]=>35
[8,5,7,2,4,1,6,3]=>[3,2,2,1]=>70
[7,4,8,2,1,5,6,3]=>[3,2,2,1]=>70
[2,3,6,7,8,5,1,4]=>[5,2,1]=>64
[8,3,7,1,6,4,2,5]=>[3,2,1,1,1]=>64
[8,2,1,7,6,5,3,4]=>[3,2,1,1,1]=>64
[6,5,1,2,8,3,4,7]=>[5,2,1]=>64
[5,6,8,1,3,7,2,4]=>[3,3,2]=>42
[1,6,8,5,3,2,4,7]=>[4,2,1,1]=>90
[5,8,1,6,7,4,2,3]=>[3,3,1,1]=>56
[7,2,8,4,6,1,3,5]=>[3,3,2]=>42
[6,2,7,4,3,8,1,5]=>[3,3,1,1]=>56
[1,7,8,4,6,2,3,5]=>[4,2,2]=>56
[7,1,8,4,6,2,3,5]=>[4,2,2]=>56
[8,1,6,5,4,7,2,3]=>[3,2,1,1,1]=>64
[4,1,6,8,7,3,2,5]=>[3,3,1,1]=>56
[5,1,4,6,7,3,8,2]=>[5,1,1,1]=>35
[7,1,3,4,6,2,8,5]=>[5,2,1]=>64
[3,4,1,6,2,5,8,7,9]=>[5,4]=>42
[3,4,1,2,6,5,8,7,9]=>[5,4]=>42
[2,4,1,6,3,5,8,7,10,9,11]=>[6,5]=>132
[3,4,1,6,2,5,8,7,10,9]=>[5,5]=>42
[3,5,1,6,2,4,8,7,9]=>[5,4]=>42
[2,5,1,6,3,4,8,7,9]=>[5,4]=>42
[3,5,1,2,6,4,8,7,9]=>[5,4]=>42
[2,5,1,3,6,4,8,7,9]=>[5,4]=>42
[8,7,1,4,6,3,2,5]=>[3,2,1,1,1]=>64
[1,4,7,5,8,6,3,2]=>[4,2,1,1]=>90
[6,1,8,3,4,7,2,5]=>[4,2,2]=>56
[1,8,6,3,5,2,7,4]=>[4,2,1,1]=>90
[4,7,1,6,8,3,5,2]=>[3,3,1,1]=>56
[3,6,5,2,8,4,1,7]=>[3,3,1,1]=>56
[7,1,8,4,2,5,3,6]=>[4,2,2]=>56
[1,4,8,7,5,2,6,3]=>[4,2,1,1]=>90
[1,5,6,4,2,3,7,8]=>[5,2,1]=>64
[5,8,7,4,2,1,3,6]=>[3,2,1,1,1]=>64
[1,8,7,3,2,5,4,6]=>[4,2,1,1]=>90
[1,2,5,4,8,7,3,6]=>[4,2,2]=>56
[1,2,4,8,6,3,5,7]=>[5,2,1]=>64
[1,5,2,4,7,3,8,6]=>[5,2,1]=>64
[8,6,3,5,7,4,1,2]=>[3,2,1,1,1]=>64
[8,5,3,2,1,4,7,6]=>[3,2,1,1,1]=>64
[1,2,7,6,8,4,3,5]=>[4,2,1,1]=>90
[1,6,3,2,5,7,8,4]=>[5,2,1]=>64
[1,7,3,4,2,6,8,5]=>[5,2,1]=>64
[1,6,3,5,8,4,2,7]=>[4,2,1,1]=>90
[1,5,6,3,2,8,4,7]=>[4,3,1]=>70
[1,2,5,8,4,6,3,7]=>[5,2,1]=>64
[1,5,3,2,7,8,4,6]=>[4,3,1]=>70
[4,1,8,6,2,3,7,5]=>[4,3,1]=>70
[7,5,8,6,2,3,4,1]=>[3,2,2,1]=>70
[1,8,5,7,6,3,2,4]=>[3,2,1,1,1]=>64
[1,4,7,3,6,8,5,2]=>[4,2,1,1]=>90
[1,6,3,5,7,8,4,2]=>[5,1,1,1]=>35
[1,5,6,3,2,7,8,4]=>[5,2,1]=>64
[1,2,7,6,8,4,5,3]=>[4,2,1,1]=>90
[1,8,4,7,5,3,2,6]=>[4,1,1,1,1]=>35
[6,8,5,2,1,7,4,3]=>[2,2,2,2]=>14
[1,2,6,8,4,3,7,5]=>[4,2,2]=>56
[5,3,7,2,6,4,1,8]=>[3,2,2,1]=>70
[7,6,2,4,3,5,1,8]=>[4,1,1,1,1]=>35
[8,4,2,7,1,6,3,5]=>[3,2,2,1]=>70
[8,7,6,1,3,5,4,2]=>[3,1,1,1,1,1]=>21
[8,6,2,7,1,5,3,4]=>[3,2,2,1]=>70
[5,3,7,2,8,1,6,4]=>[3,2,2,1]=>70
[8,3,5,4,2,1,6,7]=>[4,1,1,1,1]=>35
[7,8,4,3,1,5,2,6]=>[3,2,2,1]=>70
[8,7,6,1,2,5,4,3]=>[3,1,1,1,1,1]=>21
[4,7,5,8,6,1,3,2]=>[3,2,2,1]=>70
[6,5,7,3,8,4,1,2]=>[3,2,2,1]=>70
[8,7,5,4,1,2,6,3]=>[3,2,1,1,1]=>64
[8,6,7,1,5,3,2,4]=>[3,2,1,1,1]=>64
[5,7,1,3,4,2,8,6]=>[4,3,1]=>70
[7,3,5,6,4,8,1,2]=>[4,2,1,1]=>90
[1,5,3,7,8,4,6,2]=>[4,3,1]=>70
[1,5,7,3,8,2,6,4]=>[4,2,2]=>56
[1,3,7,5,8,6,2,4]=>[4,2,2]=>56
[3,7,5,8,4,1,2,6]=>[3,3,1,1]=>56
[5,3,7,6,8,1,2,4]=>[3,3,2]=>42
[3,1,2,7,5,8,4,6]=>[4,3,1]=>70
[3,1,2,5,7,8,6,4]=>[5,2,1]=>64
[3,7,1,2,8,5,6,4]=>[4,3,1]=>70
[5,3,1,7,4,6,8,2]=>[4,2,2]=>56
[2,4,7,3,5,6,1,8]=>[5,2,1]=>64
[5,7,6,4,2,3,1,8]=>[3,2,1,1,1]=>64
[7,4,8,2,5,6,1,3]=>[3,2,2,1]=>70
[5,8,2,4,6,1,3,7]=>[4,2,2]=>56
[6,1,4,8,5,2,7,3]=>[4,2,2]=>56
[3,4,5,8,1,6,7,2]=>[5,2,1]=>64
[5,6,8,4,7,3,1,2]=>[3,2,2,1]=>70
[3,1,6,8,5,2,7,4]=>[3,3,2]=>42
[2,3,8,1,5,6,4,7]=>[5,2,1]=>64
[5,4,8,1,2,6,7,3]=>[4,2,2]=>56
[4,1,8,2,3,6,7,5]=>[5,2,1]=>64
[5,2,3,8,1,7,4,6]=>[4,2,2]=>56
[1,5,3,8,2,4,6,7]=>[5,2,1]=>64
[8,6,2,7,5,1,4,3]=>[2,2,2,1,1]=>28
[5,7,6,1,3,2,8,4]=>[3,3,1,1]=>56
[3,5,4,6,1,7,8,2]=>[5,2,1]=>64
[8,1,5,4,6,3,7,2]=>[4,1,1,1,1]=>35
[5,4,7,2,8,6,1,3]=>[3,2,2,1]=>70
[3,7,6,1,8,5,4,2]=>[3,2,1,1,1]=>64
[8,6,4,2,1,3,5,7,9]=>[5,1,1,1,1]=>70
[8,6,2,1,4,3,5,7,9]=>[5,2,1,1]=>189
[8,4,2,1,6,3,5,7,9]=>[5,2,1,1]=>189
[6,4,2,1,8,3,5,7,9]=>[5,2,1,1]=>189
[8,6,4,2,9,1,3,5,7]=>[4,2,1,1,1]=>189
[9,6,4,2,7,1,3,5,8]=>[4,2,1,1,1]=>189
[9,7,4,2,5,1,3,6,8]=>[4,2,1,1,1]=>189
[9,7,5,2,3,1,4,6,8]=>[5,1,1,1,1]=>70
[9,7,5,3,1,2,4,6,8]=>[5,1,1,1,1]=>70
[10,8,6,4,2,1,3,5,7,9]=>[5,1,1,1,1,1]=>126
[10,8,6,2,1,4,3,5,7,9]=>[5,2,1,1,1]=>448
[8,2,1,4,3,6,5,7,9]=>[5,3,1]=>162
[10,8,4,2,1,6,3,5,7,9]=>[5,2,1,1,1]=>448
[4,2,1,6,3,5,8,7,9]=>[5,3,1]=>162
[10,6,4,2,1,8,3,5,7,9]=>[5,2,1,1,1]=>448
[6,4,2,1,8,3,5,9,7]=>[4,3,1,1]=>216
[8,6,4,2,1,10,3,5,7,9]=>[5,2,1,1,1]=>448
[6,4,2,7,1,3,5,8,9]=>[5,2,1,1]=>189
[8,6,4,2,9,1,3,5,7,10]=>[5,2,1,1,1]=>448
[6,2,8,3,1,4,5,7]=>[5,2,1]=>64
[8,9,4,2,5,1,3,6,7]=>[4,2,2,1]=>216
[9,6,4,2,7,1,3,5,8,10]=>[5,2,1,1,1]=>448
[2,7,8,3,1,4,5,6]=>[5,2,1]=>64
[9,6,7,2,3,1,4,5,8]=>[5,2,1,1]=>189
[9,7,4,2,5,1,3,6,8,10]=>[5,2,1,1,1]=>448
[9,7,4,5,1,2,3,6,8]=>[5,2,1,1]=>189
[9,7,5,2,3,1,4,6,8,10]=>[6,1,1,1,1]=>126
[9,7,5,3,1,2,4,6,8,10]=>[6,1,1,1,1]=>126
[1,5,3,2,8,6,7,4]=>[4,2,2]=>56
[1,8,5,3,2,6,7,4]=>[4,2,1,1]=>90
[1,5,6,7,3,2,8,4]=>[5,2,1]=>64
[1,7,5,2,3,4,8,6]=>[5,2,1]=>64
[1,7,5,2,4,8,6,3]=>[4,2,1,1]=>90
[1,6,7,8,3,2,4,5]=>[4,3,1]=>70
[1,4,8,6,2,3,5,7]=>[5,2,1]=>64
[1,2,8,6,3,5,7,4]=>[5,1,1,1]=>35
[1,2,7,8,4,3,5,6]=>[5,2,1]=>64
[1,8,6,7,4,2,3,5]=>[4,2,1,1]=>90
[1,6,7,8,4,2,3,5]=>[4,3,1]=>70
[1,6,7,8,3,4,2,5]=>[4,3,1]=>70
[1,7,4,2,3,8,5,6]=>[5,2,1]=>64
[1,7,8,4,2,3,5,6]=>[5,2,1]=>64
[1,7,3,5,6,2,8,4]=>[5,2,1]=>64
[1,7,8,3,4,2,5,6]=>[5,2,1]=>64
[1,2,3,7,8,5,4,6]=>[5,2,1]=>64
[1,2,7,4,6,3,8,5]=>[5,2,1]=>64
[1,7,8,4,5,2,3,6]=>[4,2,2]=>56
[1,7,8,3,4,5,2,6]=>[5,2,1]=>64
[1,2,8,4,5,6,3,7]=>[6,1,1]=>21
[6,8,7,2,3,4,1,5]=>[4,2,1,1]=>90
[3,8,7,5,2,6,1,4]=>[3,2,1,1,1]=>64
[4,8,7,3,2,5,1,6]=>[3,2,1,1,1]=>64
[5,3,8,1,6,7,4,2]=>[3,2,2,1]=>70
[5,8,2,1,3,7,6,4]=>[3,2,2,1]=>70
[5,1,8,3,6,7,4,2]=>[4,2,1,1]=>90
[3,1,8,4,6,2,7,5]=>[4,3,1]=>70
[1,8,7,6,4,3,5,2]=>[3,1,1,1,1,1]=>21
[6,1,8,7,5,3,4,2]=>[3,2,1,1,1]=>64
[2,3,7,5,6,8,4,1]=>[5,1,1,1]=>35
[2,8,7,6,4,5,1,3]=>[3,2,1,1,1]=>64
[4,8,7,6,3,1,5,2]=>[2,2,2,1,1]=>28
[3,5,2,4,7,6,8,1]=>[4,3,1]=>70
[5,3,2,6,4,7,8,1]=>[4,2,1,1]=>90
[5,3,2,6,7,4,8,1]=>[4,2,1,1]=>90
[5,3,2,7,6,4,8,1]=>[3,2,2,1]=>70
[7,3,5,2,8,4,6,1]=>[3,3,1,1]=>56
[3,5,2,7,4,6,8,1]=>[4,3,1]=>70
[3,2,5,7,4,6,8,1]=>[4,3,1]=>70
[3,2,7,5,4,8,6,1]=>[3,3,1,1]=>56
[3,7,5,2,4,8,6,1]=>[3,3,1,1]=>56
[2,3,7,5,4,8,6,1]=>[4,2,1,1]=>90
[3,4,7,6,8,2,5,1]=>[4,2,1,1]=>90
[5,2,8,4,1,3,6,7]=>[4,2,2]=>56
[3,8,5,2,1,4,6,7]=>[4,2,1,1]=>90
[7,6,4,1,8,2,5,3]=>[3,2,2,1]=>70
[7,5,4,2,1,6,3,8]=>[3,2,1,1,1]=>64
[8,1,6,7,3,4,2,5]=>[4,2,1,1]=>90
[8,2,1,6,7,4,3,5]=>[3,3,1,1]=>56
[5,2,8,6,3,7,1,4]=>[3,3,1,1]=>56
[7,6,8,1,2,5,4,3]=>[3,2,1,1,1]=>64
[1,2,9,3,4,5,6,8,7]=>[7,1,1]=>28
[1,2,3,8,4,5,9,6,7]=>[7,2]=>27
[1,2,3,4,9,5,6,8,7]=>[7,1,1]=>28
[2,1,3,4,8,5,7,6]=>[5,2,1]=>64
[1,2,3,4,5,9,6,8,7]=>[7,1,1]=>28
[7,1,2,3,4,8,5,9,6]=>[6,3]=>48
[6,9,1,2,3,4,8,5,7]=>[6,2,1]=>105
[1,2,10,3,4,5,6,7,9,8]=>[8,1,1]=>36
[5,1,9,2,3,4,8,6,7]=>[6,2,1]=>105
[1,2,3,9,4,5,6,10,7,8]=>[8,2]=>35
[4,1,2,3,5,8,6,9,7]=>[6,3]=>48
[1,2,3,4,10,5,6,7,9,8]=>[8,1,1]=>36
[3,1,2,4,9,5,8,6,7]=>[6,2,1]=>105
[1,2,3,4,5,10,6,7,9,8]=>[8,1,1]=>36
[2,1,3,4,5,9,6,8,7]=>[6,2,1]=>105
[1,2,3,4,5,6,9,10,7,8]=>[8,2]=>35
[10,1,2,3,4,5,6,7,11,8,9]=>[9,2]=>44
[8,1,2,3,4,5,9,6,10,7]=>[7,3]=>75
[1,11,2,3,4,5,6,7,8,10,9]=>[9,1,1]=>45
[1,7,2,3,4,5,9,8,6]=>[6,2,1]=>105
[7,10,1,2,3,4,5,9,6,8]=>[7,2,1]=>160
[1,2,11,3,4,5,6,7,8,10,9]=>[9,1,1]=>45
[1,6,2,3,4,5,9,8,7]=>[6,2,1]=>105
[6,1,2,3,7,4,8,9,5]=>[6,3]=>48
[6,1,10,2,3,4,5,9,7,8]=>[7,2,1]=>160
[1,2,3,10,4,5,6,7,11,8,9]=>[9,2]=>44
[5,7,1,2,6,8,3,4]=>[4,3,1]=>70
[1,2,3,8,5,4,6,9,7]=>[6,2,1]=>105
[5,9,1,2,6,3,4,8,7]=>[5,3,1]=>162
[5,1,2,3,4,6,9,7,10,8]=>[7,3]=>75
[1,2,3,4,11,5,6,7,8,10,9]=>[9,1,1]=>45
[1,4,2,3,5,6,9,8,7]=>[6,2,1]=>105
[1,5,2,3,6,8,7,4]=>[5,2,1]=>64
[4,1,9,5,2,3,6,8,7]=>[5,3,1]=>162
[4,1,2,3,10,5,6,9,7,8]=>[7,2,1]=>160
[1,2,3,4,5,11,6,7,8,10,9]=>[9,1,1]=>45
[1,3,2,4,5,6,9,8,7]=>[6,2,1]=>105
[3,4,1,2,5,6,8,9,7]=>[6,3]=>48
[3,1,2,4,5,10,6,9,7,8]=>[7,2,1]=>160
[1,2,3,4,5,6,10,7,11,8,9]=>[9,2]=>44
[2,3,1,4,9,5,6,8,7]=>[6,2,1]=>105
[1,2,3,4,5,6,7,11,8,10,9]=>[9,1,1]=>45
[1,2,3,4,5,6,7,8,11,10,9]=>[9,1,1]=>45
[3,5,7,4,1,8,2,6]=>[4,3,1]=>70
[8,6,4,7,5,1,2,3]=>[3,2,2,1]=>70
[2,8,4,3,1,6,5,7]=>[4,2,1,1]=>90
[3,8,4,6,1,5,2,7]=>[4,2,1,1]=>90
[8,3,5,6,1,4,7,2]=>[4,2,1,1]=>90
[6,8,7,3,5,4,2,1]=>[2,2,1,1,1,1]=>20
[3,1,2,8,5,7,4,6]=>[4,3,1]=>70
[8,1,2,3,4,6,9,5,7]=>[6,2,1]=>105
[8,1,2,4,6,9,3,5,7]=>[5,3,1]=>162
[6,1,2,3,4,5,9,8,7]=>[6,2,1]=>105
[5,1,2,3,4,8,6,9,7]=>[6,3]=>48
[4,1,2,3,9,6,8,5,7]=>[5,3,1]=>162
[9,1,2,3,4,5,7,10,6,8]=>[7,2,1]=>160
[7,3,1,2,5,8,4,6]=>[4,3,1]=>70
[3,1,2,8,4,6,9,5,7]=>[5,3,1]=>162
[8,3,5,7,2,1,4,6]=>[3,3,1,1]=>56
[2,1,3,8,5,7,4,6]=>[4,3,1]=>70
[2,1,9,4,6,8,3,5,7]=>[4,4,1]=>84
[9,1,2,3,5,7,10,4,6,8]=>[6,3,1]=>315
[1,8,2,4,6,9,3,5,7]=>[5,3,1]=>162
[9,1,3,5,7,10,2,4,6,8]=>[5,4,1]=>288
[7,3,1,2,8,4,5,6]=>[5,2,1]=>64
[2,1,4,7,6,3,5,8]=>[4,3,1]=>70
[7,2,4,5,3,8,1,6]=>[4,2,1,1]=>90
[8,4,2,5,6,7,3,1]=>[4,2,1,1]=>90
[5,4,1,6,3,7,8,2]=>[4,2,1,1]=>90
[4,5,1,3,6,7,8,2]=>[5,2,1]=>64
[5,1,7,6,3,4,8,2]=>[4,2,1,1]=>90
[6,1,7,5,4,8,2,3]=>[3,3,1,1]=>56
[3,7,2,1,6,8,4,5]=>[3,3,2]=>42
[1,5,8,2,4,7,6,3]=>[4,2,1,1]=>90
[5,8,1,6,4,7,3,2]=>[3,2,1,1,1]=>64
[3,8,6,5,7,2,4,1]=>[3,2,1,1,1]=>64
[6,8,1,4,7,3,5,2]=>[3,2,2,1]=>70
[1,6,8,2,7,4,5,3]=>[4,2,1,1]=>90
[5,7,2,1,8,4,3,6]=>[3,3,2]=>42
[5,7,1,6,8,3,2,4]=>[3,3,1,1]=>56
[5,6,2,1,8,3,4,7]=>[4,3,1]=>70
[6,4,1,7,3,8,2,5]=>[3,3,1,1]=>56
[8,2,5,6,7,1,4,3]=>[4,2,1,1]=>90
[7,2,4,6,8,3,1,5]=>[4,2,1,1]=>90
[6,2,4,7,8,1,3,5]=>[4,3,1]=>70
[6,1,4,3,2,8,5,7]=>[4,2,1,1]=>90
[2,7,4,8,6,1,5,3]=>[3,2,2,1]=>70
[2,4,8,6,5,7,3,1]=>[4,1,1,1,1]=>35
[3,7,8,6,4,2,5,1]=>[3,2,1,1,1]=>64
[6,2,8,4,7,5,1,3]=>[3,2,2,1]=>70
[1,4,7,2,6,8,5,3]=>[4,2,1,1]=>90
[4,2,8,5,1,6,3,7]=>[4,2,2]=>56
[6,5,8,1,4,2,3,7]=>[4,2,1,1]=>90
[2,3,8,4,1,6,5,7]=>[5,2,1]=>64
[4,5,7,3,1,6,2,8]=>[4,2,2]=>56
[5,1,8,7,4,6,3,2]=>[3,2,1,1,1]=>64
[2,4,8,7,5,1,3,6]=>[4,2,1,1]=>90
[3,5,7,6,1,8,4,2]=>[4,2,1,1]=>90
[3,5,7,6,2,8,4,1]=>[4,2,1,1]=>90
[1,5,3,2,8,7,6,4]=>[3,2,2,1]=>70
[6,1,4,3,8,7,5,2]=>[3,2,2,1]=>70
[6,3,1,8,7,4,2,5]=>[3,2,2,1]=>70
[5,3,6,2,8,7,4,1]=>[3,2,2,1]=>70
[6,3,5,2,1,8,7,4]=>[3,2,2,1]=>70
[2,8,4,1,3,7,6,5]=>[3,3,1,1]=>56
[3,8,1,4,7,6,5,2]=>[3,2,1,1,1]=>64
[6,2,3,8,7,5,4,1]=>[3,2,1,1,1]=>64
[3,4,7,5,8,1,2,6]=>[4,3,1]=>70
[2,7,8,3,4,1,5,6]=>[5,2,1]=>64
[2,8,6,7,5,4,3,1]=>[3,1,1,1,1,1]=>21
[7,2,6,8,1,4,3,5]=>[3,3,1,1]=>56
[5,3,6,2,8,4,7,1]=>[3,3,1,1]=>56
[8,1,6,3,7,4,5,2]=>[4,2,1,1]=>90
[2,4,3,7,1,8,6,5]=>[4,2,2]=>56
[2,6,5,7,3,8,4,1]=>[4,2,1,1]=>90
[6,8,2,7,4,1,5,3]=>[3,2,2,1]=>70
[6,1,7,8,5,3,2,4]=>[3,3,1,1]=>56
[2,6,5,4,7,1,8,3]=>[4,2,1,1]=>90
[5,8,3,4,6,1,7,2]=>[4,2,2]=>56
[6,1,7,4,2,5,8,3]=>[4,2,2]=>56
[6,8,7,1,5,4,2,3]=>[3,2,1,1,1]=>64
[4,8,3,1,5,7,6,2]=>[3,2,2,1]=>70
[5,3,8,2,7,1,6,4]=>[2,2,2,2]=>14
[8,3,4,5,2,7,1,6]=>[4,2,1,1]=>90
[7,1,5,2,6,3,4,8]=>[5,2,1]=>64
[3,7,1,5,2,6,8,4]=>[4,3,1]=>70
[6,7,1,8,3,4,5,2]=>[4,3,1]=>70
[3,7,1,6,8,4,5,2]=>[3,3,1,1]=>56
[3,8,5,2,6,7,1,4]=>[4,2,1,1]=>90
[3,6,5,2,7,1,4,8]=>[4,2,1,1]=>90
[6,8,3,4,7,1,5,2]=>[3,2,2,1]=>70
[3,7,1,6,5,2,8,4]=>[3,3,1,1]=>56
[8,3,5,2,7,1,6,4]=>[3,2,2,1]=>70
[3,8,6,4,7,1,5,2]=>[3,2,2,1]=>70
[3,7,1,4,8,6,5,2]=>[3,3,1,1]=>56
[3,7,1,4,5,2,8,6]=>[4,3,1]=>70
[2,3,7,6,5,8,1,4]=>[4,2,1,1]=>90
[4,3,5,6,7,8,9,1,2]=>[6,2,1]=>105
[7,8,9,5,4,3,2,1,6]=>[3,2,1,1,1,1]=>105
[6,7,8,9,4,3,2,1,5]=>[4,2,1,1,1]=>189
[6,5,4,3,2,7,8,9,1]=>[4,1,1,1,1,1]=>56
[2,1,4,3,6,5,8,7,11,12,9,10]=>[6,6]=>132
[2,1,4,3,6,5,9,10,7,8,12,11]=>[6,6]=>132
[2,1,4,3,6,5,9,11,7,12,8,10]=>[6,6]=>132
[2,1,4,3,6,5,10,11,12,7,8,9]=>[6,6]=>132
[2,1,4,3,7,8,5,6,10,9,12,11]=>[6,6]=>132
[2,1,4,3,7,8,5,6,11,12,9,10]=>[6,6]=>132
[2,1,4,3,7,9,5,10,6,8,12,11]=>[6,6]=>132
[2,1,4,3,7,9,5,11,6,12,8,10]=>[6,6]=>132
[2,1,4,3,7,10,5,11,12,6,8,9]=>[6,6]=>132
[2,1,4,3,8,9,10,5,6,7,12,11]=>[6,6]=>132
[2,1,4,3,8,9,11,5,6,12,7,10]=>[6,6]=>132
[2,1,4,3,8,10,11,5,12,6,7,9]=>[6,6]=>132
[2,1,4,3,9,10,11,12,5,6,7,8]=>[6,6]=>132
[2,1,5,6,3,4,8,7,10,9,12,11]=>[6,6]=>132
[2,1,5,6,3,4,8,7,11,12,9,10]=>[6,6]=>132
[2,1,5,6,3,4,9,10,7,8,12,11]=>[6,6]=>132
[2,1,5,6,3,4,9,11,7,12,8,10]=>[6,6]=>132
[2,1,5,6,3,4,10,11,12,7,8,9]=>[6,6]=>132
[2,1,5,7,3,8,4,6,10,9,12,11]=>[6,6]=>132
[2,1,5,7,3,8,4,6,11,12,9,10]=>[6,6]=>132
[2,1,5,7,3,9,4,10,6,8,12,11]=>[6,6]=>132
[2,1,5,7,3,9,4,11,6,12,8,10]=>[6,6]=>132
[2,1,5,7,3,10,4,11,12,6,8,9]=>[6,6]=>132
[2,1,5,8,3,9,10,4,6,7,12,11]=>[6,6]=>132
[2,1,5,8,3,9,11,4,6,12,7,10]=>[6,6]=>132
[2,1,5,8,3,10,11,4,12,6,7,9]=>[6,6]=>132
[2,1,5,9,3,10,11,12,4,6,7,8]=>[6,6]=>132
[2,1,6,7,8,3,4,5,10,9,12,11]=>[6,6]=>132
[2,1,6,7,8,3,4,5,11,12,9,10]=>[6,6]=>132
[2,1,6,7,9,3,4,10,5,8,12,11]=>[6,6]=>132
[2,1,6,7,9,3,4,11,5,12,8,10]=>[6,6]=>132
[2,1,6,7,10,3,4,11,12,5,8,9]=>[6,6]=>132
[2,1,6,8,9,3,10,4,5,7,12,11]=>[6,6]=>132
[2,1,6,8,9,3,11,4,5,12,7,10]=>[6,6]=>132
[2,1,6,8,10,3,11,4,12,5,7,9]=>[6,6]=>132
[2,1,6,9,10,3,11,12,4,5,7,8]=>[6,6]=>132
[2,1,7,8,9,10,3,4,5,6,12,11]=>[6,6]=>132
[2,1,7,8,9,11,3,4,5,12,6,10]=>[6,6]=>132
[2,1,7,8,10,11,3,4,12,5,6,9]=>[6,6]=>132
[2,1,7,9,10,11,3,12,4,5,6,8]=>[6,6]=>132
[2,1,8,9,10,11,12,3,4,5,6,7]=>[6,6]=>132
[3,4,1,2,6,5,8,7,10,9,12,11]=>[6,6]=>132
[3,4,1,2,6,5,8,7,11,12,9,10]=>[6,6]=>132
[3,4,1,2,6,5,9,10,7,8,12,11]=>[6,6]=>132
[3,4,1,2,6,5,9,11,7,12,8,10]=>[6,6]=>132
[3,4,1,2,6,5,10,11,12,7,8,9]=>[6,6]=>132
[3,4,1,2,7,8,5,6,10,9,12,11]=>[6,6]=>132
[3,4,1,2,7,8,5,6,11,12,9,10]=>[6,6]=>132
[3,4,1,2,7,9,5,10,6,8,12,11]=>[6,6]=>132
[3,4,1,2,7,9,5,11,6,12,8,10]=>[6,6]=>132
[3,4,1,2,7,10,5,11,12,6,8,9]=>[6,6]=>132
[3,4,1,2,8,9,10,5,6,7,12,11]=>[6,6]=>132
[3,4,1,2,8,9,11,5,6,12,7,10]=>[6,6]=>132
[3,4,1,2,8,10,11,5,12,6,7,9]=>[6,6]=>132
[3,4,1,2,9,10,11,12,5,6,7,8]=>[6,6]=>132
[3,5,1,6,2,4,8,7,10,9,12,11]=>[6,6]=>132
[3,5,1,6,2,4,8,7,11,12,9,10]=>[6,6]=>132
[3,5,1,6,2,4,9,10,7,8,12,11]=>[6,6]=>132
[3,5,1,6,2,4,9,11,7,12,8,10]=>[6,6]=>132
[3,5,1,6,2,4,10,11,12,7,8,9]=>[6,6]=>132
[3,5,1,7,2,8,4,6,10,9,12,11]=>[6,6]=>132
[3,5,1,7,2,8,4,6,11,12,9,10]=>[6,6]=>132
[3,5,1,7,2,9,4,10,6,8,12,11]=>[6,6]=>132
[3,5,1,7,2,9,4,11,6,12,8,10]=>[6,6]=>132
[3,5,1,7,2,10,4,11,12,6,8,9]=>[6,6]=>132
[3,5,1,8,2,9,10,4,6,7,12,11]=>[6,6]=>132
[3,5,1,8,2,9,11,4,6,12,7,10]=>[6,6]=>132
[3,5,1,8,2,10,11,4,12,6,7,9]=>[6,6]=>132
[3,5,1,9,2,10,11,12,4,6,7,8]=>[6,6]=>132
[3,6,1,7,8,2,4,5,10,9,12,11]=>[6,6]=>132
[3,6,1,7,8,2,4,5,11,12,9,10]=>[6,6]=>132
[3,6,1,7,9,2,4,10,5,8,12,11]=>[6,6]=>132
[3,6,1,7,9,2,4,11,5,12,8,10]=>[6,6]=>132
[3,6,1,7,10,2,4,11,12,5,8,9]=>[6,6]=>132
[3,6,1,8,9,2,10,4,5,7,12,11]=>[6,6]=>132
[3,6,1,8,9,2,11,4,5,12,7,10]=>[6,6]=>132
[3,6,1,8,10,2,11,4,12,5,7,9]=>[6,6]=>132
[3,6,1,9,10,2,11,12,4,5,7,8]=>[6,6]=>132
[3,7,1,8,9,10,2,4,5,6,12,11]=>[6,6]=>132
[3,7,1,8,9,11,2,4,5,12,6,10]=>[6,6]=>132
[3,7,1,8,10,11,2,4,12,5,6,9]=>[6,6]=>132
[3,7,1,9,10,11,2,12,4,5,6,8]=>[6,6]=>132
[3,8,1,9,10,11,12,2,4,5,6,7]=>[6,6]=>132
[4,5,6,1,2,3,8,7,10,9,12,11]=>[6,6]=>132
[4,5,6,1,2,3,8,7,11,12,9,10]=>[6,6]=>132
[4,5,6,1,2,3,9,10,7,8,12,11]=>[6,6]=>132
[4,5,6,1,2,3,9,11,7,12,8,10]=>[6,6]=>132
[4,5,6,1,2,3,10,11,12,7,8,9]=>[6,6]=>132
[4,5,7,1,2,8,3,6,10,9,12,11]=>[6,6]=>132
[4,5,7,1,2,8,3,6,11,12,9,10]=>[6,6]=>132
[4,5,7,1,2,9,3,10,6,8,12,11]=>[6,6]=>132
[4,5,7,1,2,9,3,11,6,12,8,10]=>[6,6]=>132
[4,5,7,1,2,10,3,11,12,6,8,9]=>[6,6]=>132
[4,5,8,1,2,9,10,3,6,7,12,11]=>[6,6]=>132
[4,5,8,1,2,9,11,3,6,12,7,10]=>[6,6]=>132
[4,5,8,1,2,10,11,3,12,6,7,9]=>[6,6]=>132
[4,5,9,1,2,10,11,12,3,6,7,8]=>[6,6]=>132
[4,6,7,1,8,2,3,5,10,9,12,11]=>[6,6]=>132
[4,6,7,1,8,2,3,5,11,12,9,10]=>[6,6]=>132
[4,6,7,1,9,2,3,10,5,8,12,11]=>[6,6]=>132
[4,6,7,1,9,2,3,11,5,12,8,10]=>[6,6]=>132
[4,6,7,1,10,2,3,11,12,5,8,9]=>[6,6]=>132
[4,6,8,1,9,2,10,3,5,7,12,11]=>[6,6]=>132
[4,6,8,1,9,2,11,3,5,12,7,10]=>[6,6]=>132
[4,6,8,1,10,2,11,3,12,5,7,9]=>[6,6]=>132
[4,6,9,1,10,2,11,12,3,5,7,8]=>[6,6]=>132
[4,7,8,1,9,10,2,3,5,6,12,11]=>[6,6]=>132
[4,7,8,1,9,11,2,3,5,12,6,10]=>[6,6]=>132
[4,7,8,1,10,11,2,3,12,5,6,9]=>[6,6]=>132
[4,7,9,1,10,11,2,12,3,5,6,8]=>[6,6]=>132
[4,8,9,1,10,11,12,2,3,5,6,7]=>[6,6]=>132
[5,6,7,8,1,2,3,4,10,9,12,11]=>[6,6]=>132
[5,6,7,8,1,2,3,4,11,12,9,10]=>[6,6]=>132
[5,6,7,9,1,2,3,10,4,8,12,11]=>[6,6]=>132
[5,6,7,9,1,2,3,11,4,12,8,10]=>[6,6]=>132
[5,6,7,10,1,2,3,11,12,4,8,9]=>[6,6]=>132
[5,6,8,9,1,2,10,3,4,7,12,11]=>[6,6]=>132
[5,6,8,9,1,2,11,3,4,12,7,10]=>[6,6]=>132
[5,6,8,10,1,2,11,3,12,4,7,9]=>[6,6]=>132
[5,6,9,10,1,2,11,12,3,4,7,8]=>[6,6]=>132
[5,7,8,9,1,10,2,3,4,6,12,11]=>[6,6]=>132
[5,7,8,9,1,11,2,3,4,12,6,10]=>[6,6]=>132
[5,7,8,10,1,11,2,3,12,4,6,9]=>[6,6]=>132
[5,7,9,10,1,11,2,12,3,4,6,8]=>[6,6]=>132
[5,8,9,10,1,11,12,2,3,4,6,7]=>[6,6]=>132
[6,7,8,9,10,1,2,3,4,5,12,11]=>[6,6]=>132
[6,7,8,9,11,1,2,3,4,12,5,10]=>[6,6]=>132
[6,7,8,10,11,1,2,3,12,4,5,9]=>[6,6]=>132
[6,7,9,10,11,1,2,12,3,4,5,8]=>[6,6]=>132
[6,8,9,10,11,1,12,2,3,4,5,7]=>[6,6]=>132
[3,5,7,6,8,2,1,4]=>[4,2,1,1]=>90
[4,2,5,3,7,6,1,8]=>[4,3,1]=>70
[6,2,4,3,7,5,1,8]=>[4,2,1,1]=>90
[1,3,6,4,7,5,2,8]=>[5,2,1]=>64
[8,2,5,3,6,4,1,7]=>[4,2,1,1]=>90
[7,2,5,3,6,4,1,8]=>[4,2,1,1]=>90
[6,2,5,3,7,4,1,8]=>[4,2,1,1]=>90
[4,2,6,3,7,5,1,8]=>[4,3,1]=>70
[5,2,7,3,6,4,1,8]=>[4,2,1,1]=>90
[7,3,6,2,5,4,1,8]=>[3,2,1,1,1]=>64
[6,3,8,2,5,4,1,7]=>[3,2,2,1]=>70
[7,3,1,4,6,5,2,8]=>[4,2,1,1]=>90
[8,3,7,2,5,4,1,6]=>[3,2,1,1,1]=>64
[5,2,8,3,6,4,1,7]=>[4,2,1,1]=>90
[3,2,8,4,6,5,1,7]=>[4,2,1,1]=>90
[1,4,7,3,6,5,2,8]=>[4,2,1,1]=>90
[8,2,5,4,1,6,3,7]=>[4,2,1,1]=>90
[8,2,6,4,1,5,3,7]=>[4,2,1,1]=>90
[1,4,8,3,7,5,2,6]=>[4,2,1,1]=>90
[6,2,1,4,8,5,3,7]=>[4,2,2]=>56
[5,2,1,4,8,6,3,7]=>[4,2,2]=>56
[3,2,1,5,8,6,4,7]=>[4,2,2]=>56
[4,2,8,3,7,5,1,6]=>[4,2,1,1]=>90
[5,2,8,3,7,4,1,6]=>[4,2,1,1]=>90
[8,3,7,2,6,4,1,5]=>[3,2,1,1,1]=>64
[7,3,1,4,8,5,2,6]=>[4,2,2]=>56
[1,3,7,4,8,5,2,6]=>[5,2,1]=>64
[8,2,6,3,7,4,1,5]=>[4,2,1,1]=>90
[7,2,6,3,8,4,1,5]=>[4,2,1,1]=>90
[5,2,7,3,8,4,1,6]=>[4,3,1]=>70
[3,2,7,4,8,5,1,6]=>[4,3,1]=>70
[5,2,6,3,8,4,1,7]=>[4,3,1]=>70
[6,2,5,3,8,4,1,7]=>[4,2,1,1]=>90
[7,2,5,3,8,4,1,6]=>[4,2,1,1]=>90
[8,2,5,3,7,4,1,6]=>[4,2,1,1]=>90
[1,3,6,4,8,5,2,7]=>[5,2,1]=>64
[1,3,5,4,8,6,2,7]=>[5,2,1]=>64
[8,2,4,3,7,5,1,6]=>[4,2,1,1]=>90
[7,2,4,3,8,5,1,6]=>[4,2,1,1]=>90
[6,2,4,3,8,5,1,7]=>[4,2,1,1]=>90
[5,2,4,3,8,6,1,7]=>[4,2,1,1]=>90
[4,2,5,3,8,6,1,7]=>[4,3,1]=>70
[4,2,5,3,1,7,6,8]=>[4,3,1]=>70
[6,2,4,3,1,7,5,8]=>[4,2,1,1]=>90
[7,2,4,3,1,6,5,8]=>[4,2,1,1]=>90
[8,5,1,3,6,4,2,7]=>[4,2,1,1]=>90
[8,4,1,3,6,5,2,7]=>[4,2,1,1]=>90
[1,5,2,4,7,6,3,8]=>[5,2,1]=>64
[7,2,5,3,1,6,4,8]=>[4,2,1,1]=>90
[6,2,5,3,1,7,4,8]=>[4,2,1,1]=>90
[4,2,6,3,1,7,5,8]=>[4,3,1]=>70
[3,2,6,4,1,7,5,8]=>[4,3,1]=>70
[3,2,7,4,1,6,5,8]=>[4,2,2]=>56
[4,2,7,3,1,6,5,8]=>[4,2,2]=>56
[5,2,7,3,1,6,4,8]=>[4,2,2]=>56
[6,2,7,3,1,5,4,8]=>[4,2,2]=>56
[7,2,6,3,1,5,4,8]=>[4,2,1,1]=>90
[1,5,2,4,8,6,3,7]=>[5,2,1]=>64
[8,4,1,3,7,5,2,6]=>[4,2,1,1]=>90
[6,2,1,5,3,7,4,8]=>[4,3,1]=>70
[3,2,1,6,4,7,5,8]=>[4,3,1]=>70
[3,2,8,5,1,6,4,7]=>[4,2,2]=>56
[6,2,8,4,1,5,3,7]=>[4,2,2]=>56
[8,3,7,4,1,5,2,6]=>[4,2,1,1]=>90
[7,1,3,2,5,6,4,8]=>[5,2,1]=>64
[6,3,5,2,4,8,1,7]=>[3,3,1,1]=>56
[1,5,2,8,7,4,3,6]=>[4,2,1,1]=>90
[5,7,2,8,1,4,3,6]=>[3,3,2]=>42
[4,8,3,1,5,2,7,6]=>[3,3,2]=>42
[7,1,5,3,2,6,8,4]=>[4,2,1,1]=>90
[8,7,6,5,3,2,1,4,9]=>[3,1,1,1,1,1,1]=>28
[8,7,6,4,3,2,1,5,9]=>[3,1,1,1,1,1,1]=>28
[8,7,5,4,3,2,1,6,9]=>[3,1,1,1,1,1,1]=>28
[8,7,6,5,4,1,2,3,9]=>[4,1,1,1,1,1]=>56
[9,8,7,6,5,4,2,1,3,10]=>[3,1,1,1,1,1,1,1]=>36
[8,7,6,5,2,3,1,4,9]=>[4,1,1,1,1,1]=>56
[9,8,7,6,5,3,2,1,4,10]=>[3,1,1,1,1,1,1,1]=>36
[8,7,6,3,4,2,1,5,9]=>[4,1,1,1,1,1]=>56
[9,8,7,6,4,3,2,1,5,10]=>[3,1,1,1,1,1,1,1]=>36
[8,7,4,5,3,2,1,6,9]=>[4,1,1,1,1,1]=>56
[9,8,7,5,4,3,2,1,6,10]=>[3,1,1,1,1,1,1,1]=>36
[8,5,6,4,3,2,1,7,9]=>[4,1,1,1,1,1]=>56
[9,8,6,5,4,3,2,1,7,10]=>[3,1,1,1,1,1,1,1]=>36
[6,7,5,4,3,2,1,8,9]=>[4,1,1,1,1,1]=>56
[8,6,2,3,1,5,7,4]=>[4,2,1,1]=>90
[1,4,2,7,3,6,8,5]=>[5,2,1]=>64
[3,2,1,7,8,5,4,6]=>[3,3,2]=>42
[7,3,4,2,1,5,8,6]=>[4,2,1,1]=>90
[2,1,6,4,7,8,5,3]=>[4,3,1]=>70
[1,6,3,2,4,7,8,5]=>[5,2,1]=>64
[1,2,3,7,5,8,4,6]=>[5,2,1]=>64
[1,8,5,3,2,4,7,6]=>[4,2,1,1]=>90
[4,7,8,1,5,6,2,3]=>[3,3,2]=>42
[3,6,7,1,8,4,2,5]=>[4,3,1]=>70
[1,3,7,6,2,4,5,8]=>[5,2,1]=>64
[2,7,3,8,4,5,6,1]=>[5,2,1]=>64
[7,1,4,3,8,5,6,2]=>[4,2,1,1]=>90
[5,6,2,7,8,3,4,1]=>[4,3,1]=>70
[7,4,1,8,5,6,2,3]=>[3,3,2]=>42
[7,2,5,8,1,6,3,4]=>[3,3,2]=>42
[6,4,8,1,5,7,2,3]=>[3,3,2]=>42
[6,2,1,4,7,5,8,3]=>[4,2,2]=>56
[6,8,7,9,5,4,3,2,1]=>[3,1,1,1,1,1,1]=>28
[5,8,7,6,9,4,3,2,1]=>[3,1,1,1,1,1,1]=>28
[4,8,7,6,5,9,3,2,1]=>[3,1,1,1,1,1,1]=>28
[3,8,7,6,5,4,9,2,1]=>[3,1,1,1,1,1,1]=>28
[2,8,7,6,5,4,3,9,1]=>[3,1,1,1,1,1,1]=>28
[2,3,6,8,4,1,7,5]=>[4,2,2]=>56
[1,7,2,8,6,3,5,4]=>[4,2,1,1]=>90
[8,4,2,3,7,1,6,5]=>[3,2,2,1]=>70
[5,2,4,8,7,3,1,6]=>[3,2,2,1]=>70
[3,2,4,6,7,8,1,5]=>[5,2,1]=>64
[5,2,6,8,1,3,7,4]=>[3,3,2]=>42
[4,8,1,6,3,7,5,2]=>[3,3,1,1]=>56
[7,1,5,2,6,4,3,8]=>[4,2,1,1]=>90
[8,3,5,2,6,1,4,7]=>[4,2,1,1]=>90
[1,8,5,6,2,7,4,3]=>[4,2,1,1]=>90
[4,2,7,6,1,8,5,3]=>[3,2,2,1]=>70
[7,2,4,8,6,3,5,1]=>[3,2,2,1]=>70
[7,3,2,1,8,5,4,6]=>[3,2,2,1]=>70
[7,3,2,1,6,4,8,5]=>[3,3,1,1]=>56
[6,7,2,4,3,5,8,1]=>[4,2,1,1]=>90
[4,3,8,2,1,5,7,6]=>[3,2,2,1]=>70
[4,3,2,8,1,6,7,5]=>[3,2,2,1]=>70
[4,5,8,3,2,7,1,6]=>[3,2,2,1]=>70
[6,8,5,2,7,3,4,1]=>[3,2,2,1]=>70
[5,4,7,8,2,3,6,1]=>[3,3,1,1]=>56
[4,3,8,2,1,6,7,5]=>[3,2,2,1]=>70
[9,1,3,4,5,6,7,8,2]=>[7,1,1]=>28
[3,5,7,4,6,2,8,1]=>[4,2,1,1]=>90
[5,3,7,6,2,4,8,1]=>[3,2,2,1]=>70
[4,6,7,2,5,3,8,1]=>[4,2,1,1]=>90
[6,4,7,8,3,1,5,2]=>[3,2,2,1]=>70
[5,8,1,7,6,4,2,3]=>[3,2,1,1,1]=>64
[5,6,7,1,8,3,4,2]=>[4,3,1]=>70
[7,1,8,6,2,5,4,3]=>[3,2,1,1,1]=>64
[1,5,8,2,6,4,7,3]=>[4,2,1,1]=>90
[1,5,7,4,6,8,3,2]=>[4,2,1,1]=>90
[1,4,7,5,6,8,3,2]=>[5,1,1,1]=>35
[5,6,7,4,8,1,3,2]=>[4,2,1,1]=>90
[8,1,2,6,4,5,7,3]=>[5,1,1,1]=>35
[4,8,1,7,2,5,6,3]=>[4,2,1,1]=>90
[2,6,7,1,5,4,8,3]=>[4,2,1,1]=>90
[3,2,7,6,5,8,1,4]=>[3,2,2,1]=>70
[1,7,3,4,5,8,2,6]=>[5,2,1]=>64
[7,1,8,4,5,6,3,2]=>[4,2,1,1]=>90
[10,1,3,4,5,6,7,8,9,2]=>[8,1,1]=>36
[1,2,3,4,5,6,7,8,11,9,10]=>[10,1]=>10
[1,8,3,4,5,6,9,2,7]=>[6,2,1]=>105
[8,2,3,4,5,1,9,7,6]=>[5,2,2]=>120
[1,2,7,4,5,8,3,6]=>[5,2,1]=>64
[8,1,9,4,5,6,7,3,2]=>[5,2,1,1]=>189
[7,9,3,4,5,6,1,8,2]=>[5,2,2]=>120
[11,1,3,4,5,6,7,8,9,10,2]=>[9,1,1]=>45
[1,2,3,4,5,6,7,8,9,12,10,11]=>[11,1]=>11
[10,2,3,4,5,6,7,8,11,1,9]=>[8,2,1]=>231
[1,9,3,4,5,6,7,10,2,8]=>[7,2,1]=>160
[9,2,3,4,5,6,1,10,8,7]=>[6,2,2]=>225
[1,2,8,4,5,6,9,3,7]=>[6,2,1]=>105
[7,8,3,4,5,2,9,1,6]=>[4,3,1,1]=>216
[8,2,3,4,1,6,9,7,5]=>[5,2,2]=>120
[6,7,3,2,5,8,1,4]=>[3,2,2,1]=>70
[8,1,3,9,5,6,7,4,2]=>[5,2,1,1]=>189
[6,1,8,4,5,3,7,2]=>[4,2,1,1]=>90
[7,8,9,4,5,6,3,1,2]=>[3,3,2,1]=>168
[9,1,10,4,5,6,7,8,3,2]=>[6,2,1,1]=>350
[6,9,3,4,5,1,7,8,2]=>[5,2,2]=>120
[8,10,3,4,5,6,7,1,9,2]=>[6,2,2]=>225
[10,11,3,4,5,6,7,8,9,1,2]=>[7,2,2]=>385
[12,1,3,4,5,6,7,8,9,10,11,2]=>[10,1,1]=>55
[4,6,2,5,1,8,7,3]=>[3,3,2]=>42
[5,1,4,6,2,8,7,3]=>[4,2,2]=>56
[7,3,5,2,1,6,8,4]=>[4,2,1,1]=>90
[8,5,1,2,6,3,7,4]=>[4,3,1]=>70
[1,5,8,7,4,6,3,2]=>[3,2,1,1,1]=>64
[5,7,2,1,3,6,8,4]=>[4,2,2]=>56
[3,7,2,6,8,1,5,4]=>[3,2,2,1]=>70
[7,4,8,6,5,1,3,2]=>[2,2,2,1,1]=>28
[2,7,6,8,5,1,4,3]=>[3,2,1,1,1]=>64
[1,6,4,5,7,3,8,2]=>[5,1,1,1]=>35
[1,5,4,7,8,6,2,3]=>[4,2,2]=>56
[7,3,1,6,8,2,5,4]=>[3,3,1,1]=>56
[7,1,6,8,5,2,4,3]=>[3,2,1,1,1]=>64
[3,5,8,7,6,4,1,2]=>[3,2,1,1,1]=>64
[1,5,7,8,6,2,4,3]=>[4,2,1,1]=>90
[3,6,2,1,4,7,8,5]=>[4,3,1]=>70
[6,8,2,7,5,4,3,1]=>[2,2,1,1,1,1]=>20
[5,8,1,7,6,4,3,2]=>[2,2,1,1,1,1]=>20
[10,6,1,2,3,4,9,5,7,8]=>[7,2,1]=>160
[10,7,1,2,3,4,9,5,6,8]=>[7,2,1]=>160
[9,10,1,2,3,4,8,5,6,7]=>[7,2,1]=>160
[10,1,5,2,3,4,6,7,8,9]=>[8,1,1]=>36
[10,1,2,5,3,4,6,7,8,9]=>[8,1,1]=>36
[5,1,2,3,10,4,6,7,8,9]=>[8,2]=>35
[7,1,2,3,4,5,11,6,8,9,10]=>[9,2]=>44
[7,6,1,2,3,4,10,9,5,8]=>[6,2,2]=>225
[11,1,2,3,4,5,8,6,7,9,10]=>[9,1,1]=>45
[9,7,1,2,3,4,8,5,10,6]=>[6,3,1]=>315
[11,1,2,3,4,5,9,6,7,8,10]=>[9,1,1]=>45
[5,9,1,2,3,4,6,7,10,8]=>[7,3]=>75
[10,8,4,9,1,2,3,5,6,7]=>[6,2,1,1]=>350
[11,10,5,1,2,3,4,6,7,8,9]=>[8,1,1,1]=>120
[2,10,1,5,3,4,6,7,8,9]=>[7,2,1]=>160
[11,10,1,5,2,3,4,6,7,8,9]=>[8,1,1,1]=>120
[3,1,5,2,10,4,6,7,8,9]=>[7,3]=>75
[5,11,1,2,10,3,4,6,7,8,9]=>[8,2,1]=>231
[4,1,2,10,3,5,6,7,8,9]=>[8,2]=>35
[5,11,1,2,3,10,4,6,7,8,9]=>[8,2,1]=>231
[4,1,5,6,7,8,9,2,3]=>[6,3]=>48
[2,3,4,5,6,7,8,10,11,1,9]=>[9,2]=>44
[2,3,4,5,8,9,1,6,7]=>[6,3]=>48
[2,3,6,7,1,8,9,4,5]=>[6,3]=>48
[2,4,5,6,7,8,9,10,11,1,3]=>[9,2]=>44
[3,4,5,6,7,8,9,10,11,1,2]=>[9,2]=>44
[8,6,3,2,1,5,4,7]=>[3,2,1,1,1]=>64
[8,5,3,2,4,1,7,6]=>[3,2,1,1,1]=>64
[7,5,2,4,3,6,8,1]=>[4,1,1,1,1]=>35
[8,5,1,4,6,3,2,7]=>[4,1,1,1,1]=>35
[8,5,1,6,3,4,2,7]=>[4,2,1,1]=>90
[8,4,3,6,1,5,2,7]=>[3,2,2,1]=>70
[8,4,3,5,2,1,7,6]=>[3,2,1,1,1]=>64
[6,4,3,2,8,7,1,5]=>[2,2,2,1,1]=>28
[8,5,1,4,3,7,2,6]=>[3,2,1,1,1]=>64
[8,5,4,2,1,3,7,6]=>[3,2,1,1,1]=>64
[4,7,3,6,1,8,5,2]=>[3,2,2,1]=>70
[7,6,2,4,1,5,8,3]=>[4,2,1,1]=>90
[8,1,6,3,7,4,2,5]=>[4,2,1,1]=>90
[5,3,8,2,6,7,1,4]=>[3,2,2,1]=>70
[8,2,5,1,7,6,3,4]=>[3,3,1,1]=>56
[8,2,4,6,3,7,1,5]=>[4,2,1,1]=>90
[7,2,6,4,3,5,8,1]=>[4,1,1,1,1]=>35
[7,3,6,2,4,5,8,1]=>[4,2,1,1]=>90
[8,3,7,2,1,4,6,5]=>[3,2,2,1]=>70
[7,6,4,1,3,2,8,5]=>[3,2,1,1,1]=>64
[7,3,8,2,1,5,6,4]=>[3,2,2,1]=>70
[6,2,5,7,4,3,8,1]=>[4,1,1,1,1]=>35
[6,2,5,4,8,7,1,3]=>[3,2,2,1]=>70
[7,2,4,8,5,1,6,3]=>[4,2,2]=>56
[4,2,7,6,8,5,1,3]=>[3,2,2,1]=>70
[7,1,6,2,8,5,4,3]=>[3,2,1,1,1]=>64
[7,1,6,3,8,5,2,4]=>[3,2,2,1]=>70
[7,2,6,8,1,3,5,4]=>[3,3,1,1]=>56
[7,2,8,5,1,3,6,4]=>[3,3,2]=>42
[7,1,8,5,3,2,6,4]=>[3,2,2,1]=>70
[7,1,8,2,5,6,4,3]=>[4,2,1,1]=>90
[6,1,5,8,7,2,4,3]=>[3,2,2,1]=>70
[6,1,5,7,4,8,3,2]=>[4,1,1,1,1]=>35
[6,1,5,7,8,3,4,2]=>[4,2,1,1]=>90
[4,6,7,3,1,8,5,2]=>[4,2,2]=>56
[4,2,6,3,1,8,7,5]=>[3,3,2]=>42
[6,1,4,2,5,8,7,3]=>[4,2,2]=>56
[1,5,3,8,4,6,2,7]=>[5,2,1]=>64
[7,2,3,5,8,4,1,6]=>[4,2,1,1]=>90
[7,6,4,2,8,5,1,3]=>[2,2,2,1,1]=>28
[1,7,6,4,8,5,3,2]=>[3,2,1,1,1]=>64
[8,7,4,2,1,5,6,3]=>[3,2,1,1,1]=>64
[8,2,3,5,1,4,6,7]=>[5,2,1]=>64
[8,7,4,1,3,2,6,5]=>[3,2,1,1,1]=>64
[7,1,4,8,3,6,2,5]=>[3,2,2,1]=>70
[4,1,8,5,7,6,2,3]=>[3,3,1,1]=>56
[3,7,5,8,4,2,1,6]=>[3,2,1,1,1]=>64
[6,1,5,8,3,4,2,7]=>[4,2,1,1]=>90
[6,7,5,1,3,2,4,8]=>[4,2,1,1]=>90
[5,2,6,1,7,3,4,8]=>[4,3,1]=>70
[4,2,6,8,3,7,1,5]=>[3,3,2]=>42
[6,8,5,1,4,2,3,7]=>[4,2,1,1]=>90
[7,8,4,5,1,3,6,2]=>[3,2,2,1]=>70
[1,7,8,5,3,4,6,2]=>[4,2,1,1]=>90
[1,5,8,3,6,4,7,2]=>[4,2,1,1]=>90
[6,3,8,1,4,2,7,5]=>[3,3,2]=>42
[4,8,1,5,6,3,7,2]=>[4,2,1,1]=>90
[1,8,2,6,5,3,7,4]=>[4,2,1,1]=>90
[3,8,1,7,2,6,5,4]=>[3,2,1,1,1]=>64
[7,3,8,1,2,6,5,4]=>[3,2,2,1]=>70
[8,1,4,2,3,5,7,6]=>[5,2,1]=>64
[8,1,2,4,6,5,7,3]=>[5,1,1,1]=>35
[5,1,8,3,7,4,6,2]=>[4,2,1,1]=>90
[8,3,7,1,5,4,6,2]=>[3,2,1,1,1]=>64
[8,4,7,1,5,3,6,2]=>[3,2,1,1,1]=>64
[7,2,5,3,4,6,1,8]=>[5,1,1,1]=>35
[7,6,4,2,5,3,1,8]=>[3,2,1,1,1]=>64
[5,8,4,3,6,2,7,1]=>[3,2,1,1,1]=>64
[1,7,2,6,3,4,8,5]=>[5,2,1]=>64
[7,5,1,6,3,2,4,8]=>[4,2,1,1]=>90
[7,1,2,6,3,4,5,8]=>[6,1,1]=>21
[7,3,1,4,6,2,5,8]=>[4,3,1]=>70
[7,1,6,5,4,2,3,8]=>[4,1,1,1,1]=>35
[5,8,4,3,1,7,2,6]=>[3,2,2,1]=>70
[3,6,8,5,2,4,7,1]=>[3,3,1,1]=>56
[5,7,8,4,3,2,6,1]=>[3,2,1,1,1]=>64
[1,3,8,4,7,2,6,5]=>[4,2,1,1]=>90
[6,7,1,3,2,8,5,4]=>[3,3,2]=>42
[1,5,3,2,6,8,4,7]=>[4,3,1]=>70
[3,7,6,5,8,2,4,1]=>[3,2,1,1,1]=>64
[5,7,4,2,8,6,1,3]=>[3,2,2,1]=>70
[5,4,3,7,8,2,6,1]=>[3,2,1,1,1]=>64
[3,8,5,7,6,2,4,1]=>[3,2,1,1,1]=>64
[1,3,6,8,7,2,5,4]=>[4,2,1,1]=>90
[5,8,7,1,4,2,3,6]=>[4,2,1,1]=>90
[2,6,3,7,1,4,5,8]=>[5,2,1]=>64
[7,6,8,4,3,1,5,2]=>[2,2,2,1,1]=>28
[1,7,6,5,3,2,4,8]=>[4,1,1,1,1]=>35
[2,7,6,5,4,1,3,8]=>[3,2,1,1,1]=>64
[6,2,3,5,8,4,1,7]=>[4,2,1,1]=>90
[4,7,6,1,5,8,3,2]=>[3,2,1,1,1]=>64
[9,8,7,6,5,4,2,3,1]=>[2,1,1,1,1,1,1,1]=>8
[2,3,9,8,7,6,5,4,1]=>[3,1,1,1,1,1,1]=>28
[9,1,3,2,4,5,6,7,8]=>[7,1,1]=>28
[6,8,7,1,5,4,3,2]=>[2,2,1,1,1,1]=>20
[9,10,1,8,7,6,5,4,3,2]=>[2,2,1,1,1,1,1,1]=>35
[3,5,2,4,7,6,9,8,1]=>[4,4,1]=>84
[2,4,3,6,5,8,7,1,9]=>[5,3,1]=>162
[3,2,5,4,7,6,9,8,1,10]=>[5,4,1]=>288
[2,4,3,6,5,8,7,10,9,1]=>[5,4,1]=>288
[7,2,6,1,5,8,3,4]=>[3,3,1,1]=>56
[4,7,3,6,8,2,1,5]=>[3,2,2,1]=>70
[5,4,7,3,8,2,1,6]=>[3,2,1,1,1]=>64
[8,7,2,4,6,3,5,1]=>[3,2,1,1,1]=>64
[1,7,2,8,5,4,3,6]=>[4,2,1,1]=>90
[5,4,8,3,6,2,1,7]=>[3,2,1,1,1]=>64
[6,8,2,5,7,1,4,3]=>[3,2,2,1]=>70
[3,8,6,2,7,5,1,4]=>[3,2,2,1]=>70
[5,8,4,2,7,3,6,1]=>[3,2,2,1]=>70
[8,2,7,3,4,5,1,6]=>[5,1,1,1]=>35
[8,1,5,2,4,6,3,7]=>[5,1,1,1]=>35
[8,6,1,3,4,5,7,2]=>[5,1,1,1]=>35
[8,5,1,2,4,6,7,3]=>[5,1,1,1]=>35
[2,6,8,7,3,4,5,1]=>[4,2,1,1]=>90
[1,7,8,5,6,4,2,3]=>[3,2,2,1]=>70
[8,3,1,2,4,6,7,5]=>[5,2,1]=>64
[3,1,7,5,8,2,4,6]=>[4,3,1]=>70
[8,1,3,2,4,6,5,7]=>[5,2,1]=>64
[8,1,5,6,4,2,3,7]=>[4,2,1,1]=>90
[8,1,6,5,4,3,2,7]=>[3,1,1,1,1,1]=>21
[2,6,8,1,5,4,3,7]=>[3,3,1,1]=>56
[3,5,8,2,1,4,7,6]=>[3,3,2]=>42
[4,2,8,5,3,7,6,1]=>[3,3,1,1]=>56
[4,2,7,5,3,8,6,1]=>[3,3,1,1]=>56
[6,4,5,1,8,3,2,7]=>[3,3,1,1]=>56
[5,4,7,8,3,1,2,6]=>[3,3,1,1]=>56
[4,5,8,1,3,7,2,6]=>[3,3,2]=>42
[1,5,3,6,8,7,2,4]=>[4,2,2]=>56
[7,6,2,8,1,4,3,5]=>[3,2,2,1]=>70
[4,7,2,6,8,3,5,1]=>[3,3,1,1]=>56
[6,3,2,8,7,4,5,1]=>[3,2,2,1]=>70
[7,4,3,8,5,6,2,1]=>[3,2,1,1,1]=>64
[3,1,5,8,7,6,2,4]=>[3,3,1,1]=>56
[8,2,1,6,5,7,3,4]=>[3,3,1,1]=>56
[3,1,8,6,5,7,2,4]=>[3,3,1,1]=>56
[1,2,7,6,4,5,8,3]=>[5,1,1,1]=>35
[7,2,6,5,1,8,3,4]=>[3,3,1,1]=>56
[4,2,8,5,6,3,1,7]=>[4,2,1,1]=>90
[4,7,3,2,5,1,6,8]=>[4,2,1,1]=>90
[4,2,5,3,8,7,1,6]=>[3,3,2]=>42
[7,2,5,3,8,4,6,1]=>[4,2,1,1]=>90
[7,5,6,1,8,3,2,4]=>[3,3,1,1]=>56
[4,5,6,2,7,3,1,8]=>[5,2,1]=>64
[3,5,1,4,6,8,2,7]=>[4,3,1]=>70
[8,5,7,4,2,1,3,6]=>[3,2,1,1,1]=>64
[4,6,2,7,5,8,1,3]=>[4,2,2]=>56
[7,8,1,4,2,3,5,6]=>[5,2,1]=>64
[6,5,2,4,8,7,1,3]=>[3,2,2,1]=>70
[8,5,2,4,1,3,7,6]=>[3,3,1,1]=>56
[5,1,2,4,3,6,8,7]=>[5,2,1]=>64
[8,6,2,7,5,3,1,4]=>[3,2,1,1,1]=>64
[4,3,8,1,5,2,6,7]=>[4,2,2]=>56
[4,1,3,6,7,2,8,5]=>[5,2,1]=>64
[3,5,1,2,4,7,6,9,8]=>[5,4]=>42
[3,7,8,6,5,1,2,4]=>[3,3,1,1]=>56
[8,4,5,7,2,6,3,1]=>[3,2,1,1,1]=>64
[4,5,8,2,7,3,1,6]=>[3,3,1,1]=>56
[6,5,8,2,7,3,1,4]=>[3,2,2,1]=>70
[6,4,8,2,7,3,1,5]=>[3,2,2,1]=>70
[7,8,1,3,6,4,2,5]=>[4,2,1,1]=>90
[5,7,3,4,2,6,8,1]=>[4,2,1,1]=>90
[5,7,4,2,3,6,8,1]=>[4,2,1,1]=>90
[5,4,7,3,2,8,1,6]=>[3,2,1,1,1]=>64
[6,8,3,2,4,5,1,7]=>[4,2,1,1]=>90
[5,8,3,4,6,1,2,7]=>[4,2,2]=>56
[6,4,3,8,5,1,2,7]=>[3,2,2,1]=>70
[6,4,8,2,3,5,1,7]=>[4,2,1,1]=>90
[5,4,6,8,2,3,1,7]=>[3,3,1,1]=>56
[5,6,8,4,1,2,3,7]=>[4,3,1]=>70
[6,4,8,5,1,2,3,7]=>[4,2,2]=>56
[7,4,8,3,1,2,5,6]=>[4,2,1,1]=>90
[5,7,8,2,3,1,4,6]=>[4,3,1]=>70
[5,4,7,8,2,1,3,6]=>[3,3,1,1]=>56
[5,8,6,3,1,2,4,7]=>[4,2,1,1]=>90
[6,8,5,2,1,3,4,7]=>[4,2,1,1]=>90
[5,6,1,3,2,4,8,7]=>[4,3,1]=>70
[4,3,8,1,2,5,7,6]=>[4,2,2]=>56
[5,3,7,2,1,8,6,4]=>[3,2,2,1]=>70
[5,4,8,3,7,2,1,6]=>[2,2,2,1,1]=>28
[3,6,8,5,2,1,7,4]=>[3,2,2,1]=>70
[6,1,5,4,7,2,8,3]=>[4,2,1,1]=>90
[5,4,8,3,2,7,1,6]=>[2,2,2,1,1]=>28
[5,4,3,7,8,2,1,6]=>[3,2,1,1,1]=>64
[3,4,5,6,7,8,2,9,1]=>[7,1,1]=>28
[1,4,8,6,3,2,7,5]=>[4,2,1,1]=>90
[4,1,8,6,2,5,7,3]=>[4,2,1,1]=>90
[6,7,2,5,3,8,4,1]=>[3,3,1,1]=>56
[6,3,4,8,1,2,7,5]=>[3,3,2]=>42
[2,6,3,1,5,8,7,4]=>[4,2,2]=>56
[7,1,3,2,6,5,8,4]=>[4,2,1,1]=>90
[8,7,6,4,5,3,2,9,1]=>[3,1,1,1,1,1,1]=>28
[2,9,8,7,5,6,4,3,1]=>[3,1,1,1,1,1,1]=>28
[1,3,5,8,4,7,2,6]=>[4,2,2]=>56
[2,3,8,7,5,1,6,4]=>[4,2,1,1]=>90
[4,1,3,5,6,2,8,7]=>[5,2,1]=>64
[6,4,8,7,3,5,2,1]=>[2,2,2,1,1]=>28
[8,2,3,5,6,1,4,7]=>[5,2,1]=>64
[3,8,2,7,6,4,1,5]=>[3,2,1,1,1]=>64
[4,3,8,6,2,7,1,5]=>[3,2,2,1]=>70
[8,3,4,5,1,6,7,2]=>[5,2,1]=>64
[7,8,1,3,5,4,6,2]=>[4,2,1,1]=>90
[3,5,7,6,4,8,1,2]=>[4,2,1,1]=>90
[1,3,7,8,5,4,6,2]=>[4,2,1,1]=>90
[1,3,2,7,8,5,4,6]=>[4,3,1]=>70
[1,5,7,6,8,3,4,2]=>[4,2,1,1]=>90
[2,1,7,4,3,8,5,6]=>[4,3,1]=>70
[7,2,3,8,5,4,1,6]=>[4,2,1,1]=>90
[3,2,5,4,7,6,1,10,8,9]=>[5,4,1]=>288
[3,2,5,4,9,8,6,7,1,10]=>[5,3,1,1]=>567
[3,2,5,4,1,8,6,10,7,9]=>[5,4,1]=>288
[3,2,5,4,1,10,9,6,7,8]=>[5,3,2]=>450
[3,2,7,6,4,5,9,8,1,10]=>[5,3,1,1]=>567
[3,2,7,6,4,5,1,10,8,9]=>[5,3,1,1]=>567
[3,2,9,6,4,8,5,7,1,10]=>[5,3,1,1]=>567
[3,2,1,6,4,8,5,10,7,9]=>[5,4,1]=>288
[3,2,1,6,4,10,9,5,7,8]=>[5,3,2]=>450
[3,2,9,8,7,4,5,6,1,10]=>[5,2,1,1,1]=>448
[3,2,1,8,7,4,5,10,6,9]=>[5,3,2]=>450
[3,2,1,10,7,4,9,5,6,8]=>[5,3,2]=>450
[3,2,1,10,9,8,4,5,6,7]=>[5,2,2,1]=>525
[5,4,2,3,7,6,9,8,1,10]=>[5,3,1,1]=>567
[5,4,2,3,7,6,1,10,8,9]=>[5,3,1,1]=>567
[5,4,2,3,9,8,6,7,1,10]=>[5,2,2,1]=>525
[5,4,2,3,1,8,6,10,7,9]=>[5,3,1,1]=>567
[5,4,2,3,1,10,9,6,7,8]=>[5,2,2,1]=>525
[7,4,2,6,3,5,9,8,1,10]=>[5,3,1,1]=>567
[7,4,2,6,3,5,1,10,8,9]=>[5,3,1,1]=>567
[9,4,2,6,3,8,5,7,1,10]=>[5,3,1,1]=>567
[1,4,2,6,3,8,5,10,7,9]=>[6,4]=>90
[1,4,2,6,3,10,9,5,7,8]=>[6,3,1]=>315
[9,4,2,8,7,3,5,6,1,10]=>[5,2,1,1,1]=>448
[1,4,2,8,7,3,5,10,6,9]=>[6,3,1]=>315
[1,4,2,10,7,3,9,5,6,8]=>[6,3,1]=>315
[1,4,2,10,9,8,3,5,6,7]=>[6,2,1,1]=>350
[7,6,5,2,3,4,9,8,1,10]=>[5,2,1,1,1]=>448
[7,6,5,2,3,4,1,10,8,9]=>[5,2,1,1,1]=>448
[9,6,5,2,3,8,4,7,1,10]=>[5,2,1,1,1]=>448
[1,6,5,2,3,8,4,10,7,9]=>[6,3,1]=>315
[1,6,5,2,3,10,9,4,7,8]=>[6,2,2]=>225
[9,8,5,2,7,3,4,6,1,10]=>[5,2,1,1,1]=>448
[1,8,5,2,7,3,4,10,6,9]=>[6,3,1]=>315
[1,10,5,2,7,3,9,4,6,8]=>[6,3,1]=>315
[1,10,5,2,9,8,3,4,6,7]=>[6,2,1,1]=>350
[9,8,7,6,2,3,4,5,1,10]=>[5,1,1,1,1,1]=>126
[1,8,7,6,2,3,4,10,5,9]=>[6,2,1,1]=>350
[1,10,7,6,2,3,9,4,5,8]=>[6,2,1,1]=>350
[1,10,9,6,2,8,3,4,5,7]=>[6,2,1,1]=>350
[1,10,9,8,7,2,3,4,5,6]=>[6,1,1,1,1]=>126
[3,2,5,4,7,6,9,8,11,10,1,12]=>[6,5,1]=>1155
[3,2,5,4,7,6,9,8,1,12,10,11]=>[6,5,1]=>1155
[3,2,5,4,7,6,11,10,8,9,1,12]=>[6,4,1,1]=>3080
[3,2,5,4,7,6,1,10,8,12,9,11]=>[6,5,1]=>1155
[3,2,5,4,7,6,1,12,11,8,9,10]=>[6,4,2]=>2673
[3,2,5,4,9,8,6,7,11,10,1,12]=>[6,4,1,1]=>3080
[3,2,5,4,9,8,6,7,1,12,10,11]=>[6,4,1,1]=>3080
[3,2,5,4,11,8,6,10,7,9,1,12]=>[6,4,1,1]=>3080
[3,2,5,4,1,8,6,10,7,12,9,11]=>[6,5,1]=>1155
[3,2,5,4,1,8,6,12,11,7,9,10]=>[6,4,2]=>2673
[3,2,5,4,11,10,9,6,7,8,1,12]=>[6,3,1,1,1]=>3696
[3,2,5,4,1,10,9,6,7,12,8,11]=>[6,4,2]=>2673
[3,2,5,4,1,12,9,6,11,7,8,10]=>[6,4,2]=>2673
[3,2,5,4,1,12,11,10,6,7,8,9]=>[6,3,2,1]=>5632
[3,2,7,6,4,5,9,8,11,10,1,12]=>[6,4,1,1]=>3080
[3,2,7,6,4,5,9,8,1,12,10,11]=>[6,4,1,1]=>3080
[3,2,7,6,4,5,11,10,8,9,1,12]=>[6,3,2,1]=>5632
[3,2,7,6,4,5,1,10,8,12,9,11]=>[6,4,1,1]=>3080
[3,2,7,6,4,5,1,12,11,8,9,10]=>[6,3,2,1]=>5632
[3,2,9,6,4,8,5,7,11,10,1,12]=>[6,4,1,1]=>3080
[3,2,9,6,4,8,5,7,1,12,10,11]=>[6,4,1,1]=>3080
[3,2,11,6,4,8,5,10,7,9,1,12]=>[6,4,1,1]=>3080
[3,2,1,6,4,8,5,10,7,12,9,11]=>[6,5,1]=>1155
[3,2,1,6,4,8,5,12,11,7,9,10]=>[6,4,2]=>2673
[3,2,11,6,4,10,9,5,7,8,1,12]=>[6,3,1,1,1]=>3696
[3,2,1,6,4,10,9,5,7,12,8,11]=>[6,4,2]=>2673
[3,2,1,6,4,12,9,5,11,7,8,10]=>[6,4,2]=>2673
[3,2,1,6,4,12,11,10,5,7,8,9]=>[6,3,2,1]=>5632
[3,2,9,8,7,4,5,6,11,10,1,12]=>[6,3,1,1,1]=>3696
[3,2,9,8,7,4,5,6,1,12,10,11]=>[6,3,1,1,1]=>3696
[3,2,11,8,7,4,5,10,6,9,1,12]=>[6,3,1,1,1]=>3696
[3,2,1,8,7,4,5,10,6,12,9,11]=>[6,4,2]=>2673
[3,2,1,8,7,4,5,12,11,6,9,10]=>[6,3,3]=>1650
[3,2,11,10,7,4,9,5,6,8,1,12]=>[6,3,1,1,1]=>3696
[3,2,1,10,7,4,9,5,6,12,8,11]=>[6,4,2]=>2673
[3,2,1,12,7,4,9,5,11,6,8,10]=>[6,4,2]=>2673
[3,2,1,12,7,4,11,10,5,6,8,9]=>[6,3,2,1]=>5632
[3,2,11,10,9,8,4,5,6,7,1,12]=>[6,2,1,1,1,1]=>2100
[3,2,1,10,9,8,4,5,6,12,7,11]=>[6,3,2,1]=>5632
[3,2,1,12,9,8,4,5,11,6,7,10]=>[6,3,2,1]=>5632
[3,2,1,12,11,8,4,10,5,6,7,9]=>[6,3,2,1]=>5632
[3,2,1,12,11,10,9,4,5,6,7,8]=>[6,2,2,1,1]=>3564
[5,4,2,3,7,6,9,8,11,10,1,12]=>[6,4,1,1]=>3080
[5,4,2,3,7,6,9,8,1,12,10,11]=>[6,4,1,1]=>3080
[5,4,2,3,7,6,11,10,8,9,1,12]=>[6,3,2,1]=>5632
[5,4,2,3,7,6,1,10,8,12,9,11]=>[6,4,1,1]=>3080
[5,4,2,3,7,6,1,12,11,8,9,10]=>[6,3,2,1]=>5632
[5,4,2,3,9,8,6,7,11,10,1,12]=>[6,3,2,1]=>5632
[5,4,2,3,9,8,6,7,1,12,10,11]=>[6,3,2,1]=>5632
[5,4,2,3,11,8,6,10,7,9,1,12]=>[6,3,2,1]=>5632
[5,4,2,3,1,8,6,10,7,12,9,11]=>[6,4,1,1]=>3080
[5,4,2,3,1,8,6,12,11,7,9,10]=>[6,3,2,1]=>5632
[5,4,2,3,11,10,9,6,7,8,1,12]=>[6,2,2,1,1]=>3564
[5,4,2,3,1,10,9,6,7,12,8,11]=>[6,3,2,1]=>5632
[5,4,2,3,1,12,9,6,11,7,8,10]=>[6,3,2,1]=>5632
[5,4,2,3,1,12,11,10,6,7,8,9]=>[6,2,2,2]=>1925
[7,4,2,6,3,5,9,8,11,10,1,12]=>[6,4,1,1]=>3080
[7,4,2,6,3,5,9,8,1,12,10,11]=>[6,4,1,1]=>3080
[7,4,2,6,3,5,11,10,8,9,1,12]=>[6,3,2,1]=>5632
[7,4,2,6,3,5,1,10,8,12,9,11]=>[6,4,1,1]=>3080
[7,4,2,6,3,5,1,12,11,8,9,10]=>[6,3,2,1]=>5632
[9,4,2,6,3,8,5,7,11,10,1,12]=>[6,4,1,1]=>3080
[9,4,2,6,3,8,5,7,1,12,10,11]=>[6,4,1,1]=>3080
[11,4,2,6,3,8,5,10,7,9,1,12]=>[6,4,1,1]=>3080
[1,4,2,6,3,8,5,10,7,12,9,11]=>[7,5]=>297
[1,4,2,6,3,8,5,12,11,7,9,10]=>[7,4,1]=>1408
[11,4,2,6,3,10,9,5,7,8,1,12]=>[6,3,1,1,1]=>3696
[1,4,2,6,3,10,9,5,7,12,8,11]=>[7,4,1]=>1408
[1,4,2,6,3,12,9,5,11,7,8,10]=>[7,4,1]=>1408
[1,4,2,6,3,12,11,10,5,7,8,9]=>[7,3,1,1]=>2376
[9,4,2,8,7,3,5,6,11,10,1,12]=>[6,3,1,1,1]=>3696
[9,4,2,8,7,3,5,6,1,12,10,11]=>[6,3,1,1,1]=>3696
[11,4,2,8,7,3,5,10,6,9,1,12]=>[6,3,1,1,1]=>3696
[1,4,2,8,7,3,5,10,6,12,9,11]=>[7,4,1]=>1408
[1,4,2,8,7,3,5,12,11,6,9,10]=>[7,3,2]=>1925
[11,4,2,10,7,3,9,5,6,8,1,12]=>[6,3,1,1,1]=>3696
[1,4,2,10,7,3,9,5,6,12,8,11]=>[7,4,1]=>1408
[1,4,2,12,7,3,9,5,11,6,8,10]=>[7,4,1]=>1408
[1,4,2,12,7,3,11,10,5,6,8,9]=>[7,3,1,1]=>2376
[11,4,2,10,9,8,3,5,6,7,1,12]=>[6,2,1,1,1,1]=>2100
[1,4,2,10,9,8,3,5,6,12,7,11]=>[7,3,1,1]=>2376
[1,4,2,12,9,8,3,5,11,6,7,10]=>[7,3,1,1]=>2376
[1,4,2,12,11,8,3,10,5,6,7,9]=>[7,3,1,1]=>2376
[1,4,2,12,11,10,9,3,5,6,7,8]=>[7,2,1,1,1]=>1728
[7,6,5,2,3,4,9,8,11,10,1,12]=>[6,3,1,1,1]=>3696
[7,6,5,2,3,4,9,8,1,12,10,11]=>[6,3,1,1,1]=>3696
[7,6,5,2,3,4,11,10,8,9,1,12]=>[6,2,2,1,1]=>3564
[7,6,5,2,3,4,1,10,8,12,9,11]=>[6,3,1,1,1]=>3696
[7,6,5,2,3,4,1,12,11,8,9,10]=>[6,2,2,1,1]=>3564
[9,6,5,2,3,8,4,7,11,10,1,12]=>[6,3,1,1,1]=>3696
[9,6,5,2,3,8,4,7,1,12,10,11]=>[6,3,1,1,1]=>3696
[11,6,5,2,3,8,4,10,7,9,1,12]=>[6,3,1,1,1]=>3696
[1,6,5,2,3,8,4,10,7,12,9,11]=>[7,4,1]=>1408
[1,6,5,2,3,8,4,12,11,7,9,10]=>[7,3,2]=>1925
[11,6,5,2,3,10,9,4,7,8,1,12]=>[6,2,2,1,1]=>3564
[1,6,5,2,3,10,9,4,7,12,8,11]=>[7,3,2]=>1925
[1,6,5,2,3,12,9,4,11,7,8,10]=>[7,3,2]=>1925
[1,6,5,2,3,12,11,10,4,7,8,9]=>[7,2,2,1]=>2079
[9,8,5,2,7,3,4,6,11,10,1,12]=>[6,3,1,1,1]=>3696
[9,8,5,2,7,3,4,6,1,12,10,11]=>[6,3,1,1,1]=>3696
[11,8,5,2,7,3,4,10,6,9,1,12]=>[6,3,1,1,1]=>3696
[1,8,5,2,7,3,4,10,6,12,9,11]=>[7,4,1]=>1408
[1,8,5,2,7,3,4,12,11,6,9,10]=>[7,3,2]=>1925
[11,10,5,2,7,3,9,4,6,8,1,12]=>[6,3,1,1,1]=>3696
[1,10,5,2,7,3,9,4,6,12,8,11]=>[7,4,1]=>1408
[1,12,5,2,7,3,9,4,11,6,8,10]=>[7,4,1]=>1408
[1,12,5,2,7,3,11,10,4,6,8,9]=>[7,3,1,1]=>2376
[11,10,5,2,9,8,3,4,6,7,1,12]=>[6,2,1,1,1,1]=>2100
[1,10,5,2,9,8,3,4,6,12,7,11]=>[7,3,1,1]=>2376
[1,12,5,2,9,8,3,4,11,6,7,10]=>[7,3,1,1]=>2376
[1,12,5,2,11,8,3,10,4,6,7,9]=>[7,3,1,1]=>2376
[1,12,5,2,11,10,9,3,4,6,7,8]=>[7,2,1,1,1]=>1728
[9,8,7,6,2,3,4,5,11,10,1,12]=>[6,2,1,1,1,1]=>2100
[9,8,7,6,2,3,4,5,1,12,10,11]=>[6,2,1,1,1,1]=>2100
[11,8,7,6,2,3,4,10,5,9,1,12]=>[6,2,1,1,1,1]=>2100
[1,8,7,6,2,3,4,10,5,12,9,11]=>[7,3,1,1]=>2376
[1,8,7,6,2,3,4,12,11,5,9,10]=>[7,2,2,1]=>2079
[11,10,7,6,2,3,9,4,5,8,1,12]=>[6,2,1,1,1,1]=>2100
[1,10,7,6,2,3,9,4,5,12,8,11]=>[7,3,1,1]=>2376
[1,12,7,6,2,3,9,4,11,5,8,10]=>[7,3,1,1]=>2376
[1,12,7,6,2,3,11,10,4,5,8,9]=>[7,2,2,1]=>2079
[11,10,9,6,2,8,3,4,5,7,1,12]=>[6,2,1,1,1,1]=>2100
[1,10,9,6,2,8,3,4,5,12,7,11]=>[7,3,1,1]=>2376
[1,12,9,6,2,8,3,4,11,5,7,10]=>[7,3,1,1]=>2376
[1,12,11,6,2,8,3,10,4,5,7,9]=>[7,3,1,1]=>2376
[1,12,11,6,2,10,9,3,4,5,7,8]=>[7,2,1,1,1]=>1728
[11,10,9,8,7,2,3,4,5,6,1,12]=>[6,1,1,1,1,1,1]=>462
[1,10,9,8,7,2,3,4,5,12,6,11]=>[7,2,1,1,1]=>1728
[1,12,9,8,7,2,3,4,11,5,6,10]=>[7,2,1,1,1]=>1728
[1,12,11,8,7,2,3,10,4,5,6,9]=>[7,2,1,1,1]=>1728
[1,12,11,10,7,2,9,3,4,5,6,8]=>[7,2,1,1,1]=>1728
[1,12,11,10,9,8,2,3,4,5,6,7]=>[7,1,1,1,1,1]=>462
[1,4,8,2,3,6,5,7]=>[5,2,1]=>64
[1,4,6,7,3,5,2,8]=>[5,2,1]=>64
[1,4,8,2,6,7,5,3]=>[4,2,1,1]=>90
[1,7,3,2,4,5,6,8]=>[6,1,1]=>21
[1,7,3,2,4,5,8,6]=>[5,2,1]=>64
[1,6,4,3,2,5,7,8]=>[5,1,1,1]=>35
[4,2,6,5,3,1,7,8]=>[4,2,1,1]=>90
[5,2,1,6,8,7,4,3]=>[3,2,2,1]=>70
[1,3,5,8,6,2,7,4]=>[5,2,1]=>64
[3,7,8,5,4,2,6,1]=>[3,2,1,1,1]=>64
[1,3,8,5,7,4,2,6]=>[4,2,1,1]=>90
[1,2,3,7,5,4,6,8]=>[6,1,1]=>21
[1,4,2,8,6,3,5,7]=>[5,2,1]=>64
[2,8,6,3,5,7,4,1]=>[4,1,1,1,1]=>35
[6,1,8,2,5,3,4,7]=>[5,2,1]=>64
[1,5,4,2,3,6,8,7]=>[5,2,1]=>64
[3,1,2,4,8,6,7,5]=>[5,2,1]=>64
[3,1,2,5,8,7,4,6]=>[4,3,1]=>70
[6,5,2,1,8,4,7,3]=>[3,2,2,1]=>70
[5,1,4,7,3,2,8,6]=>[4,2,1,1]=>90
[4,1,5,8,6,2,3,7]=>[4,3,1]=>70
[6,5,2,3,1,8,7,4]=>[3,2,2,1]=>70
[2,5,3,6,1,8,4,7]=>[4,3,1]=>70
[2,5,6,8,3,1,7,4]=>[4,2,2]=>56
[7,1,4,5,3,6,2,8]=>[5,1,1,1]=>35
[1,7,2,4,5,3,6,8]=>[6,1,1]=>21
[1,7,4,5,3,2,6,8]=>[5,1,1,1]=>35
[1,6,4,7,3,5,2,8]=>[4,2,1,1]=>90
[3,5,6,4,8,2,1,7]=>[4,2,1,1]=>90
[1,6,4,7,5,2,3,8]=>[4,2,2]=>56
[1,5,2,6,7,4,3,8]=>[5,2,1]=>64
[8,5,6,1,4,3,7,2]=>[3,2,1,1,1]=>64
[2,5,4,7,8,3,1,6]=>[4,2,1,1]=>90
[6,4,5,8,2,3,1,7]=>[3,3,1,1]=>56
[8,6,1,3,2,5,7,4]=>[4,2,1,1]=>90
[7,5,8,1,4,6,3,2]=>[3,2,1,1,1]=>64
[4,2,6,7,8,1,5,3]=>[4,2,2]=>56
[3,4,6,7,8,1,5,2]=>[5,2,1]=>64
[4,7,3,8,5,1,6,2]=>[3,3,2]=>42
[4,3,2,7,5,8,1,6]=>[3,3,1,1]=>56
[4,8,5,3,2,6,1,7]=>[4,1,1,1,1]=>35
[2,8,4,5,3,6,1,7]=>[5,1,1,1]=>35
[8,1,5,3,2,4,7,6]=>[4,2,1,1]=>90
[7,8,4,1,3,6,5,2]=>[3,2,2,1]=>70
[8,6,1,3,2,7,4,5]=>[4,2,1,1]=>90
[6,2,3,7,8,1,5,4]=>[4,2,2]=>56
[6,3,7,8,1,5,4,2]=>[3,2,2,1]=>70
[2,6,3,7,8,1,5,4]=>[4,2,2]=>56
[7,5,8,1,6,4,2,3]=>[3,2,2,1]=>70
[8,1,4,3,7,5,6,2]=>[4,2,1,1]=>90
[1,4,8,5,3,2,6,7]=>[5,1,1,1]=>35
[8,2,7,6,4,1,5,3]=>[3,2,1,1,1]=>64
[2,7,4,3,8,5,1,6]=>[4,2,1,1]=>90
[6,8,2,7,3,1,5,4]=>[3,2,2,1]=>70
[8,2,6,3,4,1,7,5]=>[4,2,1,1]=>90
[6,1,2,8,5,3,7,4]=>[4,2,2]=>56
[4,1,5,8,3,6,7,2]=>[4,3,1]=>70
[7,5,2,8,1,6,3,4]=>[3,2,2,1]=>70
[3,4,7,2,1,5,8,6]=>[4,3,1]=>70
[4,8,2,7,1,3,6,5]=>[3,2,2,1]=>70
[8,2,1,7,4,6,3,5]=>[3,3,1,1]=>56
[4,2,5,8,3,6,7,1]=>[4,3,1]=>70
[5,1,6,8,3,2,7,4]=>[3,3,2]=>42
[4,1,5,6,8,2,7,3]=>[4,3,1]=>70
[4,5,2,8,7,3,1,6]=>[3,3,1,1]=>56
[4,8,5,3,1,6,7,2]=>[4,2,1,1]=>90
[6,2,3,1,7,8,5,4]=>[4,2,2]=>56
[5,2,3,6,8,4,7,1]=>[4,3,1]=>70
[6,2,1,7,8,4,3,5]=>[3,3,2]=>42
[5,2,1,3,8,4,7,6]=>[4,2,2]=>56
[5,2,7,8,4,1,6,3]=>[3,3,2]=>42
[6,2,7,8,3,5,4,1]=>[3,3,1,1]=>56
[5,2,8,6,4,1,7,3]=>[3,2,2,1]=>70
[5,1,2,8,4,3,7,6]=>[4,2,2]=>56
[6,7,8,3,2,5,4,1]=>[3,2,2,1]=>70
[5,7,2,6,4,8,1,3]=>[3,2,2,1]=>70
[6,2,3,4,7,8,5,1]=>[5,2,1]=>64
[7,2,1,8,4,3,5,6]=>[4,2,2]=>56
[6,2,1,3,7,5,8,4]=>[4,2,2]=>56
[6,8,7,3,4,5,1,2]=>[3,2,2,1]=>70
[6,2,3,7,8,1,4,5]=>[4,3,1]=>70
[7,4,3,2,5,8,1,6]=>[3,2,1,1,1]=>64
[7,2,4,3,5,8,1,6]=>[4,2,1,1]=>90
[1,7,6,4,2,3,5,8]=>[5,1,1,1]=>35
[1,3,2,5,8,6,4,7]=>[5,2,1]=>64
[6,1,4,7,2,8,5,3]=>[4,2,2]=>56
[1,6,7,2,4,8,5,3]=>[4,3,1]=>70
[5,7,2,4,3,6,8,1]=>[4,2,1,1]=>90
[5,7,3,4,6,2,8,1]=>[4,2,1,1]=>90
[2,8,3,6,1,7,4,5]=>[4,3,1]=>70
[4,3,1,8,5,2,6,7]=>[4,2,2]=>56
[1,8,4,5,6,2,7,3]=>[5,2,1]=>64
[7,3,8,2,1,4,5,6]=>[4,2,1,1]=>90
[8,2,5,3,1,7,4,6]=>[4,2,1,1]=>90
[6,3,5,8,1,7,4,2]=>[3,2,2,1]=>70
[3,5,4,8,6,1,7,2]=>[4,2,2]=>56
[7,5,2,3,8,4,6,1]=>[4,2,1,1]=>90
[2,7,5,1,4,8,3,6]=>[3,3,1,1]=>56
[5,7,6,1,2,8,3,4]=>[4,3,1]=>70
[7,4,6,5,1,8,2,3]=>[3,3,1,1]=>56
[7,1,3,2,6,8,4,5]=>[4,3,1]=>70
[4,3,5,2,8,1,6,7]=>[4,2,1,1]=>90
[1,7,3,8,2,4,6,5]=>[4,2,2]=>56
[2,7,4,8,5,3,1,6]=>[4,2,1,1]=>90
[6,1,3,8,4,2,7,5]=>[4,2,2]=>56
[5,4,1,8,6,2,7,3]=>[3,3,2]=>42
[5,4,6,8,1,3,2,7]=>[3,3,1,1]=>56
[3,6,1,5,8,4,7,2]=>[3,3,1,1]=>56
[6,4,8,3,5,7,2,1]=>[3,2,1,1,1]=>64
[3,5,8,2,4,1,7,6]=>[3,3,2]=>42
[7,2,8,4,1,3,6,5]=>[3,3,2]=>42
[5,8,1,2,4,3,6,7]=>[5,2,1]=>64
[8,4,3,5,7,2,6,1]=>[3,2,1,1,1]=>64
[4,1,5,2,3,8,7,6]=>[4,3,1]=>70
[6,3,5,8,2,4,7,1]=>[3,3,1,1]=>56
[2,8,7,1,4,6,3,5]=>[3,3,1,1]=>56
[1,8,5,3,7,4,2,6]=>[4,2,1,1]=>90
[7,5,6,2,8,4,3,1]=>[3,2,1,1,1]=>64
[5,7,6,2,8,1,4,3]=>[3,2,2,1]=>70
[6,3,8,1,2,5,4,7]=>[4,2,2]=>56
[7,6,4,8,5,3,2,1]=>[2,2,1,1,1,1]=>20
[8,6,9,7,5,4,3,2,1]=>[2,2,1,1,1,1,1]=>27
[3,2,5,4,7,6,1,10,9,8]=>[4,4,2]=>252
[3,2,5,4,9,8,7,6,1,10]=>[4,3,1,1,1]=>525
[3,2,5,4,1,8,7,10,9,6]=>[4,4,2]=>252
[3,2,5,4,1,10,9,8,7,6]=>[3,3,2,1,1]=>450
[3,2,7,6,5,4,9,8,1,10]=>[4,3,1,1,1]=>525
[3,2,7,6,5,4,1,10,9,8]=>[3,3,2,1,1]=>450
[3,2,9,6,5,8,7,4,1,10]=>[4,3,1,1,1]=>525
[3,2,1,6,5,8,7,10,9,4]=>[4,4,2]=>252
[3,2,1,6,5,10,9,8,7,4]=>[3,3,2,1,1]=>450
[3,2,1,8,7,6,5,10,9,4]=>[3,3,2,1,1]=>450
[3,2,1,10,7,6,9,8,5,4]=>[3,3,2,1,1]=>450
[5,4,3,2,7,6,9,8,1,10]=>[4,3,1,1,1]=>525
[5,4,3,2,7,6,1,10,9,8]=>[3,3,2,1,1]=>450
[5,4,3,2,9,8,7,6,1,10]=>[3,2,2,2,1]=>288
[5,4,3,2,1,8,7,10,9,6]=>[3,3,2,1,1]=>450
[7,4,3,6,5,2,9,8,1,10]=>[4,3,1,1,1]=>525
[7,4,3,6,5,2,1,10,9,8]=>[3,3,2,1,1]=>450
[9,4,3,6,5,8,7,2,1,10]=>[4,3,1,1,1]=>525
[1,4,3,6,5,8,7,10,9,2]=>[5,4,1]=>288
[1,4,3,6,5,10,9,8,7,2]=>[4,3,1,1,1]=>525
[9,4,3,8,7,6,5,2,1,10]=>[3,2,1,1,1,1,1]=>160
[1,4,3,8,7,6,5,10,9,2]=>[4,3,1,1,1]=>525
[1,4,3,10,7,6,9,8,5,2]=>[4,3,1,1,1]=>525
[1,4,3,10,9,8,7,6,5,2]=>[3,2,1,1,1,1,1]=>160
[7,6,5,4,3,2,9,8,1,10]=>[3,2,1,1,1,1,1]=>160
[9,6,5,4,3,8,7,2,1,10]=>[3,2,1,1,1,1,1]=>160
[1,6,5,4,3,8,7,10,9,2]=>[4,3,1,1,1]=>525
[1,6,5,4,3,10,9,8,7,2]=>[3,2,2,2,1]=>288
[9,8,5,4,7,6,3,2,1,10]=>[3,2,1,1,1,1,1]=>160
[1,8,5,4,7,6,3,10,9,2]=>[4,3,1,1,1]=>525
[1,10,5,4,7,6,9,8,3,2]=>[4,3,1,1,1]=>525
[1,10,5,4,9,8,7,6,3,2]=>[3,2,1,1,1,1,1]=>160
[1,10,7,6,5,4,9,8,3,2]=>[3,2,1,1,1,1,1]=>160
[1,10,9,6,5,8,7,4,3,2]=>[3,2,1,1,1,1,1]=>160
[3,2,5,4,7,6,9,8,1,12,11,10]=>[5,5,2]=>1320
[3,2,5,4,7,6,11,10,9,8,1,12]=>[5,4,1,1,1]=>3520
[3,2,5,4,7,6,1,10,9,12,11,8]=>[5,5,2]=>1320
[3,2,5,4,7,6,1,12,11,10,9,8]=>[4,4,2,1,1]=>4455
[3,2,5,4,9,8,7,6,11,10,1,12]=>[5,4,1,1,1]=>3520
[3,2,5,4,9,8,7,6,1,12,11,10]=>[4,4,2,1,1]=>4455
[3,2,5,4,11,8,7,10,9,6,1,12]=>[5,4,1,1,1]=>3520
[3,2,5,4,1,8,7,10,9,12,11,6]=>[5,5,2]=>1320
[3,2,5,4,1,8,7,12,11,10,9,6]=>[4,4,2,1,1]=>4455
[3,2,5,4,11,10,9,8,7,6,1,12]=>[4,3,1,1,1,1,1]=>2079
[3,2,5,4,1,10,9,8,7,12,11,6]=>[4,4,2,1,1]=>4455
[3,2,5,4,1,12,9,8,11,10,7,6]=>[4,4,2,1,1]=>4455
[3,2,5,4,1,12,11,10,9,8,7,6]=>[3,3,2,1,1,1,1]=>1925
[3,2,7,6,5,4,9,8,11,10,1,12]=>[5,4,1,1,1]=>3520
[3,2,7,6,5,4,9,8,1,12,11,10]=>[4,4,2,1,1]=>4455
[3,2,7,6,5,4,11,10,9,8,1,12]=>[4,3,2,2,1]=>5775
[3,2,7,6,5,4,1,10,9,12,11,8]=>[4,4,2,1,1]=>4455
[3,2,7,6,5,4,1,12,11,10,9,8]=>[3,3,2,2,2]=>1320
[3,2,9,6,5,8,7,4,11,10,1,12]=>[5,4,1,1,1]=>3520
[3,2,9,6,5,8,7,4,1,12,11,10]=>[4,4,2,1,1]=>4455
[3,2,11,6,5,8,7,10,9,4,1,12]=>[5,4,1,1,1]=>3520
[3,2,1,6,5,8,7,10,9,12,11,4]=>[5,5,2]=>1320
[3,2,1,6,5,8,7,12,11,10,9,4]=>[4,4,2,1,1]=>4455
[3,2,11,6,5,10,9,8,7,4,1,12]=>[4,3,1,1,1,1,1]=>2079
[3,2,1,6,5,10,9,8,7,12,11,4]=>[4,4,2,1,1]=>4455
[3,2,1,6,5,12,9,8,11,10,7,4]=>[4,4,2,1,1]=>4455
[3,2,1,6,5,12,11,10,9,8,7,4]=>[3,3,2,1,1,1,1]=>1925
[3,2,9,8,7,6,5,4,11,10,1,12]=>[4,3,1,1,1,1,1]=>2079
[3,2,9,8,7,6,5,4,1,12,11,10]=>[3,3,2,1,1,1,1]=>1925
[3,2,11,8,7,6,5,10,9,4,1,12]=>[4,3,1,1,1,1,1]=>2079
[3,2,1,8,7,6,5,10,9,12,11,4]=>[4,4,2,1,1]=>4455
[3,2,1,8,7,6,5,12,11,10,9,4]=>[3,3,3,2,1]=>2112
[3,2,11,10,7,6,9,8,5,4,1,12]=>[4,3,1,1,1,1,1]=>2079
[3,2,1,10,7,6,9,8,5,12,11,4]=>[4,4,2,1,1]=>4455
[3,2,1,12,7,6,9,8,11,10,5,4]=>[4,4,2,1,1]=>4455
[3,2,1,12,7,6,11,10,9,8,5,4]=>[3,3,2,1,1,1,1]=>1925
[3,2,11,10,9,8,7,6,5,4,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[3,2,1,10,9,8,7,6,5,12,11,4]=>[3,3,2,1,1,1,1]=>1925
[3,2,1,12,9,8,7,6,11,10,5,4]=>[3,3,2,1,1,1,1]=>1925
[3,2,1,12,11,8,7,10,9,6,5,4]=>[3,3,2,1,1,1,1]=>1925
[3,2,1,12,11,10,9,8,7,6,5,4]=>[2,2,2,1,1,1,1,1,1]=>154
[5,4,3,2,7,6,9,8,11,10,1,12]=>[5,4,1,1,1]=>3520
[5,4,3,2,7,6,9,8,1,12,11,10]=>[4,4,2,1,1]=>4455
[5,4,3,2,7,6,11,10,9,8,1,12]=>[4,3,2,2,1]=>5775
[5,4,3,2,7,6,1,10,9,12,11,8]=>[4,4,2,1,1]=>4455
[5,4,3,2,7,6,1,12,11,10,9,8]=>[3,3,2,2,2]=>1320
[5,4,3,2,9,8,7,6,11,10,1,12]=>[4,3,2,2,1]=>5775
[5,4,3,2,9,8,7,6,1,12,11,10]=>[3,3,3,2,1]=>2112
[5,4,3,2,11,8,7,10,9,6,1,12]=>[4,3,2,2,1]=>5775
[5,4,3,2,1,8,7,10,9,12,11,6]=>[4,4,2,1,1]=>4455
[5,4,3,2,1,8,7,12,11,10,9,6]=>[3,3,2,2,2]=>1320
[5,4,3,2,11,10,9,8,7,6,1,12]=>[3,2,2,2,1,1,1]=>1408
[5,4,3,2,1,10,9,8,7,12,11,6]=>[3,3,2,2,2]=>1320
[5,4,3,2,1,12,9,8,11,10,7,6]=>[3,3,2,2,2]=>1320
[5,4,3,2,1,12,11,10,9,8,7,6]=>[2,2,2,2,2,1,1]=>297
[7,4,3,6,5,2,9,8,11,10,1,12]=>[5,4,1,1,1]=>3520
[7,4,3,6,5,2,9,8,1,12,11,10]=>[4,4,2,1,1]=>4455
[7,4,3,6,5,2,11,10,9,8,1,12]=>[4,3,2,2,1]=>5775
[7,4,3,6,5,2,1,10,9,12,11,8]=>[4,4,2,1,1]=>4455
[7,4,3,6,5,2,1,12,11,10,9,8]=>[3,3,2,2,2]=>1320
[9,4,3,6,5,8,7,2,11,10,1,12]=>[5,4,1,1,1]=>3520
[9,4,3,6,5,8,7,2,1,12,11,10]=>[4,4,2,1,1]=>4455
[11,4,3,6,5,8,7,10,9,2,1,12]=>[5,4,1,1,1]=>3520
[1,4,3,6,5,8,7,10,9,12,11,2]=>[6,5,1]=>1155
[1,4,3,6,5,8,7,12,11,10,9,2]=>[5,4,1,1,1]=>3520
[11,4,3,6,5,10,9,8,7,2,1,12]=>[4,3,1,1,1,1,1]=>2079
[1,4,3,6,5,10,9,8,7,12,11,2]=>[5,4,1,1,1]=>3520
[1,4,3,6,5,12,9,8,11,10,7,2]=>[5,4,1,1,1]=>3520
[1,4,3,6,5,12,11,10,9,8,7,2]=>[4,3,1,1,1,1,1]=>2079
[9,4,3,8,7,6,5,2,11,10,1,12]=>[4,3,1,1,1,1,1]=>2079
[9,4,3,8,7,6,5,2,1,12,11,10]=>[3,3,2,1,1,1,1]=>1925
[11,4,3,8,7,6,5,10,9,2,1,12]=>[4,3,1,1,1,1,1]=>2079
[1,4,3,8,7,6,5,10,9,12,11,2]=>[5,4,1,1,1]=>3520
[1,4,3,8,7,6,5,12,11,10,9,2]=>[4,3,2,2,1]=>5775
[11,4,3,10,7,6,9,8,5,2,1,12]=>[4,3,1,1,1,1,1]=>2079
[1,4,3,10,7,6,9,8,5,12,11,2]=>[5,4,1,1,1]=>3520
[1,4,3,12,7,6,9,8,11,10,5,2]=>[5,4,1,1,1]=>3520
[1,4,3,12,7,6,11,10,9,8,5,2]=>[4,3,1,1,1,1,1]=>2079
[11,4,3,10,9,8,7,6,5,2,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[1,4,3,10,9,8,7,6,5,12,11,2]=>[4,3,1,1,1,1,1]=>2079
[1,4,3,12,9,8,7,6,11,10,5,2]=>[4,3,1,1,1,1,1]=>2079
[1,4,3,12,11,8,7,10,9,6,5,2]=>[4,3,1,1,1,1,1]=>2079
[1,4,3,12,11,10,9,8,7,6,5,2]=>[3,2,1,1,1,1,1,1,1]=>320
[7,6,5,4,3,2,9,8,11,10,1,12]=>[4,3,1,1,1,1,1]=>2079
[7,6,5,4,3,2,9,8,1,12,11,10]=>[3,3,2,1,1,1,1]=>1925
[7,6,5,4,3,2,11,10,9,8,1,12]=>[3,2,2,2,1,1,1]=>1408
[7,6,5,4,3,2,1,10,9,12,11,8]=>[3,3,2,1,1,1,1]=>1925
[7,6,5,4,3,2,1,12,11,10,9,8]=>[2,2,2,2,2,1,1]=>297
[9,6,5,4,3,8,7,2,11,10,1,12]=>[4,3,1,1,1,1,1]=>2079
[9,6,5,4,3,8,7,2,1,12,11,10]=>[3,3,2,1,1,1,1]=>1925
[11,6,5,4,3,8,7,10,9,2,1,12]=>[4,3,1,1,1,1,1]=>2079
[1,6,5,4,3,8,7,10,9,12,11,2]=>[5,4,1,1,1]=>3520
[1,6,5,4,3,8,7,12,11,10,9,2]=>[4,3,2,2,1]=>5775
[11,6,5,4,3,10,9,8,7,2,1,12]=>[3,2,2,2,1,1,1]=>1408
[1,6,5,4,3,10,9,8,7,12,11,2]=>[4,3,2,2,1]=>5775
[1,6,5,4,3,12,9,8,11,10,7,2]=>[4,3,2,2,1]=>5775
[1,6,5,4,3,12,11,10,9,8,7,2]=>[3,2,2,2,1,1,1]=>1408
[9,8,5,4,7,6,3,2,11,10,1,12]=>[4,3,1,1,1,1,1]=>2079
[9,8,5,4,7,6,3,2,1,12,11,10]=>[3,3,2,1,1,1,1]=>1925
[11,8,5,4,7,6,3,10,9,2,1,12]=>[4,3,1,1,1,1,1]=>2079
[1,8,5,4,7,6,3,10,9,12,11,2]=>[5,4,1,1,1]=>3520
[1,8,5,4,7,6,3,12,11,10,9,2]=>[4,3,2,2,1]=>5775
[11,10,5,4,7,6,9,8,3,2,1,12]=>[4,3,1,1,1,1,1]=>2079
[1,10,5,4,7,6,9,8,3,12,11,2]=>[5,4,1,1,1]=>3520
[1,12,5,4,7,6,9,8,11,10,3,2]=>[5,4,1,1,1]=>3520
[1,12,5,4,7,6,11,10,9,8,3,2]=>[4,3,1,1,1,1,1]=>2079
[11,10,5,4,9,8,7,6,3,2,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[1,10,5,4,9,8,7,6,3,12,11,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,5,4,9,8,7,6,11,10,3,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,5,4,11,8,7,10,9,6,3,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,5,4,11,10,9,8,7,6,3,2]=>[3,2,1,1,1,1,1,1,1]=>320
[9,8,7,6,5,4,3,2,11,10,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[9,8,7,6,5,4,3,2,1,12,11,10]=>[2,2,2,1,1,1,1,1,1]=>154
[11,8,7,6,5,4,3,10,9,2,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[1,8,7,6,5,4,3,10,9,12,11,2]=>[4,3,1,1,1,1,1]=>2079
[1,8,7,6,5,4,3,12,11,10,9,2]=>[3,2,2,2,1,1,1]=>1408
[11,10,7,6,5,4,9,8,3,2,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[1,10,7,6,5,4,9,8,3,12,11,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,7,6,5,4,9,8,11,10,3,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,7,6,5,4,11,10,9,8,3,2]=>[3,2,2,2,1,1,1]=>1408
[11,10,9,6,5,8,7,4,3,2,1,12]=>[3,2,1,1,1,1,1,1,1]=>320
[1,10,9,6,5,8,7,4,3,12,11,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,9,6,5,8,7,4,11,10,3,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,11,6,5,8,7,10,9,4,3,2]=>[4,3,1,1,1,1,1]=>2079
[1,12,11,6,5,10,9,8,7,4,3,2]=>[3,2,1,1,1,1,1,1,1]=>320
[11,10,9,8,7,6,5,4,3,2,1,12]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[1,10,9,8,7,6,5,4,3,12,11,2]=>[3,2,1,1,1,1,1,1,1]=>320
[1,12,9,8,7,6,5,4,11,10,3,2]=>[3,2,1,1,1,1,1,1,1]=>320
[1,12,11,8,7,6,5,10,9,4,3,2]=>[3,2,1,1,1,1,1,1,1]=>320
[1,12,11,10,7,6,9,8,5,4,3,2]=>[3,2,1,1,1,1,1,1,1]=>320
[1,12,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[1,5,7,2,4,3,6,8]=>[5,2,1]=>64
[1,6,5,3,2,4,7,8]=>[5,1,1,1]=>35
[1,7,2,4,6,5,3,8]=>[5,1,1,1]=>35
[1,4,7,2,6,5,3,8]=>[4,2,1,1]=>90
[1,2,6,8,7,4,3,5]=>[4,2,1,1]=>90
[1,2,7,4,3,5,8,6]=>[5,2,1]=>64
[1,6,2,8,7,4,3,5]=>[4,2,1,1]=>90
[1,7,4,2,3,5,8,6]=>[5,2,1]=>64
[1,8,5,2,3,6,4,7]=>[5,2,1]=>64
[1,7,4,8,5,2,3,6]=>[4,2,2]=>56
[1,4,7,5,2,8,6,3]=>[4,2,2]=>56
[1,6,3,7,4,2,8,5]=>[4,3,1]=>70
[1,8,5,2,7,4,3,6]=>[4,2,1,1]=>90
[1,4,8,7,5,3,2,6]=>[4,1,1,1,1]=>35
[1,2,5,8,6,3,7,4]=>[5,2,1]=>64
[1,2,4,7,5,8,6,3]=>[5,2,1]=>64
[1,5,8,7,6,2,4,3]=>[3,2,1,1,1]=>64
[1,3,5,8,7,6,2,4]=>[4,2,1,1]=>90
[1,5,2,4,3,6,8,7]=>[5,2,1]=>64
[1,6,8,7,5,3,2,4]=>[3,2,1,1,1]=>64
[1,2,5,7,4,3,8,6]=>[5,2,1]=>64
[1,5,3,2,6,8,7,4]=>[4,2,2]=>56
[1,4,2,6,8,7,5,3]=>[4,2,1,1]=>90
[1,5,8,6,3,2,7,4]=>[4,2,1,1]=>90
[1,8,5,2,6,3,4,7]=>[5,2,1]=>64
[1,7,4,6,3,2,8,5]=>[4,2,1,1]=>90
[1,6,3,2,8,5,4,7]=>[4,2,2]=>56
[1,3,8,6,4,2,5,7]=>[5,1,1,1]=>35
[1,5,7,4,2,3,8,6]=>[4,3,1]=>70
[6,3,7,5,4,2,8,1]=>[3,2,1,1,1]=>64
[7,5,2,6,3,4,8,1]=>[4,2,1,1]=>90
[3,8,2,7,5,4,1,6]=>[3,2,1,1,1]=>64
[5,4,8,6,7,1,2,3]=>[3,3,2]=>42
[2,7,3,6,8,5,4,1]=>[4,1,1,1,1]=>35
[3,7,2,8,1,6,4,5]=>[3,3,2]=>42
[8,5,2,4,6,7,3,1]=>[4,1,1,1,1]=>35
[2,5,8,7,1,4,3,6]=>[3,3,1,1]=>56
[3,4,6,5,8,2,7,1]=>[4,2,1,1]=>90
[5,2,4,1,6,7,8,3]=>[5,2,1]=>64
[4,2,7,1,6,8,3,5]=>[3,3,2]=>42
[5,2,8,6,4,7,1,3]=>[3,2,2,1]=>70
[6,1,3,4,7,2,8,5]=>[5,2,1]=>64
[8,4,7,2,5,3,1,6]=>[3,2,1,1,1]=>64
[8,3,4,5,2,1,7,6]=>[4,2,1,1]=>90
[8,6,1,4,7,3,5,2]=>[3,2,1,1,1]=>64
[5,3,6,7,2,8,4,1]=>[4,2,1,1]=>90
[5,3,6,7,2,4,8,1]=>[4,2,1,1]=>90
[8,6,1,4,7,5,2,3]=>[3,2,2,1]=>70
[1,5,8,2,6,7,4,3]=>[4,2,1,1]=>90
[7,1,3,6,5,2,8,4]=>[4,2,1,1]=>90
[8,2,1,4,5,7,6,3]=>[4,2,1,1]=>90
[1,4,7,5,2,3,8,6]=>[4,3,1]=>70
[6,1,7,5,4,2,8,3]=>[3,3,1,1]=>56
[2,7,3,6,5,1,8,4]=>[4,2,1,1]=>90
[8,6,5,1,3,7,4,2]=>[3,2,1,1,1]=>64
[5,7,6,2,4,8,1,3]=>[3,2,2,1]=>70
[3,7,5,6,4,8,1,2]=>[4,2,1,1]=>90
[7,6,8,1,3,5,4,2]=>[3,2,1,1,1]=>64
[2,8,4,6,1,7,5,3]=>[4,2,1,1]=>90
[2,8,6,4,7,3,5,1]=>[3,2,1,1,1]=>64
[8,7,1,4,6,5,3,2]=>[3,1,1,1,1,1]=>21
[3,5,8,6,7,1,4,2]=>[4,2,1,1]=>90
[1,2,4,6,8,5,3,7]=>[5,2,1]=>64
[3,1,5,8,6,2,4,7]=>[4,3,1]=>70
[2,5,4,6,8,1,3,7]=>[4,3,1]=>70
[6,5,2,4,7,8,1,3]=>[4,2,1,1]=>90
[7,2,5,8,6,4,1,3]=>[3,2,2,1]=>70
[5,2,8,3,4,7,6,1]=>[4,2,1,1]=>90
[2,4,3,8,7,1,6,5]=>[3,2,2,1]=>70
[1,5,8,7,4,2,6,3]=>[3,2,2,1]=>70
[6,8,7,5,4,3,1,2]=>[2,2,1,1,1,1]=>20
[5,6,4,7,3,8,2,9,1]=>[5,1,1,1,1]=>70
[5,6,4,7,3,9,2,8,1]=>[4,2,1,1,1]=>189
[5,3,4,8,6,2,7,1]=>[4,2,1,1]=>90
[5,4,6,3,7,2,8,1,9]=>[5,1,1,1,1]=>70
[6,5,7,4,8,3,9,2,10,1]=>[5,1,1,1,1,1]=>126
[6,5,7,4,8,3,10,2,9,1]=>[4,2,1,1,1,1]=>350
[5,6,4,7,3,8,2,9,1,10]=>[6,1,1,1,1]=>126
[5,4,2,3,6,1,8,7]=>[4,2,1,1]=>90
[4,3,7,6,8,2,1,5]=>[3,2,2,1]=>70
[8,1,4,7,2,3,5,6]=>[5,2,1]=>64
[6,1,8,5,2,7,3,4]=>[4,2,2]=>56
[8,7,2,6,3,1,4,5]=>[4,1,1,1,1]=>35
[8,7,1,6,4,5,2,3]=>[3,2,1,1,1]=>64
[5,4,1,3,7,2,8,6]=>[4,2,1,1]=>90
[3,1,8,7,5,2,4,6]=>[4,2,1,1]=>90
[4,3,6,5,8,2,1,7]=>[3,3,1,1]=>56
[7,6,3,2,8,5,4,1]=>[2,2,2,1,1]=>28
[4,3,7,1,8,5,2,6]=>[3,3,2]=>42
[3,2,8,5,6,7,1,4]=>[4,2,2]=>56
[8,3,2,1,4,7,5,6]=>[4,2,1,1]=>90
[4,7,3,1,8,5,2,6]=>[3,3,2]=>42
[3,7,8,2,5,6,1,4]=>[3,3,2]=>42
[7,5,1,4,2,3,6,8]=>[5,1,1,1]=>35
[7,8,6,1,2,4,5,3]=>[4,2,1,1]=>90
[1,5,3,4,7,8,6,2]=>[5,2,1]=>64
[5,1,2,4,7,8,6,3]=>[5,2,1]=>64
[5,1,7,8,6,2,3,4]=>[4,3,1]=>70
[8,5,1,6,7,2,3,4]=>[4,3,1]=>70
[7,5,1,2,4,6,8,3]=>[5,1,1,1]=>35
[6,1,5,2,7,3,4,8]=>[5,2,1]=>64
[7,1,2,6,4,5,8,3]=>[5,1,1,1]=>35
[1,7,3,6,4,5,8,2]=>[5,1,1,1]=>35
[1,8,3,6,4,5,7,2]=>[5,1,1,1]=>35
[8,1,6,2,7,3,4,5]=>[5,2,1]=>64
[7,1,6,2,5,3,4,8]=>[5,1,1,1]=>35
[8,1,6,2,5,3,4,7]=>[5,1,1,1]=>35
[8,1,7,2,5,3,4,6]=>[5,1,1,1]=>35
[8,1,2,7,4,5,6,3]=>[5,1,1,1]=>35
[1,8,3,7,4,5,6,2]=>[5,1,1,1]=>35
[8,1,6,7,5,2,3,4]=>[4,2,1,1]=>90
[7,3,1,2,6,4,5,8]=>[5,2,1]=>64
[3,1,2,8,5,6,7,4]=>[5,2,1]=>64
[6,3,1,2,7,4,5,8]=>[5,2,1]=>64
[6,1,7,4,2,3,5,8]=>[5,2,1]=>64
[1,7,3,4,6,8,5,2]=>[5,1,1,1]=>35
[1,7,3,8,4,5,6,2]=>[5,2,1]=>64
[7,1,8,2,5,3,4,6]=>[5,2,1]=>64
[6,1,7,2,5,3,4,8]=>[5,2,1]=>64
[5,1,7,2,6,3,4,8]=>[5,2,1]=>64
[5,1,8,2,6,3,4,7]=>[5,2,1]=>64
[1,6,3,7,4,5,8,2]=>[5,2,1]=>64
[2,4,7,3,5,1,6,8]=>[5,2,1]=>64
[2,4,8,6,3,5,1,7]=>[4,2,1,1]=>90
[2,3,7,5,4,1,6,8]=>[5,1,1,1]=>35
[3,4,6,2,1,5,8,7]=>[4,3,1]=>70
[3,4,7,2,1,6,5,8]=>[4,2,2]=>56
[2,3,6,1,5,8,4,7]=>[4,3,1]=>70
[2,3,7,1,6,5,8,4]=>[4,2,1,1]=>90
[2,4,7,1,3,6,8,5]=>[4,3,1]=>70
[5,4,7,8,1,3,2,6]=>[3,3,1,1]=>56
[2,5,7,1,4,6,3,8]=>[4,3,1]=>70
[2,4,7,1,6,3,5,8]=>[4,3,1]=>70
[2,3,7,1,6,5,4,8]=>[4,2,1,1]=>90
[2,5,7,1,4,3,6,8]=>[4,3,1]=>70
[2,5,7,3,1,4,6,8]=>[5,2,1]=>64
[3,4,7,2,1,6,8,5]=>[4,2,2]=>56
[4,6,3,7,1,5,2,8]=>[4,2,2]=>56
[5,7,3,2,8,1,4,6]=>[3,3,1,1]=>56
[2,6,5,7,1,8,4,3]=>[4,2,1,1]=>90
[3,6,8,5,4,1,7,2]=>[3,2,2,1]=>70
[5,4,7,8,1,3,6,2]=>[3,3,1,1]=>56
[2,5,7,1,4,6,8,3]=>[4,3,1]=>70
[2,4,7,1,6,3,8,5]=>[4,3,1]=>70
[2,4,7,1,6,8,3,5]=>[4,3,1]=>70
[1,8,3,4,5,6,7,9,2]=>[7,1,1]=>28
[7,2,3,4,5,6,1,9,8]=>[6,2,1]=>105
[2,1,9,4,5,6,7,8,3]=>[6,2,1]=>105
[2,8,3,4,5,6,7,1,9]=>[7,1,1]=>28
[8,6,5,1,2,4,3,7]=>[4,1,1,1,1]=>35
[7,6,1,4,2,3,5,8]=>[5,1,1,1]=>35
[6,5,1,4,8,3,2,7]=>[3,2,1,1,1]=>64
[8,7,5,1,4,2,3,6]=>[4,1,1,1,1]=>35
[8,4,1,2,5,3,6,7]=>[5,2,1]=>64
[8,6,1,4,2,5,3,7]=>[4,2,1,1]=>90
[8,7,1,4,3,2,6,5]=>[3,2,1,1,1]=>64
[2,8,3,7,4,5,6,1]=>[5,1,1,1]=>35
[8,7,5,2,4,3,6,1]=>[3,1,1,1,1,1]=>21
[4,2,5,7,3,1,6,8]=>[4,3,1]=>70
[8,2,4,5,3,1,6,7]=>[5,1,1,1]=>35
[8,4,5,1,3,2,6,7]=>[4,2,1,1]=>90
[4,3,7,5,2,1,6,8]=>[4,2,1,1]=>90
[1,6,7,4,3,2,5,8]=>[4,2,1,1]=>90
[1,4,5,7,3,2,6,8]=>[5,2,1]=>64
[3,5,1,4,7,2,6,8]=>[4,3,1]=>70
[2,5,1,4,7,8,3,6]=>[4,3,1]=>70
[4,3,7,1,5,2,6,8]=>[4,2,2]=>56
[3,5,1,6,4,2,7,8]=>[5,2,1]=>64
[6,4,3,1,7,2,5,8]=>[4,2,1,1]=>90
[6,2,7,4,3,1,5,8]=>[4,2,1,1]=>90
[2,6,4,1,7,3,5,8]=>[4,3,1]=>70
[6,3,2,7,4,5,1,8]=>[4,2,1,1]=>90
[7,2,4,1,3,6,8,5]=>[4,3,1]=>70
[6,3,2,5,7,1,4,8]=>[4,2,1,1]=>90
[3,2,6,5,7,1,4,8]=>[4,2,2]=>56
[1,7,3,2,5,6,4,8]=>[5,2,1]=>64
[2,1,7,3,5,6,8,4]=>[5,2,1]=>64
[2,1,6,3,5,7,8,4]=>[5,2,1]=>64
[1,6,3,2,5,7,4,8]=>[5,2,1]=>64
[1,4,6,5,2,7,3,8]=>[5,2,1]=>64
[5,6,2,1,4,3,7,8]=>[4,2,2]=>56
[2,5,1,6,4,3,7,8]=>[5,2,1]=>64
[2,5,4,1,6,3,7,8]=>[5,2,1]=>64
[4,6,1,5,2,7,3,8]=>[4,3,1]=>70
[1,6,5,3,7,2,4,8]=>[4,2,1,1]=>90
[1,2,5,3,4,8,7,6]=>[5,2,1]=>64
[5,2,7,6,1,8,4,3]=>[3,2,2,1]=>70
[5,8,2,6,1,7,4,3]=>[3,2,2,1]=>70
[1,5,8,3,6,2,7,4]=>[4,2,2]=>56
[1,2,6,4,7,3,8,5]=>[5,2,1]=>64
[1,2,7,8,3,5,6,4]=>[5,2,1]=>64
[2,7,4,5,8,1,6,3]=>[4,2,2]=>56
[5,8,6,2,3,4,1,7]=>[4,2,1,1]=>90
[4,5,8,6,2,1,3,7]=>[4,2,1,1]=>90
[6,4,7,5,8,2,1,3]=>[3,2,2,1]=>70
[6,3,7,4,2,5,8,1]=>[4,2,1,1]=>90
[7,5,6,2,4,3,8,1]=>[3,2,1,1,1]=>64
[4,6,2,5,7,3,8,1]=>[4,2,1,1]=>90
[8,1,7,4,5,6,2,3]=>[4,2,1,1]=>90
[2,1,7,8,4,5,6,3]=>[4,3,1]=>70
[8,2,1,4,3,7,6,5]=>[3,3,1,1]=>56
[7,6,5,3,1,2,8,4]=>[3,2,1,1,1]=>64
[5,4,1,6,2,8,3,7]=>[4,3,1]=>70
[3,1,8,6,7,2,4,5]=>[4,3,1]=>70
[4,2,5,1,8,6,7,3]=>[4,2,2]=>56
[4,5,3,7,1,6,8,2]=>[4,2,2]=>56
[2,8,6,3,5,4,7,1]=>[4,1,1,1,1]=>35
[3,5,2,8,6,4,7,1]=>[4,2,1,1]=>90
[7,3,5,1,6,4,8,2]=>[4,2,1,1]=>90
[5,1,4,7,2,6,8,3]=>[4,2,2]=>56
[1,8,2,5,6,4,7,3]=>[5,1,1,1]=>35
[2,7,1,4,8,5,6,3]=>[4,3,1]=>70
[2,8,4,6,1,3,7,5]=>[4,3,1]=>70
[8,4,6,2,5,3,7,1]=>[3,2,1,1,1]=>64
[8,3,7,6,2,1,5,4]=>[2,2,2,1,1]=>28
[8,5,2,7,6,1,4,3]=>[2,2,2,1,1]=>28
[5,8,2,7,6,1,4,3]=>[2,2,2,1,1]=>28
[8,3,7,6,2,5,1,4]=>[2,2,2,1,1]=>28
[7,3,8,6,5,1,4,2]=>[2,2,2,1,1]=>28
[9,8,7,6,1,2,3,4,5,10]=>[6,1,1,1,1]=>126
[2,6,3,7,5,4,8,1]=>[4,2,1,1]=>90
[5,4,7,1,3,8,6,2]=>[3,3,1,1]=>56
[2,8,5,1,4,7,3,6]=>[3,3,1,1]=>56
[7,2,6,5,8,4,3,1]=>[3,1,1,1,1,1]=>21
[5,8,2,3,4,6,1,7]=>[5,2,1]=>64
[6,1,3,4,2,5,7,8]=>[6,1,1]=>21
[1,5,6,3,2,4,7,8]=>[5,2,1]=>64
[6,3,5,2,4,1,7,8]=>[4,2,1,1]=>90
[7,8,3,5,2,4,6,1]=>[3,2,2,1]=>70
[2,4,5,7,3,6,1,8]=>[5,2,1]=>64
[2,5,3,1,6,4,7,8]=>[5,2,1]=>64
[6,5,1,3,4,2,7,8]=>[5,1,1,1]=>35
[5,7,4,3,2,6,1,8]=>[3,2,1,1,1]=>64
[6,8,7,4,3,5,1,2]=>[2,2,2,1,1]=>28
[2,6,7,8,4,3,5,1]=>[4,2,1,1]=>90
[1,7,8,4,5,3,6,2]=>[4,2,1,1]=>90
[7,1,8,5,3,4,6,2]=>[4,2,1,1]=>90
[5,7,4,2,1,6,3,8]=>[3,2,2,1]=>70
[5,1,4,7,3,6,2,8]=>[4,2,1,1]=>90
[7,4,8,6,3,5,2,1]=>[2,2,2,1,1]=>28
[4,7,6,3,5,2,1,8]=>[3,2,1,1,1]=>64
[1,6,5,8,7,4,2,3]=>[3,2,2,1]=>70
[6,1,3,8,7,5,2,4]=>[3,2,2,1]=>70
[7,6,2,1,8,3,5,4]=>[3,2,2,1]=>70
[7,1,3,6,8,2,5,4]=>[4,2,1,1]=>90
[1,7,5,6,8,2,4,3]=>[4,2,1,1]=>90
[3,6,7,5,8,2,4,1]=>[4,2,1,1]=>90
[1,7,4,5,2,8,6,3]=>[4,2,2]=>56
[7,5,4,2,1,8,6,3]=>[2,2,2,1,1]=>28
[3,6,7,4,2,8,5,1]=>[4,2,1,1]=>90
[4,6,3,2,7,8,5,1]=>[4,2,1,1]=>90
[7,6,1,3,4,2,5,8]=>[5,1,1,1]=>35
[7,8,2,6,4,5,3,1]=>[3,2,1,1,1]=>64
[7,2,5,4,6,1,3,8]=>[4,2,1,1]=>90
[7,1,2,4,5,6,3,8]=>[6,1,1]=>21
[7,3,2,1,5,6,4,8]=>[4,2,1,1]=>90
[3,6,2,1,7,5,4,8]=>[4,2,2]=>56
[2,6,7,3,1,5,4,8]=>[4,2,2]=>56
[2,1,6,4,7,5,3,8]=>[4,3,1]=>70
[7,2,8,5,6,4,3,1]=>[3,2,1,1,1]=>64
[7,6,8,5,4,1,3,2]=>[2,2,1,1,1,1]=>20
[7,1,8,4,6,5,3,2]=>[3,2,1,1,1]=>64
[7,8,6,3,1,5,4,2]=>[2,2,2,1,1]=>28
[7,6,1,4,5,3,2,8]=>[4,1,1,1,1]=>35
[7,1,5,6,4,3,2,8]=>[4,1,1,1,1]=>35
[4,1,3,8,6,2,7,5]=>[4,2,2]=>56
[5,6,3,2,8,1,7,4]=>[3,2,2,1]=>70
[8,2,6,3,1,5,7,4]=>[4,2,1,1]=>90
[8,2,5,6,7,4,3,1]=>[4,1,1,1,1]=>35
[7,5,3,2,4,1,8,6]=>[3,2,1,1,1]=>64
[7,1,2,3,6,8,4,5]=>[5,2,1]=>64
[6,7,2,8,3,4,5,1]=>[4,3,1]=>70
[3,1,8,4,6,5,7,2]=>[4,2,1,1]=>90
[6,1,2,3,8,4,7,5]=>[5,2,1]=>64
[8,1,6,7,4,2,3,5]=>[4,2,1,1]=>90
[8,1,6,4,5,2,3,7]=>[4,2,1,1]=>90
[8,6,4,1,2,3,7,5]=>[4,2,1,1]=>90
[8,6,1,4,2,5,7,3]=>[4,2,1,1]=>90
[8,6,4,1,5,7,2,3]=>[3,3,1,1]=>56
[8,6,1,4,7,2,5,3]=>[3,2,2,1]=>70
[8,6,4,1,5,2,3,7]=>[4,2,1,1]=>90
[3,4,7,5,8,2,6,1]=>[4,2,1,1]=>90
[8,7,1,4,6,5,2,3]=>[3,2,1,1,1]=>64
[8,3,7,6,4,5,1,2]=>[3,2,1,1,1]=>64
[5,3,8,6,4,1,7,2]=>[3,2,2,1]=>70
[8,10,1,2,3,4,5,9,6,7]=>[7,2,1]=>160
[10,8,1,9,2,3,4,5,6,7]=>[7,2,1]=>160
[8,7,1,2,3,4,5,9,10,6]=>[7,2,1]=>160
[10,11,1,9,2,3,4,5,6,7,8]=>[8,2,1]=>231
[6,1,2,3,4,5,7,8,9]=>[8,1]=>8
[5,1,2,3,4,6,7,8,9]=>[8,1]=>8
[4,1,2,3,5,6,7,8,9]=>[8,1]=>8
[2,10,1,5,6,7,8,9,3,4]=>[6,3,1]=>315
[2,3,4,5,6,7,8,9,10,11,12,1]=>[11,1]=>11
[7,4,5,1,2,8,6,3]=>[3,3,2]=>42
[6,4,7,1,8,5,2,3]=>[3,3,2]=>42
[5,7,4,2,3,8,6,1]=>[3,3,1,1]=>56
[3,8,2,5,1,7,4,6]=>[3,3,2]=>42
[5,8,4,2,3,7,1,6]=>[3,2,2,1]=>70
[4,8,5,2,1,7,3,6]=>[3,3,1,1]=>56
[8,5,7,6,1,2,4,3]=>[3,2,1,1,1]=>64
[6,8,7,5,2,4,1,3]=>[2,2,2,1,1]=>28
[5,7,6,8,4,1,3,2]=>[3,2,1,1,1]=>64
[7,3,1,6,8,5,4,2]=>[3,2,1,1,1]=>64
[5,3,1,7,4,8,6,2]=>[3,3,2]=>42
[7,3,1,8,6,4,5,2]=>[3,2,2,1]=>70
[8,6,4,1,7,3,2,5]=>[3,2,1,1,1]=>64
[4,6,8,3,7,1,2,5]=>[3,3,2]=>42
[3,5,2,8,4,7,1,6]=>[3,3,2]=>42
[6,4,8,3,7,2,1,5]=>[2,2,2,1,1]=>28
[3,6,2,8,7,4,1,5]=>[3,3,1,1]=>56
[6,8,4,2,7,3,1,5]=>[3,2,2,1]=>70
[9,8,2,3,4,5,6,7,1]=>[6,1,1,1]=>56
[8,9,2,3,4,5,6,7,1]=>[6,2,1]=>105
[5,6,7,8,9,1,4,3,2]=>[5,2,1,1]=>189
[10,9,2,3,4,5,6,7,8,1]=>[7,1,1,1]=>84
[3,4,7,8,5,1,2,6]=>[4,3,1]=>70
[4,7,3,2,5,6,8,1]=>[4,2,1,1]=>90
[3,2,7,6,4,5,8,1]=>[4,2,1,1]=>90
[1,7,3,6,8,4,2,5]=>[4,2,1,1]=>90
[2,3,6,5,1,8,7,4]=>[4,2,2]=>56
[8,3,1,2,6,4,7,5]=>[4,3,1]=>70
[1,7,8,2,4,3,5,6]=>[5,2,1]=>64
[3,6,4,7,1,2,8,5]=>[4,3,1]=>70
[5,7,4,8,1,3,2,6]=>[3,3,1,1]=>56
[4,3,7,8,1,5,2,6]=>[3,3,2]=>42
[8,5,4,2,6,1,7,3]=>[3,2,1,1,1]=>64
[3,2,6,8,7,4,1,5]=>[3,3,1,1]=>56
[2,3,7,5,1,8,6,4]=>[4,2,2]=>56
[6,3,1,2,8,7,4,5]=>[4,2,2]=>56
[5,2,1,3,8,7,6,4]=>[3,2,2,1]=>70
[7,2,1,5,3,8,4,6]=>[4,3,1]=>70
[1,5,8,2,4,3,6,7]=>[5,2,1]=>64
[4,3,6,8,1,5,2,7]=>[3,3,2]=>42
[5,4,6,8,3,1,7,2]=>[3,2,2,1]=>70
[3,6,8,4,5,1,7,2]=>[4,2,2]=>56
[8,6,1,7,2,4,3,5]=>[4,2,1,1]=>90
[7,3,1,2,8,6,4,5]=>[4,2,2]=>56
[2,3,7,6,1,8,5,4]=>[4,2,1,1]=>90
[3,2,7,8,6,4,1,5]=>[3,3,1,1]=>56
[6,2,8,3,1,4,7,5]=>[4,2,2]=>56
[3,1,2,8,7,4,5,6]=>[5,2,1]=>64
[2,1,3,8,7,4,6,5]=>[4,2,1,1]=>90
[2,1,3,8,7,4,5,6]=>[5,2,1]=>64
[1,6,8,3,2,4,7,5]=>[4,2,2]=>56
[8,5,1,7,2,4,3,6]=>[4,2,1,1]=>90
[8,4,1,7,3,2,5,6]=>[4,2,1,1]=>90
[8,3,1,6,2,7,5,4]=>[3,3,1,1]=>56
[1,3,2,8,7,6,4,5]=>[4,2,1,1]=>90
[2,1,3,8,7,6,4,5]=>[4,2,1,1]=>90
[2,4,3,1,6,5,8,7,10,9]=>[5,4,1]=>288
[1,6,3,7,2,5,4,8]=>[4,2,2]=>56
[1,7,2,4,6,3,5,8]=>[5,2,1]=>64
[5,6,2,8,4,1,3,7]=>[3,3,2]=>42
[3,5,8,4,2,1,6,7]=>[4,2,1,1]=>90
[2,5,8,3,1,4,6,7]=>[5,2,1]=>64
[2,8,1,3,5,7,4,6]=>[4,3,1]=>70
[5,4,7,8,3,2,6,1]=>[3,2,1,1,1]=>64
[3,6,8,2,5,1,4,7]=>[3,3,2]=>42
[3,6,8,7,2,5,4,1]=>[3,2,1,1,1]=>64
[3,4,6,5,8,2,1,7]=>[4,2,1,1]=>90
[2,4,6,7,8,3,5,1]=>[5,2,1]=>64
[1,4,2,5,7,6,3,8]=>[5,2,1]=>64
[1,4,2,6,8,5,3,7]=>[4,3,1]=>70
[1,2,6,8,3,5,4,7]=>[5,2,1]=>64
[1,6,8,3,5,4,2,7]=>[4,2,1,1]=>90
[1,5,3,2,4,6,8,7]=>[5,2,1]=>64
[1,5,8,7,6,3,2,4]=>[3,2,1,1,1]=>64
[1,5,7,6,3,2,4,8]=>[4,2,1,1]=>90
[1,6,3,2,4,7,5,8]=>[5,2,1]=>64
[1,6,3,2,4,8,7,5]=>[4,2,2]=>56
[1,2,7,6,4,3,5,8]=>[5,1,1,1]=>35
[1,8,7,5,2,4,6,3]=>[4,1,1,1,1]=>35
[1,7,5,2,4,6,3,8]=>[5,1,1,1]=>35
[1,7,4,2,5,3,6,8]=>[5,2,1]=>64
[1,8,4,7,5,2,6,3]=>[4,2,1,1]=>90
[1,7,5,2,3,6,4,8]=>[5,2,1]=>64
[1,7,5,2,6,3,4,8]=>[5,2,1]=>64
[1,6,3,7,4,2,5,8]=>[5,2,1]=>64
[1,6,3,2,7,5,4,8]=>[4,2,2]=>56
[1,4,7,5,2,6,3,8]=>[5,2,1]=>64
[1,3,6,4,8,7,5,2]=>[4,2,1,1]=>90
[1,3,7,6,4,2,5,8]=>[5,1,1,1]=>35
[1,3,2,4,8,5,7,6]=>[5,2,1]=>64
[1,3,8,7,5,2,4,6]=>[4,2,1,1]=>90
[1,4,6,3,2,7,5,8]=>[5,2,1]=>64
[1,4,6,3,2,8,7,5]=>[4,2,2]=>56
[1,5,7,6,4,2,3,8]=>[4,2,1,1]=>90
[1,6,3,2,8,4,7,5]=>[4,2,2]=>56
[1,6,3,5,2,7,4,8]=>[5,2,1]=>64
[1,6,3,5,2,8,7,4]=>[4,2,2]=>56
[1,8,3,7,5,2,4,6]=>[4,2,1,1]=>90
[6,4,7,1,5,3,8,2]=>[3,2,2,1]=>70
[4,3,8,2,6,5,7,1]=>[3,2,2,1]=>70
[5,7,1,4,8,2,3,6]=>[4,3,1]=>70
[6,5,7,1,4,3,8,2]=>[3,2,1,1,1]=>64
[5,7,6,1,2,4,8,3]=>[4,2,1,1]=>90
[1,3,4,2,8,5,7,6]=>[5,2,1]=>64
[7,3,1,4,2,6,5,8]=>[4,3,1]=>70
[5,4,1,8,2,6,3,7]=>[4,2,2]=>56
[5,3,1,8,2,6,4,7]=>[4,2,2]=>56
[4,7,1,5,2,6,3,8]=>[4,3,1]=>70
[6,5,1,4,2,7,3,8]=>[4,2,1,1]=>90
[1,8,7,3,4,5,2,6]=>[5,1,1,1]=>35
[1,8,9,3,4,5,6,7,2]=>[6,2,1]=>105
[1,8,7,4,5,2,3,6]=>[4,2,1,1]=>90
[1,3,7,8,4,5,6,2]=>[5,2,1]=>64
[1,3,4,5,6,7,8,9,10,11,12,2]=>[11,1]=>11
[8,4,2,3,1,6,5,7]=>[4,2,1,1]=>90
[6,4,5,2,8,1,7,3]=>[3,2,2,1]=>70
[6,4,2,3,5,8,1,7]=>[4,2,1,1]=>90
[8,2,4,6,7,1,5,3]=>[4,2,1,1]=>90
[2,6,3,1,7,4,8,5]=>[4,3,1]=>70
[6,5,1,8,3,2,7,4]=>[3,2,2,1]=>70
[1,4,3,7,2,8,6,5]=>[4,2,2]=>56
[1,8,7,4,5,3,2,6]=>[4,1,1,1,1]=>35
[1,7,4,6,3,8,2,5]=>[4,2,1,1]=>90
[5,6,4,1,3,8,2,7]=>[3,3,1,1]=>56
[4,5,3,1,8,7,6,2]=>[3,2,2,1]=>70
[6,3,4,2,7,8,5,1]=>[4,2,1,1]=>90
[6,2,7,8,1,3,5,4]=>[3,3,2]=>42
[5,1,8,4,3,7,2,6]=>[3,2,2,1]=>70
[7,2,8,1,4,5,6,3]=>[4,2,2]=>56
[1,4,8,2,5,6,7,3]=>[5,2,1]=>64
[2,1,4,3,6,5,8,10,9,7]=>[5,4,1]=>288
[2,1,4,3,6,8,7,5,10,9]=>[5,4,1]=>288
[2,1,4,3,8,10,7,9,5,6]=>[4,4,2]=>252
[2,1,4,3,6,7,10,8,9,5]=>[6,3,1]=>315
[2,1,4,6,5,3,8,7,10,9]=>[5,4,1]=>288
[2,1,4,6,5,3,8,10,9,7]=>[5,3,2]=>450
[2,1,6,8,5,7,3,4,10,9]=>[4,4,2]=>252
[2,1,8,7,5,10,4,9,3,6]=>[3,3,2,1,1]=>450
[2,1,6,7,5,10,8,4,9,3]=>[5,3,1,1]=>567
[2,1,4,5,8,6,7,3,10,9]=>[6,3,1]=>315
[2,1,8,5,10,6,7,9,3,4]=>[5,3,2]=>450
[2,1,4,7,10,6,9,8,3,5]=>[4,3,2,1]=>768
[2,1,4,5,6,10,7,8,9,3]=>[7,2,1]=>160
[2,4,3,1,6,5,8,10,9,7]=>[5,3,2]=>450
[2,4,3,1,6,8,7,5,10,9]=>[5,3,2]=>450
[2,4,3,1,8,10,7,9,5,6]=>[4,3,3]=>210
[2,4,3,1,6,7,10,8,9,5]=>[6,2,2]=>225
[4,6,3,5,1,2,8,7,10,9]=>[4,4,2]=>252
[4,6,3,5,1,2,8,10,9,7]=>[4,3,3]=>210
[6,5,3,8,2,7,1,4,10,9]=>[3,3,2,1,1]=>450
[8,5,3,7,2,10,4,9,1,6]=>[3,3,2,1,1]=>450
[6,5,3,7,2,10,8,4,9,1]=>[4,2,2,1,1]=>567
[4,5,3,8,6,2,7,1,10,9]=>[5,3,1,1]=>567
[8,6,3,5,10,2,7,9,1,4]=>[4,2,2,1,1]=>567
[4,7,3,6,10,1,9,8,2,5]=>[3,3,3,1]=>210
[4,5,3,6,10,7,1,8,9,2]=>[6,2,2]=>225
[2,3,6,4,5,1,8,7,10,9]=>[6,3,1]=>315
[2,3,6,4,5,1,8,10,9,7]=>[6,2,2]=>225
[6,3,8,4,5,7,1,2,10,9]=>[5,3,2]=>450
[8,3,7,4,5,10,2,9,1,6]=>[4,2,2,1,1]=>567
[6,3,7,4,5,10,8,2,9,1]=>[5,3,1,1]=>567
[2,5,8,4,7,6,1,3,10,9]=>[4,3,2,1]=>768
[8,5,10,4,7,6,2,9,1,3]=>[3,2,2,2,1]=>288
[2,7,10,4,8,6,9,5,1,3]=>[4,2,2,1,1]=>567
[2,5,6,4,10,8,7,3,9,1]=>[5,2,1,1,1]=>448
[2,3,4,8,5,6,7,1,10,9]=>[7,2,1]=>160
[8,3,4,10,5,6,7,9,1,2]=>[6,2,2]=>225
[2,7,4,10,5,6,9,8,1,3]=>[5,2,2,1]=>525
[2,3,6,10,5,9,7,8,1,4]=>[5,2,2,1]=>525
[2,3,4,5,10,6,7,8,9,1]=>[8,1,1]=>36
[2,1,4,3,6,5,8,7,10,12,11,9]=>[6,5,1]=>1155
[2,1,4,3,6,5,8,10,9,7,12,11]=>[6,5,1]=>1155
[2,1,4,3,6,5,10,12,9,11,7,8]=>[5,5,2]=>1320
[2,1,4,3,6,5,8,9,12,10,11,7]=>[7,4,1]=>1408
[2,1,4,3,6,8,7,5,10,9,12,11]=>[6,5,1]=>1155
[2,1,4,3,6,8,7,5,10,12,11,9]=>[6,4,2]=>2673
[2,1,4,3,8,10,7,9,5,6,12,11]=>[5,5,2]=>1320
[2,1,4,3,10,9,7,12,6,11,5,8]=>[4,4,2,1,1]=>4455
[2,1,4,3,8,9,7,12,10,6,11,5]=>[6,4,1,1]=>3080
[2,1,4,3,6,7,10,8,9,5,12,11]=>[7,4,1]=>1408
[2,1,4,3,10,7,12,8,9,11,5,6]=>[6,4,2]=>2673
[2,1,4,3,6,9,12,8,11,10,5,7]=>[5,4,2,1]=>5775
[2,1,4,3,6,7,8,12,9,10,11,5]=>[8,3,1]=>891
[2,1,4,6,5,3,8,7,10,9,12,11]=>[6,5,1]=>1155
[2,1,4,6,5,3,8,7,10,12,11,9]=>[6,4,2]=>2673
[2,1,4,6,5,3,8,10,9,7,12,11]=>[6,4,2]=>2673
[2,1,4,6,5,3,10,12,9,11,7,8]=>[5,4,3]=>2112
[2,1,4,6,5,3,8,9,12,10,11,7]=>[7,3,2]=>1925
[2,1,6,8,5,7,3,4,10,9,12,11]=>[5,5,2]=>1320
[2,1,6,8,5,7,3,4,10,12,11,9]=>[5,4,3]=>2112
[2,1,8,7,5,10,4,9,3,6,12,11]=>[4,4,2,1,1]=>4455
[2,1,10,7,5,9,4,12,6,11,3,8]=>[4,4,2,1,1]=>4455
[2,1,8,7,5,9,4,12,10,6,11,3]=>[5,3,2,1,1]=>7700
[2,1,6,7,5,10,8,4,9,3,12,11]=>[6,4,1,1]=>3080
[2,1,10,8,5,7,12,4,9,11,3,6]=>[5,3,2,1,1]=>7700
[2,1,6,9,5,8,12,3,11,10,4,7]=>[4,4,3,1]=>2970
[2,1,6,7,5,8,12,9,3,10,11,4]=>[7,3,2]=>1925
[2,1,4,5,8,6,7,3,10,9,12,11]=>[7,4,1]=>1408
[2,1,4,5,8,6,7,3,10,12,11,9]=>[7,3,2]=>1925
[2,1,8,5,10,6,7,9,3,4,12,11]=>[6,4,2]=>2673
[2,1,10,5,9,6,7,12,4,11,3,8]=>[5,3,2,1,1]=>7700
[2,1,8,5,9,6,7,12,10,4,11,3]=>[6,4,1,1]=>3080
[2,1,4,7,10,6,9,8,3,5,12,11]=>[5,4,2,1]=>5775
[2,1,10,7,12,6,9,8,4,11,3,5]=>[4,3,2,2,1]=>5775
[2,1,4,9,12,6,10,8,11,7,3,5]=>[5,3,2,1,1]=>7700
[2,1,4,7,8,6,12,10,9,5,11,3]=>[6,3,1,1,1]=>3696
[2,1,4,5,6,10,7,8,9,3,12,11]=>[8,3,1]=>891
[2,1,10,5,6,12,7,8,9,11,3,4]=>[7,3,2]=>1925
[2,1,4,9,6,12,7,8,11,10,3,5]=>[6,3,2,1]=>5632
[2,1,4,5,8,12,7,11,9,10,3,6]=>[6,3,2,1]=>5632
[2,1,4,5,6,7,12,8,9,10,11,3]=>[9,2,1]=>320
[2,4,3,1,6,5,8,7,10,9,12,11]=>[6,5,1]=>1155
[2,4,3,1,6,5,8,7,10,12,11,9]=>[6,4,2]=>2673
[2,4,3,1,6,5,8,10,9,7,12,11]=>[6,4,2]=>2673
[2,4,3,1,6,5,10,12,9,11,7,8]=>[5,4,3]=>2112
[2,4,3,1,6,5,8,9,12,10,11,7]=>[7,3,2]=>1925
[2,4,3,1,6,8,7,5,10,9,12,11]=>[6,4,2]=>2673
[2,4,3,1,6,8,7,5,10,12,11,9]=>[6,3,3]=>1650
[2,4,3,1,8,10,7,9,5,6,12,11]=>[5,4,3]=>2112
[2,4,3,1,10,9,7,12,6,11,5,8]=>[4,3,3,1,1]=>4158
[2,4,3,1,8,9,7,12,10,6,11,5]=>[6,3,2,1]=>5632
[2,4,3,1,6,7,10,8,9,5,12,11]=>[7,3,2]=>1925
[2,4,3,1,10,7,12,8,9,11,5,6]=>[6,3,3]=>1650
[2,4,3,1,6,9,12,8,11,10,5,7]=>[5,3,3,1]=>4158
[2,4,3,1,6,7,8,12,9,10,11,5]=>[8,2,2]=>616
[4,6,3,5,1,2,8,7,10,9,12,11]=>[5,5,2]=>1320
[4,6,3,5,1,2,8,7,10,12,11,9]=>[5,4,3]=>2112
[4,6,3,5,1,2,8,10,9,7,12,11]=>[5,4,3]=>2112
[4,6,3,5,1,2,10,12,9,11,7,8]=>[4,4,4]=>462
[4,6,3,5,1,2,8,9,12,10,11,7]=>[6,3,3]=>1650
[6,5,3,8,2,7,1,4,10,9,12,11]=>[4,4,2,1,1]=>4455
[6,5,3,8,2,7,1,4,10,12,11,9]=>[4,3,3,1,1]=>4158
[8,5,3,7,2,10,4,9,1,6,12,11]=>[4,4,2,1,1]=>4455
[10,5,3,7,2,9,4,12,6,11,1,8]=>[4,4,2,1,1]=>4455
[8,5,3,7,2,9,4,12,10,6,11,1]=>[5,3,2,1,1]=>7700
[6,5,3,7,2,10,8,4,9,1,12,11]=>[5,3,2,1,1]=>7700
[10,5,3,8,2,7,12,4,9,11,1,6]=>[4,3,3,1,1]=>4158
[6,5,3,9,2,8,12,1,11,10,4,7]=>[3,3,3,2,1]=>2112
[6,5,3,7,2,8,12,9,1,10,11,4]=>[6,2,2,1,1]=>3564
[4,5,3,8,6,2,7,1,10,9,12,11]=>[6,4,1,1]=>3080
[4,5,3,8,6,2,7,1,10,12,11,9]=>[6,3,2,1]=>5632
[8,6,3,5,10,2,7,9,1,4,12,11]=>[5,3,2,1,1]=>7700
[10,6,3,5,9,2,7,12,4,11,1,8]=>[4,3,3,1,1]=>4158
[8,6,3,5,9,2,7,12,10,4,11,1]=>[5,3,2,1,1]=>7700
[4,7,3,6,10,1,9,8,2,5,12,11]=>[4,4,3,1]=>2970
[10,6,3,7,12,2,9,8,4,11,1,5]=>[4,3,2,2,1]=>5775
[4,9,3,6,12,1,10,8,11,7,2,5]=>[4,3,3,1,1]=>4158
[4,7,3,6,8,1,12,10,9,5,11,2]=>[5,3,2,1,1]=>7700
[4,5,3,6,10,7,1,8,9,2,12,11]=>[7,3,2]=>1925
[10,7,3,5,6,12,2,8,9,11,1,4]=>[6,2,2,1,1]=>3564
[4,9,3,7,6,12,1,8,11,10,2,5]=>[4,3,3,2]=>2970
[4,5,3,8,7,12,2,11,9,10,1,6]=>[5,3,2,2]=>4455
[4,5,3,6,7,12,8,2,9,10,11,1]=>[8,2,1,1]=>945
[2,3,6,4,5,1,8,7,10,9,12,11]=>[7,4,1]=>1408
[2,3,6,4,5,1,8,7,10,12,11,9]=>[7,3,2]=>1925
[2,3,6,4,5,1,8,10,9,7,12,11]=>[7,3,2]=>1925
[2,3,6,4,5,1,10,12,9,11,7,8]=>[6,3,3]=>1650
[2,3,6,4,5,1,8,9,12,10,11,7]=>[8,2,2]=>616
[6,3,8,4,5,7,1,2,10,9,12,11]=>[6,4,2]=>2673
[6,3,8,4,5,7,1,2,10,12,11,9]=>[6,3,3]=>1650
[8,3,7,4,5,10,2,9,1,6,12,11]=>[5,3,2,1,1]=>7700
[10,3,7,4,5,9,2,12,6,11,1,8]=>[5,3,2,1,1]=>7700
[8,3,7,4,5,9,2,12,10,6,11,1]=>[6,2,2,1,1]=>3564
[6,3,7,4,5,10,8,2,9,1,12,11]=>[6,4,1,1]=>3080
[10,3,8,4,5,7,12,2,9,11,1,6]=>[6,2,2,1,1]=>3564
[6,3,9,4,5,8,12,1,11,10,2,7]=>[5,3,3,1]=>4158
[6,3,7,4,5,8,12,9,1,10,11,2]=>[7,3,2]=>1925
[2,5,8,4,7,6,1,3,10,9,12,11]=>[5,4,2,1]=>5775
[2,5,8,4,7,6,1,3,10,12,11,9]=>[5,3,3,1]=>4158
[8,5,10,4,7,6,2,9,1,3,12,11]=>[4,3,2,2,1]=>5775
[10,5,9,4,7,6,2,12,3,11,1,8]=>[3,3,3,1,1,1]=>1650
[8,5,9,4,7,6,2,12,10,3,11,1]=>[4,3,2,2,1]=>5775
[2,7,10,4,8,6,9,5,1,3,12,11]=>[5,3,2,1,1]=>7700
[10,7,12,4,8,6,9,5,2,11,1,3]=>[4,2,2,2,1,1]=>3080
[2,9,8,4,12,6,10,3,11,7,1,5]=>[5,2,2,2,1]=>3520
[2,7,8,4,12,6,9,10,1,3,11,5]=>[6,3,3]=>1650
[2,5,6,4,10,8,7,3,9,1,12,11]=>[6,3,1,1,1]=>3696
[10,5,6,4,12,8,7,3,9,11,1,2]=>[5,2,2,2,1]=>3520
[2,9,8,4,6,12,7,3,11,10,1,5]=>[5,2,2,2,1]=>3520
[2,5,8,4,12,9,7,11,6,10,3,1]=>[5,3,1,1,1,1]=>3564
[2,5,6,4,7,12,9,8,1,10,11,3]=>[7,2,2,1]=>2079
[2,3,4,8,5,6,7,1,10,9,12,11]=>[8,3,1]=>891
[2,3,4,8,5,6,7,1,10,12,11,9]=>[8,2,2]=>616
[8,3,4,10,5,6,7,9,1,2,12,11]=>[7,3,2]=>1925
[10,3,4,9,5,6,7,12,2,11,1,8]=>[6,2,2,1,1]=>3564
[8,3,4,9,5,6,7,12,10,2,11,1]=>[7,3,1,1]=>2376
[2,7,4,10,5,6,9,8,1,3,12,11]=>[6,3,2,1]=>5632
[10,7,4,12,5,6,9,8,2,11,1,3]=>[5,2,2,2,1]=>3520
[2,9,4,12,5,6,10,8,11,7,1,3]=>[6,2,2,1,1]=>3564
[2,7,4,8,5,6,12,10,9,3,11,1]=>[6,3,1,1,1]=>3696
[2,3,6,10,5,9,7,8,1,4,12,11]=>[6,3,2,1]=>5632
[10,3,6,12,5,9,7,8,2,11,1,4]=>[5,2,2,2,1]=>3520
[2,9,6,12,5,11,7,8,10,1,3,4]=>[5,3,2,2]=>4455
[2,3,8,12,5,10,7,11,9,6,1,4]=>[5,3,2,1,1]=>7700
[2,3,6,7,5,12,10,8,9,4,11,1]=>[7,2,1,1,1]=>1728
[2,3,4,5,10,6,7,8,9,1,12,11]=>[9,2,1]=>320
[10,3,4,5,12,6,7,8,9,11,1,2]=>[8,2,2]=>616
[2,9,4,5,12,6,7,8,11,10,1,3]=>[7,2,2,1]=>2079
[2,3,8,5,12,6,7,11,9,10,1,4]=>[7,2,2,1]=>2079
[2,3,4,7,12,6,11,8,9,10,1,5]=>[7,2,2,1]=>2079
[2,3,4,5,6,12,7,8,9,10,11,1]=>[10,1,1]=>55
[8,1,6,7,2,5,4,3]=>[3,2,1,1,1]=>64
[7,5,2,3,6,8,4,1]=>[4,2,1,1]=>90
[8,1,4,6,5,3,2,7]=>[4,1,1,1,1]=>35
[8,1,4,7,6,5,2,3]=>[3,2,1,1,1]=>64
[8,1,2,7,6,5,4,3]=>[3,1,1,1,1,1]=>21
[4,5,8,1,6,7,2,3]=>[4,3,1]=>70
[3,7,2,5,8,4,6,1]=>[3,3,1,1]=>56
[6,7,8,4,1,5,2,3]=>[3,3,2]=>42
[6,2,8,3,5,1,4,7]=>[4,2,2]=>56
[6,2,7,4,5,3,1,8]=>[4,2,1,1]=>90
[6,8,2,5,3,4,1,7]=>[4,2,1,1]=>90
[7,4,5,6,1,8,2,3]=>[4,3,1]=>70
[6,1,8,7,4,5,2,3]=>[3,2,2,1]=>70
[4,8,7,1,6,3,2,5]=>[3,2,1,1,1]=>64
[4,8,2,7,5,3,6,1]=>[3,2,1,1,1]=>64
[1,3,2,6,8,7,4,5]=>[4,3,1]=>70
[1,3,8,2,5,4,6,7]=>[5,2,1]=>64
[1,6,2,5,8,7,3,4]=>[4,2,2]=>56
[1,6,8,7,2,3,5,4]=>[4,2,1,1]=>90
[1,6,8,7,2,5,3,4]=>[4,2,1,1]=>90
[1,5,2,4,8,3,6,7]=>[5,2,1]=>64
[1,2,4,5,8,6,3,7]=>[6,1,1]=>21
[1,2,8,3,5,4,7,6]=>[5,2,1]=>64
[1,3,8,2,5,4,7,6]=>[4,3,1]=>70
[1,6,7,5,2,4,8,3]=>[4,2,1,1]=>90
[1,5,6,4,7,2,3,8]=>[5,2,1]=>64
[1,7,4,2,5,8,3,6]=>[4,3,1]=>70
[1,6,4,3,7,5,2,8]=>[4,2,1,1]=>90
[1,6,5,4,7,2,3,8]=>[4,2,1,1]=>90
[1,7,3,2,6,4,8,5]=>[4,3,1]=>70
[1,5,8,2,3,6,7,4]=>[5,2,1]=>64
[1,3,2,6,8,5,4,7]=>[4,3,1]=>70
[1,6,3,2,7,4,5,8]=>[5,2,1]=>64
[1,7,8,5,4,2,3,6]=>[4,2,1,1]=>90
[1,8,4,2,3,6,5,7]=>[5,2,1]=>64
[1,4,2,7,5,3,8,6]=>[4,3,1]=>70
[1,5,7,6,2,4,3,8]=>[4,2,1,1]=>90
[1,8,4,7,3,2,6,5]=>[3,2,2,1]=>70
[1,3,8,4,2,6,5,7]=>[5,2,1]=>64
[1,7,4,2,6,5,8,3]=>[4,2,1,1]=>90
[1,6,5,8,3,7,4,2]=>[3,2,2,1]=>70
[1,7,4,8,3,2,5,6]=>[4,2,1,1]=>90
[1,4,8,3,2,7,5,6]=>[4,2,2]=>56
[1,8,3,6,4,5,2,7]=>[5,1,1,1]=>35
[1,6,4,7,3,2,8,5]=>[4,2,1,1]=>90
[8,2,3,7,4,5,6,1]=>[5,1,1,1]=>35
[8,5,7,2,3,6,4,1]=>[3,2,1,1,1]=>64
[7,5,2,1,6,8,3,4]=>[3,3,1,1]=>56
[7,6,1,5,4,8,2,3]=>[3,2,1,1,1]=>64
[7,6,3,2,1,8,4,5]=>[3,2,1,1,1]=>64
[2,8,7,3,4,6,1,5]=>[4,2,1,1]=>90
[6,5,1,3,7,2,8,4]=>[4,2,1,1]=>90
[8,1,7,3,4,5,2,6]=>[5,1,1,1]=>35
[7,1,8,3,4,5,2,6]=>[5,2,1]=>64
[3,8,7,1,2,4,5,6]=>[5,2,1]=>64
[1,8,5,3,4,6,2,7]=>[5,1,1,1]=>35
[7,1,6,5,4,3,8,2]=>[3,1,1,1,1,1]=>21
[7,1,3,6,4,5,8,2]=>[5,1,1,1]=>35
[7,1,5,3,6,4,8,2]=>[4,2,1,1]=>90
[6,1,5,3,7,8,2,4]=>[4,2,1,1]=>90
[5,8,7,1,2,6,3,4]=>[4,2,1,1]=>90
[6,8,2,3,4,7,1,5]=>[4,2,2]=>56
[5,1,7,3,8,6,2,4]=>[3,3,2]=>42
[6,1,3,2,4,7,8,5]=>[5,2,1]=>64
[6,2,1,3,4,7,8,5]=>[5,2,1]=>64
[3,4,5,6,1,8,9,2,7]=>[6,3]=>48
[3,4,5,6,8,1,9,2,7]=>[6,3]=>48
[3,4,5,6,8,9,1,2,7]=>[6,3]=>48
[2,4,5,1,6,7,8,9,3]=>[7,2]=>27
[2,3,4,1,6,7,8,9,5]=>[7,2]=>27
[2,3,4,5,6,1,8,9,10,7]=>[8,2]=>35
[3,4,5,6,1,2,9,7,8]=>[6,3]=>48
[3,4,5,6,8,1,2,7,9]=>[6,3]=>48
[2,3,4,5,6,8,9,1,10,7]=>[8,2]=>35
[3,4,5,1,6,7,8,2,9]=>[7,2]=>27
[5,6,1,7,8,9,2,3,4]=>[5,4]=>42
[4,5,6,1,7,8,9,10,2,3]=>[7,3]=>75
[1,3,5,2,6,7,8,9,4]=>[7,2]=>27
[3,5,6,1,7,8,9,10,2,4]=>[7,3]=>75
[2,1,4,3,6,7,8,9,5]=>[6,3]=>48
[3,4,6,1,7,8,9,10,2,5]=>[7,3]=>75
[2,3,1,5,6,7,8,9,4]=>[7,2]=>27
[3,4,5,1,7,8,9,10,2,6]=>[7,3]=>75
[3,2,5,8,7,4,1,6]=>[3,3,1,1]=>56
[4,2,5,8,7,3,1,6]=>[3,3,1,1]=>56
[8,3,4,1,6,5,2,7]=>[4,2,1,1]=>90
[3,4,8,5,7,2,1,6]=>[4,2,1,1]=>90
[3,6,4,8,5,7,2,1]=>[4,2,1,1]=>90
[5,8,4,7,3,6,2,1]=>[2,2,2,1,1]=>28
[4,2,8,7,3,1,6,5]=>[3,2,2,1]=>70
[6,5,8,2,1,7,4,3]=>[2,2,2,2]=>14
[6,1,4,3,8,7,2,5]=>[3,2,2,1]=>70
[5,1,3,2,6,8,7,4]=>[4,2,2]=>56
[6,1,3,8,7,2,4,5]=>[4,2,2]=>56
[1,2,8,4,5,7,3,6]=>[5,2,1]=>64
[4,2,1,8,7,6,3,5]=>[3,2,2,1]=>70
[3,2,5,8,7,1,4,6]=>[3,3,2]=>42
[5,6,3,8,7,2,1,4]=>[3,2,2,1]=>70
[2,5,8,4,7,1,6,3]=>[3,2,2,1]=>70
[1,6,2,4,8,5,7,3]=>[5,2,1]=>64
[3,1,6,5,8,7,2,4]=>[3,3,2]=>42
[4,8,5,3,6,7,1,2]=>[4,2,1,1]=>90
[1,8,5,3,4,7,6,2]=>[4,2,1,1]=>90
[2,7,1,3,6,4,5,8]=>[5,2,1]=>64
[8,1,7,3,5,4,6,2]=>[4,1,1,1,1]=>35
[8,1,2,4,7,5,6,3]=>[5,1,1,1]=>35
[6,4,5,8,3,1,7,2]=>[3,2,2,1]=>70
[8,6,2,1,5,7,3,4]=>[3,3,1,1]=>56
[4,6,2,8,5,3,7,1]=>[3,3,1,1]=>56
[8,7,2,4,1,5,3,6]=>[4,2,1,1]=>90
[7,5,3,4,8,6,2,1]=>[3,2,1,1,1]=>64
[2,8,3,1,4,6,7,5]=>[5,2,1]=>64
[4,3,6,5,1,2,7,8]=>[4,2,2]=>56
[5,8,3,7,6,4,2,1]=>[2,2,1,1,1,1]=>20
[1,3,8,7,6,5,2,4]=>[3,2,1,1,1]=>64
[4,8,7,2,6,3,1,5]=>[3,2,1,1,1]=>64
[1,8,7,2,6,3,5,4]=>[4,1,1,1,1]=>35
[8,7,2,1,4,3,5,6]=>[4,2,1,1]=>90
[2,8,7,1,6,3,4,5]=>[4,2,1,1]=>90
[4,2,8,7,6,5,1,3]=>[2,2,2,1,1]=>28
[1,2,5,7,4,8,6,3]=>[5,2,1]=>64
[6,2,1,8,7,5,3,4]=>[3,2,2,1]=>70
[6,3,8,7,4,5,2,1]=>[3,2,1,1,1]=>64
[2,8,3,4,1,5,6,7]=>[6,1,1]=>21
[4,5,6,3,1,8,2,7]=>[4,3,1]=>70
[1,5,6,3,8,4,2,7]=>[4,3,1]=>70
[5,7,3,8,4,2,6,1]=>[3,3,1,1]=>56
[5,3,6,2,8,4,1,7]=>[3,3,1,1]=>56
[2,3,6,5,4,8,1,7]=>[4,2,1,1]=>90
[3,7,5,4,8,2,6,1]=>[3,2,1,1,1]=>64
[5,3,7,1,2,8,4,6]=>[4,3,1]=>70
[6,3,8,7,2,5,4,1]=>[2,2,2,1,1]=>28
[9,7,8,5,4,3,2,1,6]=>[2,2,1,1,1,1,1]=>27
[1,2,3,4,6,5,7,8,9]=>[8,1]=>8
[1,2,3,5,4,6,7,8,9]=>[8,1]=>8
[6,8,4,1,7,5,2,3]=>[3,2,2,1]=>70
[8,1,4,6,7,5,2,3]=>[4,2,1,1]=>90
[2,6,8,1,4,7,5,3]=>[3,3,1,1]=>56
[6,4,8,1,2,7,5,3]=>[3,2,2,1]=>70
[4,2,8,1,6,7,5,3]=>[3,2,2,1]=>70
[8,1,2,6,4,7,5,3]=>[4,2,1,1]=>90
[8,4,1,6,2,7,5,3]=>[3,3,1,1]=>56
[4,8,1,2,6,7,5,3]=>[4,2,1,1]=>90
[4,8,2,1,6,7,5,3]=>[3,2,2,1]=>70
[8,2,4,6,1,7,5,3]=>[4,2,1,1]=>90
[2,1,4,3,6,5,8,9,10,7]=>[6,4]=>90
[2,1,4,3,6,7,8,5,10,9]=>[6,4]=>90
[2,1,4,3,8,7,9,10,5,6]=>[5,4,1]=>288
[2,1,4,3,6,7,8,9,10,5]=>[7,3]=>75
[2,1,4,5,6,3,8,7,10,9]=>[6,4]=>90
[2,1,4,5,6,3,8,9,10,7]=>[7,3]=>75
[2,1,6,5,7,8,3,4,10,9]=>[5,4,1]=>288
[2,1,8,5,9,7,3,10,6,4]=>[4,3,2,1]=>768
[2,1,6,5,7,8,9,10,3,4]=>[6,3,1]=>315
[2,1,4,5,6,7,8,3,10,9]=>[7,3]=>75
[2,1,8,5,6,7,9,10,3,4]=>[6,3,1]=>315
[2,1,4,7,6,8,9,3,10,5]=>[6,3,1]=>315
[2,1,4,5,6,7,8,9,10,3]=>[8,2]=>35
[2,3,4,1,6,5,8,7,10,9]=>[6,4]=>90
[2,3,4,1,6,5,8,9,10,7]=>[7,3]=>75
[2,3,4,1,6,7,8,5,10,9]=>[7,3]=>75
[2,3,4,1,8,7,9,10,5,6]=>[6,3,1]=>315
[2,3,4,1,6,7,8,9,10,5]=>[8,2]=>35
[4,3,5,6,1,2,8,7,10,9]=>[5,4,1]=>288
[4,3,5,6,1,2,8,9,10,7]=>[6,3,1]=>315
[6,3,7,5,1,8,4,2,10,9]=>[4,3,2,1]=>768
[8,3,9,5,1,7,4,10,6,2]=>[4,3,2,1]=>768
[6,3,7,5,1,8,9,10,4,2]=>[5,2,2,1]=>525
[4,3,5,6,7,8,1,2,10,9]=>[6,3,1]=>315
[8,3,9,5,6,7,1,10,4,2]=>[5,2,2,1]=>525
[4,3,7,8,6,10,9,2,5,1]=>[4,3,2,1]=>768
[4,3,5,6,7,8,9,10,1,2]=>[7,2,1]=>160
[2,3,4,5,6,1,8,7,10,9]=>[7,3]=>75
[6,3,4,5,7,8,1,2,10,9]=>[6,3,1]=>315
[8,3,4,5,9,7,1,10,6,2]=>[5,2,2,1]=>525
[6,3,4,5,7,8,9,10,1,2]=>[7,2,1]=>160
[2,5,4,6,7,1,8,3,10,9]=>[6,3,1]=>315
[8,5,4,6,7,1,9,10,3,2]=>[5,2,1,1,1]=>448
[2,7,4,8,6,1,9,5,10,3]=>[5,2,2,1]=>525
[2,5,4,6,7,8,9,1,10,3]=>[7,2,1]=>160
[2,3,4,5,6,7,8,1,10,9]=>[8,2]=>35
[8,3,4,5,6,7,9,10,1,2]=>[7,2,1]=>160
[2,7,4,5,6,8,9,1,10,3]=>[7,2,1]=>160
[2,3,6,5,7,8,1,9,10,4]=>[7,2,1]=>160
[2,1,4,3,6,5,8,7,10,11,12,9]=>[7,5]=>297
[2,1,4,3,6,5,8,9,10,7,12,11]=>[7,5]=>297
[2,1,4,3,6,5,10,9,11,12,7,8]=>[6,5,1]=>1155
[2,1,4,3,6,5,8,9,10,11,12,7]=>[8,4]=>275
[2,1,4,3,6,7,8,5,10,9,12,11]=>[7,5]=>297
[2,1,4,3,6,7,8,5,10,11,12,9]=>[8,4]=>275
[2,1,4,3,8,7,9,10,5,6,12,11]=>[6,5,1]=>1155
[2,1,4,3,10,7,11,9,5,12,8,6]=>[5,4,2,1]=>5775
[2,1,4,3,8,7,9,10,11,12,5,6]=>[7,4,1]=>1408
[2,1,4,3,6,7,8,9,10,5,12,11]=>[8,4]=>275
[2,1,4,3,10,7,8,9,11,12,5,6]=>[7,4,1]=>1408
[2,1,4,3,6,9,8,10,11,5,12,7]=>[7,4,1]=>1408
[2,1,4,3,6,7,8,9,10,11,12,5]=>[9,3]=>154
[2,1,4,5,6,3,8,7,10,9,12,11]=>[7,5]=>297
[2,1,4,5,6,3,8,7,10,11,12,9]=>[8,4]=>275
[2,1,4,5,6,3,8,9,10,7,12,11]=>[8,4]=>275
[2,1,4,5,6,3,10,9,11,12,7,8]=>[7,4,1]=>1408
[2,1,4,5,6,3,8,9,10,11,12,7]=>[9,3]=>154
[2,1,6,5,7,8,3,4,10,9,12,11]=>[6,5,1]=>1155
[2,1,6,5,7,8,3,4,10,11,12,9]=>[7,4,1]=>1408
[2,1,8,5,9,7,3,10,6,4,12,11]=>[5,4,2,1]=>5775
[2,1,10,5,11,7,3,9,6,12,8,4]=>[5,4,2,1]=>5775
[2,1,8,5,9,7,3,10,11,12,6,4]=>[6,3,2,1]=>5632
[2,1,6,5,7,8,9,10,3,4,12,11]=>[7,4,1]=>1408
[2,1,10,5,11,7,8,9,3,12,6,4]=>[6,3,2,1]=>5632
[2,1,6,5,9,10,8,12,11,4,7,3]=>[5,4,2,1]=>5775
[2,1,6,5,7,8,9,10,11,12,3,4]=>[8,3,1]=>891
[2,1,4,5,6,7,8,3,10,9,12,11]=>[8,4]=>275
[2,1,4,5,6,7,8,3,10,11,12,9]=>[9,3]=>154
[2,1,8,5,6,7,9,10,3,4,12,11]=>[7,4,1]=>1408
[2,1,10,5,6,7,11,9,3,12,8,4]=>[6,3,2,1]=>5632
[2,1,8,5,6,7,9,10,11,12,3,4]=>[8,3,1]=>891
[2,1,4,7,6,8,9,3,10,5,12,11]=>[7,4,1]=>1408
[2,1,10,7,6,8,9,3,11,12,5,4]=>[6,3,1,1,1]=>3696
[2,1,4,9,6,10,8,3,11,7,12,5]=>[6,3,2,1]=>5632
[2,1,4,7,6,8,9,10,11,3,12,5]=>[8,3,1]=>891
[2,1,4,5,6,7,8,9,10,3,12,11]=>[9,3]=>154
[2,1,10,5,6,7,8,9,11,12,3,4]=>[8,3,1]=>891
[2,1,4,9,6,7,8,10,11,3,12,5]=>[8,3,1]=>891
[2,1,4,5,8,7,9,10,3,11,12,6]=>[8,3,1]=>891
[2,1,4,5,6,7,8,9,10,11,12,3]=>[10,2]=>54
[2,3,4,1,6,5,8,7,10,9,12,11]=>[7,5]=>297
[2,3,4,1,6,5,8,7,10,11,12,9]=>[8,4]=>275
[2,3,4,1,6,5,8,9,10,7,12,11]=>[8,4]=>275
[2,3,4,1,6,5,10,9,11,12,7,8]=>[7,4,1]=>1408
[2,3,4,1,6,5,8,9,10,11,12,7]=>[9,3]=>154
[2,3,4,1,6,7,8,5,10,9,12,11]=>[8,4]=>275
[2,3,4,1,6,7,8,5,10,11,12,9]=>[9,3]=>154
[2,3,4,1,8,7,9,10,5,6,12,11]=>[7,4,1]=>1408
[2,3,4,1,10,7,11,9,5,12,8,6]=>[6,3,2,1]=>5632
[2,3,4,1,8,7,9,10,11,12,5,6]=>[8,3,1]=>891
[2,3,4,1,6,7,8,9,10,5,12,11]=>[9,3]=>154
[2,3,4,1,10,7,8,9,11,12,5,6]=>[8,3,1]=>891
[2,3,4,1,6,9,8,10,11,5,12,7]=>[8,3,1]=>891
[2,3,4,1,6,7,8,9,10,11,12,5]=>[10,2]=>54
[4,3,5,6,1,2,8,7,10,9,12,11]=>[6,5,1]=>1155
[4,3,5,6,1,2,8,7,10,11,12,9]=>[7,4,1]=>1408
[4,3,5,6,1,2,8,9,10,7,12,11]=>[7,4,1]=>1408
[4,3,5,6,1,2,10,9,11,12,7,8]=>[6,4,2]=>2673
[4,3,5,6,1,2,8,9,10,11,12,7]=>[8,3,1]=>891
[6,3,7,5,1,8,4,2,10,9,12,11]=>[5,4,2,1]=>5775
[6,3,7,5,1,8,4,2,10,11,12,9]=>[6,3,2,1]=>5632
[8,3,9,5,1,7,4,10,6,2,12,11]=>[5,4,2,1]=>5775
[10,3,11,5,1,7,4,9,6,12,8,2]=>[5,4,2,1]=>5775
[8,3,9,5,1,7,4,10,11,12,6,2]=>[6,3,2,1]=>5632
[6,3,7,5,1,8,9,10,4,2,12,11]=>[6,3,2,1]=>5632
[10,3,11,5,1,7,8,9,4,12,6,2]=>[6,3,2,1]=>5632
[6,3,9,5,2,10,8,12,11,4,7,1]=>[4,4,3,1]=>2970
[6,3,7,5,1,8,9,10,11,12,4,2]=>[7,2,2,1]=>2079
[4,3,5,6,7,8,1,2,10,9,12,11]=>[7,4,1]=>1408
[4,3,5,6,7,8,1,2,10,11,12,9]=>[8,3,1]=>891
[8,3,9,5,6,7,1,10,4,2,12,11]=>[6,3,2,1]=>5632
[10,3,11,5,6,7,1,9,4,12,8,2]=>[6,3,2,1]=>5632
[8,3,9,5,6,7,1,10,11,12,4,2]=>[7,2,2,1]=>2079
[4,3,7,8,6,10,9,2,5,1,12,11]=>[5,4,2,1]=>5775
[10,3,11,7,6,8,9,4,1,12,5,2]=>[5,2,2,2,1]=>3520
[4,3,9,10,6,12,8,2,11,7,5,1]=>[4,4,2,1,1]=>4455
[4,3,7,8,6,9,10,12,11,5,1,2]=>[6,3,2,1]=>5632
[4,3,5,6,7,8,9,10,1,2,12,11]=>[8,3,1]=>891
[10,3,11,5,6,7,8,9,1,12,4,2]=>[7,2,2,1]=>2079
[4,3,9,10,6,7,8,12,11,2,5,1]=>[5,4,2,1]=>5775
[4,3,5,8,9,7,12,10,1,11,6,2]=>[6,3,2,1]=>5632
[4,3,5,6,7,8,9,10,11,12,1,2]=>[9,2,1]=>320
[2,3,4,5,6,1,8,7,10,9,12,11]=>[8,4]=>275
[2,3,4,5,6,1,8,7,10,11,12,9]=>[9,3]=>154
[2,3,4,5,6,1,8,9,10,7,12,11]=>[9,3]=>154
[2,3,4,5,6,1,10,9,11,12,7,8]=>[8,3,1]=>891
[2,3,4,5,6,1,8,9,10,11,12,7]=>[10,2]=>54
[6,3,4,5,7,8,1,2,10,9,12,11]=>[7,4,1]=>1408
[6,3,4,5,7,8,1,2,10,11,12,9]=>[8,3,1]=>891
[8,3,4,5,9,7,1,10,6,2,12,11]=>[6,3,2,1]=>5632
[10,3,4,5,11,7,1,9,6,12,8,2]=>[6,3,2,1]=>5632
[8,3,4,5,9,7,1,10,11,12,6,2]=>[7,2,2,1]=>2079
[6,3,4,5,7,8,9,10,1,2,12,11]=>[8,3,1]=>891
[10,3,4,5,11,7,8,9,1,12,6,2]=>[7,2,2,1]=>2079
[6,3,4,5,9,10,8,12,11,2,7,1]=>[6,3,2,1]=>5632
[6,3,4,5,7,8,9,10,11,12,1,2]=>[9,2,1]=>320
[2,5,4,6,7,1,8,3,10,9,12,11]=>[7,4,1]=>1408
[2,5,4,6,7,1,8,3,10,11,12,9]=>[8,3,1]=>891
[8,5,4,6,7,1,9,10,3,2,12,11]=>[6,3,1,1,1]=>3696
[10,5,4,6,7,1,11,9,3,12,8,2]=>[5,3,2,1,1]=>7700
[8,5,4,6,7,1,9,10,11,12,3,2]=>[7,2,1,1,1]=>1728
[2,7,4,8,6,1,9,5,10,3,12,11]=>[6,3,2,1]=>5632
[10,7,4,8,6,1,9,5,11,12,3,2]=>[5,2,2,1,1,1]=>3696
[2,9,4,10,6,1,8,5,11,7,12,3]=>[6,3,2,1]=>5632
[2,7,4,8,6,1,9,10,11,5,12,3]=>[7,2,2,1]=>2079
[2,5,4,6,7,8,9,1,10,3,12,11]=>[8,3,1]=>891
[10,5,4,6,7,8,9,1,11,12,3,2]=>[7,2,1,1,1]=>1728
[2,9,4,10,6,7,8,1,11,5,12,3]=>[7,2,2,1]=>2079
[2,5,4,8,9,7,11,10,3,6,12,1]=>[6,3,2,1]=>5632
[2,5,4,6,7,8,9,10,11,1,12,3]=>[9,2,1]=>320
[2,3,4,5,6,7,8,1,10,9,12,11]=>[9,3]=>154
[2,3,4,5,6,7,8,1,10,11,12,9]=>[10,2]=>54
[8,3,4,5,6,7,9,10,1,2,12,11]=>[8,3,1]=>891
[10,3,4,5,6,7,11,9,1,12,8,2]=>[7,2,2,1]=>2079
[8,3,4,5,6,7,9,10,11,12,1,2]=>[9,2,1]=>320
[2,7,4,5,6,8,9,1,10,3,12,11]=>[8,3,1]=>891
[10,7,4,5,6,8,9,1,11,12,3,2]=>[7,2,1,1,1]=>1728
[2,9,4,5,6,10,8,1,11,7,12,3]=>[7,2,2,1]=>2079
[2,7,4,5,6,8,9,10,11,1,12,3]=>[9,2,1]=>320
[2,3,6,5,7,8,1,9,10,4,12,11]=>[8,3,1]=>891
[10,3,6,5,7,8,1,9,11,12,4,2]=>[7,2,1,1,1]=>1728
[2,9,6,5,7,8,1,10,11,4,12,3]=>[7,2,1,1,1]=>1728
[2,3,8,5,9,7,1,10,6,11,12,4]=>[7,2,2,1]=>2079
[2,3,6,5,7,8,9,10,1,11,12,4]=>[9,2,1]=>320
[2,3,4,5,6,7,8,9,10,1,12,11]=>[10,2]=>54
[10,3,4,5,6,7,8,9,11,12,1,2]=>[9,2,1]=>320
[2,9,4,5,6,7,8,10,11,1,12,3]=>[9,2,1]=>320
[2,3,8,5,6,7,9,10,1,11,12,4]=>[9,2,1]=>320
[2,3,4,7,6,8,9,1,10,11,12,5]=>[9,2,1]=>320
[5,4,7,6,3,1,2,8]=>[3,2,2,1]=>70
[3,6,4,8,1,5,2,7]=>[4,2,2]=>56
[3,6,8,4,1,5,2,7]=>[4,2,2]=>56
[8,7,1,4,2,3,5,6]=>[5,1,1,1]=>35
[3,8,6,4,1,5,2,7]=>[4,2,1,1]=>90
[4,6,1,3,2,8,7,5]=>[3,3,2]=>42
[7,1,4,8,2,3,6,5]=>[4,2,2]=>56
[4,5,3,6,7,1,8,2]=>[5,2,1]=>64
[1,4,7,8,3,5,2,6]=>[4,3,1]=>70
[6,1,2,5,4,8,7,3]=>[4,2,1,1]=>90
[8,4,1,7,3,5,6,2]=>[4,2,1,1]=>90
[2,4,5,6,8,3,1,7]=>[5,2,1]=>64
[4,5,1,8,6,3,7,2]=>[4,2,1,1]=>90
[1,8,2,3,4,5,9,6,7]=>[7,2]=>27
[1,3,4,5,6,8,9,2,7]=>[7,2]=>27
[8,3,7,2,1,6,5,4]=>[2,2,2,1,1]=>28
[8,4,7,6,2,5,1,3]=>[2,2,2,1,1]=>28
[8,4,7,3,6,2,1,5]=>[2,2,2,1,1]=>28
[3,8,7,5,6,4,1,2]=>[3,2,1,1,1]=>64
[3,8,7,5,6,2,1,4]=>[3,2,1,1,1]=>64
[3,8,7,5,6,2,4,1]=>[3,2,1,1,1]=>64
[2,8,7,5,6,4,1,3]=>[3,2,1,1,1]=>64
[4,5,2,3,6,7,8,9,1]=>[6,2,1]=>105
[4,3,2,5,6,7,8,9,1]=>[6,1,1,1]=>56
[5,6,7,2,3,4,8,9,1]=>[5,3,1]=>162
[5,3,6,2,4,7,8,9,1]=>[5,2,1,1]=>189
[5,4,3,2,6,7,8,9,1]=>[5,1,1,1,1]=>70
[6,3,7,8,2,4,5,9,1]=>[4,3,1,1]=>216
[6,7,4,5,2,3,8,9,1]=>[4,2,2,1]=>216
[6,4,3,7,2,5,8,9,1]=>[4,2,1,1,1]=>189
[7,8,4,5,9,2,3,6,1]=>[3,3,2,1]=>168
[7,4,3,8,9,2,5,6,1]=>[3,3,1,1,1]=>120
[7,5,8,3,6,2,4,9,1]=>[3,2,2,1,1]=>162
[7,5,4,3,8,2,6,9,1]=>[3,2,1,1,1,1]=>105
[7,6,5,4,3,2,8,9,1]=>[3,1,1,1,1,1,1]=>28
[8,6,4,9,3,7,2,5,1]=>[2,2,2,1,1,1]=>48
[8,6,5,4,3,9,2,7,1]=>[2,2,1,1,1,1,1]=>27
[4,5,2,3,6,7,8,9,10,1]=>[7,2,1]=>160
[4,3,2,5,6,7,8,9,10,1]=>[7,1,1,1]=>84
[5,6,7,2,3,4,8,9,10,1]=>[6,3,1]=>315
[5,3,6,2,4,7,8,9,10,1]=>[6,2,1,1]=>350
[5,4,3,2,6,7,8,9,10,1]=>[6,1,1,1,1]=>126
[6,7,8,9,2,3,4,5,10,1]=>[5,4,1]=>288
[6,3,7,8,2,4,5,9,10,1]=>[5,3,1,1]=>567
[6,7,4,5,2,3,8,9,10,1]=>[5,2,2,1]=>525
[6,4,3,7,2,5,8,9,10,1]=>[5,2,1,1,1]=>448
[6,5,4,3,2,7,8,9,10,1]=>[5,1,1,1,1,1]=>126
[7,8,9,10,1,3,4,5,6,2]=>[5,4,1]=>288
[7,3,8,9,10,2,4,5,6,1]=>[4,4,1,1]=>300
[7,4,3,8,9,2,5,6,10,1]=>[4,3,1,1,1]=>525
[7,5,8,3,6,2,4,9,10,1]=>[4,2,2,1,1]=>567
[7,5,4,3,8,2,6,9,10,1]=>[4,2,1,1,1,1]=>350
[7,6,5,4,3,2,8,9,10,1]=>[4,1,1,1,1,1,1]=>84
[8,5,9,3,6,10,2,4,7,1]=>[3,3,2,1,1]=>450
[8,5,4,3,9,10,2,6,7,1]=>[3,3,1,1,1,1]=>225
[8,9,6,7,4,5,2,3,10,1]=>[3,2,2,2,1]=>288
[8,6,4,9,3,7,2,5,10,1]=>[3,2,2,1,1,1]=>315
[8,6,5,4,3,9,2,7,10,1]=>[3,2,1,1,1,1,1]=>160
[8,7,6,5,4,3,2,9,10,1]=>[3,1,1,1,1,1,1,1]=>36
[9,7,5,4,10,3,8,2,6,1]=>[2,2,2,1,1,1,1]=>75
[9,7,6,5,4,3,10,2,8,1]=>[2,2,1,1,1,1,1,1]=>35
[10,1,9,2,8,3,7,4,6,5]=>[5,1,1,1,1,1]=>126
[1,5,6,3,8,2,7,4]=>[4,2,2]=>56
[1,7,5,3,6,2,8,4]=>[4,2,1,1]=>90
[1,5,7,3,4,2,8,6]=>[4,3,1]=>70
[1,4,5,3,8,2,7,6]=>[4,2,2]=>56
[5,1,6,8,3,7,2,4]=>[3,3,2]=>42
[1,2,3,4,5,6,7,8,9,10,11]=>[11]=>1
[1,4,3,6,5,10,9,7,8,2]=>[5,3,1,1]=>567
[1,4,3,8,7,5,6,10,9,2]=>[5,3,1,1]=>567
[1,4,3,10,7,5,9,6,8,2]=>[5,3,1,1]=>567
[1,4,3,10,9,8,5,6,7,2]=>[5,2,1,1,1]=>448
[1,6,5,3,4,8,7,10,9,2]=>[5,3,1,1]=>567
[1,6,5,3,4,10,9,7,8,2]=>[5,2,2,1]=>525
[1,8,5,3,7,4,6,10,9,2]=>[5,3,1,1]=>567
[1,10,5,3,7,4,9,6,8,2]=>[5,3,1,1]=>567
[1,10,5,3,9,8,4,6,7,2]=>[5,2,1,1,1]=>448
[1,8,7,6,3,4,5,10,9,2]=>[5,2,1,1,1]=>448
[1,10,7,6,3,4,9,5,8,2]=>[5,2,1,1,1]=>448
[1,10,9,6,3,8,4,5,7,2]=>[5,2,1,1,1]=>448
[1,10,9,8,7,3,4,5,6,2]=>[5,1,1,1,1,1]=>126
[3,1,2,6,5,8,7,10,9,4]=>[5,4,1]=>288
[3,1,2,6,5,10,9,7,8,4]=>[5,3,1,1]=>567
[3,1,2,8,7,5,6,10,9,4]=>[5,3,1,1]=>567
[3,1,2,10,7,5,9,6,8,4]=>[5,3,1,1]=>567
[3,1,2,10,9,8,5,6,7,4]=>[5,2,1,1,1]=>448
[3,1,5,2,4,8,7,10,9,6]=>[5,4,1]=>288
[3,1,5,2,4,10,9,7,8,6]=>[5,3,1,1]=>567
[3,1,5,2,7,4,6,10,9,8]=>[5,4,1]=>288
[3,1,5,2,9,8,4,6,7,10]=>[6,3,1]=>315
[3,1,7,6,2,4,5,10,9,8]=>[5,3,2]=>450
[3,1,7,6,2,4,9,5,8,10]=>[6,3,1]=>315
[3,1,9,6,2,8,4,5,7,10]=>[6,3,1]=>315
[3,1,9,8,7,2,4,5,6,10]=>[6,2,1,1]=>350
[5,4,1,2,3,8,7,10,9,6]=>[5,3,2]=>450
[5,4,1,2,3,10,9,7,8,6]=>[5,2,2,1]=>525
[5,4,1,2,7,3,6,10,9,8]=>[5,3,2]=>450
[5,4,1,2,7,3,9,6,8,10]=>[6,3,1]=>315
[5,4,1,2,9,8,3,6,7,10]=>[6,2,2]=>225
[7,4,1,6,2,3,5,10,9,8]=>[5,3,2]=>450
[7,4,1,6,2,3,9,5,8,10]=>[6,3,1]=>315
[9,4,1,6,2,8,3,5,7,10]=>[6,3,1]=>315
[9,4,1,8,7,2,3,5,6,10]=>[6,2,1,1]=>350
[7,6,5,1,2,3,4,10,9,8]=>[5,2,2,1]=>525
[7,6,5,1,2,3,9,4,8,10]=>[6,2,1,1]=>350
[9,6,5,1,2,8,3,4,7,10]=>[6,2,1,1]=>350
[9,8,5,1,7,2,3,4,6,10]=>[6,2,1,1]=>350
[1,4,3,6,5,8,7,12,11,9,10,2]=>[6,4,1,1]=>3080
[1,4,3,6,5,10,9,7,8,12,11,2]=>[6,4,1,1]=>3080
[1,4,3,6,5,12,9,7,11,8,10,2]=>[6,4,1,1]=>3080
[1,4,3,6,5,12,11,10,7,8,9,2]=>[6,3,1,1,1]=>3696
[1,4,3,8,7,5,6,10,9,12,11,2]=>[6,4,1,1]=>3080
[1,4,3,8,7,5,6,12,11,9,10,2]=>[6,3,2,1]=>5632
[1,4,3,10,7,5,9,6,8,12,11,2]=>[6,4,1,1]=>3080
[1,4,3,12,7,5,9,6,11,8,10,2]=>[6,4,1,1]=>3080
[1,4,3,12,7,5,11,10,6,8,9,2]=>[6,3,1,1,1]=>3696
[1,4,3,10,9,8,5,6,7,12,11,2]=>[6,3,1,1,1]=>3696
[1,4,3,12,9,8,5,6,11,7,10,2]=>[6,3,1,1,1]=>3696
[1,4,3,12,11,8,5,10,6,7,9,2]=>[6,3,1,1,1]=>3696
[1,4,3,12,11,10,9,5,6,7,8,2]=>[6,2,1,1,1,1]=>2100
[1,6,5,3,4,8,7,10,9,12,11,2]=>[6,4,1,1]=>3080
[1,6,5,3,4,8,7,12,11,9,10,2]=>[6,3,2,1]=>5632
[1,6,5,3,4,10,9,7,8,12,11,2]=>[6,3,2,1]=>5632
[1,6,5,3,4,12,9,7,11,8,10,2]=>[6,3,2,1]=>5632
[1,6,5,3,4,12,11,10,7,8,9,2]=>[6,2,2,1,1]=>3564
[1,8,5,3,7,4,6,10,9,12,11,2]=>[6,4,1,1]=>3080
[1,8,5,3,7,4,6,12,11,9,10,2]=>[6,3,2,1]=>5632
[1,10,5,3,7,4,9,6,8,12,11,2]=>[6,4,1,1]=>3080
[1,12,5,3,7,4,9,6,11,8,10,2]=>[6,4,1,1]=>3080
[1,12,5,3,7,4,11,10,6,8,9,2]=>[6,3,1,1,1]=>3696
[1,10,5,3,9,8,4,6,7,12,11,2]=>[6,3,1,1,1]=>3696
[1,12,5,3,9,8,4,6,11,7,10,2]=>[6,3,1,1,1]=>3696
[1,12,5,3,11,8,4,10,6,7,9,2]=>[6,3,1,1,1]=>3696
[1,12,5,3,11,10,9,4,6,7,8,2]=>[6,2,1,1,1,1]=>2100
[1,8,7,6,3,4,5,10,9,12,11,2]=>[6,3,1,1,1]=>3696
[1,8,7,6,3,4,5,12,11,9,10,2]=>[6,2,2,1,1]=>3564
[1,10,7,6,3,4,9,5,8,12,11,2]=>[6,3,1,1,1]=>3696
[1,12,7,6,3,4,9,5,11,8,10,2]=>[6,3,1,1,1]=>3696
[1,12,7,6,3,4,11,10,5,8,9,2]=>[6,2,2,1,1]=>3564
[1,10,9,6,3,8,4,5,7,12,11,2]=>[6,3,1,1,1]=>3696
[1,12,9,6,3,8,4,5,11,7,10,2]=>[6,3,1,1,1]=>3696
[1,12,11,6,3,8,4,10,5,7,9,2]=>[6,3,1,1,1]=>3696
[1,12,11,6,3,10,9,4,5,7,8,2]=>[6,2,1,1,1,1]=>2100
[1,10,9,8,7,3,4,5,6,12,11,2]=>[6,2,1,1,1,1]=>2100
[1,12,9,8,7,3,4,5,11,6,10,2]=>[6,2,1,1,1,1]=>2100
[1,12,11,8,7,3,4,10,5,6,9,2]=>[6,2,1,1,1,1]=>2100
[1,12,11,10,7,3,9,4,5,6,8,2]=>[6,2,1,1,1,1]=>2100
[1,12,11,10,9,8,3,4,5,6,7,2]=>[6,1,1,1,1,1,1]=>462
[3,1,2,6,5,8,7,10,9,12,11,4]=>[6,5,1]=>1155
[3,1,2,6,5,8,7,12,11,9,10,4]=>[6,4,1,1]=>3080
[3,1,2,6,5,10,9,7,8,12,11,4]=>[6,4,1,1]=>3080
[3,1,2,6,5,12,9,7,11,8,10,4]=>[6,4,1,1]=>3080
[3,1,2,6,5,12,11,10,7,8,9,4]=>[6,3,1,1,1]=>3696
[3,1,2,8,7,5,6,10,9,12,11,4]=>[6,4,1,1]=>3080
[3,1,2,8,7,5,6,12,11,9,10,4]=>[6,3,2,1]=>5632
[3,1,2,10,7,5,9,6,8,12,11,4]=>[6,4,1,1]=>3080
[3,1,2,12,7,5,9,6,11,8,10,4]=>[6,4,1,1]=>3080
[3,1,2,12,7,5,11,10,6,8,9,4]=>[6,3,1,1,1]=>3696
[3,1,2,10,9,8,5,6,7,12,11,4]=>[6,3,1,1,1]=>3696
[3,1,2,12,9,8,5,6,11,7,10,4]=>[6,3,1,1,1]=>3696
[3,1,2,12,11,8,5,10,6,7,9,4]=>[6,3,1,1,1]=>3696
[3,1,2,12,11,10,9,5,6,7,8,4]=>[6,2,1,1,1,1]=>2100
[3,1,5,2,4,8,7,10,9,12,11,6]=>[6,5,1]=>1155
[3,1,5,2,4,8,7,12,11,9,10,6]=>[6,4,1,1]=>3080
[3,1,5,2,4,10,9,7,8,12,11,6]=>[6,4,1,1]=>3080
[3,1,5,2,4,12,9,7,11,8,10,6]=>[6,4,1,1]=>3080
[3,1,5,2,4,12,11,10,7,8,9,6]=>[6,3,1,1,1]=>3696
[3,1,5,2,7,4,6,10,9,12,11,8]=>[6,5,1]=>1155
[3,1,5,2,7,4,6,12,11,9,10,8]=>[6,4,1,1]=>3080
[3,1,5,2,7,4,9,6,8,12,11,10]=>[6,5,1]=>1155
[3,1,5,2,7,4,9,6,11,8,10,12]=>[7,5]=>297
[3,1,5,2,7,4,11,10,6,8,9,12]=>[7,4,1]=>1408
[3,1,5,2,9,8,4,6,7,12,11,10]=>[6,4,2]=>2673
[3,1,5,2,9,8,4,6,11,7,10,12]=>[7,4,1]=>1408
[3,1,5,2,11,8,4,10,6,7,9,12]=>[7,4,1]=>1408
[3,1,5,2,11,10,9,4,6,7,8,12]=>[7,3,1,1]=>2376
[3,1,7,6,2,4,5,10,9,12,11,8]=>[6,4,2]=>2673
[3,1,7,6,2,4,5,12,11,9,10,8]=>[6,3,2,1]=>5632
[3,1,7,6,2,4,9,5,8,12,11,10]=>[6,4,2]=>2673
[3,1,7,6,2,4,9,5,11,8,10,12]=>[7,4,1]=>1408
[3,1,7,6,2,4,11,10,5,8,9,12]=>[7,3,2]=>1925
[3,1,9,6,2,8,4,5,7,12,11,10]=>[6,4,2]=>2673
[3,1,9,6,2,8,4,5,11,7,10,12]=>[7,4,1]=>1408
[3,1,11,6,2,8,4,10,5,7,9,12]=>[7,4,1]=>1408
[3,1,11,6,2,10,9,4,5,7,8,12]=>[7,3,1,1]=>2376
[3,1,9,8,7,2,4,5,6,12,11,10]=>[6,3,2,1]=>5632
[3,1,9,8,7,2,4,5,11,6,10,12]=>[7,3,1,1]=>2376
[3,1,11,8,7,2,4,10,5,6,9,12]=>[7,3,1,1]=>2376
[3,1,11,10,7,2,9,4,5,6,8,12]=>[7,3,1,1]=>2376
[3,1,11,10,9,8,2,4,5,6,7,12]=>[7,2,1,1,1]=>1728
[5,4,1,2,3,8,7,10,9,12,11,6]=>[6,4,2]=>2673
[5,4,1,2,3,8,7,12,11,9,10,6]=>[6,3,2,1]=>5632
[5,4,1,2,3,10,9,7,8,12,11,6]=>[6,3,2,1]=>5632
[5,4,1,2,3,12,9,7,11,8,10,6]=>[6,3,2,1]=>5632
[5,4,1,2,3,12,11,10,7,8,9,6]=>[6,2,2,1,1]=>3564
[5,4,1,2,7,3,6,10,9,12,11,8]=>[6,4,2]=>2673
[5,4,1,2,7,3,6,12,11,9,10,8]=>[6,3,2,1]=>5632
[5,4,1,2,7,3,9,6,8,12,11,10]=>[6,4,2]=>2673
[5,4,1,2,7,3,9,6,11,8,10,12]=>[7,4,1]=>1408
[5,4,1,2,7,3,11,10,6,8,9,12]=>[7,3,2]=>1925
[5,4,1,2,9,8,3,6,7,12,11,10]=>[6,3,3]=>1650
[5,4,1,2,9,8,3,6,11,7,10,12]=>[7,3,2]=>1925
[5,4,1,2,11,8,3,10,6,7,9,12]=>[7,3,2]=>1925
[5,4,1,2,11,10,9,3,6,7,8,12]=>[7,2,2,1]=>2079
[7,4,1,6,2,3,5,10,9,12,11,8]=>[6,4,2]=>2673
[7,4,1,6,2,3,5,12,11,9,10,8]=>[6,3,2,1]=>5632
[7,4,1,6,2,3,9,5,8,12,11,10]=>[6,4,2]=>2673
[7,4,1,6,2,3,9,5,11,8,10,12]=>[7,4,1]=>1408
[7,4,1,6,2,3,11,10,5,8,9,12]=>[7,3,2]=>1925
[9,4,1,6,2,8,3,5,7,12,11,10]=>[6,4,2]=>2673
[9,4,1,6,2,8,3,5,11,7,10,12]=>[7,4,1]=>1408
[11,4,1,6,2,8,3,10,5,7,9,12]=>[7,4,1]=>1408
[11,4,1,6,2,10,9,3,5,7,8,12]=>[7,3,1,1]=>2376
[9,4,1,8,7,2,3,5,6,12,11,10]=>[6,3,2,1]=>5632
[9,4,1,8,7,2,3,5,11,6,10,12]=>[7,3,1,1]=>2376
[11,4,1,8,7,2,3,10,5,6,9,12]=>[7,3,1,1]=>2376
[11,4,1,10,7,2,9,3,5,6,8,12]=>[7,3,1,1]=>2376
[11,4,1,10,9,8,2,3,5,6,7,12]=>[7,2,1,1,1]=>1728
[7,6,5,1,2,3,4,10,9,12,11,8]=>[6,3,2,1]=>5632
[7,6,5,1,2,3,4,12,11,9,10,8]=>[6,2,2,2]=>1925
[7,6,5,1,2,3,9,4,8,12,11,10]=>[6,3,2,1]=>5632
[7,6,5,1,2,3,9,4,11,8,10,12]=>[7,3,1,1]=>2376
[7,6,5,1,2,3,11,10,4,8,9,12]=>[7,2,2,1]=>2079
[9,6,5,1,2,8,3,4,7,12,11,10]=>[6,3,2,1]=>5632
[9,6,5,1,2,8,3,4,11,7,10,12]=>[7,3,1,1]=>2376
[11,6,5,1,2,8,3,10,4,7,9,12]=>[7,3,1,1]=>2376
[11,6,5,1,2,10,9,3,4,7,8,12]=>[7,2,2,1]=>2079
[9,8,5,1,7,2,3,4,6,12,11,10]=>[6,3,2,1]=>5632
[9,8,5,1,7,2,3,4,11,6,10,12]=>[7,3,1,1]=>2376
[11,8,5,1,7,2,3,10,4,6,9,12]=>[7,3,1,1]=>2376
[11,10,5,1,7,2,9,3,4,6,8,12]=>[7,3,1,1]=>2376
[11,10,5,1,9,8,2,3,4,6,7,12]=>[7,2,1,1,1]=>1728
[9,8,7,6,1,2,3,4,5,12,11,10]=>[6,2,2,1,1]=>3564
[9,8,7,6,1,2,3,4,11,5,10,12]=>[7,2,1,1,1]=>1728
[11,8,7,6,1,2,3,10,4,5,9,12]=>[7,2,1,1,1]=>1728
[11,10,7,6,1,2,9,3,4,5,8,12]=>[7,2,1,1,1]=>1728
[11,10,9,6,1,8,2,3,4,5,7,12]=>[7,2,1,1,1]=>1728
[11,10,9,8,7,1,2,3,4,5,6,12]=>[7,1,1,1,1,1]=>462
[5,4,7,1,8,6,3,2]=>[3,2,2,1]=>70
[2,4,1,5,3,6,7,8,9]=>[7,2]=>27
[1,4,8,2,6,5,3,7]=>[4,2,1,1]=>90
[8,5,1,3,6,2,4,7]=>[4,2,1,1]=>90
[5,2,8,1,7,4,3,6]=>[3,2,2,1]=>70
[1,2,5,6,8,7,3,4]=>[5,2,1]=>64
[1,5,6,8,2,7,4,3]=>[4,2,1,1]=>90
[2,6,7,3,4,1,8,5]=>[4,3,1]=>70
[1,6,5,7,8,2,4,3]=>[4,2,1,1]=>90
[1,5,6,7,2,8,4,3]=>[5,2,1]=>64
[3,7,6,1,8,2,4,5]=>[4,3,1]=>70
[1,3,7,2,6,4,8,5]=>[4,3,1]=>70
[1,5,8,6,7,3,4,2]=>[4,2,1,1]=>90
[1,6,5,8,7,2,4,3]=>[3,2,2,1]=>70
[1,5,7,6,2,8,3,4]=>[4,3,1]=>70
[1,2,5,8,6,7,4,3]=>[5,1,1,1]=>35
[1,2,6,5,7,3,8,4]=>[5,2,1]=>64
[1,7,5,8,6,4,2,3]=>[3,2,2,1]=>70
[3,6,5,8,1,2,7,4]=>[3,3,2]=>42
[5,4,7,8,1,6,3,2]=>[3,2,2,1]=>70
[2,5,6,8,1,3,7,4]=>[4,3,1]=>70
[5,3,6,8,1,2,7,4]=>[3,3,2]=>42
[4,6,5,8,3,2,7,1]=>[3,2,1,1,1]=>64
[4,5,6,8,2,3,7,1]=>[4,3,1]=>70
[2,5,8,7,1,6,4,3]=>[3,2,1,1,1]=>64
[4,7,5,8,3,6,2,1]=>[3,2,1,1,1]=>64
[7,3,6,8,5,2,1,4]=>[3,2,1,1,1]=>64
[8,3,6,7,5,2,4,1]=>[3,2,1,1,1]=>64
[8,4,5,7,3,6,2,1]=>[3,2,1,1,1]=>64
[2,4,7,8,5,6,3,1]=>[4,2,1,1]=>90
[3,6,8,7,5,2,4,1]=>[3,2,1,1,1]=>64
[6,4,7,8,5,1,3,2]=>[3,2,2,1]=>70
[7,8,4,6,5,3,1,2]=>[2,2,2,1,1]=>28
[6,8,4,7,5,1,3,2]=>[2,2,2,1,1]=>28
[8,9,2,3,4,5,1,6,7]=>[6,2,1]=>105
[6,5,7,8,9,1,2,3,4]=>[4,4,1]=>84
[2,8,7,5,1,6,3,4]=>[3,3,1,1]=>56
[8,7,6,4,2,1,5,3]=>[2,2,1,1,1,1]=>20
[3,8,7,5,2,6,4,1]=>[3,2,1,1,1]=>64
[5,8,3,7,1,4,6,2]=>[3,2,2,1]=>70
[5,3,8,2,4,6,1,7]=>[4,2,1,1]=>90
[4,5,8,3,2,6,1,7]=>[4,2,1,1]=>90
[5,8,2,1,4,6,3,7]=>[4,2,2]=>56
[4,1,5,8,3,6,2,7]=>[4,3,1]=>70
[4,5,8,3,6,1,2,7]=>[4,2,2]=>56
[3,2,7,1,8,5,4,6]=>[3,3,2]=>42
[4,7,8,5,2,3,1,6]=>[3,3,1,1]=>56
[6,2,7,8,1,5,3,4]=>[3,3,2]=>42
[2,7,1,3,8,5,4,6]=>[4,3,1]=>70
[2,6,7,8,4,1,3,5]=>[4,3,1]=>70
[2,6,7,8,4,3,1,5]=>[4,2,1,1]=>90
[7,1,2,3,4,5,8,6,9]=>[7,2]=>27
[6,1,2,3,4,7,5,8,9]=>[7,2]=>27
[5,1,2,3,6,4,7,8,9]=>[7,2]=>27
[4,1,2,5,3,6,7,8,9]=>[7,2]=>27
[7,1,2,6,3,8,4,5]=>[5,2,1]=>64
[8,1,2,6,5,3,7,4]=>[4,2,1,1]=>90
[7,4,1,8,2,5,3,6]=>[4,2,2]=>56
[7,4,8,3,1,2,6,5]=>[3,2,2,1]=>70
[8,4,5,3,1,6,7,2]=>[4,2,1,1]=>90
[8,2,1,7,4,3,5,6]=>[4,2,1,1]=>90
[7,2,6,8,4,1,3,5]=>[3,3,1,1]=>56
[7,2,5,1,6,8,3,4]=>[4,3,1]=>70
[6,2,1,7,4,8,3,5]=>[3,3,2]=>42
[1,7,4,3,2,5,6,8]=>[5,1,1,1]=>35
[1,7,4,3,6,2,5,8]=>[4,2,1,1]=>90
[3,7,5,8,2,4,6,1]=>[3,3,1,1]=>56
[5,2,1,6,3,4,8,7]=>[4,3,1]=>70
[5,1,3,4,6,2,8,7]=>[5,2,1]=>64
[3,8,4,5,7,2,6,1]=>[4,2,1,1]=>90
[3,8,4,7,5,6,2,1]=>[4,1,1,1,1]=>35
[4,2,8,6,3,7,5,1]=>[3,3,1,1]=>56
[4,1,7,6,3,8,5,2]=>[3,3,1,1]=>56
[7,4,1,8,5,3,6,2]=>[3,2,2,1]=>70
[3,5,6,8,4,7,1,2]=>[4,2,2]=>56
[5,4,1,8,6,7,2,3]=>[3,3,2]=>42
[6,2,8,4,5,3,7,1]=>[4,2,1,1]=>90
[4,5,2,1,8,7,3,6]=>[3,3,2]=>42
[4,7,3,8,2,6,5,1]=>[3,2,2,1]=>70
[4,7,3,1,8,6,2,5]=>[3,3,2]=>42
[6,2,1,3,7,4,8,5]=>[4,3,1]=>70
[6,3,7,1,2,5,8,4]=>[4,2,2]=>56
[5,1,4,7,8,2,6,3]=>[4,2,2]=>56
[7,2,5,8,1,3,6,4]=>[3,3,2]=>42
[8,3,6,7,2,4,5,1]=>[3,3,1,1]=>56
[3,8,7,5,2,1,6,4]=>[3,2,1,1,1]=>64
[3,8,5,6,2,7,4,1]=>[4,2,1,1]=>90
[3,6,5,8,4,2,7,1]=>[3,2,1,1,1]=>64
[6,8,3,2,5,7,4,1]=>[3,2,2,1]=>70
[4,1,5,6,8,7,3,2]=>[4,2,1,1]=>90
[8,4,2,3,6,7,5,1]=>[4,2,1,1]=>90
[6,1,2,4,5,7,8,3]=>[6,1,1]=>21
[4,5,1,3,7,6,8,2]=>[4,3,1]=>70
[3,5,4,8,6,2,7,1]=>[4,2,1,1]=>90
[3,6,2,4,5,8,7,1]=>[4,3,1]=>70
[9,1,2,3,8,5,6,7,4]=>[6,1,1,1]=>56
[8,1,3,7,4,5,6,2]=>[5,1,1,1]=>35
[10,1,2,3,4,9,6,7,8,5]=>[7,1,1,1]=>84
[10,1,9,3,4,5,6,7,8,2]=>[7,1,1,1]=>84
[8,1,5,3,6,4,7,2]=>[4,2,1,1]=>90
[2,6,4,8,3,1,5,7]=>[4,2,1,1]=>90
[2,6,4,1,5,8,7,3]=>[4,2,2]=>56
[8,1,5,4,7,3,6,2]=>[3,2,1,1,1]=>64
[7,6,5,4,1,8,2,3]=>[3,2,1,1,1]=>64
[8,1,5,4,7,6,3,2]=>[3,2,1,1,1]=>64
[2,5,1,4,6,7,3,8]=>[5,2,1]=>64
[3,6,4,1,5,7,8,2]=>[5,2,1]=>64
[7,6,5,2,8,4,1,3]=>[2,2,2,1,1]=>28
[3,1,6,5,2,8,7,4]=>[3,3,2]=>42
[1,7,2,4,3,5,8,6]=>[5,2,1]=>64
[3,8,1,7,4,2,6,5]=>[3,3,1,1]=>56
[8,1,7,4,3,5,6,2]=>[4,1,1,1,1]=>35
[6,8,2,4,5,3,7,1]=>[4,2,1,1]=>90
[4,8,5,3,6,1,7,2]=>[4,2,1,1]=>90
[2,8,3,1,4,7,5,6]=>[5,2,1]=>64
[8,6,3,2,7,4,1,5]=>[3,2,1,1,1]=>64
[2,7,3,1,8,4,5,6]=>[5,2,1]=>64
[1,2,8,3,5,6,4,7]=>[6,1,1]=>21
[2,8,1,3,5,4,6,7]=>[5,2,1]=>64
[1,5,2,8,6,4,3,7]=>[4,2,1,1]=>90
[7,4,8,6,3,1,2,5]=>[3,2,2,1]=>70
[3,6,8,4,1,2,5,7]=>[4,3,1]=>70
[4,7,8,5,2,1,3,6]=>[3,3,1,1]=>56
[6,1,5,2,8,7,3,4]=>[4,2,2]=>56
[8,1,3,5,7,4,2,6]=>[4,2,1,1]=>90
[3,1,8,5,4,7,2,6]=>[3,3,1,1]=>56
[3,1,6,4,8,5,2,7]=>[4,3,1]=>70
[5,1,3,4,2,6,8,7]=>[5,2,1]=>64
[3,2,6,4,1,5,7,8]=>[5,2,1]=>64
[5,4,2,1,8,3,6,7]=>[4,2,1,1]=>90
[4,2,5,1,8,7,3,6]=>[3,3,2]=>42
[6,8,2,7,1,4,3,5]=>[3,2,2,1]=>70
[1,8,4,7,3,2,5,6]=>[4,2,1,1]=>90
[8,6,3,1,5,7,2,4]=>[3,3,1,1]=>56
[5,8,3,1,4,7,6,2]=>[3,2,2,1]=>70
[1,2,5,4,7,8,3,6]=>[5,2,1]=>64
[1,8,3,2,6,4,7,5]=>[4,3,1]=>70
[4,7,1,2,5,3,6,8]=>[5,2,1]=>64
[6,8,4,1,3,7,2,5]=>[3,2,2,1]=>70
[3,2,6,1,7,8,5,4]=>[4,2,2]=>56
[7,6,4,1,8,3,5,2]=>[3,2,1,1,1]=>64
[5,4,1,6,7,3,2,8]=>[4,2,1,1]=>90
[7,4,1,6,5,8,2,3]=>[3,3,1,1]=>56
[8,5,4,1,6,7,3,2]=>[3,2,1,1,1]=>64
[5,2,1,6,4,7,8,3]=>[4,2,2]=>56
[1,6,2,3,5,7,8,4]=>[6,1,1]=>21
[1,3,4,8,5,2,6,7]=>[6,1,1]=>21
[8,2,4,6,1,7,3,5]=>[4,3,1]=>70
[1,5,7,2,3,6,8,4]=>[5,2,1]=>64
[7,3,1,4,2,5,8,6]=>[4,3,1]=>70
[4,3,5,1,6,2,7,8]=>[5,2,1]=>64
[8,6,3,5,4,1,2,7]=>[3,2,1,1,1]=>64
[8,3,2,6,1,5,4,7]=>[3,2,2,1]=>70
[8,5,1,7,4,6,2,3]=>[3,2,2,1]=>70
[4,8,1,7,6,3,5,2]=>[3,2,1,1,1]=>64
[8,5,1,7,4,3,6,2]=>[3,2,1,1,1]=>64
[8,5,7,6,2,1,3,4]=>[3,2,1,1,1]=>64
[5,4,8,3,1,7,2,6]=>[3,2,2,1]=>70
[5,1,4,8,3,2,7,6]=>[3,2,2,1]=>70
[4,8,1,7,6,5,2,3]=>[3,2,1,1,1]=>64
[4,3,8,7,2,6,1,5]=>[2,2,2,2]=>14
[3,8,7,2,6,4,1,5]=>[3,2,1,1,1]=>64
[8,2,5,7,4,3,6,1]=>[3,2,1,1,1]=>64
[3,8,7,4,6,1,2,5]=>[3,3,1,1]=>56
[8,7,6,3,5,4,1,2]=>[2,2,1,1,1,1]=>20
[2,8,4,7,6,1,5,3]=>[3,2,1,1,1]=>64
[2,5,4,8,3,1,7,6]=>[3,2,2,1]=>70
[5,4,8,2,1,3,7,6]=>[3,2,2,1]=>70
[3,8,7,2,6,1,5,4]=>[2,2,2,1,1]=>28
[1,8,4,7,6,3,5,2]=>[3,2,1,1,1]=>64
[1,8,3,7,6,5,2,4]=>[3,2,1,1,1]=>64
[1,4,3,8,7,2,6,5]=>[3,2,2,1]=>70
[7,1,5,4,6,2,3,8]=>[4,2,1,1]=>90
[7,4,1,3,6,2,5,8]=>[4,2,1,1]=>90
[2,6,8,3,1,7,4,5]=>[4,2,2]=>56
[2,5,4,8,1,7,3,6]=>[3,3,2]=>42
[7,2,6,5,8,3,4,1]=>[3,2,1,1,1]=>64
[5,6,3,1,4,2,7,8]=>[4,2,2]=>56
[2,6,1,5,3,4,7,8]=>[5,2,1]=>64
[3,4,7,8,5,1,6,2]=>[4,2,2]=>56
[5,3,6,4,8,7,2,1]=>[3,3,1,1]=>56
[1,5,4,8,6,2,7,3]=>[4,2,2]=>56
[7,6,2,5,3,8,4,1]=>[3,2,1,1,1]=>64
[8,4,6,1,3,7,2,5]=>[3,3,1,1]=>56
[4,8,5,1,2,3,6,7]=>[5,2,1]=>64
[4,5,1,3,8,6,2,7]=>[4,3,1]=>70
[2,1,6,7,4,8,3,5]=>[4,3,1]=>70
[7,8,3,1,6,2,5,4]=>[3,2,2,1]=>70
[7,5,2,8,1,4,6,3]=>[3,2,2,1]=>70
[6,7,8,2,5,4,3,1]=>[3,2,1,1,1]=>64
[7,8,1,6,2,5,4,3]=>[3,2,1,1,1]=>64
[5,1,6,8,3,4,7,2]=>[4,3,1]=>70
[7,1,6,8,5,4,3,2]=>[3,1,1,1,1,1]=>21
[5,6,8,1,2,3,7,4]=>[4,3,1]=>70
[4,8,1,2,7,6,5,3]=>[3,2,1,1,1]=>64
[4,6,1,2,8,5,7,3]=>[4,3,1]=>70
[6,4,7,3,5,2,1,8]=>[3,2,1,1,1]=>64
[5,7,8,4,2,1,3,6]=>[3,3,1,1]=>56
[3,1,6,2,5,7,8,4]=>[5,2,1]=>64
[1,6,4,5,2,7,3,8]=>[5,2,1]=>64
[6,2,1,4,5,3,7,8]=>[5,2,1]=>64
[1,2,3,4,5,8,9,6,7]=>[7,2]=>27
[1,2,3,4,7,9,5,8,6]=>[6,2,1]=>105
[1,2,3,6,9,4,7,8,5]=>[6,2,1]=>105
[1,2,4,6,8,3,7,5]=>[5,2,1]=>64
[1,2,5,9,3,6,7,8,4]=>[6,2,1]=>105
[1,3,5,8,2,6,7,4]=>[5,2,1]=>64
[1,4,9,2,5,6,7,8,3]=>[6,2,1]=>105
[3,9,1,4,5,6,7,8,2]=>[6,2,1]=>105
[6,1,3,7,2,8,5,4]=>[4,2,2]=>56
[6,4,5,8,3,7,1,2]=>[3,2,2,1]=>70
[8,1,4,3,6,7,2,5]=>[4,2,1,1]=>90
[2,6,8,4,3,1,7,5]=>[3,2,2,1]=>70
[8,1,5,2,6,4,3,7]=>[4,2,1,1]=>90
[1,6,7,4,2,8,3,5]=>[4,3,1]=>70
[1,7,8,4,3,6,2,5]=>[3,2,2,1]=>70
[1,4,7,2,3,6,8,5]=>[5,2,1]=>64
[3,1,2,6,7,8,5,4]=>[5,2,1]=>64
[3,8,1,6,4,2,7,5]=>[3,3,1,1]=>56
[1,6,3,4,7,8,2,5]=>[5,2,1]=>64
[3,1,5,7,6,2,8,4]=>[4,3,1]=>70
[6,3,1,4,2,7,8,5]=>[4,3,1]=>70
[2,4,3,7,6,1,8,5]=>[4,2,2]=>56
[3,1,7,6,5,2,8,4]=>[3,3,1,1]=>56
[1,4,7,6,8,3,2,5]=>[4,2,1,1]=>90
[7,2,1,5,6,3,8,4]=>[4,3,1]=>70
[4,3,1,8,6,2,7,5]=>[3,3,2]=>42
[3,1,5,2,8,7,6,4]=>[3,3,1,1]=>56
[1,2,8,4,3,7,6,5]=>[4,2,1,1]=>90
[2,6,1,8,7,4,3,5]=>[3,3,1,1]=>56
[7,5,1,8,3,2,6,4]=>[3,2,2,1]=>70
[4,7,6,3,1,8,2,5]=>[3,3,1,1]=>56
[5,3,1,8,6,2,4,7]=>[4,2,2]=>56
[5,1,8,6,3,2,4,7]=>[4,2,1,1]=>90
[1,5,4,2,8,6,3,7]=>[4,2,2]=>56
[1,4,2,8,5,3,7,6]=>[4,3,1]=>70
[8,3,1,6,4,2,5,7]=>[4,2,1,1]=>90
[1,7,4,8,3,5,2,6]=>[4,2,1,1]=>90
[7,3,2,4,8,5,1,6]=>[4,2,1,1]=>90
[5,7,8,1,4,2,6,3]=>[3,3,2]=>42
[2,6,3,8,1,7,5,4]=>[3,2,2,1]=>70
[2,5,1,8,6,3,7,4]=>[4,3,1]=>70
[2,8,6,4,1,7,3,5]=>[3,3,1,1]=>56
[1,8,4,2,7,5,3,6]=>[4,2,1,1]=>90
[6,5,1,7,2,8,4,3]=>[3,3,1,1]=>56
[2,8,1,7,5,3,6,4]=>[3,3,1,1]=>56
[1,2,8,7,6,4,3,5]=>[4,1,1,1,1]=>35
[4,1,7,8,6,3,5,2]=>[3,3,1,1]=>56
[1,6,5,7,8,4,2,3]=>[4,2,1,1]=>90
[4,1,8,7,6,3,5,2]=>[3,2,1,1,1]=>64
[4,8,2,6,3,5,1,7]=>[4,2,1,1]=>90
[4,1,8,5,3,6,2,7]=>[4,2,1,1]=>90
[2,6,1,8,5,7,4,3]=>[3,3,1,1]=>56
[6,3,8,4,5,2,7,1]=>[4,2,1,1]=>90
[2,1,6,8,5,3,7,4]=>[3,3,2]=>42
[10,1,11,2,3,4,5,6,7,8,9]=>[9,2]=>44
[1,9,2,10,3,4,5,6,7,8]=>[8,2]=>35
[2,8,1,9,3,4,5,6,7]=>[6,3]=>48
[10,11,1,2,3,4,5,6,7,8,9]=>[9,2]=>44
[3,6,2,4,8,5,7,1]=>[4,3,1]=>70
[3,5,1,8,4,7,6,2]=>[3,3,1,1]=>56
[3,6,1,8,5,4,7,2]=>[3,3,1,1]=>56
[2,4,8,3,7,6,5,1]=>[3,2,1,1,1]=>64
[3,6,8,2,5,7,4,1]=>[3,3,1,1]=>56
[2,6,8,5,4,3,7,1]=>[3,2,1,1,1]=>64
[3,6,8,2,5,4,7,1]=>[3,3,1,1]=>56
[4,6,8,3,2,5,7,1]=>[3,3,1,1]=>56
[4,6,2,8,3,5,7,1]=>[4,3,1]=>70
[3,6,1,8,5,7,4,2]=>[3,3,1,1]=>56
[5,2,6,8,4,1,7,3]=>[3,3,2]=>42
[3,5,8,2,7,4,6,1]=>[3,3,1,1]=>56
[2,6,8,5,7,4,3,1]=>[3,2,1,1,1]=>64
[2,4,8,7,6,3,5,1]=>[3,2,1,1,1]=>64
[7,5,1,6,3,2,8,4]=>[3,3,1,1]=>56
[2,7,6,3,4,1,8,5]=>[4,2,1,1]=>90
[4,8,2,1,7,5,6,3]=>[3,2,2,1]=>70
[6,3,8,5,7,2,4,1]=>[3,2,2,1]=>70
[1,5,4,8,6,2,3,7]=>[4,2,2]=>56
[8,2,1,7,5,3,6,4]=>[3,3,1,1]=>56
[8,2,1,6,7,3,5,4]=>[3,3,1,1]=>56
[6,2,8,1,7,5,3,4]=>[3,2,2,1]=>70
[3,5,1,8,7,6,2,4]=>[3,3,1,1]=>56
[1,4,2,3,6,5,8,7,9]=>[6,3]=>48
[1,3,4,2,6,5,8,7,9]=>[6,3]=>48
[1,4,2,3,6,5,8,7,10,9]=>[6,4]=>90
[2,3,1,4,6,5,8,7,9]=>[6,3]=>48
[4,6,1,2,3,5,8,7,9]=>[6,3]=>48
[3,4,5,1,6,2,8,7,9]=>[6,3]=>48
[3,1,2,4,6,5,8,7,9]=>[6,3]=>48
[1,3,4,2,6,5,8,7,10,9]=>[6,4]=>90
[3,1,4,2,6,5,8,7,10,9,11]=>[6,5]=>132
[4,7,8,3,5,6,1,2]=>[3,3,2]=>42
[2,1,3,4,5,6,9,7,8]=>[7,2]=>27
[1,2,3,4,5,6,7,8,10,9,11]=>[10,1]=>10
[1,2,3,4,5,7,8,6,9]=>[8,1]=>8
[2,1,3,4,5,6,7,10,8,9]=>[8,2]=>35
[3,2,5,6,8,4,7,1]=>[4,3,1]=>70
[2,5,6,4,8,3,7,1]=>[4,2,1,1]=>90
[4,2,5,7,3,8,1,6]=>[4,3,1]=>70
[4,7,3,1,6,8,2,5]=>[3,3,2]=>42
[4,2,7,6,8,1,3,5]=>[3,3,2]=>42
[1,7,4,6,8,3,2,5]=>[4,2,1,1]=>90
[2,4,3,6,5,8,7,10,9,12,11,1]=>[6,5,1]=>1155
[4,7,2,5,6,3,1,8]=>[4,2,1,1]=>90
[5,4,1,3,7,8,2,6]=>[4,2,1,1]=>90
[6,1,5,8,3,7,2,4]=>[3,2,2,1]=>70
[7,2,1,6,8,3,5,4]=>[3,3,1,1]=>56
[5,6,4,1,8,3,2,7]=>[3,3,1,1]=>56
[1,2,6,7,4,3,5,8]=>[5,2,1]=>64
[10,2,3,4,5,6,7,8,1,9]=>[8,1,1]=>36
[7,1,9,3,4,5,6,2,8]=>[6,2,1]=>105
[5,8,6,3,4,1,2,7]=>[3,2,2,1]=>70
[3,10,1,4,5,6,7,8,9,2]=>[7,2,1]=>160
[11,2,3,4,5,6,7,8,9,1,10]=>[9,1,1]=>45
[8,1,10,3,4,5,6,7,2,9]=>[7,2,1]=>160
[7,2,1,9,4,5,6,3,8]=>[5,2,2]=>120
[6,9,7,3,4,5,1,2,8]=>[4,2,2,1]=>216
[6,2,3,1,8,5,4,7]=>[4,2,2]=>56
[5,1,2,6,4,8,3,7]=>[4,3,1]=>70
[8,6,2,3,7,5,1,4]=>[3,2,2,1]=>70
[3,8,1,2,9,5,6,7,4]=>[5,3,1]=>162
[8,7,9,1,2,3,4,5,6]=>[6,2,1]=>105
[3,11,1,4,5,6,7,8,9,10,2]=>[8,2,1]=>231
[12,2,3,4,5,6,7,8,9,10,1,11]=>[10,1,1]=>55
[9,1,11,3,4,5,6,7,8,2,10]=>[8,2,1]=>231
[8,2,1,10,4,5,6,7,3,9]=>[6,2,2]=>225
[7,10,8,3,4,5,6,1,2,9]=>[5,2,2,1]=>525
[7,2,3,1,9,5,6,4,8]=>[5,2,2]=>120
[6,1,2,7,4,5,9,3,8]=>[5,3,1]=>162
[5,9,6,3,4,1,7,2,8]=>[4,2,2,1]=>216
[4,5,2,8,6,1,3,7]=>[4,2,2]=>56
[3,4,8,2,5,6,1,7]=>[5,2,1]=>64
[3,8,1,4,2,9,6,7,5]=>[4,3,2]=>168
[9,7,2,3,8,5,6,1,4]=>[4,2,2,1]=>216
[3,9,1,2,10,5,6,7,8,4]=>[6,3,1]=>315
[3,12,1,4,5,6,7,8,9,10,11,2]=>[9,2,1]=>320
[6,8,2,7,5,3,1,4]=>[3,2,1,1,1]=>64
[5,6,7,2,8,4,1,3]=>[4,2,2]=>56
[5,8,3,6,4,1,7,2]=>[3,2,2,1]=>70
[4,3,8,5,2,7,1,6]=>[3,2,2,1]=>70
[2,8,4,5,1,6,3,7]=>[5,2,1]=>64
[3,5,1,8,7,4,2,6]=>[3,3,1,1]=>56
[4,6,1,3,8,2,7,5]=>[3,3,2]=>42
[8,6,1,2,3,5,7,4]=>[5,1,1,1]=>35
[5,1,7,8,3,2,4,6]=>[4,3,1]=>70
[5,3,6,7,4,2,8,1]=>[4,2,1,1]=>90
[5,4,2,8,6,7,3,1]=>[3,2,2,1]=>70
[6,1,4,2,8,7,3,5]=>[4,2,2]=>56
[3,7,2,6,8,4,5,1]=>[3,3,1,1]=>56
[4,6,5,2,7,8,3,1]=>[4,2,1,1]=>90
[5,4,6,2,7,8,3,1]=>[4,2,1,1]=>90
[5,1,8,6,4,2,7,3]=>[3,3,1,1]=>56
[6,2,1,8,5,7,4,3]=>[3,2,2,1]=>70
[5,4,6,2,3,1,8,7]=>[3,3,1,1]=>56
[6,5,7,8,1,3,4,2]=>[3,3,1,1]=>56
[2,1,7,6,8,4,5,3]=>[3,3,1,1]=>56
[6,4,7,2,8,3,1,5]=>[3,3,1,1]=>56
[6,3,2,7,8,4,5,1]=>[3,3,1,1]=>56
[4,7,3,1,5,2,8,6]=>[3,3,2]=>42
[4,7,6,3,1,5,8,2]=>[3,2,2,1]=>70
[2,7,3,1,8,5,4,6]=>[4,2,2]=>56
[2,8,3,1,7,4,5,6]=>[5,2,1]=>64
[7,6,8,9,1,2,3,4,5]=>[5,3,1]=>162
[5,4,6,7,8,9,1,2,3]=>[5,3,1]=>162
[1,8,2,7,3,5,6,4]=>[5,1,1,1]=>35
[1,7,4,8,6,5,3,2]=>[3,2,1,1,1]=>64
[1,6,3,5,7,4,8,2]=>[5,1,1,1]=>35
[1,5,4,7,2,8,3,6]=>[4,3,1]=>70
[3,8,5,2,6,1,7,4]=>[4,2,1,1]=>90
[3,7,4,8,5,2,6,1]=>[4,2,1,1]=>90
[8,1,2,6,5,3,4,7]=>[5,1,1,1]=>35
[3,7,4,2,5,6,1,8]=>[5,1,1,1]=>35
[6,8,7,1,3,4,2,5]=>[4,2,1,1]=>90
[3,4,2,8,6,7,5,1]=>[4,2,1,1]=>90
[3,7,8,6,1,4,2,5]=>[3,3,1,1]=>56
[3,6,1,5,2,7,8,4]=>[4,3,1]=>70
[8,1,2,6,3,5,7,4]=>[5,1,1,1]=>35
[6,2,8,4,7,1,3,5]=>[3,3,2]=>42
[3,7,8,4,2,5,6,1]=>[4,2,1,1]=>90
[3,4,2,8,5,1,6,7]=>[5,2,1]=>64
[1,4,3,2,5,6,7,8,9]=>[7,1,1]=>28
[6,8,2,7,5,4,1,3]=>[2,2,2,1,1]=>28
[1,8,4,3,7,6,2,5]=>[3,2,2,1]=>70
[4,3,8,7,1,2,6,5]=>[3,2,2,1]=>70
[2,7,8,5,1,4,6,3]=>[3,3,1,1]=>56
[2,7,8,1,4,5,6,3]=>[4,3,1]=>70
[5,7,6,8,2,1,3,4]=>[3,3,1,1]=>56
[5,4,7,8,6,3,1,2]=>[3,2,2,1]=>70
[4,5,7,8,2,6,1,3]=>[4,2,2]=>56
[6,1,5,3,8,4,7,2]=>[4,2,1,1]=>90
[1,8,6,2,5,4,7,3]=>[4,1,1,1,1]=>35
[6,2,7,4,8,3,1,5]=>[3,3,1,1]=>56
[2,8,5,1,4,3,7,6]=>[3,3,1,1]=>56
[6,8,2,7,5,1,4,3]=>[2,2,2,1,1]=>28
[8,3,4,5,6,1,7,2]=>[5,2,1]=>64
[5,3,6,4,7,2,1,8]=>[4,2,1,1]=>90
[4,2,6,5,7,3,1,8]=>[4,2,1,1]=>90
[5,4,6,2,7,3,1,8]=>[4,2,1,1]=>90
[3,2,6,5,8,4,1,7]=>[3,3,1,1]=>56
[3,2,6,5,8,7,1,4]=>[3,3,2]=>42
[4,2,6,5,8,7,1,3]=>[3,3,2]=>42
[5,2,6,4,8,7,1,3]=>[3,3,2]=>42
[5,4,7,6,8,2,1,3]=>[3,2,2,1]=>70
[6,4,7,5,8,3,1,2]=>[3,2,2,1]=>70
[4,2,7,5,8,6,1,3]=>[3,3,2]=>42
[3,2,7,5,8,4,1,6]=>[3,3,1,1]=>56
[4,3,7,2,8,5,1,6]=>[3,3,1,1]=>56
[4,3,6,2,8,5,1,7]=>[3,3,1,1]=>56
[4,3,7,6,8,5,1,2]=>[3,2,2,1]=>70
[5,3,7,6,8,2,1,4]=>[3,2,2,1]=>70
[5,3,7,2,8,6,1,4]=>[3,2,2,1]=>70
[3,2,6,4,8,7,1,5]=>[3,3,2]=>42
[4,2,7,3,8,6,1,5]=>[3,3,2]=>42
[5,2,7,6,8,3,1,4]=>[3,3,1,1]=>56
[3,2,7,6,8,4,1,5]=>[3,3,1,1]=>56
[3,2,7,6,8,5,1,4]=>[3,2,2,1]=>70
[6,2,7,5,8,4,1,3]=>[3,2,2,1]=>70
[4,8,1,7,3,2,5,6]=>[4,2,1,1]=>90
[3,7,4,8,2,1,5,6]=>[4,2,1,1]=>90
[3,7,8,2,5,4,6,1]=>[3,3,1,1]=>56
[4,7,5,8,3,2,6,1]=>[3,2,1,1,1]=>64
[6,7,1,3,2,5,8,4]=>[4,2,2]=>56
[8,7,6,4,1,5,3,2]=>[2,2,1,1,1,1]=>20
[3,8,5,2,6,4,7,1]=>[4,2,1,1]=>90
[7,2,5,3,4,8,1,6]=>[4,2,1,1]=>90
[4,2,5,3,7,8,6,1]=>[4,3,1]=>70
[5,3,6,2,4,1,8,7]=>[3,3,1,1]=>56
[7,8,6,2,3,5,4,1]=>[3,2,1,1,1]=>64
[5,8,2,6,3,7,4,1]=>[3,3,1,1]=>56
[4,8,2,3,7,5,6,1]=>[4,2,1,1]=>90
[7,5,6,2,3,8,4,1]=>[3,3,1,1]=>56
[2,7,5,6,4,3,8,1]=>[4,1,1,1,1]=>35
[2,8,4,3,7,5,6,1]=>[4,2,1,1]=>90
[3,8,5,7,6,4,2,1]=>[3,1,1,1,1,1]=>21
[7,8,6,3,5,4,2,1]=>[2,2,1,1,1,1]=>20
[2,7,6,3,8,5,4,1]=>[3,2,1,1,1]=>64
[7,4,2,5,6,3,8,1]=>[4,2,1,1]=>90
[6,2,7,5,3,8,4,1]=>[3,3,1,1]=>56
[2,4,8,3,7,5,6,1]=>[4,2,1,1]=>90
[4,8,3,7,5,6,2,1]=>[3,2,1,1,1]=>64
[6,2,5,8,3,7,4,1]=>[3,2,2,1]=>70
[4,7,3,8,2,5,6,1]=>[3,3,1,1]=>56
[8,2,5,6,3,7,4,1]=>[4,2,1,1]=>90
[4,5,3,7,1,2,6,8]=>[4,3,1]=>70
[8,5,6,4,1,3,2,7]=>[3,2,1,1,1]=>64
[6,7,2,8,4,3,1,5]=>[3,3,1,1]=>56
[6,7,3,2,8,4,1,5]=>[3,3,1,1]=>56
[4,7,8,3,1,5,2,6]=>[3,3,2]=>42
[4,5,8,1,3,2,6,7]=>[4,3,1]=>70
[4,7,8,1,6,3,2,5]=>[3,3,1,1]=>56
[4,7,1,3,8,6,5,2]=>[3,3,1,1]=>56
[5,7,2,8,3,4,6,1]=>[4,3,1]=>70
[3,7,2,8,5,6,4,1]=>[3,3,1,1]=>56
[3,1,5,8,6,4,7,2]=>[4,2,1,1]=>90
[2,5,6,1,8,7,3,4]=>[4,3,1]=>70
[3,6,2,8,4,7,5,1]=>[3,3,1,1]=>56
[8,5,6,3,1,4,2,7]=>[3,2,2,1]=>70
[5,7,8,3,4,6,2,1]=>[3,3,1,1]=>56
[3,5,1,8,6,4,2,7]=>[4,2,1,1]=>90
[7,5,3,8,6,4,2,1]=>[2,2,2,1,1]=>28
[5,1,3,8,6,4,2,7]=>[4,2,1,1]=>90
[1,5,8,3,6,4,2,7]=>[4,2,1,1]=>90
[7,5,8,3,6,4,2,1]=>[2,2,2,1,1]=>28
[1,5,8,6,3,4,2,7]=>[4,2,1,1]=>90
[3,7,5,8,2,6,4,1]=>[3,2,2,1]=>70
[5,7,8,1,4,6,2,3]=>[3,3,2]=>42
[1,3,7,8,4,2,6,5]=>[4,2,2]=>56
[6,1,2,5,3,4,7,8]=>[6,1,1]=>21
[1,4,6,5,7,2,3,8]=>[5,2,1]=>64
[6,7,3,5,4,1,2,8]=>[3,2,2,1]=>70
[4,2,5,1,3,7,6,8]=>[4,3,1]=>70
[1,3,2,6,8,4,7,5]=>[4,3,1]=>70
[8,1,7,5,4,2,6,3]=>[3,2,1,1,1]=>64
[1,2,6,4,7,3,5,8]=>[5,2,1]=>64
[1,6,4,3,7,2,5,8]=>[4,2,1,1]=>90
[5,7,8,3,2,6,1,4]=>[3,2,2,1]=>70
[2,3,4,5,6,9,8,7,1]=>[6,1,1,1]=>56
[2,3,4,5,8,7,9,6,1]=>[6,1,1,1]=>56
[2,3,6,5,7,8,9,4,1]=>[6,1,1,1]=>56
[2,3,4,5,6,7,8,9,11,10,1]=>[9,1,1]=>45
[2,3,4,5,6,7,10,9,8,1]=>[7,1,1,1]=>84
[2,3,4,5,6,9,8,10,7,1]=>[7,1,1,1]=>84
[8,4,5,1,3,7,6,2]=>[3,3,1,1]=>56
[8,6,4,3,7,1,5,2]=>[2,2,2,1,1]=>28
[7,3,1,8,6,5,2,4]=>[3,2,2,1]=>70
[3,4,5,6,7,1,2,8,9]=>[7,2]=>27
[2,7,3,1,4,8,6,5]=>[4,2,2]=>56
[3,1,6,5,7,8,4,2]=>[4,2,1,1]=>90
[4,3,1,5,8,7,6,2]=>[3,2,2,1]=>70
[1,7,2,5,6,8,4,3]=>[5,1,1,1]=>35
[4,7,6,8,3,1,5,2]=>[3,2,2,1]=>70
[3,5,4,7,1,8,6,2]=>[4,2,2]=>56
[7,1,5,4,2,3,6,8]=>[5,1,1,1]=>35
[7,1,3,6,4,5,2,8]=>[5,1,1,1]=>35
[6,1,3,8,4,5,2,7]=>[5,2,1]=>64
[5,8,2,7,1,3,6,4]=>[3,2,2,1]=>70
[2,6,5,4,1,3,7,8]=>[4,2,1,1]=>90
[4,1,5,7,6,3,2,8]=>[4,2,1,1]=>90
[4,5,1,7,6,3,2,8]=>[4,2,1,1]=>90
[5,4,2,1,8,7,3,6]=>[3,2,2,1]=>70
[6,2,1,5,4,3,8,7]=>[3,3,1,1]=>56
[1,4,2,6,7,8,5,3]=>[5,2,1]=>64
[1,4,2,5,6,8,7,3]=>[5,2,1]=>64
[2,5,3,6,7,8,4,1]=>[5,2,1]=>64
[1,8,6,2,4,3,5,7]=>[5,1,1,1]=>35
[2,3,4,7,5,8,6,1]=>[5,2,1]=>64
[6,5,2,8,7,4,3,1]=>[2,2,2,1,1]=>28
[7,8,5,4,2,1,6,3]=>[2,2,2,1,1]=>28
[7,5,2,8,6,4,3,1]=>[2,2,2,1,1]=>28
[7,8,3,2,6,5,4,1]=>[2,2,2,1,1]=>28
[8,2,6,3,7,5,1,4]=>[3,2,2,1]=>70
[8,6,7,2,5,3,1,4]=>[3,2,1,1,1]=>64
[1,6,2,7,8,4,5,3]=>[4,3,1]=>70
[8,6,2,7,5,4,1,3]=>[2,2,2,1,1]=>28
[1,6,8,2,7,5,3,4]=>[4,2,1,1]=>90
[7,6,3,2,8,1,5,4]=>[2,2,2,1,1]=>28
[8,6,3,7,2,4,1,5]=>[3,2,1,1,1]=>64
[1,7,8,6,4,2,3,5]=>[4,2,1,1]=>90
[7,2,8,6,4,1,3,5]=>[3,2,2,1]=>70
[1,5,3,7,4,2,6,8]=>[5,2,1]=>64
[1,7,6,3,4,2,5,8]=>[5,1,1,1]=>35
[1,2,7,4,3,8,6,5]=>[4,2,2]=>56
[1,5,4,2,3,8,7,6]=>[4,2,2]=>56
[1,5,3,2,4,6,7,8]=>[6,1,1]=>21
[1,5,4,2,3,7,8,6]=>[5,2,1]=>64
[1,2,7,6,3,5,8,4]=>[5,1,1,1]=>35
[8,1,3,2,6,5,7,4]=>[4,2,1,1]=>90
[3,2,7,5,6,1,8,4]=>[4,2,2]=>56
[7,5,6,1,4,3,8,2]=>[3,2,1,1,1]=>64
[8,1,4,3,5,2,7,6]=>[4,2,1,1]=>90
[10,5,9,4,8,3,7,2,6,1]=>[2,2,2,2,1,1]=>90
[1,3,5,2,4,7,6,9,8,10]=>[6,4]=>90
[2,3,5,1,4,7,6,9,8]=>[5,4]=>42
[3,4,1,5,2,7,6,9,8]=>[5,4]=>42
[4,1,2,5,3,7,6,9,8]=>[5,4]=>42
[1,4,2,5,3,7,6,9,8,10]=>[6,4]=>90
[8,3,6,5,4,1,2,7]=>[3,2,1,1,1]=>64
[1,7,5,8,4,6,3,2]=>[3,2,1,1,1]=>64
[6,5,7,1,2,8,3,4]=>[4,3,1]=>70
[7,1,4,2,3,8,6,5]=>[4,2,2]=>56
[8,1,2,5,3,7,6,4]=>[4,2,1,1]=>90
[8,6,5,2,4,1,7,3]=>[3,2,1,1,1]=>64
[6,8,5,2,4,3,1,7]=>[3,2,1,1,1]=>64
[3,4,2,8,6,7,1,5]=>[4,2,2]=>56
[4,6,7,2,5,1,8,3]=>[4,2,2]=>56
[3,6,2,5,1,7,8,4]=>[4,2,2]=>56
[3,4,2,7,8,1,5,6]=>[4,3,1]=>70
[3,1,11,5,6,7,8,9,10,2,4]=>[7,3,1]=>550
[10,3,1,5,6,7,8,9,2,4]=>[6,3,1]=>315
[10,4,1,5,6,7,8,9,2,3]=>[6,3,1]=>315
[12,3,4,5,6,7,8,9,10,11,1,2]=>[9,2,1]=>320
[7,1,4,2,5,8,6,3]=>[4,2,2]=>56
[7,8,5,1,2,4,3,6]=>[4,2,1,1]=>90
[5,8,1,4,3,6,7,2]=>[4,2,1,1]=>90
[5,2,3,8,7,4,1,6]=>[4,2,1,1]=>90
[4,2,6,8,1,3,5,7,9]=>[5,3,1]=>162
[4,6,2,8,1,3,5,7,9]=>[5,3,1]=>162
[4,6,8,2,1,3,5,7,9]=>[5,3,1]=>162
[4,6,2,7,8,1,3,5]=>[4,3,1]=>70
[4,6,8,2,9,1,3,5,7]=>[4,4,1]=>84
[4,6,2,7,9,1,3,5,8]=>[4,4,1]=>84
[6,2,3,7,1,4,5,8]=>[5,2,1]=>64
[4,2,5,7,9,1,3,6,8]=>[4,4,1]=>84
[2,3,5,7,9,1,4,6,8]=>[5,4]=>42
[4,2,6,8,10,1,3,5,7,9]=>[5,4,1]=>288
[6,4,2,8,1,3,5,7,9]=>[5,2,1,1]=>189
[4,6,2,8,10,1,3,5,7,9]=>[5,4,1]=>288
[8,4,6,2,1,3,5,7,9]=>[5,2,1,1]=>189
[4,6,8,2,10,1,3,5,7,9]=>[5,4,1]=>288
[4,6,8,9,2,1,3,5,7]=>[4,4,1]=>84
[4,6,8,10,2,1,3,5,7,9]=>[5,4,1]=>288
[4,6,7,8,2,1,3,5]=>[4,3,1]=>70
[4,6,2,7,1,3,5,8,9]=>[5,3,1]=>162
[4,6,8,2,9,1,3,5,7,10]=>[5,4,1]=>288
[4,8,2,5,9,1,3,6,7]=>[4,3,2]=>168
[4,6,2,7,9,1,3,5,8,10]=>[5,4,1]=>288
[6,2,3,7,9,1,4,5,8]=>[5,3,1]=>162
[4,2,5,7,9,1,3,6,8,10]=>[5,4,1]=>288
[1,4,5,7,9,2,3,6,8]=>[5,4]=>42
[2,3,5,7,9,1,4,6,8,10]=>[6,4]=>90
[8,6,3,2,1,7,5,4]=>[2,2,2,1,1]=>28
[8,6,4,9,7,5,3,2,1]=>[2,2,2,1,1,1]=>48
[8,6,4,2,9,7,5,3,1]=>[2,2,2,2,1]=>42
[6,2,7,3,8,4,9,5,1]=>[4,4,1]=>84
[4,5,6,7,8,2,9,3,1]=>[6,2,1]=>105
[4,5,6,7,1,8,2,9,3]=>[6,3]=>48
[9,7,10,8,6,5,4,3,2,1]=>[2,2,1,1,1,1,1,1]=>35
[9,7,5,10,8,6,4,3,2,1]=>[2,2,2,1,1,1,1]=>75
[8,5,2,9,6,3,10,7,4,1]=>[3,3,3,1]=>210
[7,3,8,4,9,5,1,10,6,2]=>[4,4,2]=>252
[6,1,3,4,2,5,8,7]=>[5,2,1]=>64
[5,1,3,6,2,4,8,7]=>[4,3,1]=>70
[1,5,7,6,8,2,4,3]=>[4,2,1,1]=>90
[5,7,1,3,8,4,2,6]=>[4,3,1]=>70
[2,6,1,4,3,7,8,5]=>[4,3,1]=>70
[1,6,2,4,3,5,8,7]=>[5,2,1]=>64
[5,3,7,6,1,8,4,2]=>[3,2,2,1]=>70
[1,5,6,3,7,8,4,2]=>[5,2,1]=>64
[1,5,7,6,3,8,4,2]=>[4,2,1,1]=>90
[7,3,5,6,1,8,4,2]=>[4,2,1,1]=>90
[1,6,3,7,8,5,4,2]=>[4,2,1,1]=>90
[1,7,8,6,3,5,4,2]=>[3,2,1,1,1]=>64
[3,7,5,6,1,8,4,2]=>[4,2,1,1]=>90
[5,6,2,8,4,7,3,1]=>[3,3,1,1]=>56
[7,3,5,4,1,2,6,8]=>[4,2,1,1]=>90
[7,8,5,1,3,2,4,6]=>[4,2,1,1]=>90
[7,5,1,3,8,6,2,4]=>[3,2,2,1]=>70
[3,1,5,4,7,2,6,8]=>[4,3,1]=>70
[5,7,6,1,3,8,2,4]=>[3,3,1,1]=>56
[5,7,6,3,8,1,4,2]=>[3,2,2,1]=>70
[5,1,3,7,6,2,4,8]=>[4,2,2]=>56
[1,6,3,7,2,4,5,8]=>[5,2,1]=>64
[5,3,2,4,8,1,7,6]=>[3,2,2,1]=>70
[6,8,5,3,2,7,1,4]=>[2,2,2,1,1]=>28
[8,3,7,2,6,5,1,4]=>[2,2,2,1,1]=>28
[4,6,2,7,1,3,8,5]=>[4,3,1]=>70
[3,5,1,4,7,2,8,6]=>[4,3,1]=>70
[5,1,4,8,7,3,2,6]=>[3,2,2,1]=>70
[6,1,3,4,2,7,8,5]=>[5,2,1]=>64
[6,5,2,3,7,8,1,4]=>[4,2,1,1]=>90
[1,5,3,8,4,2,7,6]=>[4,2,2]=>56
[5,4,2,1,8,3,7,6]=>[3,2,2,1]=>70
[3,1,7,4,2,6,8,5]=>[4,3,1]=>70
[7,4,8,2,3,5,1,6]=>[4,2,1,1]=>90
[8,4,1,3,2,6,7,5]=>[4,2,1,1]=>90
[8,1,7,3,2,5,6,4]=>[4,2,1,1]=>90
[8,6,5,2,7,3,1,4]=>[3,2,1,1,1]=>64
[3,1,6,8,4,2,7,5]=>[3,3,2]=>42
[2,3,4,5,9,6,7,8,1]=>[7,1,1]=>28
[2,3,4,9,5,6,7,8,1]=>[7,1,1]=>28
[2,3,9,4,5,6,7,8,1]=>[7,1,1]=>28
[2,3,4,5,6,7,10,8,9,1]=>[8,1,1]=>36
[2,3,4,5,9,7,6,8,1]=>[6,1,1,1]=>56
[2,3,4,5,6,10,7,8,9,1]=>[8,1,1]=>36
[2,3,4,9,6,5,7,8,1]=>[6,1,1,1]=>56
[2,3,9,5,4,6,7,8,1]=>[6,1,1,1]=>56
[2,3,4,10,5,6,7,8,9,1]=>[8,1,1]=>36
[2,9,4,3,5,6,7,8,1]=>[6,1,1,1]=>56
[2,3,10,4,5,6,7,8,9,1]=>[8,1,1]=>36
[2,3,4,5,9,7,8,6,1]=>[6,1,1,1]=>56
[5,6,2,3,7,4,1,8]=>[4,3,1]=>70
[6,2,4,7,3,5,1,8]=>[4,2,1,1]=>90
[1,4,8,5,3,6,7,2]=>[5,1,1,1]=>35
[2,5,6,3,1,8,4,7]=>[4,3,1]=>70
[4,5,1,2,7,8,6,3]=>[4,3,1]=>70
[4,8,5,1,2,6,7,3]=>[4,3,1]=>70
[4,6,7,5,1,2,8,3]=>[4,3,1]=>70
[7,2,8,1,4,5,3,6]=>[4,2,2]=>56
[6,1,4,7,3,8,2,5]=>[4,2,1,1]=>90
[7,1,6,3,4,8,2,5]=>[4,2,1,1]=>90
[2,8,4,6,3,1,5,7]=>[4,2,1,1]=>90
[8,2,6,3,5,1,4,7]=>[4,2,1,1]=>90
[3,7,4,1,5,8,2,6]=>[4,3,1]=>70
[3,8,4,1,7,2,5,6]=>[4,3,1]=>70
[6,7,5,1,3,8,2,4]=>[3,3,1,1]=>56
[8,5,1,3,6,7,2,4]=>[4,2,1,1]=>90
[7,8,6,2,4,1,3,5]=>[3,2,2,1]=>70
[8,2,4,1,3,6,7,5]=>[4,3,1]=>70
[8,1,3,6,2,5,7,4]=>[4,2,1,1]=>90
[1,5,6,3,8,4,7,2]=>[4,3,1]=>70
[5,6,1,3,7,2,8,4]=>[4,3,1]=>70
[5,6,1,8,2,3,7,4]=>[4,3,1]=>70
[5,6,1,2,8,4,7,3]=>[4,3,1]=>70
[3,7,8,1,6,4,2,5]=>[3,3,1,1]=>56
[1,7,8,6,3,4,2,5]=>[4,2,1,1]=>90
[5,7,1,8,6,4,2,3]=>[3,3,1,1]=>56
[7,8,1,5,6,4,2,3]=>[3,2,2,1]=>70
[7,1,8,5,6,4,2,3]=>[3,2,2,1]=>70
[7,1,5,8,6,4,2,3]=>[3,2,2,1]=>70
[8,1,3,5,6,4,2,7]=>[5,1,1,1]=>35
[1,3,8,5,6,4,2,7]=>[5,1,1,1]=>35
[1,3,5,8,6,4,2,7]=>[5,1,1,1]=>35
[1,5,7,8,6,4,2,3]=>[4,2,1,1]=>90
[3,2,4,1,6,5,8,7,10,9]=>[5,4,1]=>288
[3,2,5,4,7,6,9,8,10,1]=>[5,4,1]=>288
[3,2,5,4,7,6,9,8,11,10,12,1]=>[6,5,1]=>1155
[1,8,2,6,5,3,4,7]=>[5,1,1,1]=>35
[8,6,1,5,2,3,4,7]=>[5,1,1,1]=>35
[8,5,1,6,2,3,4,7]=>[5,2,1]=>64
[7,6,1,2,3,8,4,5]=>[5,2,1]=>64
[2,7,8,4,1,3,5,6]=>[4,3,1]=>70
[6,8,1,2,3,7,4,5]=>[5,2,1]=>64
[8,1,3,5,6,7,2,4]=>[5,2,1]=>64
[8,1,2,5,3,4,7,6]=>[5,2,1]=>64
[5,2,7,3,4,8,1,6]=>[4,3,1]=>70
[2,7,5,4,1,3,6,8]=>[4,2,1,1]=>90
[2,7,4,6,5,1,8,3]=>[4,2,1,1]=>90
[6,8,7,5,2,1,4,3]=>[2,2,2,1,1]=>28
[2,8,6,3,5,1,4,7]=>[4,2,1,1]=>90
[1,5,8,7,6,3,4,2]=>[3,2,1,1,1]=>64
[1,6,4,8,5,7,3,2]=>[4,2,1,1]=>90
[1,6,8,5,2,7,3,4]=>[4,2,2]=>56
[2,1,8,3,4,5,6,7,9]=>[7,2]=>27
[3,1,6,4,2,5,8,7]=>[4,3,1]=>70
[5,4,2,3,6,8,1,7]=>[4,2,1,1]=>90
[3,1,7,8,6,2,5,4]=>[3,3,1,1]=>56
[2,8,1,6,5,3,7,4]=>[3,3,1,1]=>56
[2,1,5,7,6,3,8,4]=>[4,3,1]=>70
[4,3,5,1,7,8,6,2]=>[4,2,2]=>56
[1,8,5,2,3,4,7,6]=>[5,2,1]=>64
[1,9,6,2,3,4,5,8,7]=>[6,2,1]=>105
[1,5,8,2,3,4,7,6]=>[5,2,1]=>64
[1,2,7,8,4,5,6,3]=>[5,2,1]=>64
[1,2,3,4,5,6,9,7,10,8]=>[8,2]=>35
[2,3,4,5,6,9,10,1,7,8]=>[7,3]=>75
[4,3,8,7,6,2,5,1]=>[2,2,2,1,1]=>28
[5,4,8,2,7,6,3,1]=>[2,2,2,1,1]=>28
[2,3,6,1,7,5,8,4]=>[5,2,1]=>64
[4,6,5,2,1,7,8,3]=>[4,2,1,1]=>90
[4,6,1,7,5,8,3,2]=>[4,2,1,1]=>90
[4,1,5,7,6,8,3,2]=>[4,2,1,1]=>90
[3,5,6,2,1,4,7,8]=>[5,2,1]=>64
[4,3,6,5,1,7,8,2]=>[4,2,2]=>56
[1,2,3,4,5,7,6,8,9,10]=>[9,1]=>9
[1,2,3,5,4,6,7,8,9,10]=>[9,1]=>9
[1,2,3,5,4,7,6,9,8,10]=>[7,3]=>75
[5,8,1,4,2,3,6,7]=>[5,2,1]=>64
[4,5,8,2,3,1,6,7]=>[4,3,1]=>70
[3,5,4,8,1,7,2,6]=>[3,3,2]=>42
[5,3,6,8,1,4,7,2]=>[3,3,2]=>42
[3,5,1,8,6,4,7,2]=>[4,2,1,1]=>90
[4,7,2,8,3,1,6,5]=>[3,3,2]=>42
[1,2,5,6,8,3,7,4]=>[5,2,1]=>64
[5,3,8,4,6,2,7,1]=>[4,2,1,1]=>90
[7,4,8,1,5,2,6,3]=>[3,3,2]=>42
[8,3,2,1,6,5,7,4]=>[3,2,2,1]=>70
[4,1,5,6,8,7,2,3]=>[4,3,1]=>70
[1,2,5,6,8,4,7,3]=>[5,2,1]=>64
[1,5,6,8,4,7,2,3]=>[4,2,2]=>56
[5,6,8,1,2,4,7,3]=>[4,3,1]=>70
[6,8,1,4,5,7,2,3]=>[4,2,2]=>56
[4,3,5,1,8,6,7,2]=>[4,2,2]=>56
[1,3,5,6,8,4,7,2]=>[5,2,1]=>64
[5,6,8,2,3,4,7,1]=>[4,3,1]=>70
[9,8,7,4,5,6,3,2,1]=>[3,1,1,1,1,1,1]=>28
[6,5,1,2,4,8,7,3]=>[4,2,1,1]=>90
[5,8,7,2,1,3,6,4]=>[3,2,2,1]=>70
[5,1,7,2,8,6,3,4]=>[4,3,1]=>70
[6,1,5,3,4,8,7,2]=>[4,2,1,1]=>90
[5,8,6,3,2,1,4,7]=>[3,2,1,1,1]=>64
[8,7,1,6,3,5,4,2]=>[3,1,1,1,1,1]=>21
[3,2,1,7,8,6,4,5]=>[3,3,2]=>42
[8,6,7,1,2,5,3,4]=>[4,2,1,1]=>90
[1,5,6,4,2,8,7,3]=>[4,2,2]=>56
[7,5,1,4,8,2,3,6]=>[4,2,1,1]=>90
[3,2,8,1,7,5,6,4]=>[3,2,2,1]=>70
[8,4,3,1,7,5,6,2]=>[3,2,2,1]=>70
[6,1,7,8,4,2,3,5]=>[4,3,1]=>70
[7,4,3,1,8,5,2,6]=>[3,2,2,1]=>70
[7,8,1,6,3,4,5,2]=>[4,2,1,1]=>90
[6,8,1,7,3,4,2,5]=>[4,2,1,1]=>90
[1,5,6,7,8,9,2,3,4]=>[6,3]=>48
[1,8,9,10,2,3,4,5,6,7]=>[7,3]=>75
[1,7,2,8,9,3,4,5,6]=>[6,3]=>48
[1,6,2,7,8,9,3,4,5]=>[5,4]=>42
[1,5,2,6,7,8,9,3,4]=>[6,3]=>48
[1,5,6,7,8,9,10,2,3,4]=>[7,3]=>75
[3,4,2,5,1,6,7,8,9]=>[7,1,1]=>28
[3,1,2,4,5,6,7,8,9,10,11]=>[10,1]=>10
[4,6,5,3,8,2,7,1]=>[3,2,1,1,1]=>64
[4,5,6,3,8,1,7,2]=>[4,2,2]=>56
[7,8,3,5,2,1,6,4]=>[3,2,2,1]=>70
[6,3,7,5,2,4,1,8]=>[3,2,2,1]=>70
[6,2,4,5,7,3,1,8]=>[5,1,1,1]=>35
[7,8,1,5,6,4,3,2]=>[3,2,1,1,1]=>64
[6,3,7,5,1,4,2,8]=>[3,2,2,1]=>70
[1,3,8,2,4,6,7,5]=>[5,2,1]=>64
[6,1,7,3,4,2,5,8]=>[5,2,1]=>64
[3,1,7,2,5,8,6,4]=>[4,3,1]=>70
[2,8,7,6,3,5,1,4]=>[3,2,1,1,1]=>64
[2,8,7,1,5,6,4,3]=>[3,2,1,1,1]=>64
[7,1,6,8,2,5,3,4]=>[4,2,1,1]=>90
[1,6,5,7,4,2,3,8]=>[4,2,1,1]=>90
[8,5,4,3,9,1,2,6,7]=>[4,2,1,1,1]=>189
[9,6,5,4,3,10,1,2,7,8]=>[4,2,1,1,1,1]=>350
[6,8,7,3,2,4,5,1]=>[3,2,1,1,1]=>64
[3,8,6,1,4,5,7,2]=>[4,2,1,1]=>90
[7,5,8,6,4,1,3,2]=>[2,2,2,1,1]=>28
[2,7,6,3,8,5,1,4]=>[3,2,2,1]=>70
[2,3,1,8,4,6,5,7]=>[5,2,1]=>64
[2,3,1,8,4,6,7,5]=>[5,2,1]=>64
[4,2,3,5,1,8,6,7]=>[5,2,1]=>64
[2,3,4,5,9,7,1,8,6]=>[6,2,1]=>105
[2,3,4,9,6,7,1,8,5]=>[6,2,1]=>105
[2,3,9,5,6,1,7,8,4]=>[6,2,1]=>105
[2,3,9,5,1,7,4,8,6]=>[5,3,1]=>162
[2,3,4,5,6,7,10,9,1,8]=>[7,2,1]=>160
[2,3,4,5,6,10,8,9,1,7]=>[7,2,1]=>160
[2,3,4,5,6,10,8,1,9,7]=>[7,2,1]=>160
[2,3,4,5,6,10,8,1,7,9]=>[7,2,1]=>160
[2,3,4,5,6,10,1,7,8,9]=>[8,2]=>35
[2,3,4,5,10,7,8,9,1,6]=>[7,2,1]=>160
[2,3,4,5,10,7,8,1,9,6]=>[7,2,1]=>160
[2,3,4,5,10,7,8,1,6,9]=>[7,2,1]=>160
[2,3,4,5,10,7,1,9,6,8]=>[6,3,1]=>315
[2,3,4,5,10,7,1,6,8,9]=>[7,2,1]=>160
[2,3,4,5,10,1,6,7,8,9]=>[8,2]=>35
[2,3,4,10,6,7,8,1,9,5]=>[7,2,1]=>160
[2,3,4,10,6,7,8,1,5,9]=>[7,2,1]=>160
[2,3,4,10,6,7,1,8,9,5]=>[7,2,1]=>160
[2,3,4,10,6,7,1,9,5,8]=>[6,3,1]=>315
[2,3,4,10,6,7,1,5,8,9]=>[7,2,1]=>160
[2,3,4,10,6,1,8,5,9,7]=>[6,3,1]=>315
[2,3,4,10,6,1,8,5,7,9]=>[6,3,1]=>315
[2,3,4,10,6,1,5,7,8,9]=>[7,2,1]=>160
[2,3,4,10,1,5,6,7,8,9]=>[8,2]=>35
[2,3,10,5,6,1,8,9,4,7]=>[6,3,1]=>315
[2,3,10,5,6,1,8,4,9,7]=>[6,3,1]=>315
[2,3,10,5,6,1,8,4,7,9]=>[6,3,1]=>315
[2,3,10,5,6,1,4,7,8,9]=>[7,2,1]=>160
[2,3,10,5,1,7,4,9,6,8]=>[5,4,1]=>288
[2,3,10,5,1,7,4,6,8,9]=>[6,3,1]=>315
[2,3,10,5,1,4,6,7,8,9]=>[7,2,1]=>160
[2,10,4,1,6,3,8,5,9,7]=>[5,4,1]=>288
[2,10,4,1,6,3,8,5,7,9]=>[5,4,1]=>288
[2,10,4,1,6,3,5,7,8,9]=>[6,3,1]=>315
[2,10,4,1,3,5,6,7,8,9]=>[7,2,1]=>160
[5,8,7,2,6,4,1,3]=>[2,2,2,1,1]=>28
[6,8,5,1,7,4,3,2]=>[2,2,2,1,1]=>28
[6,8,5,2,7,4,1,3]=>[2,2,2,2]=>14
[7,5,8,1,6,4,3,2]=>[2,2,2,1,1]=>28
[7,5,8,2,6,4,1,3]=>[2,2,2,2]=>14
[6,3,2,8,1,7,5,4]=>[2,2,2,2]=>14
[2,1,3,4,5,6,8,7,9]=>[7,2]=>27
[2,3,4,5,6,8,7,9,1]=>[7,1,1]=>28
[2,6,8,7,1,3,5,4]=>[3,3,1,1]=>56
[5,3,8,7,6,2,1,4]=>[2,2,2,1,1]=>28
[3,7,6,1,4,5,2,8]=>[4,2,1,1]=>90
[4,1,6,2,7,5,3,8]=>[4,3,1]=>70
[7,6,2,5,3,1,4,8]=>[4,1,1,1,1]=>35
[4,3,1,7,6,2,5,8]=>[4,2,2]=>56
[4,5,3,1,2,8,6,7]=>[4,3,1]=>70
[2,4,5,3,1,8,6,7]=>[5,2,1]=>64
[5,7,6,2,3,1,4,8]=>[4,2,1,1]=>90
[4,1,3,7,5,2,6,8]=>[5,2,1]=>64
[4,1,6,3,2,7,5,8]=>[4,3,1]=>70
[7,5,4,1,3,2,6,8]=>[4,1,1,1,1]=>35
[2,4,8,5,6,3,1,7]=>[5,1,1,1]=>35
[2,5,7,4,1,3,6,8]=>[4,3,1]=>70
[5,7,4,1,3,2,6,8]=>[4,2,1,1]=>90
[2,6,8,4,5,3,1,7]=>[4,2,1,1]=>90
[5,2,3,7,4,1,6,8]=>[5,2,1]=>64
[4,5,1,6,3,2,7,8]=>[5,2,1]=>64
[5,1,6,3,2,4,7,8]=>[5,2,1]=>64
[4,2,5,1,6,3,7,8]=>[5,2,1]=>64
[5,1,6,2,4,3,7,8]=>[5,2,1]=>64
[5,3,4,8,7,6,2,1]=>[3,2,1,1,1]=>64
[8,3,1,6,7,5,4,2]=>[3,2,1,1,1]=>64
[8,4,6,5,7,2,3,1]=>[3,2,1,1,1]=>64
[1,8,2,6,7,4,5,3]=>[4,2,1,1]=>90
[8,5,7,2,4,3,6,1]=>[3,2,1,1,1]=>64
[8,5,3,6,4,7,2,1]=>[3,2,1,1,1]=>64
[8,2,5,3,6,7,4,1]=>[4,2,1,1]=>90
[1,2,8,3,4,7,6,5]=>[5,1,1,1]=>35
[6,8,5,2,7,1,3,4]=>[3,2,2,1]=>70
[7,6,4,5,2,1,8,3]=>[3,2,1,1,1]=>64
[8,2,4,7,6,3,1,5]=>[3,2,1,1,1]=>64
[7,3,8,5,4,2,1,6]=>[3,2,1,1,1]=>64
[6,3,4,7,2,8,5,1]=>[4,2,1,1]=>90
[8,1,7,3,6,4,2,5]=>[4,1,1,1,1]=>35
[7,1,8,5,3,4,2,6]=>[4,2,1,1]=>90
[6,8,4,3,1,5,2,7]=>[3,2,2,1]=>70
[1,4,5,8,3,2,6,7]=>[5,2,1]=>64
[1,5,2,4,7,8,6,3]=>[5,2,1]=>64
[5,2,7,4,3,8,6,1]=>[3,3,1,1]=>56
[2,7,3,4,8,5,6,1]=>[5,2,1]=>64
[2,7,6,8,3,5,4,1]=>[3,2,1,1,1]=>64
[2,7,4,5,3,8,6,1]=>[4,2,1,1]=>90
[6,2,3,7,4,5,8,1]=>[5,2,1]=>64
[1,6,3,2,7,5,8,4]=>[4,2,2]=>56
[7,3,5,2,6,8,1,4]=>[4,2,1,1]=>90
[6,4,2,7,1,5,8,3]=>[3,2,2,1]=>70
[2,5,3,6,4,7,8,1]=>[5,2,1]=>64
[4,2,5,3,6,7,8,1]=>[5,2,1]=>64
[1,6,5,2,4,7,3,8]=>[5,1,1,1]=>35
[1,8,7,2,4,6,3,5]=>[4,2,1,1]=>90
[1,8,7,2,5,4,3,6]=>[4,1,1,1,1]=>35
[1,5,4,2,7,3,6,8]=>[5,2,1]=>64
[1,5,4,2,8,7,3,6]=>[4,2,2]=>56
[1,6,8,3,5,2,4,7]=>[4,2,2]=>56
[1,7,6,2,3,5,8,4]=>[5,1,1,1]=>35
[1,2,8,3,6,5,4,7]=>[5,1,1,1]=>35
[1,3,8,6,5,2,4,7]=>[4,2,1,1]=>90
[1,4,7,3,2,8,6,5]=>[4,2,2]=>56
[1,8,6,5,2,4,7,3]=>[4,1,1,1,1]=>35
[1,6,8,4,3,2,5,7]=>[4,2,1,1]=>90
[1,7,5,3,2,6,4,8]=>[4,2,1,1]=>90
[1,2,6,5,3,8,4,7]=>[5,2,1]=>64
[1,7,3,2,8,4,6,5]=>[4,2,2]=>56
[1,6,5,2,8,4,7,3]=>[4,2,1,1]=>90
[1,8,3,7,2,4,6,5]=>[4,2,1,1]=>90
[5,4,2,8,7,6,1,3]=>[2,2,2,2]=>14
[8,6,3,2,5,7,4,1]=>[3,2,1,1,1]=>64
[7,3,2,1,6,5,8,4]=>[3,2,2,1]=>70
[7,3,2,6,1,5,8,4]=>[3,2,2,1]=>70
[6,8,5,2,7,1,4,3]=>[2,2,2,2]=>14
[6,8,2,5,1,7,4,3]=>[3,2,2,1]=>70
[6,8,5,7,2,1,4,3]=>[2,2,2,2]=>14
[6,5,8,2,7,4,1,3]=>[2,2,2,2]=>14
[6,2,1,7,5,8,4,3]=>[3,2,2,1]=>70
[1,6,4,8,5,3,7,2]=>[4,2,1,1]=>90
[4,2,6,7,8,1,3,5]=>[4,3,1]=>70
[4,6,5,1,3,7,8,2]=>[4,2,1,1]=>90
[5,1,7,2,6,4,8,3]=>[4,2,1,1]=>90
[4,1,7,6,5,8,2,3]=>[3,3,1,1]=>56
[4,2,3,6,7,8,1,5]=>[5,2,1]=>64
[4,7,2,1,6,5,8,3]=>[3,2,2,1]=>70
[2,4,3,6,7,8,1,5]=>[5,2,1]=>64
[6,8,5,2,7,3,1,4]=>[3,2,2,1]=>70
[6,5,1,3,7,8,2,4]=>[4,2,1,1]=>90
[7,2,1,4,3,5,8,6]=>[4,3,1]=>70
[6,1,2,4,3,7,8,5]=>[5,2,1]=>64
[8,1,5,4,2,3,6,7]=>[5,1,1,1]=>35
[7,1,2,4,6,3,8,5]=>[5,2,1]=>64
[7,1,2,6,5,3,8,4]=>[4,2,1,1]=>90
[7,5,6,1,2,4,8,3]=>[4,2,1,1]=>90
[7,1,4,5,2,3,6,8]=>[5,2,1]=>64
[6,1,4,8,7,2,3,5]=>[4,2,2]=>56
[6,1,8,5,7,2,3,4]=>[4,2,2]=>56
[1,6,7,5,8,3,4,2]=>[4,2,1,1]=>90
[6,1,7,5,8,2,3,4]=>[4,3,1]=>70
[6,1,4,7,8,2,3,5]=>[4,3,1]=>70
[8,1,2,3,7,5,4,6]=>[5,1,1,1]=>35
[5,8,6,1,2,4,7,3]=>[4,2,1,1]=>90
[1,6,8,7,5,3,4,2]=>[3,2,1,1,1]=>64
[6,1,8,7,5,2,3,4]=>[4,2,1,1]=>90
[8,3,1,2,4,6,5,7]=>[5,2,1]=>64
[8,3,1,2,4,5,7,6]=>[5,2,1]=>64
[6,3,1,2,4,7,5,8]=>[5,2,1]=>64
[6,7,1,4,2,3,5,8]=>[5,2,1]=>64
[6,1,7,4,8,2,3,5]=>[4,3,1]=>70
[6,7,8,5,1,2,4,3]=>[3,3,1,1]=>56
[9,2,3,4,5,6,1,7,8]=>[7,1,1]=>28
[3,1,5,6,7,8,9,2,4]=>[6,3]=>48
[2,1,3,5,6,7,8,9,4]=>[7,2]=>27
[4,3,8,5,6,2,7,1]=>[4,2,1,1]=>90
[4,3,8,6,7,2,5,1]=>[3,2,2,1]=>70
[7,6,8,1,5,3,4,2]=>[3,2,1,1,1]=>64
[7,4,6,1,5,3,8,2]=>[3,2,1,1,1]=>64
[6,3,8,1,7,2,5,4]=>[3,2,2,1]=>70
[6,1,5,4,8,2,7,3]=>[3,2,2,1]=>70
[6,2,5,4,7,1,8,3]=>[4,2,1,1]=>90
[8,3,6,7,5,1,2,4]=>[3,3,1,1]=>56
[4,6,8,2,3,5,1,7]=>[4,3,1]=>70
[6,8,2,1,3,5,4,7]=>[4,2,2]=>56
[3,5,1,6,4,8,2,7]=>[4,3,1]=>70
[3,5,8,6,2,1,4,7]=>[4,2,1,1]=>90
[2,4,8,5,6,1,3,7]=>[5,2,1]=>64
[4,8,2,5,6,1,3,7]=>[4,2,2]=>56
[5,3,8,4,2,7,6,1]=>[3,2,2,1]=>70
[2,8,5,3,1,4,7,6]=>[4,2,1,1]=>90
[1,7,8,4,6,3,2,5]=>[3,2,2,1]=>70
[8,7,2,4,6,3,1,5]=>[3,2,1,1,1]=>64
[8,7,3,2,1,6,4,5]=>[3,2,1,1,1]=>64
[7,8,3,4,6,5,2,1]=>[3,2,1,1,1]=>64
[8,7,3,6,5,2,4,1]=>[2,2,1,1,1,1]=>20
[3,1,2,8,6,5,7,4]=>[4,2,1,1]=>90
[3,8,2,7,5,4,6,1]=>[3,2,1,1,1]=>64
[8,7,1,4,5,3,6,2]=>[4,1,1,1,1]=>35
[2,8,7,4,6,3,5,1]=>[3,2,1,1,1]=>64
[2,8,7,4,6,3,1,5]=>[3,2,1,1,1]=>64
[8,3,4,1,2,5,7,6]=>[4,3,1]=>70
[8,4,1,3,2,5,7,6]=>[4,2,1,1]=>90
[7,3,8,6,2,1,4,5]=>[3,2,2,1]=>70
[7,2,8,4,6,5,1,3]=>[3,2,2,1]=>70
[5,8,6,4,7,2,3,1]=>[3,2,1,1,1]=>64
[4,7,2,6,5,8,3,1]=>[3,2,1,1,1]=>64
[3,6,8,5,7,4,2,1]=>[3,2,1,1,1]=>64
[6,7,5,2,4,8,3,1]=>[3,2,1,1,1]=>64
[8,1,2,7,5,6,3,4]=>[4,2,1,1]=>90
[8,2,7,3,4,6,1,5]=>[4,2,1,1]=>90
[6,7,5,4,8,1,3,2]=>[3,2,1,1,1]=>64
[8,3,5,6,4,7,2,1]=>[4,1,1,1,1]=>35
[8,5,6,2,4,3,7,1]=>[3,2,1,1,1]=>64
[6,5,8,1,3,4,2,7]=>[4,2,1,1]=>90
[6,8,4,5,1,3,2,7]=>[3,2,2,1]=>70
[6,4,8,7,5,3,2,1]=>[2,2,1,1,1,1]=>20
[6,7,1,4,3,2,8,5]=>[3,3,1,1]=>56
[7,2,5,1,4,8,3,6]=>[3,3,1,1]=>56
[5,8,1,3,4,2,7,6]=>[4,2,2]=>56
[1,5,6,3,2,8,7,4]=>[4,2,2]=>56
[1,3,7,6,8,4,2,5]=>[4,2,1,1]=>90
[1,6,7,3,2,8,5,4]=>[4,2,2]=>56
[3,2,7,6,8,4,5,1]=>[3,3,1,1]=>56
[1,3,8,5,2,7,6,4]=>[4,2,1,1]=>90
[6,4,1,5,2,8,7,3]=>[3,3,2]=>42
[7,6,5,3,1,8,2,4]=>[3,2,1,1,1]=>64
[2,6,1,5,7,4,8,3]=>[4,2,1,1]=>90
[3,6,5,1,7,2,4,8]=>[4,3,1]=>70
[5,4,2,6,3,7,8,1]=>[4,2,1,1]=>90
[3,5,7,6,2,4,1,8]=>[4,2,1,1]=>90
[3,5,8,2,1,4,6,7]=>[4,3,1]=>70
[3,5,8,2,4,6,7,1]=>[4,3,1]=>70
[5,3,8,2,1,4,6,7]=>[4,2,1,1]=>90
[5,3,1,8,2,4,6,7]=>[5,2,1]=>64
[5,1,3,8,2,4,6,7]=>[5,2,1]=>64
[1,5,8,4,2,3,6,7]=>[5,2,1]=>64
[5,8,2,1,4,3,6,7]=>[4,2,2]=>56
[5,8,2,4,1,6,7,3]=>[4,2,2]=>56
[5,8,2,4,6,3,1,7]=>[4,2,1,1]=>90
[5,8,2,4,3,6,1,7]=>[4,2,1,1]=>90
[5,8,1,4,6,2,3,7]=>[4,2,2]=>56
[1,5,8,4,6,7,2,3]=>[4,2,2]=>56
[5,1,8,4,6,7,2,3]=>[4,2,2]=>56
[5,8,2,4,6,3,7,1]=>[4,2,1,1]=>90
[3,8,4,6,7,2,1,5]=>[4,2,1,1]=>90
[3,8,4,6,7,2,5,1]=>[4,2,1,1]=>90
[8,4,3,6,7,2,5,1]=>[3,2,1,1,1]=>64
[8,4,3,6,7,2,1,5]=>[3,2,1,1,1]=>64
[8,6,2,4,5,3,7,1]=>[4,1,1,1,1]=>35
[1,8,6,4,5,7,2,3]=>[4,2,1,1]=>90
[8,6,2,4,5,3,1,7]=>[4,1,1,1,1]=>35
[1,8,6,4,2,3,5,7]=>[5,1,1,1]=>35
[3,8,1,6,2,4,5,7]=>[5,2,1]=>64
[3,8,6,2,1,4,5,7]=>[4,2,1,1]=>90
[3,8,6,2,4,1,5,7]=>[4,2,1,1]=>90
[3,8,6,2,4,5,7,1]=>[4,2,1,1]=>90
[8,3,6,2,4,5,1,7]=>[4,2,1,1]=>90
[8,1,3,6,2,4,5,7]=>[5,2,1]=>64
[8,3,6,7,2,1,4,5]=>[3,3,1,1]=>56
[3,8,6,7,2,1,4,5]=>[3,3,1,1]=>56
[8,2,6,4,5,1,7,3]=>[4,2,1,1]=>90
[1,8,4,6,7,5,2,3]=>[4,2,1,1]=>90
[8,4,6,2,3,7,5,1]=>[3,3,1,1]=>56
[2,7,1,6,3,5,8,4]=>[4,2,1,1]=>90
[8,2,1,4,7,3,6,5]=>[3,3,1,1]=>56
[1,6,2,5,8,4,7,3]=>[4,2,1,1]=>90
[2,1,5,8,7,3,6,4]=>[3,3,1,1]=>56
[3,2,1,6,7,4,8,5]=>[4,3,1]=>70
[4,3,1,7,8,5,2,6]=>[3,3,2]=>42
[2,8,5,3,6,4,7,1]=>[4,2,1,1]=>90
[5,3,2,7,8,6,4,1]=>[3,2,2,1]=>70
[4,2,7,8,3,5,6,1]=>[4,3,1]=>70
[2,8,3,7,1,4,6,5]=>[4,2,1,1]=>90
[2,8,7,1,5,3,6,4]=>[3,3,1,1]=>56
[7,3,5,6,4,2,8,1]=>[4,1,1,1,1]=>35
[3,8,4,2,7,6,5,1]=>[3,2,1,1,1]=>64
[3,2,4,8,7,5,6,1]=>[4,2,1,1]=>90
[2,6,8,1,5,3,4,7]=>[4,3,1]=>70
[3,2,5,6,8,1,4,7]=>[4,3,1]=>70
[3,8,1,6,4,5,2,7]=>[4,2,1,1]=>90
[8,1,3,6,5,4,2,7]=>[4,1,1,1,1]=>35
[7,4,3,6,2,1,8,5]=>[3,2,1,1,1]=>64
[1,2,4,8,6,3,7,5]=>[5,2,1]=>64
[7,2,1,5,3,4,8,6]=>[4,3,1]=>70
[5,7,2,3,1,4,8,6]=>[4,3,1]=>70
[7,1,5,2,4,6,8,3]=>[5,1,1,1]=>35
[8,4,2,7,3,5,6,1]=>[4,2,1,1]=>90
[1,8,6,4,7,5,3,2]=>[3,2,1,1,1]=>64
[7,4,1,5,8,6,3,2]=>[3,2,2,1]=>70
[4,5,8,7,3,1,2,6]=>[3,3,1,1]=>56
[1,3,8,7,6,4,2,5]=>[4,1,1,1,1]=>35
[2,8,5,1,7,4,6,3]=>[3,3,1,1]=>56
[1,8,6,4,7,5,2,3]=>[3,2,2,1]=>70
[2,7,4,6,3,8,5,1]=>[4,2,1,1]=>90
[1,2,8,6,4,7,5,3]=>[4,2,1,1]=>90
[3,4,5,6,7,9,1,2,8]=>[6,3]=>48
[3,4,5,7,8,9,1,2,6]=>[6,3]=>48
[3,5,6,7,8,9,1,2,4]=>[6,3]=>48
[3,4,5,6,8,9,10,1,2,7]=>[7,3]=>75
[3,5,6,7,8,9,10,1,2,4]=>[7,3]=>75
[3,4,5,6,7,8,9,10,1,2,11]=>[9,2]=>44
[3,4,5,6,7,8,1,2,9,10]=>[8,2]=>35
[3,4,5,6,9,1,2,7,8]=>[6,3]=>48
[3,4,5,6,1,2,7,8,9]=>[7,2]=>27
[3,4,5,6,7,9,10,11,1,2,8]=>[8,3]=>110
[5,1,6,7,8,9,2,3,4]=>[5,4]=>42
[3,4,6,7,8,9,10,11,1,2,5]=>[8,3]=>110
[4,1,8,6,3,7,5,2]=>[3,3,1,1]=>56
[8,4,3,1,6,2,5,7]=>[4,2,1,1]=>90
[7,5,4,3,8,1,6,2]=>[2,2,2,1,1]=>28
[5,3,1,6,2,8,7,4]=>[3,3,2]=>42
[3,5,4,1,7,8,2,6]=>[4,3,1]=>70
[3,2,5,7,8,4,6,1]=>[4,3,1]=>70
[3,1,5,7,8,4,2,6]=>[4,3,1]=>70
[6,1,3,7,4,5,2,8]=>[5,2,1]=>64
[1,8,6,3,5,4,2,7]=>[4,1,1,1,1]=>35
[2,6,1,8,5,3,4,7]=>[4,3,1]=>70
[4,5,7,8,1,6,3,2]=>[4,2,1,1]=>90
[2,5,7,8,4,6,3,1]=>[4,2,1,1]=>90
[1,8,2,7,5,3,4,6]=>[5,1,1,1]=>35
[2,5,4,1,8,6,7,3]=>[4,2,2]=>56
[7,3,5,1,4,8,6,2]=>[3,3,1,1]=>56
[7,1,3,2,4,5,6,8]=>[6,1,1]=>21
[3,8,7,1,4,2,5,6]=>[4,2,1,1]=>90
[5,1,7,8,2,4,3,6]=>[4,3,1]=>70
[8,5,4,6,1,7,3,2]=>[3,2,1,1,1]=>64
[5,3,2,1,4,6,8,7]=>[4,2,1,1]=>90
[5,3,2,4,7,1,8,6]=>[4,2,1,1]=>90
[4,8,1,7,3,5,6,2]=>[4,2,1,1]=>90
[5,3,2,4,6,8,1,7]=>[4,2,1,1]=>90
[1,2,5,6,7,3,8,9,4]=>[7,2]=>27
[1,2,4,3,5,7,8,9,6]=>[7,2]=>27
[4,6,8,3,7,1,5,2]=>[3,2,2,1]=>70
[1,7,6,4,2,5,3,8]=>[4,2,1,1]=>90
[7,6,4,2,8,3,1,5]=>[3,2,1,1,1]=>64
[8,5,2,4,3,7,1,6]=>[3,2,1,1,1]=>64
[8,5,1,4,3,7,6,2]=>[3,2,1,1,1]=>64
[3,6,7,2,5,1,8,4]=>[4,2,2]=>56
[2,6,5,7,1,4,8,3]=>[4,2,1,1]=>90
[3,5,1,7,8,4,6,2]=>[4,3,1]=>70
[1,5,2,4,6,8,7,3]=>[5,2,1]=>64
[8,1,2,4,7,6,5,3]=>[4,1,1,1,1]=>35
[3,4,1,8,6,7,5,2]=>[4,2,1,1]=>90
[4,3,8,5,1,7,6,2]=>[3,2,2,1]=>70
[6,1,3,2,8,5,7,4]=>[4,2,2]=>56
[3,1,2,4,5,6,7,9,8]=>[7,2]=>27
[8,5,3,2,4,7,1,6]=>[3,2,1,1,1]=>64
[6,7,4,2,5,8,3,1]=>[3,2,2,1]=>70
[8,5,4,2,6,3,1,7]=>[3,2,1,1,1]=>64
[8,5,2,1,6,4,3,7]=>[3,2,2,1]=>70
[8,4,6,5,1,3,2,7]=>[3,2,1,1,1]=>64
[1,3,8,4,7,5,2,6]=>[5,1,1,1]=>35
[5,3,7,1,4,6,8,2]=>[4,2,2]=>56
[5,7,2,6,1,4,8,3]=>[3,2,2,1]=>70
[3,8,5,7,6,1,2,4]=>[3,3,1,1]=>56
[8,4,7,5,2,1,3,6]=>[3,2,1,1,1]=>64
[3,8,6,4,7,2,1,5]=>[3,2,1,1,1]=>64
[5,2,7,4,6,8,3,1]=>[4,2,1,1]=>90
[4,8,6,3,7,2,1,5]=>[3,2,1,1,1]=>64
[2,8,3,1,7,6,4,5]=>[4,2,1,1]=>90
[2,5,6,4,8,1,7,3]=>[4,2,2]=>56
[5,7,2,1,6,8,3,4]=>[3,3,2]=>42
[4,7,8,5,1,6,2,3]=>[3,3,2]=>42
[4,5,2,1,6,7,8,3]=>[5,2,1]=>64
[4,5,6,3,1,7,8,2]=>[5,2,1]=>64
[3,5,6,7,4,1,8,2]=>[5,2,1]=>64
[3,5,1,4,2,8,7,6]=>[3,3,2]=>42
[3,5,1,4,2,6,8,7]=>[4,3,1]=>70
[3,5,1,4,2,6,7,8]=>[5,2,1]=>64
[1,3,8,4,6,2,5,7]=>[5,2,1]=>64
[1,8,4,2,3,7,5,6]=>[5,2,1]=>64
[1,4,8,3,2,7,6,5]=>[3,2,2,1]=>70
[1,3,7,6,5,2,4,8]=>[4,2,1,1]=>90
[1,2,8,6,7,5,4,3]=>[4,1,1,1,1]=>35
[1,7,5,4,3,2,6,8]=>[4,1,1,1,1]=>35
[8,9,10,1,5,6,7,3,4,2]=>[4,3,2,1]=>768
[8,9,10,5,6,7,1,3,4,2]=>[3,3,3,1]=>210
[8,9,10,1,5,6,3,4,7,2]=>[4,3,2,1]=>768
[8,9,10,5,6,1,3,4,7,2]=>[4,3,2,1]=>768
[8,9,10,5,6,3,4,7,1,2]=>[3,3,2,2]=>252
[8,9,5,6,10,1,3,4,7,2]=>[4,3,2,1]=>768
[8,9,5,6,10,3,4,7,1,2]=>[3,3,2,2]=>252
[8,9,10,1,5,6,7,3,2,4]=>[4,3,2,1]=>768
[8,9,10,5,6,7,1,3,2,4]=>[3,3,3,1]=>210
[8,9,10,1,5,6,3,7,2,4]=>[4,3,2,1]=>768
[8,9,10,5,6,1,3,7,2,4]=>[3,3,3,1]=>210
[8,9,10,5,6,3,7,1,2,4]=>[3,3,3,1]=>210
[8,9,5,6,10,1,3,7,2,4]=>[3,3,3,1]=>210
[8,9,5,6,10,3,7,1,2,4]=>[3,3,3,1]=>210
[8,9,10,1,5,6,3,2,4,7]=>[4,3,2,1]=>768
[8,9,10,5,6,1,3,2,4,7]=>[4,3,2,1]=>768
[8,9,10,5,6,3,1,2,4,7]=>[4,3,2,1]=>768
[8,9,10,5,6,3,2,4,7,1]=>[3,3,2,1,1]=>450
[8,9,5,6,10,1,3,2,4,7]=>[4,3,2,1]=>768
[8,9,5,6,10,3,1,2,4,7]=>[4,3,2,1]=>768
[8,9,5,6,10,3,2,4,7,1]=>[3,3,2,1,1]=>450
[8,9,10,1,5,3,6,7,2,4]=>[4,3,2,1]=>768
[8,9,10,5,1,3,6,7,2,4]=>[4,3,2,1]=>768
[8,9,10,5,3,6,7,1,2,4]=>[3,3,3,1]=>210
[8,9,5,10,1,3,6,7,2,4]=>[4,3,2,1]=>768
[8,9,5,10,3,6,7,1,2,4]=>[3,3,3,1]=>210
[8,9,10,1,5,3,6,2,4,7]=>[4,3,2,1]=>768
[8,9,10,5,1,3,6,2,4,7]=>[4,3,2,1]=>768
[8,9,10,5,3,6,1,2,4,7]=>[4,3,2,1]=>768
[8,9,10,5,3,6,2,4,7,1]=>[3,3,2,1,1]=>450
[8,9,5,10,1,3,6,2,4,7]=>[4,3,2,1]=>768
[8,9,5,10,3,6,1,2,4,7]=>[4,3,2,1]=>768
[8,9,5,10,3,6,2,4,7,1]=>[3,3,2,1,1]=>450
[8,9,5,3,6,10,1,2,4,7]=>[4,3,2,1]=>768
[8,9,5,3,6,10,2,4,7,1]=>[3,3,2,1,1]=>450
[8,5,9,10,1,3,6,7,2,4]=>[4,3,2,1]=>768
[8,5,9,10,3,6,7,1,2,4]=>[3,3,3,1]=>210
[8,5,9,10,1,3,6,2,4,7]=>[4,3,2,1]=>768
[8,5,9,10,3,6,1,2,4,7]=>[4,3,2,1]=>768
[8,5,9,10,3,6,2,4,7,1]=>[3,3,2,1,1]=>450
[3,8,5,7,4,6,2,1]=>[3,2,1,1,1]=>64
[7,6,3,2,5,1,8,4]=>[3,2,1,1,1]=>64
[4,2,5,7,8,6,3,1]=>[4,2,1,1]=>90
[6,7,2,4,5,1,8,3]=>[4,2,2]=>56
[5,2,7,8,3,6,1,4]=>[3,3,2]=>42
[8,5,1,2,3,7,4,6]=>[5,2,1]=>64
[8,7,2,5,1,4,3,6]=>[3,2,1,1,1]=>64
[8,4,1,3,2,7,6,5]=>[3,2,2,1]=>70
[8,3,5,1,2,4,7,6]=>[4,3,1]=>70
[3,8,6,2,7,1,5,4]=>[3,2,2,1]=>70
[3,8,4,2,1,7,6,5]=>[3,2,2,1]=>70
[8,4,1,7,5,2,6,3]=>[3,3,1,1]=>56
[8,4,2,7,5,3,1,6]=>[3,2,1,1,1]=>64
[8,5,7,6,4,3,1,2]=>[2,2,1,1,1,1]=>20
[1,4,6,8,2,5,7,3]=>[4,3,1]=>70
[7,3,8,2,4,6,1,5]=>[3,2,2,1]=>70
[1,5,2,6,8,3,7,4]=>[4,3,1]=>70
[4,5,3,1,8,2,6,7]=>[4,3,1]=>70
[7,2,8,4,1,3,5,6]=>[4,2,2]=>56
[6,1,7,3,2,8,4,5]=>[4,3,1]=>70
[6,2,1,7,3,8,4,5]=>[4,3,1]=>70
[5,8,2,1,3,4,6,7]=>[5,2,1]=>64
[4,2,5,1,8,3,6,7]=>[4,3,1]=>70
[7,4,2,8,3,1,5,6]=>[4,2,1,1]=>90
[7,4,2,8,3,5,1,6]=>[4,2,1,1]=>90
[10,1,9,5,6,7,8,2,3,4]=>[5,3,1,1]=>567
[9,1,10,8,6,7,2,3,4,5]=>[5,2,2,1]=>525
[8,1,9,10,7,2,3,4,5,6]=>[6,3,1]=>315
[10,1,8,9,2,3,4,5,6,7]=>[7,2,1]=>160
[11,1,10,5,6,7,8,9,2,3,4]=>[6,3,1,1]=>1232
[3,1,10,9,6,7,8,2,4,5]=>[4,4,1,1]=>300
[10,1,11,9,6,7,8,2,3,4,5]=>[5,3,2,1]=>2310
[3,1,9,10,8,7,2,4,5,6]=>[5,3,1,1]=>567
[9,1,10,11,8,7,2,3,4,5,6]=>[6,3,1,1]=>1232
[3,1,8,9,10,2,4,5,6,7]=>[6,4]=>90
[8,1,9,10,11,2,3,4,5,6,7]=>[7,4]=>165
[11,1,10,9,2,3,4,5,6,7,8]=>[8,1,1,1]=>120
[7,3,4,1,8,6,2,5]=>[3,3,2]=>42
[4,7,6,3,5,8,2,1]=>[3,2,1,1,1]=>64
[3,7,6,5,2,4,8,1]=>[3,2,1,1,1]=>64
[1,4,7,8,6,2,5,3]=>[4,2,1,1]=>90
[1,6,7,8,3,2,5,4]=>[4,2,2]=>56
[1,3,2,7,8,4,6,5]=>[4,3,1]=>70
[5,7,1,4,6,2,8,3]=>[4,2,2]=>56
[6,3,1,4,7,8,2,5]=>[4,3,1]=>70
[9,8,7,1,5,6,4,3,2]=>[3,1,1,1,1,1,1]=>28
[9,1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1,1]=>28
[4,5,7,1,8,6,2,3]=>[4,3,1]=>70
[4,3,8,6,5,2,7,1]=>[3,2,1,1,1]=>64
[5,4,7,3,1,2,6,8]=>[4,2,1,1]=>90
[3,1,2,6,5,7,8,4]=>[5,2,1]=>64
[7,3,2,6,1,4,8,5]=>[3,3,1,1]=>56
[3,2,5,6,8,4,1,7]=>[4,3,1]=>70
[7,2,6,8,5,4,3,1]=>[3,1,1,1,1,1]=>21
[3,7,5,6,2,4,1,8]=>[4,2,1,1]=>90
[1,3,4,5,6,7,2,9,8]=>[7,2]=>27
[3,4,5,6,7,1,9,2,8]=>[6,3]=>48
[3,2,4,1,6,5,8,7,9]=>[5,3,1]=>162
[4,2,5,1,6,3,8,7,9]=>[5,3,1]=>162
[4,2,6,1,7,3,8,5,9]=>[5,3,1]=>162
[4,2,6,1,8,3,9,5,7]=>[4,4,1]=>84
[4,2,6,1,7,3,5,9,8]=>[4,4,1]=>84
[4,2,5,1,3,7,6,9,8]=>[4,4,1]=>84
[3,2,5,4,6,1,8,7,9]=>[5,3,1]=>162
[4,2,5,1,6,3,8,7,10,9]=>[5,4,1]=>288
[4,2,5,1,7,6,8,3,9]=>[5,2,2]=>120
[4,2,6,1,7,3,8,5,10,9]=>[5,4,1]=>288
[4,2,6,1,7,3,9,8,5]=>[4,3,2]=>168
[4,2,6,1,8,3,9,5,10,7]=>[5,4,1]=>288
[4,2,5,1,3,6,8,7]=>[4,3,1]=>70
[4,2,6,1,7,3,5,8,9]=>[5,3,1]=>162
[4,2,6,1,8,3,9,5,7,10]=>[5,4,1]=>288
[4,2,5,1,3,8,9,6,7]=>[4,4,1]=>84
[4,2,6,1,7,3,5,9,8,10]=>[5,4,1]=>288
[3,2,1,6,7,4,5,9,8]=>[4,4,1]=>84
[4,2,5,1,3,7,6,9,8,10]=>[5,4,1]=>288
[1,4,5,2,3,7,6,9,8]=>[5,4]=>42
[5,3,4,2,7,1,8,6]=>[4,2,1,1]=>90
[6,5,2,1,3,8,4,7]=>[4,2,1,1]=>90
[2,4,3,5,6,8,1,7]=>[5,2,1]=>64
[6,3,1,2,7,8,4,5]=>[4,3,1]=>70
[8,4,7,1,2,5,3,6]=>[4,2,1,1]=>90
[7,4,6,1,8,5,2,3]=>[3,3,1,1]=>56
[2,5,6,3,8,4,7,1]=>[4,3,1]=>70
[1,7,6,2,8,3,5,4]=>[4,2,1,1]=>90
[4,1,3,8,5,2,7,6]=>[4,2,2]=>56
[1,8,5,4,7,2,3,6]=>[4,2,1,1]=>90
[8,2,5,6,4,3,1,7]=>[4,1,1,1,1]=>35
[2,4,3,8,6,5,1,7]=>[4,2,1,1]=>90
[1,8,3,2,5,4,6,7]=>[5,2,1]=>64
[5,1,7,3,2,8,4,6]=>[4,3,1]=>70
[5,7,8,1,3,2,4,6]=>[4,3,1]=>70
[8,2,4,1,6,7,3,5]=>[4,3,1]=>70
[8,7,3,6,2,4,1,5]=>[3,2,1,1,1]=>64
[1,7,4,8,3,6,2,5]=>[3,2,2,1]=>70
[7,8,6,1,3,5,4,2]=>[3,2,1,1,1]=>64
[1,7,5,8,4,3,2,6]=>[3,2,1,1,1]=>64
[6,3,1,2,7,8,5,4]=>[4,2,2]=>56
[8,2,7,5,3,4,1,6]=>[4,1,1,1,1]=>35
[6,3,1,2,8,7,5,4]=>[3,2,2,1]=>70
[8,4,7,2,6,3,1,5]=>[3,2,1,1,1]=>64
[7,6,3,4,2,1,8,5]=>[3,2,1,1,1]=>64
[8,4,6,2,3,7,1,5]=>[3,3,1,1]=>56
[3,4,5,8,1,7,2,6]=>[4,3,1]=>70
[6,3,4,2,7,8,1,5]=>[4,2,1,1]=>90
[5,6,3,7,8,2,1,4]=>[4,2,1,1]=>90
[8,6,3,4,7,2,1,5]=>[3,2,1,1,1]=>64
[4,3,8,6,7,5,1,2]=>[3,2,2,1]=>70
[4,5,6,2,7,8,3,1]=>[5,2,1]=>64
[4,5,6,2,7,1,8,3]=>[5,2,1]=>64
[4,5,6,2,1,7,8,3]=>[5,2,1]=>64
[4,5,6,2,1,7,3,8]=>[5,2,1]=>64
[6,8,7,2,3,1,4,5]=>[4,2,1,1]=>90
[4,5,1,6,7,3,2,8]=>[5,2,1]=>64
[2,5,1,8,3,7,4,6]=>[4,3,1]=>70
[5,7,2,1,3,8,4,6]=>[4,3,1]=>70
[7,1,5,4,2,6,3,8]=>[4,2,1,1]=>90
[9,8,7,6,5,4,3,2,1,11,10]=>[2,2,1,1,1,1,1,1,1]=>44
[2,7,4,5,6,8,1,3]=>[5,2,1]=>64
[2,3,4,6,8,1,7,5]=>[5,2,1]=>64
[2,3,4,8,6,7,9,5,1]=>[6,1,1,1]=>56
[2,3,8,5,6,7,9,1,4]=>[6,2,1]=>105
[2,8,4,5,6,7,9,3,1]=>[6,1,1,1]=>56
[8,3,4,5,6,7,9,2,1]=>[6,1,1,1]=>56
[2,3,4,5,7,9,1,8,6]=>[6,2,1]=>105
[2,3,4,6,7,1,9,5,8]=>[6,3]=>48
[2,3,4,5,9,7,8,10,6,1]=>[7,1,1,1]=>84
[2,3,5,8,1,6,7,4]=>[5,2,1]=>64
[2,3,5,6,1,7,9,4,8]=>[6,3]=>48
[2,3,4,9,6,7,8,10,1,5]=>[7,2,1]=>160
[2,4,5,1,6,7,9,8,3]=>[6,2,1]=>105
[2,3,9,5,6,7,8,10,4,1]=>[7,1,1,1]=>84
[2,4,7,5,6,8,1,3]=>[5,2,1]=>64
[3,4,1,5,6,7,9,2,8]=>[6,3]=>48
[2,9,4,5,6,7,8,10,3,1]=>[7,1,1,1]=>84
[3,2,4,5,6,7,9,1,8]=>[6,2,1]=>105
[9,3,4,5,6,7,8,10,1,2]=>[7,2,1]=>160
[2,3,4,5,6,8,10,1,9,7]=>[7,2,1]=>160
[2,3,4,5,6,7,10,9,11,8,1]=>[8,1,1,1]=>120
[2,3,4,7,6,9,8,5,1]=>[5,2,1,1]=>189
[2,3,4,5,7,8,1,10,6,9]=>[7,3]=>75
[2,3,4,5,6,10,8,9,11,7,1]=>[8,1,1,1]=>120
[2,3,4,6,9,1,7,8,5]=>[6,2,1]=>105
[2,3,4,6,7,1,8,10,5,9]=>[7,3]=>75
[2,3,4,5,10,7,8,9,11,1,6]=>[8,2,1]=>231
[7,3,4,6,2,8,1,5]=>[4,2,1,1]=>90
[2,5,4,6,8,7,9,1,3]=>[5,2,2]=>120
[2,3,5,7,1,6,9,4,8]=>[5,3,1]=>162
[2,3,5,6,1,7,8,10,9,4]=>[7,2,1]=>160
[2,3,4,10,6,7,8,9,11,5,1]=>[8,1,1,1]=>120
[4,7,6,5,2,8,3,1]=>[3,2,1,1,1]=>64
[4,3,5,8,6,7,9,2,1]=>[5,2,1,1]=>189
[2,5,4,8,6,7,3,1]=>[4,2,1,1]=>90
[2,4,6,1,5,7,9,3,8]=>[5,3,1]=>162
[2,4,5,1,6,7,8,10,3,9]=>[7,3]=>75
[2,3,10,5,6,7,8,9,11,4,1]=>[8,1,1,1]=>120
[7,5,4,1,6,8,2,3]=>[3,3,1,1]=>56
[2,4,8,5,6,7,9,1,3]=>[6,2,1]=>105
[3,5,1,4,6,7,9,8,2]=>[5,3,1]=>162
[3,4,1,5,6,7,8,10,2,9]=>[7,3]=>75
[2,10,4,5,6,7,8,9,11,1,3]=>[8,2,1]=>231
[4,2,3,5,6,7,9,1,8]=>[6,2,1]=>105
[3,2,4,5,6,7,8,10,9,1]=>[7,2,1]=>160
[10,3,4,5,6,7,8,9,11,2,1]=>[8,1,1,1]=>120
[8,5,2,1,7,6,3,4]=>[3,2,2,1]=>70
[7,2,1,8,5,6,4,3]=>[3,2,2,1]=>70
[3,6,5,1,4,8,2,7]=>[3,3,1,1]=>56
[2,5,1,4,6,3,8,7]=>[4,3,1]=>70
[3,1,5,6,4,2,8,7]=>[4,3,1]=>70
[8,5,6,4,3,1,7,2]=>[3,2,1,1,1]=>64
[8,3,5,6,7,1,2,4]=>[4,3,1]=>70
[2,1,4,7,3,6,8,5]=>[4,3,1]=>70
[5,3,7,6,4,8,2,1]=>[3,2,1,1,1]=>64
[3,7,6,4,2,8,1,5]=>[3,2,1,1,1]=>64
[8,6,1,4,3,7,2,5]=>[3,2,1,1,1]=>64
[8,4,7,5,1,6,3,2]=>[3,2,1,1,1]=>64
[2,1,5,3,7,8,6,4]=>[4,3,1]=>70
[5,1,4,7,6,8,2,3]=>[4,2,2]=>56
[8,4,1,3,7,6,5,2]=>[3,2,1,1,1]=>64
[8,3,4,1,6,7,5,2]=>[4,2,1,1]=>90
[8,1,4,2,6,5,7,3]=>[4,2,1,1]=>90
[5,8,1,4,3,2,6,7]=>[4,2,1,1]=>90
[5,6,4,3,8,2,7,1]=>[3,2,1,1,1]=>64
[1,6,4,3,8,2,7,5]=>[3,2,2,1]=>70
[7,8,1,4,3,2,5,6]=>[4,2,1,1]=>90
[7,1,8,4,5,3,6,2]=>[4,2,1,1]=>90
[4,3,1,8,6,5,7,2]=>[3,2,2,1]=>70
[4,3,2,7,5,1,8,6]=>[3,3,1,1]=>56
[5,2,3,7,4,1,8,6]=>[4,3,1]=>70
[2,1,7,4,3,6,8,5]=>[4,3,1]=>70
[7,1,2,4,5,6,8,3]=>[6,1,1]=>21
[2,8,7,1,4,5,6,3]=>[4,2,1,1]=>90
[8,7,1,3,4,5,6,2]=>[5,1,1,1]=>35
[5,8,3,1,4,6,7,2]=>[4,2,2]=>56
[1,7,2,5,4,6,8,3]=>[5,1,1,1]=>35
[2,5,3,8,1,6,7,4]=>[4,2,2]=>56
[1,6,4,2,5,7,8,3]=>[5,2,1]=>64
[6,5,3,4,1,7,8,2]=>[4,2,1,1]=>90
[5,6,3,4,1,7,8,2]=>[4,2,2]=>56
[2,5,3,1,4,7,8,6]=>[5,2,1]=>64
[6,8,2,3,1,5,7,4]=>[4,2,2]=>56
[4,3,1,5,2,7,8,6]=>[4,3,1]=>70
[5,2,3,1,4,7,8,6]=>[5,2,1]=>64
[7,2,1,3,5,6,8,4]=>[5,2,1]=>64
[5,2,4,7,8,6,3,1]=>[4,2,1,1]=>90
[5,4,8,7,2,3,1,6]=>[3,2,2,1]=>70
[8,1,4,5,3,6,2,7]=>[5,1,1,1]=>35
[8,3,5,1,4,6,2,7]=>[4,2,1,1]=>90
[5,8,2,1,7,4,3,6]=>[3,2,2,1]=>70
[6,5,7,2,1,8,4,3]=>[3,2,2,1]=>70
[1,5,4,7,3,8,6,2]=>[4,2,1,1]=>90
[7,4,1,3,8,5,6,2]=>[4,2,1,1]=>90
[3,6,8,4,1,7,2,5]=>[3,3,2]=>42
[2,1,8,4,7,6,3,5]=>[3,3,1,1]=>56
[2,7,5,6,8,4,3,1]=>[4,1,1,1,1]=>35
[3,5,2,4,7,8,6,1]=>[4,3,1]=>70
[7,5,6,3,8,2,1,4]=>[3,2,1,1,1]=>64
[1,6,2,7,4,5,8,3]=>[5,2,1]=>64
[7,4,2,6,1,5,8,3]=>[3,2,2,1]=>70
[8,4,1,6,2,5,7,3]=>[4,2,1,1]=>90
[7,3,4,5,1,6,8,2]=>[5,2,1]=>64
[1,3,2,5,4,7,6,9,8,11,10]=>[6,5]=>132
[1,4,2,6,3,7,5,9,8]=>[5,4]=>42
[1,3,2,6,4,7,5,9,8]=>[5,4]=>42
[2,1,6,3,7,4,8,5,9]=>[5,4]=>42
[8,4,2,7,6,1,5,3]=>[2,2,2,1,1]=>28
[8,4,7,1,2,6,5,3]=>[3,2,1,1,1]=>64
[8,4,7,6,1,2,5,3]=>[3,2,1,1,1]=>64
[8,7,6,2,1,5,3,4]=>[3,2,1,1,1]=>64
[5,7,8,1,6,2,4,3]=>[3,3,1,1]=>56
[6,8,7,4,2,5,1,3]=>[2,2,2,1,1]=>28
[6,8,4,5,7,2,1,3]=>[3,2,2,1]=>70
[6,5,4,3,2,7,1,8,9]=>[4,1,1,1,1,1]=>56
[5,4,3,2,6,1,7,8,9]=>[5,1,1,1,1]=>70
[4,3,2,5,1,6,7,8,9]=>[6,1,1,1]=>56
[3,2,4,1,5,6,7,8,9]=>[7,1,1]=>28
[4,1,2,6,5,3,7,8]=>[5,2,1]=>64
[4,6,1,3,5,2,7,8]=>[5,2,1]=>64
[4,2,6,3,5,1,7,8]=>[5,2,1]=>64
[4,6,1,2,5,3,7,8]=>[5,2,1]=>64
[5,8,4,7,1,3,6,2]=>[3,2,2,1]=>70
[6,8,3,1,5,4,7,2]=>[3,2,2,1]=>70
[5,1,3,6,7,4,2,8]=>[5,2,1]=>64
[4,2,8,6,7,1,3,5]=>[3,3,2]=>42
[6,1,2,4,7,3,5,8]=>[5,2,1]=>64
[4,2,8,1,6,5,7,3]=>[3,2,2,1]=>70
[1,3,5,2,7,4,6,9,8]=>[5,4]=>42
[1,2,4,3,6,5,8,7,9]=>[6,3]=>48
[1,3,5,7,2,4,6,9,8]=>[5,4]=>42
[1,3,5,7,2,4,6,9,8,10]=>[6,4]=>90
[1,3,5,7,2,9,4,6,8]=>[5,4]=>42
[5,6,1,4,8,3,2,7]=>[3,3,1,1]=>56
[3,6,4,1,7,2,8,5]=>[4,3,1]=>70
[5,6,2,1,3,7,4,8,9]=>[5,3,1]=>162
[3,2,5,1,6,4,7,8,9]=>[6,2,1]=>105
[6,7,2,1,8,3,4,9,5]=>[4,4,1]=>84
[3,6,4,1,7,2,8,5,9]=>[5,3,1]=>162
[3,6,7,2,1,4,8,5,9]=>[5,3,1]=>162
[4,2,6,1,7,5,3,8,9]=>[5,2,2]=>120
[4,3,2,6,1,7,5,8,9]=>[5,2,1,1]=>189
[4,7,2,5,1,8,3,9,6]=>[4,3,2]=>168
[4,3,7,8,2,1,5,9,6]=>[4,3,1,1]=>216
[3,5,2,7,1,8,6,4,9]=>[5,2,2]=>120
[5,4,3,2,7,1,8,6,9]=>[4,2,1,1,1]=>189
[6,4,2,8,1,9,7,5,3]=>[3,2,2,2]=>84
[4,3,6,2,8,1,9,7,5]=>[4,2,2,1]=>216
[6,5,4,3,2,8,1,9,7]=>[3,2,1,1,1,1]=>105
[2,4,1,5,3,6,7,8,9,10]=>[8,2]=>35
[5,6,2,1,3,7,4,8,9,10]=>[6,3,1]=>315
[3,2,5,1,6,4,7,8,9,10]=>[7,2,1]=>160
[6,7,2,1,8,3,4,9,5,10]=>[5,4,1]=>288
[3,6,4,1,7,2,8,5,9,10]=>[6,3,1]=>315
[3,6,7,2,1,4,8,5,9,10]=>[6,3,1]=>315
[4,2,6,1,7,5,3,8,9,10]=>[6,2,2]=>225
[4,3,2,6,1,7,5,8,9,10]=>[6,2,1,1]=>350
[3,4,7,1,8,2,9,5,10,6]=>[6,4]=>90
[7,8,9,3,2,1,4,5,10,6]=>[4,4,1,1]=>300
[4,7,2,5,1,8,3,9,6,10]=>[5,3,2]=>450
[4,3,7,8,2,1,5,9,6,10]=>[5,3,1,1]=>567
[3,5,2,7,1,8,6,4,9,10]=>[6,2,2]=>225
[5,4,3,2,7,1,8,6,9,10]=>[5,2,1,1,1]=>448
[5,8,9,2,1,6,3,10,7,4]=>[4,3,3]=>210
[5,3,8,6,4,1,9,2,10,7]=>[4,3,2,1]=>768
[3,5,8,2,6,1,9,4,10,7]=>[5,3,2]=>450
[5,4,3,8,9,2,1,6,10,7]=>[4,3,1,1,1]=>525
[6,4,2,8,1,9,7,5,3,10]=>[4,2,2,2]=>300
[4,3,6,2,8,1,9,7,5,10]=>[5,2,2,1]=>525
[6,5,4,3,2,8,1,9,7,10]=>[4,2,1,1,1,1]=>350
[5,3,7,2,9,1,10,8,6,4]=>[4,2,2,2]=>300
[5,4,3,7,2,9,1,10,8,6]=>[4,2,2,1,1]=>567
[7,6,5,4,3,2,9,1,10,8]=>[3,2,1,1,1,1,1]=>160
[5,2,6,3,7,8,4,1]=>[4,3,1]=>70
[2,4,1,3,7,8,6,5]=>[4,3,1]=>70
[2,6,1,5,7,8,4,3]=>[4,2,1,1]=>90
[5,1,6,4,7,8,2,3]=>[4,3,1]=>70
[8,4,6,3,7,5,1,2]=>[3,2,2,1]=>70
[4,7,6,8,2,3,5,1]=>[3,3,1,1]=>56
[5,7,4,8,1,2,6,3]=>[3,3,2]=>42
[3,6,7,5,8,1,4,2]=>[4,2,1,1]=>90
[3,7,5,6,8,2,4,1]=>[4,2,1,1]=>90
[2,7,1,6,8,4,5,3]=>[3,3,1,1]=>56
[1,5,4,7,2,6,3,8]=>[4,2,2]=>56
[2,4,5,8,3,1,7,6]=>[4,2,2]=>56
[1,4,7,5,8,3,6,2]=>[4,2,1,1]=>90
[2,6,8,7,3,5,1,4]=>[3,2,2,1]=>70
[4,7,8,6,2,5,1,3]=>[3,2,2,1]=>70
[4,8,7,3,5,6,2,1]=>[3,2,1,1,1]=>64
[1,7,6,3,5,4,2,8]=>[4,1,1,1,1]=>35
[4,3,8,1,6,5,7,2]=>[3,2,2,1]=>70
[1,3,6,2,5,8,7,4]=>[4,3,1]=>70
[5,8,7,1,4,6,3,2]=>[3,2,1,1,1]=>64
[5,7,1,4,3,2,6,8]=>[4,2,1,1]=>90
[7,8,5,3,2,1,6,4]=>[2,2,2,1,1]=>28
[1,2,6,7,8,4,5,3]=>[5,2,1]=>64
[6,1,4,8,2,7,5,3]=>[3,2,2,1]=>70
[5,2,3,7,1,8,4,6]=>[4,3,1]=>70
[7,2,3,1,8,4,6,5]=>[4,2,2]=>56
[7,3,4,5,1,8,6,2]=>[4,2,2]=>56
[1,5,6,7,4,8,2,3]=>[5,2,1]=>64
[6,3,2,5,7,4,8,1]=>[4,2,1,1]=>90
[4,5,2,7,6,3,1,8]=>[4,2,1,1]=>90
[4,5,2,1,7,6,3,8]=>[4,2,2]=>56
[2,6,7,8,3,1,4,5]=>[4,3,1]=>70
[6,3,2,5,1,7,8,4]=>[4,2,1,1]=>90
[4,6,3,7,8,2,1,5]=>[4,2,1,1]=>90
[5,6,7,1,8,4,2,3]=>[4,3,1]=>70
[1,7,8,4,6,5,2,3]=>[3,2,2,1]=>70
[1,7,3,2,8,6,5,4]=>[3,2,2,1]=>70
[3,7,1,2,8,6,5,4]=>[3,3,1,1]=>56
[2,7,8,1,6,5,3,4]=>[3,3,1,1]=>56
[8,1,5,7,3,4,6,2]=>[4,2,1,1]=>90
[2,8,4,7,6,3,1,5]=>[3,2,1,1,1]=>64
[1,8,2,4,7,6,3,5]=>[4,2,1,1]=>90
[4,5,8,7,1,6,2,3]=>[3,3,1,1]=>56
[1,8,2,4,6,7,5,3]=>[5,1,1,1]=>35
[3,4,2,8,1,7,6,5]=>[3,2,2,1]=>70
[3,1,8,2,6,7,5,4]=>[4,2,1,1]=>90
[1,6,5,2,8,7,3,4]=>[4,2,2]=>56
[8,1,7,3,5,2,4,6]=>[4,2,1,1]=>90
[8,1,3,2,7,6,4,5]=>[4,2,1,1]=>90
[7,3,4,8,6,2,5,1]=>[3,2,2,1]=>70
[7,5,8,1,6,2,3,4]=>[4,2,2]=>56
[6,2,5,3,8,1,4,7]=>[4,2,1,1]=>90
[7,6,1,3,5,2,4,8]=>[4,2,1,1]=>90
[6,2,4,5,3,8,1,7]=>[4,2,1,1]=>90
[6,1,5,4,7,2,3,8]=>[4,2,1,1]=>90
[6,8,5,4,7,1,3,2]=>[2,2,2,1,1]=>28
[1,6,8,4,2,5,7,3]=>[4,2,2]=>56
[7,5,8,1,3,4,2,6]=>[4,2,1,1]=>90
[1,4,2,8,3,5,7,6]=>[5,2,1]=>64
[1,6,2,4,8,3,7,5]=>[4,2,2]=>56
[1,7,8,5,4,2,6,3]=>[3,2,2,1]=>70
[1,5,2,8,6,4,7,3]=>[4,2,1,1]=>90
[1,6,5,2,7,4,8,3]=>[4,2,1,1]=>90
[5,1,6,7,4,2,8,3]=>[4,3,1]=>70
[1,5,4,2,8,6,7,3]=>[4,2,2]=>56
[1,7,5,4,6,2,8,3]=>[4,2,1,1]=>90
[5,8,4,1,6,2,7,3]=>[3,3,2]=>42
[4,8,1,3,7,6,2,5]=>[3,2,2,1]=>70
[4,5,3,1,2,8,7,6]=>[3,3,2]=>42
[6,4,2,3,1,8,7,5]=>[3,2,2,1]=>70
[6,5,2,1,3,8,7,4]=>[3,2,2,1]=>70
[7,6,1,8,2,5,3,4]=>[4,2,1,1]=>90
[8,4,2,3,7,6,1,5]=>[3,2,2,1]=>70
[5,7,8,1,2,4,3,6]=>[4,3,1]=>70
[1,7,6,8,3,5,4,2]=>[3,2,1,1,1]=>64
[5,7,6,4,2,1,3,8]=>[3,2,1,1,1]=>64
[6,5,7,4,1,3,2,8]=>[3,2,1,1,1]=>64
[4,6,1,8,3,5,2,7]=>[4,3,1]=>70
[7,1,6,8,2,5,4,3]=>[3,2,1,1,1]=>64
[4,7,1,8,3,2,5,6]=>[4,3,1]=>70
[4,8,3,6,1,5,2,7]=>[3,2,2,1]=>70
[1,7,8,6,4,5,3,2]=>[3,2,1,1,1]=>64
[3,2,8,6,4,5,1,7]=>[4,2,1,1]=>90
[8,4,3,6,2,5,1,7]=>[3,2,1,1,1]=>64
[1,6,8,7,4,3,5,2]=>[3,2,1,1,1]=>64
[3,1,2,6,8,7,5,4]=>[4,2,1,1]=>90
[5,7,4,2,1,8,6,3]=>[3,2,2,1]=>70
[8,6,5,7,2,4,3,1]=>[2,2,1,1,1,1]=>20
[7,4,6,1,8,5,3,2]=>[3,2,1,1,1]=>64
[7,4,6,3,8,1,5,2]=>[3,2,2,1]=>70
[7,4,8,1,6,3,2,5]=>[3,2,2,1]=>70
[7,4,8,3,6,2,1,5]=>[2,2,2,1,1]=>28
[4,6,8,2,5,7,1,3]=>[3,3,2]=>42
[6,4,8,2,5,7,1,3]=>[3,2,2,1]=>70
[6,2,4,5,8,3,7,1]=>[4,2,1,1]=>90
[6,8,2,4,7,3,5,1]=>[3,2,2,1]=>70
[8,4,6,2,7,1,3,5]=>[3,3,1,1]=>56
[6,8,4,2,7,1,3,5]=>[3,2,2,1]=>70
[6,8,2,4,1,7,3,5]=>[3,3,2]=>42
[7,5,1,6,2,4,8,3]=>[4,2,1,1]=>90
[4,2,5,7,1,6,8,3]=>[4,2,2]=>56
[4,5,2,3,8,7,1,6]=>[3,3,2]=>42
[2,5,4,7,6,1,3,8]=>[4,2,2]=>56
[5,2,3,7,6,1,4,8]=>[4,2,2]=>56
[4,2,3,7,6,1,5,8]=>[4,2,2]=>56
[4,2,7,3,5,1,6,8]=>[5,2,1]=>64
[5,6,2,3,8,4,7,1]=>[4,3,1]=>70
[5,6,2,3,1,7,8,4]=>[4,3,1]=>70
[5,7,2,3,4,1,6,8]=>[5,2,1]=>64
[6,2,7,3,5,1,4,8]=>[4,2,2]=>56
[7,2,6,3,5,1,4,8]=>[4,2,1,1]=>90
[6,5,2,3,1,7,8,4]=>[4,2,1,1]=>90
[6,5,2,3,8,4,7,1]=>[4,2,1,1]=>90
[7,5,2,1,4,6,8,3]=>[4,2,1,1]=>90
[8,5,2,3,1,6,4,7]=>[4,2,1,1]=>90
[8,6,2,3,1,5,4,7]=>[4,2,1,1]=>90
[8,2,6,3,1,7,4,5]=>[4,2,1,1]=>90
[1,6,3,4,2,7,5,8]=>[5,2,1]=>64
[8,5,2,7,3,4,6,1]=>[4,2,1,1]=>90
[1,7,2,4,5,6,8,3]=>[6,1,1]=>21
[1,8,3,2,5,6,4,7]=>[5,2,1]=>64
[7,2,8,1,4,6,3,5]=>[3,3,2]=>42
[2,7,8,1,5,6,3,4]=>[3,3,2]=>42
[6,8,2,3,1,5,4,7]=>[4,2,2]=>56
[5,8,2,3,1,6,4,7]=>[4,2,2]=>56
[5,7,2,1,4,6,8,3]=>[4,2,2]=>56
[4,2,7,1,5,6,8,3]=>[4,2,2]=>56
[4,2,3,8,1,7,5,6]=>[4,2,2]=>56
[4,2,1,5,3,7,6,8]=>[4,3,1]=>70
[5,1,3,8,4,6,7,2]=>[5,2,1]=>64
[5,1,3,2,6,7,8,4]=>[5,2,1]=>64
[5,1,3,4,2,7,6,8]=>[5,2,1]=>64
[6,1,3,4,2,7,5,8]=>[5,2,1]=>64
[7,2,1,3,5,8,4,6]=>[4,3,1]=>70
[6,8,7,2,3,4,5,1]=>[4,2,1,1]=>90
[6,2,7,3,4,5,1,8]=>[5,2,1]=>64
[3,1,2,9,4,5,6,7,8]=>[7,2]=>27
[4,1,2,3,9,5,6,7,8]=>[7,2]=>27
[5,1,2,3,4,9,6,7,8]=>[7,2]=>27
[6,1,2,3,4,5,9,7,8]=>[7,2]=>27
[2,1,10,3,4,5,6,7,8,9]=>[8,2]=>35
[3,1,2,10,4,5,6,7,8,9]=>[8,2]=>35
[3,4,1,2,9,5,6,7,8]=>[6,3]=>48
[4,1,2,3,10,5,6,7,8,9]=>[8,2]=>35
[4,5,1,2,3,9,6,7,8]=>[6,3]=>48
[5,1,2,3,4,10,6,7,8,9]=>[8,2]=>35
[5,6,1,2,3,4,9,7,8]=>[6,3]=>48
[6,1,2,3,4,5,10,7,8,9]=>[8,2]=>35
[6,7,1,2,3,4,5,9,8]=>[6,3]=>48
[7,1,2,3,4,5,6,10,8,9]=>[8,2]=>35
[4,5,7,2,8,3,6,1]=>[4,3,1]=>70
[9,7,5,3,1,8,6,4,2]=>[2,2,2,2,1]=>42
[9,6,3,8,5,2,7,4,1]=>[3,2,2,1,1]=>162
[8,5,2,9,6,3,7,4,1]=>[3,3,2,1]=>168
[9,5,1,6,2,7,3,8,4]=>[4,4,1]=>84
[9,5,1,8,4,7,3,6,2]=>[3,2,2,1,1]=>162
[8,4,7,3,6,2,9,5,1]=>[3,2,2,1,1]=>162
[7,3,8,4,6,2,9,5,1]=>[4,2,2,1]=>216
[9,4,7,2,5,8,3,6,1]=>[3,3,1,1,1]=>120
[9,4,6,1,8,3,5,7,2]=>[4,3,1,1]=>216
[8,3,5,7,2,9,4,6,1]=>[4,3,1,1]=>216
[7,2,8,3,9,4,5,6,1]=>[5,3,1]=>162
[8,3,7,2,9,4,5,6,1]=>[4,3,1,1]=>216
[5,8,3,7,2,9,4,6,1]=>[3,3,2,1]=>168
[4,5,6,9,3,8,2,7,1]=>[4,2,2,1]=>216
[4,5,6,8,2,9,3,7,1]=>[5,3,1]=>162
[9,3,6,5,4,7,1,8,2]=>[4,2,1,1,1]=>189
[8,2,9,3,6,5,4,7,1]=>[4,2,1,1,1]=>189
[6,5,4,8,2,9,3,7,1]=>[3,3,1,1,1]=>120
[5,6,4,8,2,9,3,7,1]=>[4,3,1,1]=>216
[9,2,7,4,5,6,3,8,1]=>[5,1,1,1,1]=>70
[7,4,5,6,3,9,2,8,1]=>[4,2,1,1,1]=>189
[5,7,4,6,3,9,2,8,1]=>[3,3,1,1,1]=>120
[10,8,6,4,2,9,7,5,3,1]=>[2,2,2,2,1,1]=>90
[10,7,4,1,8,5,2,9,6,3]=>[3,3,3,1]=>210
[9,6,3,8,5,2,10,7,4,1]=>[3,3,2,1,1]=>450
[9,5,1,7,3,10,6,2,8,4]=>[4,3,2,1]=>768
[10,6,2,7,3,8,4,9,5,1]=>[4,4,1,1]=>300
[7,3,8,4,10,6,2,9,5,1]=>[4,3,2,1]=>768
[8,4,7,3,10,6,2,9,5,1]=>[3,3,2,1,1]=>450
[10,5,8,3,6,1,9,4,7,2]=>[3,3,2,1,1]=>450
[9,4,7,2,10,5,8,3,6,1]=>[3,3,2,1,1]=>450
[10,5,7,2,8,3,9,4,6,1]=>[4,4,1,1]=>300
[8,3,10,5,7,2,9,4,6,1]=>[4,3,2,1]=>768
[8,3,9,4,7,2,10,5,6,1]=>[4,3,2,1]=>768
[9,3,5,7,1,10,4,6,8,2]=>[4,4,1,1]=>300
[10,4,6,8,2,9,3,5,7,1]=>[4,4,1,1]=>300
[10,4,5,6,7,1,8,2,9,3]=>[6,3,1]=>315
[8,2,9,3,10,4,5,6,7,1]=>[6,3,1]=>315
[9,3,8,2,10,4,5,6,7,1]=>[5,3,1,1]=>567
[5,6,9,3,7,1,10,4,8,2]=>[4,3,2,1]=>768
[5,6,10,4,8,2,9,3,7,1]=>[4,3,2,1]=>768
[5,6,9,3,8,2,10,4,7,1]=>[4,3,2,1]=>768
[6,5,9,3,8,2,10,4,7,1]=>[3,3,2,1,1]=>450
[9,2,7,6,5,4,10,3,8,1]=>[3,2,1,1,1,1,1]=>160
[10,3,7,6,5,4,8,1,9,2]=>[4,2,1,1,1,1]=>350
[9,2,10,3,7,6,5,4,8,1]=>[4,2,1,1,1,1]=>350
[7,6,5,4,9,2,10,3,8,1]=>[3,3,1,1,1,1]=>225
[6,4,7,5,10,3,9,2,8,1]=>[3,3,2,1,1]=>450
[6,4,7,5,9,2,10,3,8,1]=>[4,3,2,1]=>768
[7,5,6,4,9,2,10,3,8,1]=>[4,3,1,1,1]=>525
[6,5,7,4,9,2,10,3,8,1]=>[4,3,1,1,1]=>525
[5,6,7,3,8,4,9,1,10,2]=>[6,2,2]=>225
[5,6,7,3,8,4,10,2,9,1]=>[5,3,1,1]=>567
[5,6,8,4,7,3,10,2,9,1]=>[4,3,1,1,1]=>525
[6,5,8,4,7,3,10,2,9,1]=>[3,3,1,1,1,1]=>225
[5,2,1,3,6,7,8,4]=>[5,2,1]=>64
[7,5,2,6,1,8,4,3]=>[3,2,2,1]=>70
[6,1,5,2,7,8,4,3]=>[4,2,1,1]=>90
[7,5,6,8,4,1,3,2]=>[3,2,1,1,1]=>64
[8,3,7,5,1,4,2,6]=>[3,2,1,1,1]=>64
[8,1,5,7,3,6,2,4]=>[3,2,2,1]=>70
[8,3,2,6,4,5,1,7]=>[4,2,1,1]=>90
[8,5,3,7,4,1,2,6]=>[3,2,2,1]=>70
[8,5,6,2,7,1,3,4]=>[3,3,1,1]=>56
[8,4,7,2,6,5,1,3]=>[2,2,2,1,1]=>28
[8,5,7,3,2,6,1,4]=>[2,2,2,1,1]=>28
[8,1,2,3,6,4,7,5]=>[5,2,1]=>64
[7,6,2,3,5,8,1,4]=>[4,2,1,1]=>90
[4,5,3,7,8,1,6,2]=>[4,2,2]=>56
[3,4,2,8,1,6,7,5]=>[4,2,2]=>56
[8,3,4,1,5,7,6,2]=>[4,2,1,1]=>90
[4,3,7,5,1,6,2,8]=>[4,2,2]=>56
[5,2,6,1,4,3,7,8]=>[4,2,2]=>56
[5,3,7,4,2,8,6,1]=>[3,3,1,1]=>56
[7,2,5,8,6,1,4,3]=>[3,2,2,1]=>70
[5,3,1,4,6,7,8,2]=>[5,2,1]=>64
[4,6,2,1,3,7,8,5]=>[4,3,1]=>70
[2,5,4,1,3,6,7,8]=>[5,2,1]=>64
[4,2,5,6,7,8,9,1,3]=>[6,2,1]=>105
[3,1,6,7,8,4,5,2]=>[4,3,1]=>70
[7,4,5,6,2,1,8,3]=>[4,2,1,1]=>90
[4,2,5,6,7,8,9,10,1,3]=>[7,2,1]=>160
[3,4,5,6,7,8,9,10,1,11,2]=>[9,2]=>44
[3,7,5,6,2,1,8,4]=>[4,2,1,1]=>90
[1,7,6,3,8,4,5,2]=>[4,2,1,1]=>90
[6,4,1,2,7,8,3,5]=>[4,3,1]=>70
[6,4,1,3,5,2,7,8]=>[5,1,1,1]=>35
[5,1,8,3,4,6,2,7]=>[5,2,1]=>64
[4,5,8,2,3,7,1,6]=>[3,3,2]=>42
[7,3,4,8,2,5,1,6]=>[4,2,1,1]=>90
[4,7,2,5,1,6,8,3]=>[4,2,2]=>56
[7,2,8,1,5,6,4,3]=>[3,2,2,1]=>70
[2,4,3,5,8,1,6,7]=>[5,2,1]=>64
[2,6,5,3,8,1,4,7]=>[4,2,1,1]=>90
[6,1,2,4,3,5,7,8]=>[6,1,1]=>21
[6,5,8,2,7,3,4,1]=>[3,2,2,1]=>70
[1,7,6,8,4,3,2,5]=>[3,2,1,1,1]=>64
[1,7,6,5,3,8,2,4]=>[3,2,1,1,1]=>64
[6,1,2,4,3,5,8,7]=>[5,2,1]=>64
[4,6,1,3,7,8,5,2]=>[4,3,1]=>70
[1,5,6,3,8,7,2,4]=>[4,2,2]=>56
[5,3,2,6,8,7,1,4]=>[3,2,2,1]=>70
[6,3,5,2,7,1,4,8]=>[4,2,1,1]=>90
[8,5,2,6,7,1,4,3]=>[3,2,2,1]=>70
[5,3,8,7,1,4,2,6]=>[3,2,2,1]=>70
[6,4,5,3,1,8,7,2]=>[3,2,2,1]=>70
[8,5,1,2,3,6,7,4]=>[5,2,1]=>64
[2,8,6,1,5,4,7,3]=>[3,2,1,1,1]=>64
[8,3,2,6,1,5,7,4]=>[3,2,2,1]=>70
[3,8,6,4,7,1,2,5]=>[3,3,1,1]=>56
[1,8,7,5,4,3,2,6]=>[3,1,1,1,1,1]=>21
[8,6,4,7,1,3,2,5]=>[3,2,1,1,1]=>64
[3,1,4,7,6,2,5,8]=>[4,3,1]=>70
[5,3,4,1,6,2,7,8]=>[5,2,1]=>64
[2,7,1,4,6,3,5,8]=>[4,3,1]=>70
[7,3,1,6,5,2,4,8]=>[4,2,1,1]=>90
[7,1,5,2,4,6,3,8]=>[5,1,1,1]=>35
[6,1,4,5,2,7,3,8]=>[5,2,1]=>64
[6,1,5,8,2,7,4,3]=>[3,2,2,1]=>70
[7,1,2,3,6,4,5,8]=>[6,1,1]=>21
[2,8,4,6,5,1,7,3]=>[4,2,1,1]=>90
[7,4,1,3,6,5,2,8]=>[4,2,1,1]=>90
[5,7,2,8,1,3,6,4]=>[3,3,2]=>42
[6,5,1,4,7,3,2,8]=>[4,1,1,1,1]=>35
[2,7,8,4,1,3,6,5]=>[3,3,2]=>42
[2,4,6,5,7,8,1,3]=>[5,2,1]=>64
[2,4,6,7,5,8,1,3]=>[5,2,1]=>64
[2,4,6,3,7,8,1,5]=>[5,2,1]=>64
[2,4,5,6,8,7,1,3]=>[5,2,1]=>64
[2,4,5,6,8,3,7,1]=>[5,2,1]=>64
[2,4,5,6,3,8,1,7]=>[5,2,1]=>64
[2,3,4,6,8,5,1,7]=>[5,2,1]=>64
[5,2,8,3,4,1,6,7]=>[5,2,1]=>64
[3,6,4,1,2,7,8,5]=>[4,3,1]=>70
[4,1,7,3,8,6,2,5]=>[3,3,2]=>42
[8,4,1,2,5,3,7,6]=>[4,3,1]=>70
[1,5,2,7,6,8,4,3]=>[4,2,1,1]=>90
[4,7,6,8,3,1,2,5]=>[3,3,1,1]=>56
[4,8,2,7,6,5,1,3]=>[2,2,2,1,1]=>28
[7,4,2,8,6,5,1,3]=>[2,2,2,2]=>14
[8,6,5,2,7,1,4,3]=>[2,2,2,1,1]=>28
[6,5,8,2,7,1,4,3]=>[2,2,2,2]=>14
[7,5,8,2,1,6,4,3]=>[2,2,2,2]=>14
[3,2,1,6,5,8,4,7]=>[3,3,2]=>42
[2,6,4,8,5,7,3,1]=>[4,2,1,1]=>90
[6,3,1,4,5,8,2,7]=>[4,3,1]=>70
[3,4,8,5,2,1,7,6]=>[4,2,1,1]=>90
[4,8,7,1,3,2,6,5]=>[3,2,2,1]=>70
[5,8,7,4,6,1,3,2]=>[2,2,2,1,1]=>28
[3,4,1,8,7,6,2,5]=>[3,3,1,1]=>56
[1,3,5,6,8,7,2,4]=>[5,2,1]=>64
[2,8,7,5,4,1,6,3]=>[3,2,1,1,1]=>64
[8,1,5,7,4,2,6,3]=>[3,2,2,1]=>70
[5,8,7,3,4,1,6,2]=>[3,2,2,1]=>70
[4,6,1,3,2,8,5,7]=>[4,3,1]=>70
[2,6,5,8,3,1,4,7]=>[4,2,1,1]=>90
[6,7,8,2,4,5,3,1]=>[3,3,1,1]=>56
[3,2,8,4,5,7,1,6]=>[4,2,2]=>56
[6,1,8,2,4,5,3,7]=>[5,2,1]=>64
[8,3,6,4,2,7,1,5]=>[3,2,1,1,1]=>64
[1,3,8,4,7,6,2,5]=>[4,2,1,1]=>90
[8,3,7,5,4,1,2,6]=>[3,2,1,1,1]=>64
[2,6,4,7,8,5,1,3]=>[4,2,2]=>56
[5,4,3,7,6,1,8,2]=>[3,2,2,1]=>70
[8,6,3,7,1,4,2,5]=>[3,2,2,1]=>70
[3,1,2,8,7,6,4,5]=>[4,2,1,1]=>90
[8,5,4,1,2,3,7,6]=>[4,2,1,1]=>90
[8,3,2,1,6,4,7,5]=>[3,3,1,1]=>56
[2,3,8,4,1,7,5,6]=>[5,2,1]=>64
[4,6,1,3,2,7,8,5]=>[4,3,1]=>70
[6,7,2,5,8,4,1,3]=>[3,2,2,1]=>70
[4,1,7,8,2,5,6,3]=>[4,3,1]=>70
[3,4,6,7,1,5,8,2]=>[5,2,1]=>64
[3,4,5,7,8,1,6,2]=>[5,2,1]=>64
[2,4,5,8,1,3,7,6]=>[4,3,1]=>70
[6,3,1,5,8,4,2,7]=>[3,3,1,1]=>56
[2,8,3,5,6,1,4,7]=>[5,2,1]=>64
[1,3,6,4,2,7,5,8]=>[5,2,1]=>64
[2,3,7,5,8,1,4,6]=>[4,3,1]=>70
[3,2,8,5,6,1,4,7]=>[4,2,2]=>56
[7,2,5,8,1,4,6,3]=>[3,3,1,1]=>56
[4,7,5,8,1,2,6,3]=>[3,3,2]=>42
[4,7,5,8,1,2,3,6]=>[4,3,1]=>70
[3,4,7,5,2,8,1,6]=>[4,2,1,1]=>90
[4,3,2,5,7,8,1,6]=>[4,2,1,1]=>90
[2,4,7,5,8,3,1,6]=>[4,2,1,1]=>90
[2,5,4,7,3,8,1,6]=>[4,2,1,1]=>90
[3,7,8,4,2,1,6,5]=>[3,2,2,1]=>70
[5,6,7,9,1,2,3,4,8]=>[5,4]=>42
[4,5,6,7,9,1,2,3,8]=>[5,4]=>42
[7,8,10,1,2,3,4,5,6,9]=>[7,3]=>75
[4,5,6,7,8,10,1,2,3,9]=>[6,4]=>90
[8,5,4,7,6,3,1,2]=>[2,2,2,1,1]=>28
[1,5,4,8,7,6,2,3]=>[3,2,2,1]=>70
[3,2,4,5,8,1,6,7]=>[5,2,1]=>64
[3,6,8,4,2,7,1,5]=>[3,2,2,1]=>70
[7,4,1,6,2,8,5,3]=>[3,3,1,1]=>56
[1,3,6,8,2,4,7,5]=>[4,3,1]=>70
[1,6,7,4,3,8,2,5]=>[4,2,1,1]=>90
[8,5,4,1,6,2,7,3]=>[3,3,1,1]=>56
[4,7,2,8,5,1,6,3]=>[3,3,2]=>42
[7,8,6,2,1,5,4,3]=>[2,2,2,1,1]=>28
[2,1,3,8,7,5,6,4]=>[4,2,1,1]=>90
[8,1,7,3,6,5,2,4]=>[3,2,1,1,1]=>64
[1,6,5,7,4,8,3,9,2]=>[5,1,1,1,1]=>70
[5,4,6,3,8,2,7,1,9]=>[4,2,1,1,1]=>189
[1,6,7,5,8,4,9,3,10,2]=>[6,1,1,1,1]=>126
[6,5,7,4,8,3,9,2,10,1,11]=>[6,1,1,1,1,1]=>252
[1,7,6,8,5,9,4,10,3,11,2]=>[6,1,1,1,1,1]=>252
[1,2,3,4,5,6,8,10,7,9]=>[8,2]=>35
[3,4,5,6,7,8,2,1,9]=>[7,1,1]=>28
[4,5,6,7,8,1,2,3,9]=>[6,3]=>48
[4,8,1,6,3,7,2,5]=>[3,3,1,1]=>56
[1,7,6,2,4,8,5,3]=>[4,2,1,1]=>90
[2,8,4,6,3,5,1,7]=>[4,2,1,1]=>90
[3,8,1,4,6,5,2,7]=>[4,2,1,1]=>90
[2,7,5,4,1,8,3,6]=>[3,3,1,1]=>56
[4,6,1,8,5,3,2,7]=>[3,3,1,1]=>56
[3,8,5,2,1,6,4,7]=>[4,2,1,1]=>90
[5,1,4,8,2,6,3,7]=>[4,2,2]=>56
[4,5,8,1,3,7,6,2]=>[3,3,1,1]=>56
[8,6,7,1,4,3,2,5]=>[3,2,1,1,1]=>64
[1,4,7,8,6,3,5,2]=>[4,2,1,1]=>90
[8,5,2,6,3,4,7,1]=>[4,2,1,1]=>90
[8,3,6,1,2,7,4,5]=>[4,3,1]=>70
[3,8,6,1,2,5,7,4]=>[4,2,1,1]=>90
[3,7,6,2,1,8,5,4]=>[3,2,2,1]=>70
[4,3,7,6,1,8,5,2]=>[3,2,2,1]=>70
[8,6,3,2,7,1,5,4]=>[2,2,2,1,1]=>28
[6,8,1,5,4,7,2,3]=>[3,2,2,1]=>70
[6,7,2,5,4,8,1,3]=>[3,2,2,1]=>70
[7,6,2,4,8,5,1,3]=>[3,2,2,1]=>70
[4,6,8,7,3,1,2,5]=>[3,3,1,1]=>56
[4,7,5,2,6,3,8,1]=>[4,2,1,1]=>90
[3,5,6,2,8,1,4,7]=>[4,3,1]=>70
[8,9,10,4,5,6,2,3,1,7]=>[4,3,2,1]=>768
[8,9,4,5,6,10,2,3,1,7]=>[4,3,2,1]=>768
[8,9,10,4,5,2,3,6,1,7]=>[4,3,2,1]=>768
[8,9,4,5,10,2,3,6,1,7]=>[4,3,2,1]=>768
[8,9,4,5,2,3,6,10,1,7]=>[4,3,2,1]=>768
[8,4,5,9,10,2,3,6,1,7]=>[4,4,1,1]=>300
[8,4,5,9,2,3,6,10,1,7]=>[4,4,1,1]=>300
[8,9,10,4,5,6,2,1,3,7]=>[4,3,2,1]=>768
[8,9,4,5,6,10,2,1,3,7]=>[4,3,2,1]=>768
[8,9,10,4,5,2,6,1,3,7]=>[4,3,2,1]=>768
[8,9,4,5,10,2,6,1,3,7]=>[4,3,2,1]=>768
[8,9,4,5,2,6,10,1,3,7]=>[4,3,2,1]=>768
[8,4,5,9,10,2,6,1,3,7]=>[4,3,2,1]=>768
[8,4,5,9,2,6,10,1,3,7]=>[4,3,2,1]=>768
[8,9,10,4,5,2,1,3,6,7]=>[4,3,2,1]=>768
[8,9,4,5,10,2,1,3,6,7]=>[4,3,2,1]=>768
[8,9,4,5,2,10,1,3,6,7]=>[4,3,2,1]=>768
[8,9,4,5,2,1,3,6,10,7]=>[4,3,2,1]=>768
[8,4,5,9,10,2,1,3,6,7]=>[4,4,1,1]=>300
[8,4,5,9,2,10,1,3,6,7]=>[4,4,1,1]=>300
[8,4,5,9,2,1,3,6,10,7]=>[4,4,1,1]=>300
[8,9,10,4,2,5,6,1,3,7]=>[4,3,2,1]=>768
[8,9,4,10,2,5,6,1,3,7]=>[4,3,2,1]=>768
[8,9,4,2,5,6,10,1,3,7]=>[4,3,2,1]=>768
[8,4,9,10,2,5,6,1,3,7]=>[4,3,2,1]=>768
[8,4,9,2,5,6,10,1,3,7]=>[4,3,2,1]=>768
[8,9,10,4,2,5,1,3,6,7]=>[4,3,2,1]=>768
[8,9,4,10,2,5,1,3,6,7]=>[4,3,2,1]=>768
[8,9,4,2,5,10,1,3,6,7]=>[4,3,2,1]=>768
[8,9,4,2,5,1,3,6,10,7]=>[4,3,2,1]=>768
[8,4,9,10,2,5,1,3,6,7]=>[4,3,2,1]=>768
[8,4,9,2,5,1,3,6,10,7]=>[4,3,2,1]=>768
[8,4,2,5,9,10,1,3,6,7]=>[4,4,1,1]=>300
[8,4,2,5,9,1,3,6,10,7]=>[4,4,1,1]=>300
[4,8,9,10,2,5,6,1,3,7]=>[4,4,2]=>252
[4,8,9,2,5,6,10,1,3,7]=>[4,4,2]=>252
[4,8,9,10,2,5,1,3,6,7]=>[4,4,2]=>252
[4,8,9,2,5,10,1,3,6,7]=>[4,4,2]=>252
[4,8,9,2,5,1,3,6,10,7]=>[4,4,2]=>252
[4,8,2,5,9,10,1,3,6,7]=>[4,4,2]=>252
[4,8,2,5,9,1,3,6,10,7]=>[4,4,2]=>252
[6,1,8,2,4,3,5,7]=>[5,2,1]=>64
[1,6,8,2,5,3,4,7]=>[5,2,1]=>64
[5,4,8,7,1,2,6,3]=>[3,2,2,1]=>70
[2,5,6,4,3,8,1,7]=>[4,2,1,1]=>90
[8,6,3,5,2,1,4,7]=>[3,2,1,1,1]=>64
[8,7,3,5,2,4,6,1]=>[3,2,1,1,1]=>64
[4,6,3,8,5,2,7,1]=>[3,3,1,1]=>56
[4,1,3,8,5,6,2,7]=>[5,2,1]=>64
[5,2,8,3,1,6,7,4]=>[4,2,2]=>56
[1,7,8,6,3,2,5,4]=>[3,2,2,1]=>70
[3,4,6,7,2,1,5,8]=>[5,2,1]=>64
[3,2,7,4,8,5,6,1]=>[4,3,1]=>70
[5,8,2,7,4,6,3,1]=>[3,2,1,1,1]=>64
[4,5,2,8,3,7,1,6]=>[3,3,2]=>42
[7,8,5,1,6,4,3,2]=>[2,2,2,1,1]=>28
[8,7,5,1,6,4,3,2]=>[2,2,1,1,1,1]=>20
[4,5,8,3,1,2,7,6]=>[3,3,2]=>42
[1,4,6,3,7,5,2,8]=>[5,2,1]=>64
[1,3,8,7,4,5,6,2]=>[5,1,1,1]=>35
[7,3,1,8,4,5,6,2]=>[4,2,2]=>56
[6,2,4,3,7,5,8,1]=>[4,2,1,1]=>90
[3,8,2,1,5,7,6,4]=>[3,2,2,1]=>70
[1,3,2,8,7,4,6,5]=>[4,2,1,1]=>90
[7,5,2,8,3,1,6,4]=>[3,2,2,1]=>70
[4,6,3,7,8,1,2,5]=>[4,3,1]=>70
[6,2,5,4,1,7,8,3]=>[4,2,1,1]=>90
[8,5,1,6,3,2,4,7]=>[4,2,1,1]=>90
[2,8,5,1,3,7,6,4]=>[3,3,1,1]=>56
[5,6,4,1,8,2,7,3]=>[3,3,2]=>42
[6,4,5,1,3,8,7,2]=>[3,3,1,1]=>56
[6,1,3,5,4,8,2,7]=>[4,2,1,1]=>90
[1,3,8,7,2,5,6,4]=>[4,2,1,1]=>90
[2,5,4,1,8,3,7,6]=>[3,3,2]=>42
[5,1,4,8,3,7,6,2]=>[3,2,2,1]=>70
[8,4,1,2,7,6,5,3]=>[3,2,1,1,1]=>64
[4,8,3,2,7,6,5,1]=>[2,2,2,1,1]=>28
[1,8,7,3,4,6,5,2]=>[4,1,1,1,1]=>35
[4,3,1,2,6,5,8,7,9]=>[5,3,1]=>162
[6,5,3,1,2,4,8,7,9]=>[5,2,1,1]=>189
[8,7,5,3,1,2,4,6,9]=>[5,1,1,1,1]=>70
[7,5,3,1,2,4,6,9,8]=>[5,2,1,1]=>189
[5,3,1,2,4,7,6,9,8]=>[5,3,1]=>162
[4,1,2,6,5,3,8,7,9]=>[5,3,1]=>162
[6,5,3,1,2,4,8,7,10,9]=>[5,3,1,1]=>567
[6,3,1,2,4,8,7,5,9]=>[5,2,2]=>120
[8,7,5,3,1,2,4,6,10,9]=>[5,2,1,1,1]=>448
[8,5,3,1,2,4,6,9,7]=>[5,2,1,1]=>189
[10,9,7,5,3,1,2,4,6,8]=>[5,1,1,1,1,1]=>126
[5,3,1,2,4,6,8,7]=>[5,2,1]=>64
[8,5,7,3,1,2,4,6]=>[4,2,1,1]=>90
[7,5,3,1,2,4,6,8,9]=>[6,1,1,1]=>56
[3,1,2,8,7,5,4,6]=>[4,2,1,1]=>90
[5,3,1,2,4,9,7,6,8]=>[5,2,2]=>120
[7,5,3,1,2,4,6,9,8,10]=>[6,2,1,1]=>350
[3,1,2,7,5,4,6,9,8]=>[5,3,1]=>162
[5,3,1,2,4,7,6,9,8,10]=>[6,3,1]=>315
[1,5,3,2,4,7,6,9,8]=>[5,3,1]=>162
[1,4,3,8,5,7,2,6]=>[4,2,2]=>56
[6,7,1,5,2,8,4,3]=>[3,3,1,1]=>56
[1,5,3,7,6,4,8,2]=>[4,2,1,1]=>90
[4,8,1,3,6,2,7,5]=>[4,2,2]=>56
[2,7,3,4,8,6,5,1]=>[4,2,1,1]=>90
[1,8,2,4,7,3,6,5]=>[4,2,1,1]=>90
[6,2,3,8,1,5,7,4]=>[4,2,2]=>56
[2,5,7,4,8,3,6,1]=>[4,2,1,1]=>90
[8,5,6,2,4,7,1,3]=>[3,2,2,1]=>70
[8,1,5,7,3,6,4,2]=>[3,2,1,1,1]=>64
[3,8,6,2,7,5,4,1]=>[3,2,1,1,1]=>64
[4,8,1,6,2,5,3,7]=>[4,2,1,1]=>90
[1,8,4,2,5,7,3,6]=>[4,3,1]=>70
[5,8,3,1,2,4,6,7]=>[5,2,1]=>64
[1,4,8,5,2,3,6,7]=>[5,2,1]=>64
[1,4,8,5,2,3,7,6]=>[4,3,1]=>70
[1,5,8,7,2,4,3,6]=>[4,2,1,1]=>90
[1,5,4,2,8,3,7,6]=>[4,2,2]=>56
[1,2,8,7,3,5,4,6]=>[5,1,1,1]=>35
[8,7,1,3,2,5,4,6]=>[4,2,1,1]=>90
[6,7,4,2,8,1,3,5]=>[3,3,1,1]=>56
[4,1,6,8,7,2,3,5]=>[4,3,1]=>70
[6,1,7,3,5,8,2,4]=>[4,2,2]=>56
[2,6,4,8,7,3,1,5]=>[3,2,2,1]=>70
[2,1,8,7,3,5,4,6]=>[4,2,1,1]=>90
[6,1,8,5,7,4,3,2]=>[3,2,1,1,1]=>64
[8,5,1,4,7,6,3,2]=>[3,2,1,1,1]=>64
[5,3,1,6,4,8,2,7]=>[3,3,2]=>42
[4,7,5,3,2,8,1,6]=>[3,2,1,1,1]=>64
[4,7,5,2,8,6,1,3]=>[3,2,2,1]=>70
[5,8,1,2,7,4,3,6]=>[4,2,1,1]=>90
[4,6,3,7,8,1,5,2]=>[4,2,2]=>56
[6,3,1,8,4,5,2,7]=>[4,2,2]=>56
[7,6,2,4,8,3,1,5]=>[3,2,1,1,1]=>64
[6,5,8,1,4,3,7,2]=>[3,2,1,1,1]=>64
[8,1,4,2,7,5,6,3]=>[4,2,1,1]=>90
[9,3,4,5,6,7,1,2,10,8]=>[6,3,1]=>315
[1,7,2,8,3,9,4,10,5,6]=>[6,4]=>90
[1,7,2,8,3,9,10,4,5,6]=>[6,4]=>90
[1,7,2,8,9,3,4,10,5,6]=>[6,4]=>90
[1,7,2,8,9,3,10,4,5,6]=>[6,4]=>90
[1,7,2,8,9,10,3,4,5,6]=>[6,4]=>90
[1,7,8,2,3,9,4,10,5,6]=>[6,4]=>90
[1,7,8,2,3,9,10,4,5,6]=>[6,4]=>90
[1,7,8,2,9,3,4,10,5,6]=>[6,4]=>90
[1,7,8,2,9,3,10,4,5,6]=>[6,4]=>90
[1,7,8,2,9,10,3,4,5,6]=>[6,4]=>90
[1,7,8,9,2,3,4,10,5,6]=>[6,4]=>90
[1,7,8,9,2,3,10,4,5,6]=>[6,4]=>90
[1,7,8,9,2,10,3,4,5,6]=>[6,4]=>90
[7,1,2,8,3,9,4,10,5,6]=>[6,4]=>90
[7,1,2,8,3,9,10,4,5,6]=>[6,4]=>90
[7,1,2,8,9,3,4,10,5,6]=>[6,4]=>90
[7,1,2,8,9,3,10,4,5,6]=>[6,4]=>90
[7,1,2,8,9,10,3,4,5,6]=>[6,4]=>90
[7,1,8,2,3,9,4,10,5,6]=>[6,4]=>90
[7,1,8,2,3,9,10,4,5,6]=>[6,4]=>90
[7,1,8,2,9,3,4,10,5,6]=>[6,4]=>90
[7,1,8,2,9,10,3,4,5,6]=>[6,4]=>90
[7,1,8,9,2,3,4,10,5,6]=>[6,4]=>90
[7,1,8,9,2,3,10,4,5,6]=>[6,4]=>90
[7,1,8,9,2,10,3,4,5,6]=>[6,4]=>90
[7,1,8,9,10,2,3,4,5,6]=>[6,4]=>90
[7,8,1,2,3,9,4,10,5,6]=>[6,4]=>90
[7,8,1,2,3,9,10,4,5,6]=>[6,4]=>90
[7,8,1,2,9,3,4,10,5,6]=>[6,4]=>90
[7,8,1,2,9,3,10,4,5,6]=>[6,4]=>90
[7,8,1,2,9,10,3,4,5,6]=>[6,4]=>90
[7,8,1,9,2,3,4,10,5,6]=>[6,4]=>90
[7,8,1,9,2,3,10,4,5,6]=>[6,4]=>90
[7,8,1,9,2,10,3,4,5,6]=>[6,4]=>90
[7,8,1,9,10,2,3,4,5,6]=>[6,4]=>90
[7,8,9,1,2,3,4,10,5,6]=>[6,4]=>90
[7,8,9,1,2,3,10,4,5,6]=>[6,4]=>90
[7,8,9,1,2,10,3,4,5,6]=>[6,4]=>90
[7,8,9,1,10,2,3,4,5,6]=>[6,4]=>90
[1,8,2,9,3,10,4,11,5,12,6,7]=>[7,5]=>297
[1,8,2,9,3,10,4,11,12,5,6,7]=>[7,5]=>297
[1,8,2,9,3,10,11,4,5,12,6,7]=>[7,5]=>297
[1,8,2,9,3,10,11,4,12,5,6,7]=>[7,5]=>297
[1,8,2,9,3,10,11,12,4,5,6,7]=>[7,5]=>297
[1,8,2,9,10,3,4,11,5,12,6,7]=>[7,5]=>297
[1,8,2,9,10,3,4,11,12,5,6,7]=>[7,5]=>297
[1,8,2,9,10,3,11,4,5,12,6,7]=>[7,5]=>297
[1,8,2,9,10,3,11,4,12,5,6,7]=>[7,5]=>297
[1,8,2,9,10,3,11,12,4,5,6,7]=>[7,5]=>297
[1,8,2,9,10,11,3,4,5,12,6,7]=>[7,5]=>297
[1,8,2,9,10,11,3,4,12,5,6,7]=>[7,5]=>297
[1,8,2,9,10,11,3,12,4,5,6,7]=>[7,5]=>297
[1,8,2,9,10,11,12,3,4,5,6,7]=>[7,5]=>297
[1,8,9,2,3,10,4,11,5,12,6,7]=>[7,5]=>297
[1,8,9,2,3,10,4,11,12,5,6,7]=>[7,5]=>297
[1,8,9,2,3,10,11,4,5,12,6,7]=>[7,5]=>297
[1,8,9,2,3,10,11,4,12,5,6,7]=>[7,5]=>297
[1,8,9,2,3,10,11,12,4,5,6,7]=>[7,5]=>297
[1,8,9,2,10,3,4,11,5,12,6,7]=>[7,5]=>297
[1,8,9,2,10,3,4,11,12,5,6,7]=>[7,5]=>297
[1,8,9,2,10,3,11,4,5,12,6,7]=>[7,5]=>297
[1,8,9,2,10,3,11,4,12,5,6,7]=>[7,5]=>297
[1,8,9,2,10,3,11,12,4,5,6,7]=>[7,5]=>297
[1,8,9,2,10,11,3,4,5,12,6,7]=>[7,5]=>297
[1,8,9,2,10,11,3,4,12,5,6,7]=>[7,5]=>297
[1,8,9,2,10,11,3,12,4,5,6,7]=>[7,5]=>297
[1,8,9,2,10,11,12,3,4,5,6,7]=>[7,5]=>297
[1,8,9,10,2,3,4,11,5,12,6,7]=>[7,5]=>297
[1,8,9,10,2,3,4,11,12,5,6,7]=>[7,5]=>297
[1,8,9,10,2,3,11,4,5,12,6,7]=>[7,5]=>297
[1,8,9,10,2,3,11,4,12,5,6,7]=>[7,5]=>297
[1,8,9,10,2,3,11,12,4,5,6,7]=>[7,5]=>297
[1,8,9,10,2,11,3,4,5,12,6,7]=>[7,5]=>297
[1,8,9,10,2,11,3,4,12,5,6,7]=>[7,5]=>297
[1,8,9,10,2,11,3,12,4,5,6,7]=>[7,5]=>297
[1,8,9,10,2,11,12,3,4,5,6,7]=>[7,5]=>297
[1,8,9,10,11,2,3,4,5,12,6,7]=>[7,5]=>297
[1,8,9,10,11,2,3,4,12,5,6,7]=>[7,5]=>297
[1,8,9,10,11,2,3,12,4,5,6,7]=>[7,5]=>297
[1,8,9,10,11,2,12,3,4,5,6,7]=>[7,5]=>297
[1,8,9,10,11,12,2,3,4,5,6,7]=>[7,5]=>297
[8,1,2,9,3,10,4,11,5,12,6,7]=>[7,5]=>297
[8,1,2,9,3,10,4,11,12,5,6,7]=>[7,5]=>297
[8,1,2,9,3,10,11,4,5,12,6,7]=>[7,5]=>297
[8,1,2,9,3,10,11,4,12,5,6,7]=>[7,5]=>297
[8,1,2,9,3,10,11,12,4,5,6,7]=>[7,5]=>297
[8,1,2,9,10,3,4,11,5,12,6,7]=>[7,5]=>297
[8,1,2,9,10,3,4,11,12,5,6,7]=>[7,5]=>297
[8,1,2,9,10,3,11,4,5,12,6,7]=>[7,5]=>297
[8,1,2,9,10,3,11,4,12,5,6,7]=>[7,5]=>297
[8,1,2,9,10,3,11,12,4,5,6,7]=>[7,5]=>297
[8,1,2,9,10,11,3,4,5,12,6,7]=>[7,5]=>297
[8,1,2,9,10,11,3,4,12,5,6,7]=>[7,5]=>297
[8,1,2,9,10,11,3,12,4,5,6,7]=>[7,5]=>297
[8,1,2,9,10,11,12,3,4,5,6,7]=>[7,5]=>297
[8,1,9,2,3,10,4,11,5,12,6,7]=>[7,5]=>297
[8,1,9,2,3,10,4,11,12,5,6,7]=>[7,5]=>297
[8,1,9,2,3,10,11,4,5,12,6,7]=>[7,5]=>297
[8,1,9,2,3,10,11,4,12,5,6,7]=>[7,5]=>297
[8,1,9,2,3,10,11,12,4,5,6,7]=>[7,5]=>297
[8,1,9,2,10,3,4,11,5,12,6,7]=>[7,5]=>297
[8,1,9,2,10,3,4,11,12,5,6,7]=>[7,5]=>297
[8,1,9,2,10,3,11,4,5,12,6,7]=>[7,5]=>297
[8,1,9,2,10,3,11,4,12,5,6,7]=>[7,5]=>297
[8,1,9,2,10,3,11,12,4,5,6,7]=>[7,5]=>297
[8,1,9,2,10,11,3,4,5,12,6,7]=>[7,5]=>297
[8,1,9,2,10,11,3,4,12,5,6,7]=>[7,5]=>297
[8,1,9,2,10,11,3,12,4,5,6,7]=>[7,5]=>297
[8,1,9,2,10,11,12,3,4,5,6,7]=>[7,5]=>297
[8,1,9,10,2,3,4,11,5,12,6,7]=>[7,5]=>297
[8,1,9,10,2,3,4,11,12,5,6,7]=>[7,5]=>297
[8,1,9,10,2,3,11,4,5,12,6,7]=>[7,5]=>297
[8,1,9,10,2,3,11,4,12,5,6,7]=>[7,5]=>297
[8,1,9,10,2,3,11,12,4,5,6,7]=>[7,5]=>297
[8,1,9,10,2,11,3,4,5,12,6,7]=>[7,5]=>297
[8,1,9,10,2,11,3,4,12,5,6,7]=>[7,5]=>297
[8,1,9,10,2,11,3,12,4,5,6,7]=>[7,5]=>297
[8,1,9,10,2,11,12,3,4,5,6,7]=>[7,5]=>297
[8,1,9,10,11,2,3,4,5,12,6,7]=>[7,5]=>297
[8,1,9,10,11,2,3,4,12,5,6,7]=>[7,5]=>297
[8,1,9,10,11,2,3,12,4,5,6,7]=>[7,5]=>297
[8,1,9,10,11,2,12,3,4,5,6,7]=>[7,5]=>297
[8,1,9,10,11,12,2,3,4,5,6,7]=>[7,5]=>297
[8,9,1,2,3,10,4,11,5,12,6,7]=>[7,5]=>297
[8,9,1,2,3,10,4,11,12,5,6,7]=>[7,5]=>297
[8,9,1,2,3,10,11,4,5,12,6,7]=>[7,5]=>297
[8,9,1,2,3,10,11,4,12,5,6,7]=>[7,5]=>297
[8,9,1,2,3,10,11,12,4,5,6,7]=>[7,5]=>297
[8,9,1,2,10,3,4,11,5,12,6,7]=>[7,5]=>297
[8,9,1,2,10,3,4,11,12,5,6,7]=>[7,5]=>297
[8,9,1,2,10,3,11,4,5,12,6,7]=>[7,5]=>297
[8,9,1,2,10,3,11,4,12,5,6,7]=>[7,5]=>297
[8,9,1,2,10,3,11,12,4,5,6,7]=>[7,5]=>297
[8,9,1,2,10,11,3,4,5,12,6,7]=>[7,5]=>297
[8,9,1,2,10,11,3,4,12,5,6,7]=>[7,5]=>297
[8,9,1,2,10,11,3,12,4,5,6,7]=>[7,5]=>297
[8,9,1,2,10,11,12,3,4,5,6,7]=>[7,5]=>297
[8,9,1,10,2,3,4,11,5,12,6,7]=>[7,5]=>297
[8,9,1,10,2,3,4,11,12,5,6,7]=>[7,5]=>297
[8,9,1,10,2,3,11,4,5,12,6,7]=>[7,5]=>297
[8,9,1,10,2,3,11,4,12,5,6,7]=>[7,5]=>297
[8,9,1,10,2,3,11,12,4,5,6,7]=>[7,5]=>297
[8,9,1,10,2,11,3,4,5,12,6,7]=>[7,5]=>297
[8,9,1,10,2,11,3,4,12,5,6,7]=>[7,5]=>297
[8,9,1,10,2,11,3,12,4,5,6,7]=>[7,5]=>297
[8,9,1,10,2,11,12,3,4,5,6,7]=>[7,5]=>297
[8,9,1,10,11,2,3,4,5,12,6,7]=>[7,5]=>297
[8,9,1,10,11,2,3,4,12,5,6,7]=>[7,5]=>297
[8,9,1,10,11,2,3,12,4,5,6,7]=>[7,5]=>297
[8,9,1,10,11,2,12,3,4,5,6,7]=>[7,5]=>297
[8,9,1,10,11,12,2,3,4,5,6,7]=>[7,5]=>297
[8,9,10,1,2,3,4,11,5,12,6,7]=>[7,5]=>297
[8,9,10,1,2,3,4,11,12,5,6,7]=>[7,5]=>297
[8,9,10,1,2,3,11,4,5,12,6,7]=>[7,5]=>297
[8,9,10,1,2,3,11,4,12,5,6,7]=>[7,5]=>297
[8,9,10,1,2,3,11,12,4,5,6,7]=>[7,5]=>297
[8,9,10,1,2,11,3,4,5,12,6,7]=>[7,5]=>297
[8,9,10,1,2,11,3,4,12,5,6,7]=>[7,5]=>297
[8,9,10,1,2,11,3,12,4,5,6,7]=>[7,5]=>297
[8,9,10,1,2,11,12,3,4,5,6,7]=>[7,5]=>297
[8,9,10,1,11,2,3,4,5,12,6,7]=>[7,5]=>297
[8,9,10,1,11,2,3,4,12,5,6,7]=>[7,5]=>297
[8,9,10,1,11,2,3,12,4,5,6,7]=>[7,5]=>297
[8,9,10,1,11,2,12,3,4,5,6,7]=>[7,5]=>297
[8,9,10,1,11,12,2,3,4,5,6,7]=>[7,5]=>297
[8,9,10,11,1,2,3,4,5,12,6,7]=>[7,5]=>297
[8,9,10,11,1,2,3,4,12,5,6,7]=>[7,5]=>297
[8,9,10,11,1,2,3,12,4,5,6,7]=>[7,5]=>297
[8,9,10,11,1,2,12,3,4,5,6,7]=>[7,5]=>297
[8,9,10,11,1,12,2,3,4,5,6,7]=>[7,5]=>297
[8,9,10,11,12,1,2,3,4,5,6,7]=>[7,5]=>297
[8,6,3,5,2,1,7,4]=>[3,2,1,1,1]=>64
[6,8,3,1,2,5,4,7]=>[4,2,2]=>56
[5,8,6,4,7,1,2,3]=>[3,3,1,1]=>56
[2,5,1,8,7,3,4,6]=>[4,3,1]=>70
[7,2,4,3,8,6,1,5]=>[3,2,2,1]=>70
[1,7,6,5,4,3,2,9,8]=>[3,2,1,1,1,1]=>105
[6,8,4,3,5,1,7,2]=>[3,2,2,1]=>70
[1,4,7,3,6,8,2,5]=>[4,2,2]=>56
[3,7,1,4,6,8,2,5]=>[4,3,1]=>70
[2,4,7,3,6,8,1,5]=>[4,2,2]=>56
[8,5,7,6,1,3,2,4]=>[3,2,1,1,1]=>64
[2,7,5,6,1,8,4,3]=>[4,2,1,1]=>90
[1,2,6,7,4,5,8,3]=>[5,2,1]=>64
[6,5,2,8,7,1,4,3]=>[2,2,2,2]=>14
[7,2,3,6,8,1,4,5]=>[4,3,1]=>70
[2,6,1,3,8,5,4,7]=>[4,3,1]=>70
[6,4,1,8,3,2,5,7]=>[4,2,1,1]=>90
[5,8,1,4,2,7,3,6]=>[4,2,2]=>56
[6,4,8,2,1,7,3,5]=>[3,2,2,1]=>70
[2,3,1,8,7,5,6,4]=>[4,2,1,1]=>90
[1,5,6,7,2,4,3,8]=>[5,2,1]=>64
[2,8,6,4,1,5,3,7]=>[4,2,1,1]=>90
[6,7,4,5,1,3,8,2]=>[3,2,2,1]=>70
[1,6,5,3,8,2,4,7]=>[4,2,1,1]=>90
[8,5,1,2,7,4,3,6]=>[4,2,1,1]=>90
[4,1,8,7,2,5,3,6]=>[4,2,1,1]=>90
[3,2,4,6,1,8,7,5]=>[4,2,2]=>56
[3,6,7,4,1,2,5,8]=>[4,3,1]=>70
[1,4,7,5,8,2,3,6]=>[4,3,1]=>70
[1,6,8,4,7,3,2,5]=>[3,2,2,1]=>70
[3,6,7,5,4,8,1,2]=>[4,2,1,1]=>90
[4,5,7,2,6,3,8,1]=>[4,2,1,1]=>90
[2,1,5,7,4,6,8,3]=>[4,3,1]=>70
[2,3,5,7,8,1,6,4]=>[5,2,1]=>64
[1,5,7,4,2,3,6,8]=>[5,2,1]=>64
[2,4,7,5,3,6,8,1]=>[5,1,1,1]=>35
[8,1,7,2,4,6,3,5]=>[4,2,1,1]=>90
[1,2,4,7,8,6,3,5]=>[5,2,1]=>64
[1,3,6,2,5,8,4,7]=>[4,3,1]=>70
[1,5,3,6,8,2,4,7]=>[4,3,1]=>70
[4,8,1,2,6,3,7,5]=>[4,3,1]=>70
[5,8,1,2,6,3,7,4]=>[4,3,1]=>70
[1,6,2,3,7,5,8,4]=>[5,2,1]=>64
[4,1,2,6,5,7,8,3]=>[5,2,1]=>64
[1,8,4,2,7,3,6,5]=>[4,2,1,1]=>90
[1,7,5,2,3,8,6,4]=>[4,2,2]=>56
[8,1,4,7,3,5,2,6]=>[4,2,1,1]=>90
[8,4,3,6,1,7,2,5]=>[3,3,1,1]=>56
[2,6,1,8,3,7,4,5]=>[4,3,1]=>70
[8,4,2,1,3,7,5,6]=>[4,2,1,1]=>90
[2,5,1,7,6,8,3,4]=>[4,3,1]=>70
[5,3,1,8,2,4,7,6]=>[4,2,2]=>56
[1,2,6,3,7,5,8,4]=>[5,2,1]=>64
[5,1,8,3,2,4,7,6]=>[4,2,2]=>56
[3,1,5,4,6,7,8,2]=>[5,2,1]=>64
[2,8,5,7,3,1,4,6]=>[4,2,1,1]=>90
[2,6,8,7,3,1,4,5]=>[4,2,1,1]=>90
[7,4,2,1,3,8,5,6]=>[4,2,1,1]=>90
[7,2,1,3,8,5,4,6]=>[4,2,2]=>56
[2,1,7,3,8,6,4,5]=>[4,3,1]=>70
[1,7,5,3,2,4,8,6]=>[4,2,1,1]=>90
[1,4,2,7,6,5,8,3]=>[4,2,1,1]=>90
[3,4,1,6,5,7,8,2]=>[5,2,1]=>64
[2,8,7,3,4,1,5,6]=>[5,1,1,1]=>35
[5,7,6,2,3,8,1,4]=>[3,3,1,1]=>56
[4,5,7,6,2,8,1,3]=>[4,2,1,1]=>90
[3,1,8,7,5,2,6,4]=>[3,3,1,1]=>56
[4,5,6,8,7,2,1,3]=>[4,2,1,1]=>90
[2,8,3,1,5,4,7,6]=>[4,3,1]=>70
[3,8,4,1,5,2,7,6]=>[4,3,1]=>70
[4,8,3,1,6,2,7,5]=>[3,3,2]=>42
[2,8,3,1,6,4,7,5]=>[4,3,1]=>70
[6,2,7,1,5,8,4,3]=>[3,2,2,1]=>70
[1,4,5,6,7,8,9,3,2]=>[7,1,1]=>28
[4,8,5,1,3,2,6,7]=>[4,2,1,1]=>90
[5,4,3,1,2,7,6,8]=>[4,2,1,1]=>90
[4,1,6,5,2,3,7,8]=>[5,2,1]=>64
[7,1,5,2,3,6,4,8]=>[5,2,1]=>64
[4,1,6,3,7,2,5,8]=>[4,3,1]=>70
[4,6,1,2,8,3,7,5]=>[4,3,1]=>70
[4,1,3,6,7,2,5,8]=>[5,2,1]=>64
[2,6,5,1,3,4,7,8]=>[5,2,1]=>64
[2,6,7,4,3,1,5,8]=>[4,2,1,1]=>90
[2,6,3,1,7,4,5,8]=>[5,2,1]=>64
[6,5,3,7,2,4,1,8]=>[3,2,1,1,1]=>64
[2,3,6,7,1,5,4,8]=>[5,2,1]=>64
[2,7,5,8,1,3,6,4]=>[3,3,2]=>42
[5,1,6,7,3,2,4,8]=>[4,3,1]=>70
[5,6,1,4,7,2,3,8]=>[4,3,1]=>70
[1,2,5,7,8,6,3,4]=>[5,2,1]=>64
[1,2,7,8,4,6,3,5]=>[4,2,2]=>56
[8,6,5,2,1,7,4,3]=>[2,2,2,1,1]=>28
[4,3,8,6,7,1,5,2]=>[3,2,2,1]=>70
[7,3,2,8,6,1,5,4]=>[2,2,2,2]=>14
[7,5,8,2,6,1,4,3]=>[2,2,2,2]=>14
[7,4,1,2,6,5,8,3]=>[4,2,1,1]=>90
[5,2,7,4,6,1,8,3]=>[4,2,2]=>56
[5,4,8,6,3,2,1,7]=>[3,2,1,1,1]=>64
[8,4,6,7,3,1,5,2]=>[3,2,2,1]=>70
[6,3,5,7,1,2,8,4]=>[4,3,1]=>70
[1,8,5,3,2,4,6,7]=>[5,1,1,1]=>35
[1,6,7,3,4,2,5,8]=>[5,2,1]=>64
[1,6,8,3,4,2,5,7]=>[5,2,1]=>64
[1,8,7,5,3,4,2,6]=>[4,1,1,1,1]=>35
[1,7,8,5,3,4,2,6]=>[4,2,1,1]=>90
[1,7,6,8,4,2,3,5]=>[4,2,1,1]=>90
[1,7,8,6,4,3,2,5]=>[3,2,1,1,1]=>64
[7,2,8,9,10,1,3,4,5,6]=>[5,4,1]=>288
[9,7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[5,1,7,8,4,2,3,6]=>[4,3,1]=>70
[3,8,2,1,6,7,5,4]=>[3,2,2,1]=>70
[2,8,3,1,7,5,6,4]=>[4,2,1,1]=>90
[9,10,6,4,2,1,3,5,8,7]=>[4,2,2,1,1]=>567
[10,7,8,4,2,1,3,6,5,9]=>[4,2,2,1,1]=>567
[9,7,10,4,2,1,3,6,8,5]=>[4,2,2,1,1]=>567
[8,9,10,4,2,1,3,7,6,5]=>[3,3,2,2]=>252
[10,8,5,6,2,1,4,3,7,9]=>[4,2,2,1,1]=>567
[9,10,5,6,2,1,4,3,8,7]=>[3,3,2,2]=>252
[10,7,5,8,2,1,4,6,3,9]=>[4,2,2,1,1]=>567
[9,7,5,10,2,1,4,6,8,3]=>[4,2,2,1,1]=>567
[8,9,5,10,2,1,4,7,6,3]=>[3,3,2,2]=>252
[10,6,7,8,2,1,5,4,3,9]=>[4,2,2,1,1]=>567
[9,6,7,10,2,1,5,4,8,3]=>[3,3,2,1,1]=>450
[8,6,9,10,2,1,5,7,4,3]=>[3,3,2,1,1]=>450
[7,8,9,10,2,1,6,5,4,3]=>[4,2,2,1,1]=>567
[10,8,6,3,4,2,1,5,7,9]=>[5,1,1,1,1,1]=>126
[9,10,6,3,4,2,1,5,8,7]=>[4,2,2,1,1]=>567
[10,7,8,3,4,2,1,6,5,9]=>[4,2,2,1,1]=>567
[9,7,10,3,4,2,1,6,8,5]=>[4,2,2,1,1]=>567
[8,9,10,3,4,2,1,7,6,5]=>[3,3,2,2]=>252
[10,8,5,3,6,2,4,1,7,9]=>[4,2,1,1,1,1]=>350
[9,10,5,3,6,2,4,1,8,7]=>[3,3,2,1,1]=>450
[10,7,5,3,8,2,4,6,1,9]=>[4,2,1,1,1,1]=>350
[9,7,5,3,10,2,4,6,8,1]=>[4,2,1,1,1,1]=>350
[8,9,5,3,10,2,4,7,6,1]=>[3,3,2,1,1]=>450
[10,6,7,3,8,2,5,4,1,9]=>[4,2,2,1,1]=>567
[9,6,7,3,10,2,5,4,8,1]=>[3,3,2,1,1]=>450
[8,6,9,3,10,2,5,7,4,1]=>[3,3,2,1,1]=>450
[7,8,9,3,10,2,6,5,4,1]=>[4,2,2,1,1]=>567
[10,8,4,5,6,3,2,1,7,9]=>[5,1,1,1,1,1]=>126
[9,10,4,5,6,3,2,1,8,7]=>[4,2,2,1,1]=>567
[10,7,4,5,8,3,2,6,1,9]=>[4,2,1,1,1,1]=>350
[9,7,4,5,10,3,2,6,8,1]=>[4,2,1,1,1,1]=>350
[8,9,4,5,10,3,2,7,6,1]=>[3,3,2,1,1]=>450
[10,6,4,7,8,3,5,2,1,9]=>[4,2,1,1,1,1]=>350
[9,6,4,7,10,3,5,2,8,1]=>[3,3,1,1,1,1]=>225
[8,6,4,9,10,3,5,7,2,1]=>[3,3,1,1,1,1]=>225
[7,8,4,9,10,3,6,5,2,1]=>[4,2,2,1,1]=>567
[10,5,6,7,8,4,3,2,1,9]=>[5,1,1,1,1,1]=>126
[9,5,6,7,10,4,3,2,8,1]=>[4,2,1,1,1,1]=>350
[8,5,6,9,10,4,3,7,2,1]=>[4,2,1,1,1,1]=>350
[7,5,8,9,10,4,6,3,2,1]=>[4,2,1,1,1,1]=>350
[12,10,8,6,4,2,1,3,5,7,9,11]=>[6,1,1,1,1,1,1]=>462
[11,12,8,6,4,2,1,3,5,7,10,9]=>[5,2,2,1,1,1]=>3696
[12,9,10,6,4,2,1,3,5,8,7,11]=>[5,2,2,1,1,1]=>3696
[11,9,12,6,4,2,1,3,5,8,10,7]=>[5,2,2,1,1,1]=>3696
[10,11,12,6,4,2,1,3,5,9,8,7]=>[4,3,2,2,1]=>5775
[12,10,7,8,4,2,1,3,6,5,9,11]=>[5,2,2,1,1,1]=>3696
[11,12,7,8,4,2,1,3,6,5,10,9]=>[4,3,2,2,1]=>5775
[12,9,7,10,4,2,1,3,6,8,5,11]=>[5,2,2,1,1,1]=>3696
[11,9,7,12,4,2,1,3,6,8,10,5]=>[5,2,2,1,1,1]=>3696
[10,11,7,12,4,2,1,3,6,9,8,5]=>[4,3,2,2,1]=>5775
[12,8,9,10,4,2,1,3,7,6,5,11]=>[4,3,2,2,1]=>5775
[11,8,9,12,4,2,1,3,7,6,10,5]=>[4,3,2,2,1]=>5775
[10,8,11,12,4,2,1,3,7,9,6,5]=>[4,3,2,2,1]=>5775
[9,10,11,12,4,2,1,3,8,7,6,5]=>[4,3,2,2,1]=>5775
[12,10,8,5,6,2,1,4,3,7,9,11]=>[5,2,2,1,1,1]=>3696
[11,12,8,5,6,2,1,4,3,7,10,9]=>[4,3,2,2,1]=>5775
[12,9,10,5,6,2,1,4,3,8,7,11]=>[4,3,2,2,1]=>5775
[11,9,12,5,6,2,1,4,3,8,10,7]=>[4,3,2,2,1]=>5775
[10,11,12,5,6,2,1,4,3,9,8,7]=>[3,3,3,3]=>462
[12,10,7,5,8,2,1,4,6,3,9,11]=>[5,2,2,1,1,1]=>3696
[11,12,7,5,8,2,1,4,6,3,10,9]=>[4,3,2,2,1]=>5775
[12,9,7,5,10,2,1,4,6,8,3,11]=>[5,2,2,1,1,1]=>3696
[11,9,7,5,12,2,1,4,6,8,10,3]=>[5,2,2,1,1,1]=>3696
[10,11,7,5,12,2,1,4,6,9,8,3]=>[4,3,2,2,1]=>5775
[12,8,9,5,10,2,1,4,7,6,3,11]=>[4,3,2,2,1]=>5775
[11,8,9,5,12,2,1,4,7,6,10,3]=>[4,3,2,2,1]=>5775
[10,8,11,5,12,2,1,4,7,9,6,3]=>[4,3,2,2,1]=>5775
[9,10,11,5,12,2,1,4,8,7,6,3]=>[4,3,2,2,1]=>5775
[12,10,6,7,8,2,1,5,4,3,9,11]=>[5,2,2,1,1,1]=>3696
[11,12,6,7,8,2,1,5,4,3,10,9]=>[4,3,2,2,1]=>5775
[12,9,6,7,10,2,1,5,4,8,3,11]=>[4,3,2,1,1,1]=>5632
[11,9,6,7,12,2,1,5,4,8,10,3]=>[4,3,2,1,1,1]=>5632
[10,11,6,7,12,2,1,5,4,9,8,3]=>[3,3,3,2,1]=>2112
[12,8,6,9,10,2,1,5,7,4,3,11]=>[4,3,2,1,1,1]=>5632
[11,8,6,9,12,2,1,5,7,4,10,3]=>[4,3,2,1,1,1]=>5632
[10,8,6,11,12,2,1,5,7,9,4,3]=>[4,3,2,1,1,1]=>5632
[9,10,6,11,12,2,1,5,8,7,4,3]=>[4,3,2,2,1]=>5775
[12,7,8,9,10,2,1,6,5,4,3,11]=>[5,2,2,1,1,1]=>3696
[11,7,8,9,12,2,1,6,5,4,10,3]=>[4,3,2,1,1,1]=>5632
[10,7,8,11,12,2,1,6,5,9,4,3]=>[4,3,2,1,1,1]=>5632
[9,7,10,11,12,2,1,6,8,5,4,3]=>[4,3,2,1,1,1]=>5632
[8,9,10,11,12,2,1,7,6,5,4,3]=>[5,2,2,1,1,1]=>3696
[12,10,8,6,3,4,2,1,5,7,9,11]=>[6,1,1,1,1,1,1]=>462
[11,12,8,6,3,4,2,1,5,7,10,9]=>[5,2,2,1,1,1]=>3696
[12,9,10,6,3,4,2,1,5,8,7,11]=>[5,2,2,1,1,1]=>3696
[11,9,12,6,3,4,2,1,5,8,10,7]=>[5,2,2,1,1,1]=>3696
[10,11,12,6,3,4,2,1,5,9,8,7]=>[4,3,2,2,1]=>5775
[12,10,7,8,3,4,2,1,6,5,9,11]=>[5,2,2,1,1,1]=>3696
[11,12,7,8,3,4,2,1,6,5,10,9]=>[4,3,2,2,1]=>5775
[12,9,7,10,3,4,2,1,6,8,5,11]=>[5,2,2,1,1,1]=>3696
[11,9,7,12,3,4,2,1,6,8,10,5]=>[5,2,2,1,1,1]=>3696
[10,11,7,12,3,4,2,1,6,9,8,5]=>[4,3,2,2,1]=>5775
[12,8,9,10,3,4,2,1,7,6,5,11]=>[4,3,2,2,1]=>5775
[11,8,9,12,3,4,2,1,7,6,10,5]=>[4,3,2,2,1]=>5775
[10,8,11,12,3,4,2,1,7,9,6,5]=>[4,3,2,2,1]=>5775
[9,10,11,12,3,4,2,1,8,7,6,5]=>[4,3,2,2,1]=>5775
[12,10,8,5,3,6,2,4,1,7,9,11]=>[5,2,1,1,1,1,1]=>1728
[11,12,8,5,3,6,2,4,1,7,10,9]=>[4,3,2,1,1,1]=>5632
[12,9,10,5,3,6,2,4,1,8,7,11]=>[4,3,2,1,1,1]=>5632
[11,9,12,5,3,6,2,4,1,8,10,7]=>[4,3,2,1,1,1]=>5632
[10,11,12,5,3,6,2,4,1,9,8,7]=>[3,3,3,2,1]=>2112
[12,10,7,5,3,8,2,4,6,1,9,11]=>[5,2,1,1,1,1,1]=>1728
[11,12,7,5,3,8,2,4,6,1,10,9]=>[4,3,2,1,1,1]=>5632
[12,9,7,5,3,10,2,4,6,8,1,11]=>[5,2,1,1,1,1,1]=>1728
[11,9,7,5,3,12,2,4,6,8,10,1]=>[5,2,1,1,1,1,1]=>1728
[10,11,7,5,3,12,2,4,6,9,8,1]=>[4,3,2,1,1,1]=>5632
[12,8,9,5,3,10,2,4,7,6,1,11]=>[4,3,2,1,1,1]=>5632
[11,8,9,5,3,12,2,4,7,6,10,1]=>[4,3,2,1,1,1]=>5632
[10,8,11,5,3,12,2,4,7,9,6,1]=>[4,3,2,1,1,1]=>5632
[9,10,11,5,3,12,2,4,8,7,6,1]=>[4,3,2,2,1]=>5775
[12,10,6,7,3,8,2,5,4,1,9,11]=>[5,2,2,1,1,1]=>3696
[11,12,6,7,3,8,2,5,4,1,10,9]=>[4,3,2,2,1]=>5775
[12,9,6,7,3,10,2,5,4,8,1,11]=>[4,3,2,1,1,1]=>5632
[11,9,6,7,3,12,2,5,4,8,10,1]=>[4,3,2,1,1,1]=>5632
[10,11,6,7,3,12,2,5,4,9,8,1]=>[3,3,3,2,1]=>2112
[12,8,6,9,3,10,2,5,7,4,1,11]=>[4,3,2,1,1,1]=>5632
[11,8,6,9,3,12,2,5,7,4,10,1]=>[4,3,2,1,1,1]=>5632
[10,8,6,11,3,12,2,5,7,9,4,1]=>[4,3,2,1,1,1]=>5632
[9,10,6,11,3,12,2,5,8,7,4,1]=>[4,3,2,2,1]=>5775
[12,7,8,9,3,10,2,6,5,4,1,11]=>[5,2,2,1,1,1]=>3696
[11,7,8,9,3,12,2,6,5,4,10,1]=>[4,3,2,1,1,1]=>5632
[10,7,8,11,3,12,2,6,5,9,4,1]=>[4,3,2,1,1,1]=>5632
[9,7,10,11,3,12,2,6,8,5,4,1]=>[4,3,2,1,1,1]=>5632
[8,9,10,11,3,12,2,7,6,5,4,1]=>[5,2,2,1,1,1]=>3696
[12,10,8,4,5,6,3,2,1,7,9,11]=>[6,1,1,1,1,1,1]=>462
[11,12,8,4,5,6,3,2,1,7,10,9]=>[5,2,2,1,1,1]=>3696
[12,9,10,4,5,6,3,2,1,8,7,11]=>[5,2,2,1,1,1]=>3696
[11,9,12,4,5,6,3,2,1,8,10,7]=>[5,2,2,1,1,1]=>3696
[10,11,12,4,5,6,3,2,1,9,8,7]=>[4,3,2,2,1]=>5775
[12,10,7,4,5,8,3,2,6,1,9,11]=>[5,2,1,1,1,1,1]=>1728
[11,12,7,4,5,8,3,2,6,1,10,9]=>[4,3,2,1,1,1]=>5632
[12,9,7,4,5,10,3,2,6,8,1,11]=>[5,2,1,1,1,1,1]=>1728
[11,9,7,4,5,12,3,2,6,8,10,1]=>[5,2,1,1,1,1,1]=>1728
[10,11,7,4,5,12,3,2,6,9,8,1]=>[4,3,2,1,1,1]=>5632
[12,8,9,4,5,10,3,2,7,6,1,11]=>[4,3,2,1,1,1]=>5632
[11,8,9,4,5,12,3,2,7,6,10,1]=>[4,3,2,1,1,1]=>5632
[10,8,11,4,5,12,3,2,7,9,6,1]=>[4,3,2,1,1,1]=>5632
[9,10,11,4,5,12,3,2,8,7,6,1]=>[4,3,2,2,1]=>5775
[12,10,6,4,7,8,3,5,2,1,9,11]=>[5,2,1,1,1,1,1]=>1728
[11,12,6,4,7,8,3,5,2,1,10,9]=>[4,3,2,1,1,1]=>5632
[12,9,6,4,7,10,3,5,2,8,1,11]=>[4,3,1,1,1,1,1]=>2079
[11,9,6,4,7,12,3,5,2,8,10,1]=>[4,3,1,1,1,1,1]=>2079
[10,11,6,4,7,12,3,5,2,9,8,1]=>[3,3,3,1,1,1]=>1650
[12,8,6,4,9,10,3,5,7,2,1,11]=>[4,3,1,1,1,1,1]=>2079
[11,8,6,4,9,12,3,5,7,2,10,1]=>[4,3,1,1,1,1,1]=>2079
[10,8,6,4,11,12,3,5,7,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[9,10,6,4,11,12,3,5,8,7,2,1]=>[4,3,2,1,1,1]=>5632
[12,7,8,4,9,10,3,6,5,2,1,11]=>[5,2,2,1,1,1]=>3696
[11,7,8,4,9,12,3,6,5,2,10,1]=>[4,3,2,1,1,1]=>5632
[10,7,8,4,11,12,3,6,5,9,2,1]=>[4,3,2,1,1,1]=>5632
[9,7,10,4,11,12,3,6,8,5,2,1]=>[4,3,2,1,1,1]=>5632
[8,9,10,4,11,12,3,7,6,5,2,1]=>[5,2,2,1,1,1]=>3696
[12,10,5,6,7,8,4,3,2,1,9,11]=>[6,1,1,1,1,1,1]=>462
[11,12,5,6,7,8,4,3,2,1,10,9]=>[5,2,2,1,1,1]=>3696
[12,9,5,6,7,10,4,3,2,8,1,11]=>[5,2,1,1,1,1,1]=>1728
[11,9,5,6,7,12,4,3,2,8,10,1]=>[5,2,1,1,1,1,1]=>1728
[10,11,5,6,7,12,4,3,2,9,8,1]=>[4,3,2,1,1,1]=>5632
[12,8,5,6,9,10,4,3,7,2,1,11]=>[5,2,1,1,1,1,1]=>1728
[11,8,5,6,9,12,4,3,7,2,10,1]=>[4,3,1,1,1,1,1]=>2079
[10,8,5,6,11,12,4,3,7,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[9,10,5,6,11,12,4,3,8,7,2,1]=>[4,3,2,1,1,1]=>5632
[12,7,5,8,9,10,4,6,3,2,1,11]=>[5,2,1,1,1,1,1]=>1728
[11,7,5,8,9,12,4,6,3,2,10,1]=>[4,3,1,1,1,1,1]=>2079
[10,7,5,8,11,12,4,6,3,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[9,7,5,10,11,12,4,6,8,3,2,1]=>[4,3,1,1,1,1,1]=>2079
[8,9,5,10,11,12,4,7,6,3,2,1]=>[5,2,2,1,1,1]=>3696
[12,6,7,8,9,10,5,4,3,2,1,11]=>[6,1,1,1,1,1,1]=>462
[11,6,7,8,9,12,5,4,3,2,10,1]=>[5,2,1,1,1,1,1]=>1728
[10,6,7,8,11,12,5,4,3,9,2,1]=>[5,2,1,1,1,1,1]=>1728
[9,6,7,10,11,12,5,4,8,3,2,1]=>[5,2,1,1,1,1,1]=>1728
[8,6,9,10,11,12,5,7,4,3,2,1]=>[5,2,1,1,1,1,1]=>1728
[2,3,4,5,6,7,8,11,10,1,9]=>[8,2,1]=>231
[2,3,4,5,6,7,8,9,12,11,1,10]=>[9,2,1]=>320
[11,3,4,5,6,7,8,10,1,2,9]=>[7,3,1]=>550
[2,10,4,5,6,7,9,1,3,8]=>[6,3,1]=>315
[10,3,4,5,6,7,1,9,2,8]=>[6,3,1]=>315
[2,7,4,1,5,8,3,6]=>[4,3,1]=>70
[2,1,6,4,7,8,3,5]=>[4,3,1]=>70
[5,7,8,3,4,2,1,6]=>[3,3,1,1]=>56
[4,7,5,3,8,2,6,1]=>[3,2,1,1,1]=>64
[7,8,4,5,6,1,3,2]=>[3,2,2,1]=>70
[2,5,1,8,4,6,7,3]=>[4,3,1]=>70
[6,5,8,3,4,2,1,7]=>[3,2,1,1,1]=>64
[8,2,7,6,3,4,5,1]=>[4,1,1,1,1]=>35
[6,8,7,3,2,1,4,5]=>[3,2,1,1,1]=>64
[3,4,8,2,7,1,5,6]=>[4,2,2]=>56
[7,2,6,1,4,8,3,5]=>[3,3,1,1]=>56
[7,8,1,2,4,6,3,5]=>[4,2,2]=>56
[7,2,8,3,4,5,1,6]=>[5,2,1]=>64
[6,1,8,3,4,2,5,7]=>[5,2,1]=>64
[7,5,1,2,4,3,8,6]=>[4,2,1,1]=>90
[7,6,8,1,4,2,3,5]=>[4,2,1,1]=>90
[2,4,3,7,8,5,6,1]=>[4,3,1]=>70
[2,1,7,6,3,4,5,8]=>[5,2,1]=>64
[6,1,5,3,8,2,4,7]=>[4,2,1,1]=>90
[2,3,6,8,5,1,7,4]=>[4,2,2]=>56
[3,2,4,8,6,1,7,5]=>[4,2,2]=>56
[2,1,3,8,4,5,7,6]=>[5,2,1]=>64
[3,1,2,8,5,4,7,6]=>[4,3,1]=>70
[2,1,3,7,8,4,6,5]=>[4,3,1]=>70
[2,1,3,8,4,7,6,5]=>[4,2,1,1]=>90
[3,1,2,8,4,5,7,6]=>[5,2,1]=>64
[1,2,8,7,5,4,6,3]=>[4,1,1,1,1]=>35
[4,6,7,2,3,8,1,5]=>[4,3,1]=>70
[3,2,6,5,7,8,1,4]=>[4,2,2]=>56
[6,1,5,8,4,7,3,2]=>[3,2,1,1,1]=>64
[1,4,6,8,5,7,2,3]=>[4,2,2]=>56
[2,4,7,1,8,3,6,5]=>[4,3,1]=>70
[6,1,5,4,2,3,8,7]=>[4,2,1,1]=>90
[6,4,5,1,2,8,3,7]=>[4,3,1]=>70
[8,4,1,5,7,6,3,2]=>[3,2,1,1,1]=>64
[8,1,6,3,5,2,4,7]=>[4,2,1,1]=>90
[4,6,2,5,3,8,1,7]=>[3,3,1,1]=>56
[4,6,5,2,1,8,3,7]=>[3,3,1,1]=>56
[5,8,4,3,6,7,2,1]=>[3,2,1,1,1]=>64
[6,8,2,1,5,3,4,7]=>[4,2,2]=>56
[2,5,3,8,6,7,4,1]=>[4,2,1,1]=>90
[3,2,6,5,1,8,4,7]=>[3,3,2]=>42
[7,4,5,8,1,6,2,3]=>[3,3,2]=>42
[4,5,8,1,6,7,3,2]=>[4,2,1,1]=>90
[5,1,8,4,6,7,3,2]=>[4,2,1,1]=>90
[6,5,3,8,1,7,2,4]=>[3,2,2,1]=>70
[8,3,7,1,6,2,4,5]=>[4,2,1,1]=>90
[8,1,4,6,5,7,2,3]=>[4,2,1,1]=>90
[8,1,7,5,6,4,2,3]=>[3,2,1,1,1]=>64
[8,6,1,5,3,7,2,4]=>[3,2,1,1,1]=>64
[7,2,3,6,8,1,5,4]=>[4,2,1,1]=>90
[2,6,3,7,8,1,4,5]=>[4,3,1]=>70
[6,3,8,7,2,1,5,4]=>[2,2,2,2]=>14
[7,2,5,6,3,4,8,1]=>[4,2,1,1]=>90
[7,2,8,6,3,1,5,4]=>[3,2,2,1]=>70
[7,2,4,5,8,6,3,1]=>[4,2,1,1]=>90
[6,3,8,4,7,2,5,1]=>[3,2,2,1]=>70
[7,2,3,6,8,5,4,1]=>[4,1,1,1,1]=>35
[7,2,8,5,4,1,3,6]=>[3,2,2,1]=>70
[7,4,5,2,8,1,6,3]=>[3,2,2,1]=>70
[7,5,4,2,8,1,6,3]=>[2,2,2,1,1]=>28
[7,6,3,2,8,4,5,1]=>[3,2,1,1,1]=>64
[7,2,3,6,8,4,5,1]=>[4,2,1,1]=>90
[7,2,5,4,8,3,6,1]=>[3,2,1,1,1]=>64
[7,2,8,3,6,1,4,5]=>[4,2,2]=>56
[7,4,5,2,8,3,6,1]=>[3,3,1,1]=>56
[5,1,3,2,4,6,8,7]=>[5,2,1]=>64
[6,4,5,3,8,1,2,7]=>[3,3,1,1]=>56
[7,2,4,6,3,8,5,1]=>[4,2,1,1]=>90
[2,8,3,7,6,1,5,4]=>[3,2,1,1,1]=>64
[5,4,2,6,8,7,3,1]=>[3,2,2,1]=>70
[3,7,2,5,8,6,4,1]=>[3,3,1,1]=>56
[2,4,8,7,6,1,5,3]=>[3,2,1,1,1]=>64
[3,2,8,7,4,6,5,1]=>[3,2,1,1,1]=>64
[8,2,6,5,1,4,3,7]=>[3,2,1,1,1]=>64
[4,8,5,2,7,6,3,1]=>[3,2,1,1,1]=>64
[2,8,6,5,7,1,3,4]=>[3,3,1,1]=>56
[3,8,4,7,2,1,6,5]=>[3,2,2,1]=>70
[4,8,5,1,7,6,3,2]=>[3,2,1,1,1]=>64
[5,8,1,7,6,2,3,4]=>[4,2,1,1]=>90
[3,4,6,2,5,7,1,8]=>[5,2,1]=>64
[1,7,5,2,6,8,3,4]=>[4,3,1]=>70
[7,4,8,3,6,5,1,2]=>[2,2,2,2]=>14
[1,5,4,3,8,7,2,6]=>[3,2,2,1]=>70
[1,5,8,2,6,4,3,7]=>[4,2,1,1]=>90
[10,9,8,6,4,2,1,3,5,7]=>[4,1,1,1,1,1,1]=>84
[10,8,7,6,4,2,1,3,5,9]=>[4,1,1,1,1,1,1]=>84
[10,7,9,6,4,2,1,3,8,5]=>[3,2,2,1,1,1]=>315
[10,9,8,7,6,4,2,1,3,5]=>[3,1,1,1,1,1,1,1]=>36
[10,8,6,5,4,2,1,3,7,9]=>[4,1,1,1,1,1,1]=>84
[10,9,8,6,5,4,2,1,3,7]=>[3,1,1,1,1,1,1,1]=>36
[10,8,5,7,4,2,1,6,3,9]=>[3,2,2,1,1,1]=>315
[10,5,9,7,4,2,1,6,8,3]=>[3,2,2,1,1,1]=>315
[10,9,8,5,7,4,2,1,6,3]=>[2,2,2,1,1,1,1]=>75
[10,8,7,6,5,4,2,1,3,9]=>[3,1,1,1,1,1,1,1]=>36
[10,7,9,6,5,4,2,1,8,3]=>[2,2,2,1,1,1,1]=>75
[10,6,9,8,5,7,2,1,4,3]=>[2,2,2,2,1,1]=>90
[10,8,6,4,3,2,1,5,7,9]=>[4,1,1,1,1,1,1]=>84
[10,9,8,6,4,3,2,1,5,7]=>[3,1,1,1,1,1,1,1]=>36
[10,8,7,6,4,3,2,1,5,9]=>[3,1,1,1,1,1,1,1]=>36
[10,7,9,6,4,3,2,1,8,5]=>[2,2,2,1,1,1,1]=>75
[10,8,6,3,5,2,4,1,7,9]=>[4,2,1,1,1,1]=>350
[10,9,8,6,3,5,2,4,1,7]=>[3,2,1,1,1,1,1]=>160
[10,8,3,7,5,2,4,6,1,9]=>[4,2,1,1,1,1]=>350
[10,3,9,7,5,2,4,6,8,1]=>[4,2,1,1,1,1]=>350
[10,9,8,3,7,5,2,4,6,1]=>[3,2,1,1,1,1,1]=>160
[10,8,7,6,3,5,2,4,1,9]=>[3,2,1,1,1,1,1]=>160
[10,7,9,6,3,5,2,4,8,1]=>[3,2,2,1,1,1]=>315
[10,9,3,8,6,5,2,7,4,1]=>[3,2,1,1,1,1,1]=>160
[10,9,8,7,6,3,5,2,4,1]=>[2,2,1,1,1,1,1,1]=>35
[10,8,6,5,4,3,2,1,7,9]=>[3,1,1,1,1,1,1,1]=>36
[10,8,5,7,4,3,2,6,1,9]=>[3,2,1,1,1,1,1]=>160
[10,5,9,7,4,3,2,6,8,1]=>[3,2,1,1,1,1,1]=>160
[10,9,8,5,7,4,3,2,6,1]=>[2,2,1,1,1,1,1,1]=>35
[10,8,4,7,6,3,5,2,1,9]=>[3,2,1,1,1,1,1]=>160
[10,4,9,7,6,3,5,2,8,1]=>[3,2,1,1,1,1,1]=>160
[10,4,9,6,8,3,5,7,2,1]=>[3,3,1,1,1,1]=>225
[10,9,8,4,7,6,3,5,2,1]=>[2,2,1,1,1,1,1,1]=>35
[10,7,9,6,5,4,3,2,8,1]=>[2,2,1,1,1,1,1,1]=>35
[10,6,9,8,5,4,3,7,2,1]=>[2,2,1,1,1,1,1,1]=>35
[10,5,9,8,7,4,6,3,2,1]=>[2,2,1,1,1,1,1,1]=>35
[12,11,10,8,6,4,2,1,3,5,7,9]=>[5,1,1,1,1,1,1,1]=>330
[12,10,9,8,6,4,2,1,3,5,7,11]=>[5,1,1,1,1,1,1,1]=>330
[12,9,11,8,6,4,2,1,3,5,10,7]=>[4,2,2,1,1,1,1]=>2376
[12,11,10,9,8,6,4,2,1,3,5,7]=>[4,1,1,1,1,1,1,1,1]=>165
[12,10,8,7,6,4,2,1,3,5,9,11]=>[5,1,1,1,1,1,1,1]=>330
[12,11,10,8,7,6,4,2,1,3,5,9]=>[4,1,1,1,1,1,1,1,1]=>165
[12,10,7,9,6,4,2,1,3,8,5,11]=>[4,2,2,1,1,1,1]=>2376
[12,7,11,9,6,4,2,1,3,8,10,5]=>[4,2,2,1,1,1,1]=>2376
[12,11,10,7,9,6,4,2,1,3,8,5]=>[3,2,2,1,1,1,1,1]=>891
[12,10,9,8,7,6,4,2,1,3,5,11]=>[4,1,1,1,1,1,1,1,1]=>165
[12,9,11,8,7,6,4,2,1,3,10,5]=>[3,2,2,1,1,1,1,1]=>891
[12,8,11,10,7,9,4,2,1,3,6,5]=>[3,2,2,2,1,1,1]=>1408
[12,11,10,9,8,7,6,4,2,1,3,5]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,10,8,6,5,4,2,1,3,7,9,11]=>[5,1,1,1,1,1,1,1]=>330
[12,11,10,8,6,5,4,2,1,3,7,9]=>[4,1,1,1,1,1,1,1,1]=>165
[12,10,9,8,6,5,4,2,1,3,7,11]=>[4,1,1,1,1,1,1,1,1]=>165
[12,9,11,8,6,5,4,2,1,3,10,7]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,9,8,6,5,4,2,1,3,7]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,10,8,5,7,4,2,1,6,3,9,11]=>[4,2,2,1,1,1,1]=>2376
[12,11,10,8,5,7,4,2,1,6,3,9]=>[3,2,2,1,1,1,1,1]=>891
[12,10,5,9,7,4,2,1,6,8,3,11]=>[4,2,2,1,1,1,1]=>2376
[12,5,11,9,7,4,2,1,6,8,10,3]=>[4,2,2,1,1,1,1]=>2376
[12,11,10,5,9,7,4,2,1,6,8,3]=>[3,2,2,1,1,1,1,1]=>891
[12,10,9,8,5,7,4,2,1,6,3,11]=>[3,2,2,1,1,1,1,1]=>891
[12,9,11,8,5,7,4,2,1,6,10,3]=>[3,2,2,2,1,1,1]=>1408
[12,11,5,10,8,7,4,2,1,9,6,3]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,9,8,5,7,4,2,1,6,3]=>[2,2,2,1,1,1,1,1,1]=>154
[12,10,8,7,6,5,4,2,1,3,9,11]=>[4,1,1,1,1,1,1,1,1]=>165
[12,11,10,8,7,6,5,4,2,1,3,9]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,10,7,9,6,5,4,2,1,8,3,11]=>[3,2,2,1,1,1,1,1]=>891
[12,7,11,9,6,5,4,2,1,8,10,3]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,7,9,6,5,4,2,1,8,3]=>[2,2,2,1,1,1,1,1,1]=>154
[12,10,6,9,8,5,7,2,1,4,3,11]=>[3,2,2,2,1,1,1]=>1408
[12,6,11,9,8,5,7,2,1,4,10,3]=>[3,2,2,2,1,1,1]=>1408
[12,6,11,8,10,5,7,2,1,9,4,3]=>[3,3,2,2,1,1]=>2673
[12,11,10,6,9,8,5,7,2,1,4,3]=>[2,2,2,2,1,1,1,1]=>275
[12,10,9,8,7,6,5,4,2,1,3,11]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,9,11,8,7,6,5,4,2,1,10,3]=>[2,2,2,1,1,1,1,1,1]=>154
[12,8,11,10,7,6,5,9,2,1,4,3]=>[2,2,2,2,1,1,1,1]=>275
[12,7,11,10,9,6,8,5,2,1,4,3]=>[2,2,2,2,1,1,1,1]=>275
[12,11,10,9,8,7,6,5,4,2,1,3]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[12,10,8,6,4,3,2,1,5,7,9,11]=>[5,1,1,1,1,1,1,1]=>330
[12,11,10,8,6,4,3,2,1,5,7,9]=>[4,1,1,1,1,1,1,1,1]=>165
[12,10,9,8,6,4,3,2,1,5,7,11]=>[4,1,1,1,1,1,1,1,1]=>165
[12,9,11,8,6,4,3,2,1,5,10,7]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,9,8,6,4,3,2,1,5,7]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,10,8,7,6,4,3,2,1,5,9,11]=>[4,1,1,1,1,1,1,1,1]=>165
[12,11,10,8,7,6,4,3,2,1,5,9]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,10,7,9,6,4,3,2,1,8,5,11]=>[3,2,2,1,1,1,1,1]=>891
[12,7,11,9,6,4,3,2,1,8,10,5]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,7,9,6,4,3,2,1,8,5]=>[2,2,2,1,1,1,1,1,1]=>154
[12,10,9,8,7,6,4,3,2,1,5,11]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,9,11,8,7,6,4,3,2,1,10,5]=>[2,2,2,1,1,1,1,1,1]=>154
[12,8,11,10,7,9,4,3,2,1,6,5]=>[2,2,2,2,1,1,1,1]=>275
[12,11,10,9,8,7,6,4,3,2,1,5]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[12,10,8,6,3,5,2,4,1,7,9,11]=>[5,2,1,1,1,1,1]=>1728
[12,11,10,8,6,3,5,2,4,1,7,9]=>[4,2,1,1,1,1,1,1]=>945
[12,10,9,8,6,3,5,2,4,1,7,11]=>[4,2,1,1,1,1,1,1]=>945
[12,9,11,8,6,3,5,2,4,1,10,7]=>[3,3,2,1,1,1,1]=>1925
[12,11,10,9,8,6,3,5,2,4,1,7]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,8,3,7,5,2,4,6,1,9,11]=>[5,2,1,1,1,1,1]=>1728
[12,11,10,8,3,7,5,2,4,6,1,9]=>[4,2,1,1,1,1,1,1]=>945
[12,10,3,9,7,5,2,4,6,8,1,11]=>[5,2,1,1,1,1,1]=>1728
[12,3,11,9,7,5,2,4,6,8,10,1]=>[5,2,1,1,1,1,1]=>1728
[12,11,10,3,9,7,5,2,4,6,8,1]=>[4,2,1,1,1,1,1,1]=>945
[12,10,9,8,3,7,5,2,4,6,1,11]=>[4,2,1,1,1,1,1,1]=>945
[12,9,11,8,3,7,5,2,4,6,10,1]=>[4,2,2,1,1,1,1]=>2376
[12,11,3,10,8,7,5,2,4,9,6,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,10,9,8,3,7,5,2,4,6,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,8,7,6,3,5,2,4,1,9,11]=>[4,2,1,1,1,1,1,1]=>945
[12,11,10,8,7,6,3,5,2,4,1,9]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,7,9,6,3,5,2,4,8,1,11]=>[4,2,2,1,1,1,1]=>2376
[12,7,11,9,6,3,5,2,4,8,10,1]=>[4,2,2,1,1,1,1]=>2376
[12,11,10,7,9,6,3,5,2,4,8,1]=>[3,2,2,1,1,1,1,1]=>891
[12,10,9,3,8,6,5,2,7,4,1,11]=>[4,2,1,1,1,1,1,1]=>945
[12,9,11,3,8,6,5,2,7,4,10,1]=>[4,2,2,1,1,1,1]=>2376
[12,11,3,8,10,6,5,2,7,9,4,1]=>[4,2,2,1,1,1,1]=>2376
[12,11,10,9,3,8,6,5,2,7,4,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,9,8,7,6,3,5,2,4,1,11]=>[3,2,1,1,1,1,1,1,1]=>320
[12,9,11,8,7,6,3,5,2,4,10,1]=>[3,2,2,1,1,1,1,1]=>891
[12,8,11,10,7,6,3,5,2,9,4,1]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,3,9,7,6,8,2,5,4,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,11,10,9,8,7,6,3,5,2,4,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,10,8,6,5,4,3,2,1,7,9,11]=>[4,1,1,1,1,1,1,1,1]=>165
[12,11,10,8,6,5,4,3,2,1,7,9]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,10,9,8,6,5,4,3,2,1,7,11]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,9,11,8,6,5,4,3,2,1,10,7]=>[2,2,2,1,1,1,1,1,1]=>154
[12,11,10,9,8,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[12,10,8,5,7,4,3,2,6,1,9,11]=>[4,2,1,1,1,1,1,1]=>945
[12,11,10,8,5,7,4,3,2,6,1,9]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,5,9,7,4,3,2,6,8,1,11]=>[4,2,1,1,1,1,1,1]=>945
[12,5,11,9,7,4,3,2,6,8,10,1]=>[4,2,1,1,1,1,1,1]=>945
[12,11,10,5,9,7,4,3,2,6,8,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,9,8,5,7,4,3,2,6,1,11]=>[3,2,1,1,1,1,1,1,1]=>320
[12,9,11,8,5,7,4,3,2,6,10,1]=>[3,2,2,1,1,1,1,1]=>891
[12,11,5,10,8,7,4,3,2,9,6,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,11,10,9,8,5,7,4,3,2,6,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,10,8,4,7,6,3,5,2,1,9,11]=>[4,2,1,1,1,1,1,1]=>945
[12,11,10,8,4,7,6,3,5,2,1,9]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,4,9,7,6,3,5,2,8,1,11]=>[4,2,1,1,1,1,1,1]=>945
[12,4,11,9,7,6,3,5,2,8,10,1]=>[4,2,1,1,1,1,1,1]=>945
[12,11,10,4,9,7,6,3,5,2,8,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,10,4,9,6,8,3,5,7,2,1,11]=>[4,3,1,1,1,1,1]=>2079
[12,4,11,9,6,8,3,5,7,2,10,1]=>[4,3,1,1,1,1,1]=>2079
[12,4,11,6,10,8,3,5,7,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[12,11,10,4,9,6,8,3,5,7,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,10,9,8,4,7,6,3,5,2,1,11]=>[3,2,1,1,1,1,1,1,1]=>320
[12,9,11,8,4,7,6,3,5,2,10,1]=>[3,2,2,1,1,1,1,1]=>891
[12,8,11,10,4,7,6,3,5,9,2,1]=>[3,2,2,1,1,1,1,1]=>891
[12,11,4,10,7,9,6,3,8,5,2,1]=>[3,2,2,1,1,1,1,1]=>891
[12,11,10,9,8,4,7,6,3,5,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,10,8,7,6,5,4,3,2,1,9,11]=>[3,1,1,1,1,1,1,1,1,1]=>55
[12,11,10,8,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[12,10,7,9,6,5,4,3,2,8,1,11]=>[3,2,1,1,1,1,1,1,1]=>320
[12,7,11,9,6,5,4,3,2,8,10,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,11,10,7,9,6,5,4,3,2,8,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,10,6,9,8,5,4,3,7,2,1,11]=>[3,2,1,1,1,1,1,1,1]=>320
[12,6,11,9,8,5,4,3,7,2,10,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,6,11,8,10,5,4,3,7,9,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,10,6,9,8,5,4,3,7,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,10,5,9,8,7,4,6,3,2,1,11]=>[3,2,1,1,1,1,1,1,1]=>320
[12,5,11,9,8,7,4,6,3,2,10,1]=>[3,2,1,1,1,1,1,1,1]=>320
[12,5,11,8,10,7,4,6,3,9,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,5,11,7,10,9,4,6,8,3,2,1]=>[3,3,1,1,1,1,1,1]=>616
[12,11,10,5,9,8,7,4,6,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,9,11,8,7,6,5,4,3,2,10,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,8,11,10,7,6,5,4,3,9,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,7,11,10,9,6,5,4,8,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[12,6,11,10,9,8,5,7,4,3,2,1]=>[2,2,1,1,1,1,1,1,1,1]=>54
[3,5,6,2,4,7,8,1]=>[5,2,1]=>64
[3,5,6,7,2,4,8,1]=>[5,2,1]=>64
[3,5,7,6,8,2,4,1]=>[4,2,1,1]=>90
[3,5,7,2,6,8,4,1]=>[4,2,1,1]=>90
[3,5,2,7,6,8,4,1]=>[4,2,1,1]=>90
[3,5,7,4,2,6,8,1]=>[4,2,1,1]=>90
[3,5,4,7,2,6,8,1]=>[4,2,1,1]=>90
[3,4,5,7,2,6,8,1]=>[5,2,1]=>64
[3,4,5,7,2,8,6,1]=>[5,2,1]=>64
[3,5,4,7,8,2,6,1]=>[4,2,1,1]=>90
[3,5,4,7,2,8,6,1]=>[4,2,1,1]=>90
[3,2,5,7,4,8,6,1]=>[4,3,1]=>70
[3,5,7,4,2,8,6,1]=>[4,2,1,1]=>90
[3,5,7,8,4,2,6,1]=>[4,2,1,1]=>90
[2,3,5,7,8,4,6,1]=>[5,2,1]=>64
[3,5,2,7,8,6,4,1]=>[4,2,1,1]=>90
[3,5,7,8,2,6,4,1]=>[4,2,1,1]=>90
[3,5,7,8,6,2,4,1]=>[4,2,1,1]=>90
[3,2,5,6,7,8,9,1,4]=>[6,2,1]=>105
[4,2,5,6,7,3,8,1]=>[5,2,1]=>64
[4,2,5,6,7,8,9,3,1]=>[6,2,1]=>105
[3,2,4,5,6,7,8,9,10,11,1]=>[9,1,1]=>45
[8,6,1,4,3,5,2,7]=>[4,1,1,1,1]=>35
[6,1,8,4,3,5,2,7]=>[4,2,1,1]=>90
[5,1,6,4,8,2,3,7]=>[4,3,1]=>70
[8,1,4,2,5,3,6,7]=>[5,2,1]=>64
[2,8,4,1,5,3,6,7]=>[5,2,1]=>64
[8,4,1,3,5,2,6,7]=>[5,1,1,1]=>35
[4,1,8,3,5,2,6,7]=>[5,2,1]=>64
[8,3,1,2,5,4,6,7]=>[5,2,1]=>64
[3,1,8,2,5,4,6,7]=>[5,2,1]=>64
[4,2,5,1,8,7,6,3]=>[3,2,2,1]=>70
[5,2,4,8,1,7,6,3]=>[3,2,2,1]=>70
[7,3,2,4,6,8,1,5]=>[4,2,1,1]=>90
[1,4,8,6,7,2,5,3]=>[4,2,1,1]=>90
[1,4,5,7,3,8,2,6]=>[5,2,1]=>64
[4,6,8,1,2,5,3,7]=>[4,3,1]=>70
[3,5,6,8,2,1,4,7]=>[4,3,1]=>70
[8,2,5,4,1,3,7,6]=>[3,3,1,1]=>56
[2,4,5,8,6,3,1,7]=>[5,1,1,1]=>35
[5,4,8,2,3,1,7,6]=>[3,2,2,1]=>70
[4,7,5,8,2,3,1,6]=>[3,3,1,1]=>56
[4,6,7,5,1,8,3,2]=>[4,2,1,1]=>90
[1,7,3,6,5,8,2,4]=>[4,2,1,1]=>90
[8,3,4,2,6,7,1,5]=>[4,2,1,1]=>90
[7,5,3,8,6,2,1,4]=>[2,2,2,1,1]=>28
[7,3,1,8,2,6,5,4]=>[3,2,2,1]=>70
[4,6,7,5,2,8,3,1]=>[4,2,1,1]=>90
[5,8,7,2,4,3,1,6]=>[3,2,1,1,1]=>64
[5,1,2,8,6,7,3,4]=>[4,3,1]=>70
[2,5,7,8,6,1,4,3]=>[4,2,1,1]=>90
[7,2,6,8,4,5,1,3]=>[3,2,2,1]=>70
[5,1,7,6,8,2,3,4]=>[4,3,1]=>70
[1,7,6,2,4,3,8,5]=>[4,2,1,1]=>90
[7,1,6,2,4,5,3,8]=>[5,1,1,1]=>35
[5,7,1,6,2,3,4,8]=>[5,2,1]=>64
[6,2,5,8,3,4,1,7]=>[4,2,1,1]=>90
[1,5,3,4,8,2,6,7]=>[5,2,1]=>64
[2,1,3,6,5,8,4,7]=>[4,3,1]=>70
[5,1,2,8,6,3,7,4]=>[4,3,1]=>70
[6,1,5,7,8,4,2,3]=>[4,2,1,1]=>90
[4,6,1,5,7,2,8,3]=>[4,3,1]=>70
[2,5,8,4,6,3,7,1]=>[4,2,1,1]=>90
[4,3,7,1,2,6,8,5]=>[4,2,2]=>56
[8,1,6,5,2,7,4,3]=>[3,2,1,1,1]=>64
[6,8,1,5,2,7,4,3]=>[3,2,2,1]=>70
[4,5,8,2,3,7,6,1]=>[3,3,1,1]=>56
[1,7,3,2,4,8,6,5]=>[4,2,2]=>56
[4,3,1,8,2,6,7,5]=>[4,2,2]=>56
[4,8,1,3,2,5,7,6]=>[4,2,2]=>56
[1,7,5,3,8,6,2,4]=>[3,2,2,1]=>70
[2,5,3,8,1,4,7,6]=>[4,2,2]=>56
[4,2,5,8,1,3,7,6]=>[3,3,2]=>42
[8,1,2,4,3,5,7,6]=>[5,2,1]=>64
[2,4,3,8,1,5,7,6]=>[4,2,2]=>56
[3,1,7,4,8,6,5,2]=>[3,3,1,1]=>56
[6,4,5,3,2,8,7,1]=>[3,2,1,1,1]=>64
[2,7,3,8,5,1,6,4]=>[4,2,2]=>56
[8,7,3,2,5,6,4,1]=>[3,2,1,1,1]=>64
[3,1,8,2,6,5,4,7]=>[4,2,1,1]=>90
[7,6,2,8,1,4,5,3]=>[3,2,2,1]=>70
[2,3,8,4,1,5,7,6]=>[5,2,1]=>64
[8,4,2,3,1,5,7,6]=>[4,2,1,1]=>90
[8,2,3,4,1,5,7,6]=>[5,2,1]=>64
[7,1,6,2,4,8,3,5]=>[4,2,1,1]=>90
[2,7,8,1,4,3,6,5]=>[3,3,2]=>42
[6,5,8,1,3,2,4,7]=>[4,2,1,1]=>90
[2,1,8,5,3,4,6,7]=>[5,2,1]=>64
[8,4,1,3,2,5,6,7]=>[5,1,1,1]=>35
[8,6,1,2,3,5,4,7]=>[5,1,1,1]=>35
[7,8,1,5,2,4,6,3]=>[4,2,1,1]=>90
[2,8,6,3,1,5,4,7]=>[4,2,1,1]=>90
[5,7,2,8,4,1,6,3]=>[3,3,2]=>42
[2,5,6,3,8,1,4,7]=>[4,3,1]=>70
[1,3,4,5,6,7,2,8,9]=>[8,1]=>8
[7,4,5,6,8,1,3,2]=>[4,2,1,1]=>90
[7,6,8,1,4,5,3,2]=>[3,2,1,1,1]=>64
[7,5,1,8,4,6,3,2]=>[3,2,1,1,1]=>64
[1,7,8,5,6,4,3,2]=>[3,2,1,1,1]=>64
[7,3,6,2,5,4,8,1]=>[3,2,1,1,1]=>64
[1,6,2,3,5,8,4,7]=>[5,2,1]=>64
[1,8,5,6,4,3,7,2]=>[4,1,1,1,1]=>35
[5,3,2,1,7,8,4,6]=>[3,3,1,1]=>56
[8,4,1,3,6,7,2,5]=>[4,2,1,1]=>90
[5,3,8,1,4,7,6,2]=>[3,2,2,1]=>70
[4,3,5,8,1,7,6,2]=>[3,2,2,1]=>70
[2,5,3,6,8,4,1,7]=>[4,3,1]=>70
[4,6,2,5,1,7,8,3]=>[4,2,2]=>56
[2,3,1,7,4,8,6,5]=>[4,3,1]=>70
[1,8,3,6,4,2,7,5]=>[4,2,1,1]=>90
[2,1,7,4,8,5,3,6]=>[4,3,1]=>70
[8,1,7,3,2,5,4,6]=>[4,2,1,1]=>90
[7,8,5,2,6,4,3,1]=>[2,2,2,1,1]=>28
[8,1,2,5,7,4,6,3]=>[4,2,1,1]=>90
[8,2,5,3,6,1,4,7]=>[4,2,1,1]=>90
[6,8,7,4,1,5,2,3]=>[3,2,2,1]=>70
[8,6,4,7,5,1,3,2]=>[2,2,2,1,1]=>28
[6,1,2,4,7,8,3,5]=>[5,2,1]=>64
[3,2,8,9,10,1,4,5,6,7]=>[5,4,1]=>288
[3,5,2,1,7,8,6,4]=>[4,2,2]=>56
[4,2,7,8,6,5,1,3]=>[3,2,2,1]=>70
[4,8,1,2,6,5,3,7]=>[4,2,1,1]=>90
[6,4,8,1,2,3,7,5]=>[4,2,2]=>56
[5,2,7,1,4,6,3,8]=>[4,2,2]=>56
[6,3,8,5,7,1,4,2]=>[3,2,2,1]=>70
[2,4,3,8,5,7,1,6]=>[4,2,2]=>56
[2,8,3,1,4,6,5,7]=>[5,2,1]=>64
[4,5,7,6,1,3,8,2]=>[4,2,1,1]=>90
[3,7,1,6,5,8,2,4]=>[3,3,1,1]=>56
[7,4,3,6,8,2,1,5]=>[3,2,1,1,1]=>64
[3,8,5,4,7,6,1,2]=>[3,2,2,1]=>70
[1,4,6,8,7,3,5,2]=>[4,2,1,1]=>90
[4,6,5,1,3,8,7,2]=>[3,3,1,1]=>56
[5,4,6,2,1,8,7,3]=>[3,2,2,1]=>70
[3,2,8,5,1,4,6,7]=>[4,2,2]=>56
[3,5,4,1,2,8,6,7]=>[4,3,1]=>70
[5,3,8,1,4,2,6,7]=>[4,2,2]=>56
[5,3,8,1,4,2,7,6]=>[3,3,2]=>42
[1,4,7,5,8,6,2,3]=>[4,2,2]=>56
[8,5,7,6,3,4,1,2]=>[2,2,2,1,1]=>28
[7,5,2,6,1,4,8,3]=>[3,2,2,1]=>70
[2,4,5,1,8,3,7,6]=>[4,3,1]=>70
[7,2,8,5,3,4,1,6]=>[4,2,1,1]=>90
[6,4,5,3,1,7,8,2]=>[4,2,1,1]=>90
[7,3,5,6,4,1,8,2]=>[4,2,1,1]=>90
[2,3,4,7,8,9,1,5,6]=>[6,3]=>48
[2,3,6,7,8,9,1,4,5]=>[6,3]=>48
[2,5,6,7,8,9,1,3,4]=>[6,3]=>48
[2,3,4,5,1,9,6,7,8]=>[7,2]=>27
[2,3,4,1,8,9,5,6,7]=>[6,3]=>48
[2,3,4,5,8,9,10,1,6,7]=>[7,3]=>75
[2,3,1,7,8,9,4,5,6]=>[5,4]=>42
[2,3,4,7,8,9,10,1,5,6]=>[7,3]=>75
[2,1,6,7,8,9,3,4,5]=>[5,4]=>42
[2,3,6,7,8,9,10,1,4,5]=>[7,3]=>75
[2,5,6,7,8,9,10,1,3,4]=>[7,3]=>75
[2,5,6,3,4,1,8,7]=>[4,3,1]=>70
[4,6,2,1,5,8,3,7]=>[3,3,2]=>42
[4,6,7,2,3,8,5,1]=>[4,3,1]=>70
[4,5,3,7,8,1,2,6]=>[4,3,1]=>70
[2,3,5,8,1,6,4,7]=>[5,2,1]=>64
[1,7,4,5,8,3,6,2]=>[4,2,1,1]=>90
[2,8,5,6,3,1,4,7]=>[4,2,1,1]=>90
[4,8,2,6,1,5,7,3]=>[3,2,2,1]=>70
[2,3,7,8,1,5,4,6]=>[4,3,1]=>70
[5,2,6,7,8,3,1,4]=>[4,3,1]=>70
[5,6,2,7,8,3,1,4]=>[4,3,1]=>70
[2,3,7,5,8,4,6,1]=>[4,2,1,1]=>90
[3,7,8,5,1,4,6,2]=>[3,3,1,1]=>56
[2,5,6,7,1,8,4,3]=>[5,2,1]=>64
[6,4,7,8,1,2,5,3]=>[3,3,2]=>42
[7,5,8,1,2,3,6,4]=>[4,2,2]=>56
[1,2,8,7,4,6,5,3]=>[4,1,1,1,1]=>35
[5,1,4,8,7,3,6,2]=>[3,2,2,1]=>70
[4,3,1,8,7,5,6,2]=>[3,2,2,1]=>70
[4,3,2,7,6,1,5,8]=>[3,2,2,1]=>70
[7,2,6,5,3,1,4,8]=>[4,1,1,1,1]=>35
[1,3,7,6,2,4,8,5]=>[4,3,1]=>70
[1,3,8,2,7,4,6,5]=>[4,2,1,1]=>90
[8,2,7,1,6,4,3,5]=>[3,2,1,1,1]=>64
[4,3,2,8,1,7,5,6]=>[3,2,2,1]=>70
[7,5,4,1,6,3,8,2]=>[3,2,1,1,1]=>64
[1,6,5,3,2,4,8,7]=>[4,2,1,1]=>90
[1,7,3,5,2,4,8,6]=>[4,3,1]=>70
[4,3,7,2,5,1,6,8]=>[4,2,1,1]=>90
[5,1,4,3,2,6,8,7]=>[4,2,1,1]=>90
[7,2,1,3,5,4,6,8]=>[5,2,1]=>64
[8,3,7,5,4,2,6,1]=>[3,1,1,1,1,1]=>21
[1,6,8,7,5,2,3,4]=>[4,2,1,1]=>90
[1,3,6,2,5,4,8,7]=>[4,3,1]=>70
[1,2,7,3,8,4,9,5,10,6]=>[6,4]=>90
[4,5,7,6,3,1,8,2]=>[4,2,1,1]=>90
[4,6,7,5,1,3,8,2]=>[4,2,1,1]=>90
[3,6,5,1,4,7,8,2]=>[4,2,1,1]=>90
[4,6,7,3,1,5,8,2]=>[4,2,2]=>56
[6,2,4,7,5,3,1,8]=>[4,2,1,1]=>90
[6,2,5,1,8,7,3,4]=>[3,3,2]=>42
[3,2,6,1,5,8,7,4]=>[3,3,2]=>42
[4,2,3,6,7,5,1,8]=>[5,2,1]=>64
[6,2,3,5,7,4,1,8]=>[5,1,1,1]=>35
[1,6,3,8,4,7,2,5]=>[4,2,2]=>56
[8,1,5,2,4,7,3,6]=>[4,2,1,1]=>90
[7,5,8,1,4,2,3,6]=>[4,2,1,1]=>90
[4,1,2,3,6,5,8,7,9]=>[6,3]=>48
[4,1,2,3,6,5,8,7,10,9]=>[6,4]=>90
[4,1,6,2,3,5,8,7,9]=>[6,3]=>48
[3,2,7,1,8,6,5,4]=>[3,2,2,1]=>70
[6,2,4,1,5,7,8,3]=>[5,2,1]=>64
[5,8,4,1,3,6,7,2]=>[4,2,1,1]=>90
[6,7,2,3,8,1,4,5]=>[4,3,1]=>70
[5,2,8,1,7,4,6,3]=>[3,2,2,1]=>70
[2,5,4,7,3,1,8,6]=>[4,2,1,1]=>90
[4,6,3,1,2,5,7,8]=>[5,2,1]=>64
[7,4,6,8,3,1,2,5]=>[3,3,1,1]=>56
[8,5,4,7,3,1,2,6]=>[3,2,1,1,1]=>64
[7,3,2,1,5,4,8,6]=>[3,3,1,1]=>56
[2,5,6,4,8,1,3,7]=>[4,3,1]=>70
[1,3,6,5,2,4,7,8]=>[5,2,1]=>64
[5,4,1,2,7,6,3,8]=>[4,2,2]=>56
[5,8,7,3,1,2,4,6]=>[4,2,1,1]=>90
[2,7,8,1,4,5,3,6]=>[4,3,1]=>70
[4,1,2,8,7,3,6,5]=>[4,2,1,1]=>90
[6,1,2,4,3,8,7,5]=>[4,2,2]=>56
[3,7,8,1,2,4,6,5]=>[4,3,1]=>70
[7,3,4,1,2,6,8,5]=>[4,3,1]=>70
[8,4,3,1,2,6,5,7]=>[4,2,1,1]=>90
[3,8,2,7,4,5,1,6]=>[4,2,1,1]=>90
[8,6,2,3,5,4,1,7]=>[4,1,1,1,1]=>35
[8,2,6,1,3,5,4,7]=>[4,2,1,1]=>90
[8,4,3,7,2,5,6,1]=>[3,2,1,1,1]=>64
[8,3,1,7,4,5,2,6]=>[4,2,1,1]=>90
[8,2,4,5,1,7,3,6]=>[4,3,1]=>70
[6,8,2,4,5,1,7,3]=>[4,2,2]=>56
[4,3,8,1,7,5,6,2]=>[3,2,2,1]=>70
[8,4,3,7,1,5,6,2]=>[3,2,2,1]=>70
[8,3,4,7,2,6,5,1]=>[3,2,1,1,1]=>64
[8,1,3,7,6,4,5,2]=>[4,1,1,1,1]=>35
[8,3,7,1,4,5,6,2]=>[4,2,1,1]=>90
[8,7,3,6,1,2,5,4]=>[3,2,1,1,1]=>64
[8,3,7,6,2,4,5,1]=>[3,2,1,1,1]=>64
[8,7,2,3,6,1,5,4]=>[3,2,1,1,1]=>64
[8,2,7,1,3,4,6,5]=>[4,2,1,1]=>90
[5,1,8,4,2,3,7,6]=>[4,2,2]=>56
[8,2,4,7,3,1,6,5]=>[3,2,2,1]=>70
[8,2,7,6,3,1,4,5]=>[4,1,1,1,1]=>35
[6,8,1,4,7,3,2,5]=>[3,2,2,1]=>70
[8,5,7,2,6,3,1,4]=>[3,2,1,1,1]=>64
[5,8,2,7,3,1,6,4]=>[3,2,2,1]=>70
[8,1,2,6,7,5,4,3]=>[4,1,1,1,1]=>35
[8,4,1,7,5,6,2,3]=>[3,3,1,1]=>56
[8,2,4,7,6,5,1,3]=>[3,2,1,1,1]=>64
[8,2,7,6,4,5,1,3]=>[3,2,1,1,1]=>64
[8,4,7,2,3,6,5,1]=>[3,2,1,1,1]=>64
[8,2,4,7,3,6,5,1]=>[3,2,1,1,1]=>64
[8,1,7,6,4,5,2,3]=>[3,2,1,1,1]=>64
[8,1,2,7,6,4,5,3]=>[4,1,1,1,1]=>35
[8,1,4,7,3,6,5,2]=>[3,2,1,1,1]=>64
[2,3,1,9,8,7,6,5,4]=>[3,2,1,1,1,1]=>105
[2,8,1,5,3,7,6,4]=>[3,3,1,1]=>56
[1,8,2,4,7,5,6,3]=>[5,1,1,1]=>35
[2,3,8,4,7,1,6,5]=>[4,2,1,1]=>90
[1,8,2,3,5,6,4,7]=>[6,1,1]=>21
[1,4,7,6,2,3,5,8]=>[5,2,1]=>64
[1,7,6,2,3,8,4,5]=>[5,2,1]=>64
[1,8,2,3,7,6,4,5]=>[5,1,1,1]=>35
[1,7,3,8,6,2,5,4]=>[3,2,2,1]=>70
[5,8,2,3,7,4,1,6]=>[4,2,1,1]=>90
[1,3,5,6,4,8,2,7]=>[5,2,1]=>64
[7,1,2,3,4,5,9,6,10,8]=>[7,3]=>75
[4,6,1,8,2,7,5,3]=>[3,3,1,1]=>56
[3,4,8,5,6,1,2,7]=>[5,2,1]=>64
[1,7,6,2,5,4,8,3]=>[4,1,1,1,1]=>35
[5,6,1,7,4,3,8,2]=>[4,2,1,1]=>90
[3,1,5,6,4,2,7,8]=>[5,2,1]=>64
[8,1,6,4,3,5,2,7]=>[4,1,1,1,1]=>35
[2,1,6,5,3,8,7,4]=>[3,3,2]=>42
[3,7,5,6,4,2,1,8]=>[4,1,1,1,1]=>35
[6,1,4,3,7,5,8,2]=>[4,2,1,1]=>90
[3,8,6,4,5,2,7,1]=>[4,1,1,1,1]=>35
[4,5,8,6,2,3,7,1]=>[4,2,1,1]=>90
[4,6,8,5,3,7,2,1]=>[3,2,1,1,1]=>64
[4,5,7,2,8,6,3,1]=>[4,2,1,1]=>90
[3,7,4,5,1,6,8,2]=>[5,2,1]=>64
[4,6,8,1,2,5,7,3]=>[4,3,1]=>70
[4,6,8,5,1,3,7,2]=>[3,3,1,1]=>56
[3,7,4,5,2,8,6,1]=>[4,2,1,1]=>90
[3,7,8,4,6,1,5,2]=>[3,2,2,1]=>70
[4,5,7,2,1,6,8,3]=>[4,2,2]=>56
[4,5,1,6,8,3,7,2]=>[4,3,1]=>70
[8,3,5,4,6,1,2,7]=>[4,2,1,1]=>90
[3,4,5,6,1,7,2,9,8]=>[6,3]=>48
[1,7,4,5,2,6,8,3]=>[5,2,1]=>64
[1,4,5,9,6,7,2,8,3]=>[6,2,1]=>105
[3,4,5,6,7,1,8,2,10,9]=>[7,3]=>75
[2,4,5,9,6,1,7,3,8]=>[6,2,1]=>105
[3,4,5,7,6,1,9,2,8]=>[5,3,1]=>162
[1,4,2,6,5,3,8,7]=>[4,3,1]=>70
[3,1,5,8,4,6,2,7]=>[4,3,1]=>70
[3,5,6,9,7,1,8,2,4]=>[5,3,1]=>162
[1,4,8,5,6,2,7,9,3]=>[6,2,1]=>105
[1,4,5,6,10,7,8,2,9,3]=>[7,2,1]=>160
[3,4,5,6,7,8,1,9,2,11,10]=>[8,3]=>110
[2,4,5,6,10,7,1,8,3,9]=>[7,2,1]=>160
[3,4,5,6,8,7,1,10,2,9]=>[6,3,1]=>315
[2,5,9,6,7,3,1,4,8]=>[5,2,1,1]=>189
[4,1,5,2,7,6,3,9,8]=>[4,4,1]=>84
[3,4,1,6,9,5,7,2,8]=>[5,3,1]=>162
[8,2,6,3,4,1,5,7]=>[5,1,1,1]=>35
[4,6,5,8,2,1,3,7]=>[3,3,1,1]=>56
[1,4,8,3,5,6,2,7]=>[5,2,1]=>64
[1,8,7,4,2,3,6,5]=>[4,2,1,1]=>90
[6,7,9,8,1,3,4,2,5]=>[4,3,1,1]=>216
[9,1,5,2,8,6,3,7,4]=>[4,3,1,1]=>216
[3,5,6,7,10,8,1,9,2,4]=>[6,3,1]=>315
[1,7,4,5,2,6,8,9,3]=>[6,2,1]=>105
[1,4,5,9,6,7,2,8,10,3]=>[7,2,1]=>160
[1,4,5,6,7,11,8,9,2,10,3]=>[8,2,1]=>231
[7,4,6,2,1,3,8,5]=>[3,3,1,1]=>56
[5,4,8,7,6,2,3,1]=>[2,2,2,1,1]=>28
[5,2,3,8,7,1,6,4]=>[3,2,2,1]=>70
[7,5,2,4,1,3,8,6]=>[3,3,1,1]=>56
[7,2,6,8,5,1,3,4]=>[3,3,1,1]=>56
[8,2,3,4,1,6,7,5]=>[5,2,1]=>64
[7,4,3,8,1,6,5,2]=>[2,2,2,2]=>14
[6,5,1,4,3,8,7,2]=>[3,2,1,1,1]=>64
[4,7,6,2,5,8,1,3]=>[3,2,2,1]=>70
[2,6,4,5,8,3,1,7]=>[4,2,1,1]=>90
[7,3,5,2,8,1,4,6]=>[3,3,1,1]=>56
[1,5,8,7,4,2,3,6]=>[4,2,1,1]=>90
[1,7,2,4,5,8,6,3]=>[5,2,1]=>64
[1,4,6,8,7,2,5,3]=>[4,2,1,1]=>90
[1,6,2,7,5,3,4,8]=>[5,2,1]=>64
[1,3,7,2,6,4,5,8]=>[5,2,1]=>64
[1,7,3,2,8,5,6,4]=>[4,2,2]=>56
[1,6,5,2,4,8,3,7]=>[4,2,1,1]=>90
[1,7,3,8,4,2,5,6]=>[5,2,1]=>64
[1,6,2,4,7,5,8,3]=>[5,2,1]=>64
[1,6,2,7,4,3,8,5]=>[4,3,1]=>70
[1,5,8,2,3,6,4,7]=>[5,2,1]=>64
[6,8,9,1,2,3,4,5,7]=>[6,3]=>48
[5,8,9,1,2,3,4,6,7]=>[6,3]=>48
[2,5,3,6,7,1,4,8]=>[5,2,1]=>64
[6,4,1,5,7,2,3,8]=>[4,3,1]=>70
[6,4,1,5,7,3,8,2]=>[4,2,1,1]=>90
[1,2,7,3,8,5,6,4]=>[5,2,1]=>64
[7,4,1,6,3,8,2,5]=>[3,3,1,1]=>56
[1,5,7,4,3,8,6,2]=>[4,2,1,1]=>90
[2,7,3,1,4,5,8,6]=>[5,2,1]=>64
[2,3,4,5,1,7,6,9,8]=>[6,3]=>48
[2,3,4,1,6,5,8,7,9]=>[6,3]=>48
[2,3,4,5,6,7,1,9,8,10]=>[8,2]=>35
[2,3,4,5,1,8,6,9,7]=>[6,3]=>48
[2,3,4,1,7,5,8,6,9]=>[6,3]=>48
[2,3,4,5,1,7,6,9,8,10]=>[7,3]=>75
[6,5,8,3,2,7,1,4]=>[2,2,2,1,1]=>28
[8,4,3,1,7,6,5,2]=>[2,2,2,1,1]=>28
[3,4,5,6,7,9,1,8,2]=>[6,2,1]=>105
[3,4,5,6,8,2,7,1]=>[5,2,1]=>64
[3,4,5,6,7,8,10,1,9,2]=>[7,2,1]=>160
[3,4,5,6,7,9,2,8,1]=>[6,2,1]=>105
[3,4,5,6,7,1,9,8,2]=>[6,2,1]=>105
[7,2,1,4,5,6,3,8]=>[5,2,1]=>64
[1,5,6,7,3,4,2,8]=>[5,2,1]=>64
[4,6,8,5,2,1,7,3]=>[3,2,2,1]=>70
[1,6,7,8,2,4,5,3]=>[4,3,1]=>70
[5,7,8,2,3,1,6,4]=>[3,3,2]=>42
[5,3,4,2,1,9,8,7,6]=>[3,2,2,2]=>84
[6,5,3,4,2,1,9,8,7]=>[3,2,2,1,1]=>162
[7,6,4,5,3,2,1,9,8]=>[3,2,1,1,1,1]=>105
[4,5,2,7,8,6,1,3]=>[4,2,2]=>56
[1,3,5,8,7,2,6,4]=>[4,2,1,1]=>90
[6,4,1,8,5,7,3,2]=>[3,2,2,1]=>70
[4,1,3,8,7,5,2,6]=>[4,2,1,1]=>90
[8,5,1,6,7,2,4,3]=>[3,3,1,1]=>56
[3,6,7,2,1,5,8,4]=>[4,2,2]=>56
[2,5,6,1,3,8,7,4]=>[4,3,1]=>70
[7,2,5,6,1,3,8,4]=>[4,3,1]=>70
[4,7,3,5,2,6,8,1]=>[4,2,1,1]=>90
[6,8,4,1,5,7,3,2]=>[3,2,2,1]=>70
[8,1,6,2,3,7,5,4]=>[4,2,1,1]=>90
[7,8,9,6,1,2,3,4,10,5]=>[5,4,1]=>288
[2,8,9,10,7,1,3,4,5,6]=>[5,4,1]=>288
[8,9,10,7,6,1,2,3,4,11,5]=>[5,4,1,1]=>1155
[8,9,7,5,6,1,2,3,10,4]=>[4,3,2,1]=>768
[2,9,10,8,6,7,1,3,4,5]=>[4,3,2,1]=>768
[2,9,10,11,8,7,1,3,4,5,6]=>[5,4,1,1]=>1155
[8,9,10,11,7,1,2,3,4,5,12,6]=>[6,5,1]=>1155
[7,8,9,10,1,2,3,4,5,11,6]=>[6,5]=>132
[7,8,9,5,1,2,3,4,10,6]=>[5,4,1]=>288
[7,8,9,1,6,2,3,4,10,5]=>[5,4,1]=>288
[2,8,9,10,6,1,3,4,5,7]=>[5,4,1]=>288
[2,8,9,10,1,7,3,4,5,6]=>[5,4,1]=>288
[2,8,9,10,11,1,3,4,5,6,7]=>[6,5]=>132
[2,9,10,11,12,8,1,3,4,5,6,7]=>[6,5,1]=>1155
[2,8,3,6,4,1,7,5]=>[4,2,1,1]=>90
[6,5,3,4,8,2,1,7]=>[3,2,1,1,1]=>64
[3,4,5,1,2,6,7,8,9]=>[7,2]=>27
[5,2,7,6,8,3,4,1]=>[3,3,1,1]=>56
[8,4,5,2,7,3,6,1]=>[3,3,1,1]=>56
[6,3,7,4,5,2,8,1]=>[4,2,1,1]=>90
[7,3,4,2,8,5,6,1]=>[4,2,1,1]=>90
[4,3,6,5,8,2,7,1]=>[3,3,1,1]=>56
[8,2,7,4,5,3,6,1]=>[4,1,1,1,1]=>35
[7,2,8,4,5,3,6,1]=>[4,2,1,1]=>90
[6,3,8,2,7,4,5,1]=>[3,2,2,1]=>70
[3,2,8,4,7,5,6,1]=>[4,2,1,1]=>90
[8,3,6,2,7,4,5,1]=>[3,3,1,1]=>56
[2,3,4,5,6,7,8,11,1,9,10]=>[9,2]=>44
[2,3,4,5,6,7,11,1,8,9,10]=>[9,2]=>44
[2,3,4,5,6,11,1,7,8,9,10]=>[9,2]=>44
[2,3,4,5,11,1,6,7,8,9,10]=>[9,2]=>44
[2,3,4,11,1,5,6,7,8,9,10]=>[9,2]=>44
[2,3,11,1,4,5,6,7,8,9,10]=>[9,2]=>44
[1,7,8,4,3,6,5,2]=>[3,2,2,1]=>70
[1,7,8,3,6,5,4,2]=>[3,2,1,1,1]=>64
[5,8,1,7,2,4,3,6]=>[4,2,1,1]=>90
[2,5,7,3,8,1,4,6]=>[4,3,1]=>70
[8,3,5,2,1,6,7,4]=>[4,2,1,1]=>90
[2,6,4,7,1,8,5,3]=>[4,2,2]=>56
[1,8,5,3,7,6,2,4]=>[3,2,2,1]=>70
[6,1,4,2,7,8,3,5]=>[4,3,1]=>70
[6,5,1,3,7,8,4,2]=>[4,2,1,1]=>90
[5,8,7,3,2,4,6,1]=>[3,2,1,1,1]=>64
[2,4,1,7,5,6,3,8]=>[5,2,1]=>64
[1,4,3,7,6,2,8,5]=>[4,2,2]=>56
[1,6,2,5,7,3,8,4]=>[5,2,1]=>64
[1,4,3,8,2,5,7,6]=>[4,2,2]=>56
[1,5,7,3,6,4,2,8]=>[4,2,1,1]=>90
[1,6,7,2,4,8,3,5]=>[4,3,1]=>70
[3,7,2,8,4,1,5,6]=>[4,3,1]=>70
[2,4,1,5,3,6,8,7,9]=>[6,3]=>48
[2,4,1,7,3,8,5,6,9]=>[5,4]=>42
[5,3,4,1,7,8,6,2]=>[4,2,2]=>56
[4,7,6,5,8,2,3,1]=>[3,2,1,1,1]=>64
[1,2,6,8,4,3,5,7]=>[5,2,1]=>64
[7,2,6,3,1,8,4,5]=>[4,2,1,1]=>90
[5,8,4,1,3,7,2,6]=>[3,2,2,1]=>70
[3,4,2,1,6,8,5,7]=>[4,3,1]=>70
[8,1,3,5,6,4,7,2]=>[5,1,1,1]=>35
[3,4,7,1,5,6,2,8]=>[5,2,1]=>64
[4,8,2,6,5,3,7,1]=>[3,2,1,1,1]=>64
[4,8,7,2,5,6,1,3]=>[3,2,2,1]=>70
[5,8,6,4,7,3,2,1]=>[3,1,1,1,1,1]=>21
[8,5,2,3,1,6,7,4]=>[4,2,1,1]=>90
[2,8,6,3,5,1,7,4]=>[4,2,1,1]=>90
[8,3,2,6,4,1,7,5]=>[3,3,1,1]=>56
[8,4,1,5,3,6,7,2]=>[4,2,1,1]=>90
[8,3,5,1,4,6,7,2]=>[4,2,1,1]=>90
[8,5,1,3,4,6,7,2]=>[5,1,1,1]=>35
[3,8,6,2,5,4,7,1]=>[3,2,1,1,1]=>64
[3,8,4,6,5,2,7,1]=>[4,1,1,1,1]=>35
[8,1,7,4,2,5,3,6]=>[4,2,1,1]=>90
[8,3,2,5,1,4,7,6]=>[3,3,1,1]=>56
[8,4,5,1,2,6,7,3]=>[4,3,1]=>70
[8,1,5,3,2,6,7,4]=>[4,2,1,1]=>90
[8,1,5,2,4,6,7,3]=>[5,1,1,1]=>35
[5,2,6,4,1,3,8,7]=>[3,3,2]=>42
[8,6,4,7,1,3,5,2]=>[3,2,1,1,1]=>64
[2,1,8,5,4,3,7,6]=>[3,3,1,1]=>56
[6,4,8,5,3,2,7,1]=>[3,2,1,1,1]=>64
[9,10,6,7,4,5,2,3,1,8]=>[3,2,2,2,1]=>288
[6,8,5,4,7,2,3,1]=>[2,2,2,1,1]=>28
[2,5,7,3,4,8,1,6]=>[4,3,1]=>70
[5,2,4,7,8,1,3,6]=>[4,3,1]=>70
[8,5,9,3,6,1,2,4,7]=>[4,2,2,1]=>216
[9,7,1,5,8,3,6,2,4]=>[3,2,2,1,1]=>162
[9,7,5,4,1,3,8,2,6]=>[3,2,1,1,1,1]=>105
[8,9,4,5,10,1,2,3,6,7]=>[5,3,2]=>450
[8,4,3,9,10,1,2,5,6,7]=>[5,3,1,1]=>567
[9,6,10,1,3,7,8,2,4,5]=>[4,3,2,1]=>768
[9,10,6,7,4,5,1,2,3,8]=>[4,2,2,2]=>300
[9,6,4,10,3,7,1,2,5,8]=>[4,2,2,1,1]=>567
[10,1,8,9,6,7,4,5,2,3]=>[3,2,2,2,1]=>288
[10,8,6,1,4,9,3,7,2,5]=>[3,2,2,1,1,1]=>315
[10,8,6,5,4,1,3,9,2,7]=>[3,2,1,1,1,1,1]=>160
[10,8,7,6,5,4,3,1,2,9]=>[3,1,1,1,1,1,1,1]=>36
[4,8,5,6,1,2,7,3]=>[4,3,1]=>70
[2,5,6,8,7,1,4,3]=>[4,2,1,1]=>90
[1,7,8,5,4,6,2,3]=>[3,2,2,1]=>70
[4,6,8,1,5,2,7,3]=>[3,3,2]=>42
[2,3,7,5,8,6,1,4]=>[4,2,2]=>56
[1,3,6,4,8,2,7,5]=>[4,2,2]=>56
[1,2,3,4,6,5,7,8,9,10]=>[9,1]=>9
[1,2,3,4,5,6,8,7,9,10]=>[9,1]=>9
[1,7,6,2,8,5,3,4]=>[4,2,1,1]=>90
[1,5,8,6,4,7,2,3]=>[4,2,1,1]=>90
[5,6,2,8,1,7,3,4]=>[3,3,2]=>42
[6,8,4,5,1,3,7,2]=>[3,2,2,1]=>70
[5,2,3,8,1,4,6,7]=>[5,2,1]=>64
[1,6,8,3,2,4,5,7]=>[5,2,1]=>64
[9,6,5,4,3,2,1,7,8]=>[3,1,1,1,1,1,1]=>28
[10,7,6,5,4,3,2,1,8,9]=>[3,1,1,1,1,1,1,1]=>36
[7,3,5,4,8,2,6,1]=>[3,2,1,1,1]=>64
[7,3,6,8,4,5,1,2]=>[3,2,2,1]=>70
[1,6,5,7,4,2,8,3]=>[4,2,1,1]=>90
[1,2,7,4,8,5,6,3]=>[5,2,1]=>64
[2,6,7,4,8,5,1,3]=>[4,2,2]=>56
[2,5,8,6,4,3,7,1]=>[4,1,1,1,1]=>35
[6,4,2,5,7,1,8,3]=>[4,2,1,1]=>90
[9,1,2,3,4,5,8,7,6]=>[6,1,1,1]=>56
[9,1,2,3,4,8,6,7,5]=>[6,1,1,1]=>56
[8,1,4,7,3,5,6,2]=>[4,2,1,1]=>90
[9,1,2,8,4,5,6,7,3]=>[6,1,1,1]=>56
[8,3,7,2,4,5,6,1]=>[4,2,1,1]=>90
[9,1,8,3,4,5,6,7,2]=>[6,1,1,1]=>56
[10,1,2,3,4,5,6,9,8,7]=>[7,1,1,1]=>84
[9,1,2,3,4,7,8,6,5]=>[6,1,1,1]=>56
[10,1,2,3,4,5,9,7,8,6]=>[7,1,1,1]=>84
[9,1,2,3,6,8,5,7,4]=>[5,2,1,1]=>189
[9,1,2,5,8,4,6,7,3]=>[5,2,1,1]=>189
[10,1,2,3,9,5,6,7,8,4]=>[7,1,1,1]=>84
[8,1,4,5,7,3,6,2]=>[4,2,1,1]=>90
[9,1,4,8,3,5,6,7,2]=>[5,2,1,1]=>189
[10,1,2,9,4,5,6,7,8,3]=>[7,1,1,1]=>84
[9,3,8,2,4,5,6,7,1]=>[5,2,1,1]=>189
[5,6,3,4,2,8,7,1]=>[3,3,1,1]=>56
[2,5,7,4,6,8,1,3]=>[4,2,2]=>56
[2,5,6,4,1,3,8,7]=>[4,3,1]=>70
[4,6,1,3,5,7,2,8]=>[5,2,1]=>64
[3,6,5,8,1,7,4,2]=>[3,2,2,1]=>70
[4,5,2,8,6,7,3,1]=>[4,2,1,1]=>90
[4,2,3,6,8,5,1,7]=>[4,3,1]=>70
[6,4,1,3,7,8,2,5]=>[4,2,1,1]=>90
[6,3,1,2,5,4,8,7]=>[4,3,1]=>70
[1,5,8,2,4,3,7,6]=>[4,2,2]=>56
[4,3,7,8,2,6,5,1]=>[3,2,2,1]=>70
[3,8,5,1,2,6,7,4]=>[4,3,1]=>70
[2,4,7,8,3,6,5,1]=>[4,2,1,1]=>90
[5,4,7,8,3,6,1,2]=>[3,2,2,1]=>70
[6,8,1,3,2,5,7,4]=>[4,2,2]=>56
[1,4,8,5,7,2,3,6]=>[4,3,1]=>70
[1,8,7,3,2,4,5,6]=>[5,1,1,1]=>35
[8,6,2,7,3,4,1,5]=>[4,2,1,1]=>90
[8,6,2,7,3,4,5,1]=>[4,2,1,1]=>90
[5,6,3,2,8,7,1,4]=>[3,2,2,1]=>70
[5,1,6,7,8,3,2,4]=>[4,3,1]=>70
[1,5,6,3,7,2,4,8]=>[5,2,1]=>64
[1,5,6,7,4,2,3,8]=>[5,2,1]=>64
[5,1,6,7,3,4,2,8]=>[4,3,1]=>70
[8,6,1,7,3,4,5,2]=>[4,2,1,1]=>90
[6,8,5,1,7,4,2,3]=>[3,2,2,1]=>70
[8,4,2,3,5,7,6,1]=>[4,2,1,1]=>90
[4,8,5,2,3,1,6,7]=>[4,2,1,1]=>90
[5,4,8,3,1,2,6,7]=>[4,2,1,1]=>90
[8,4,7,3,2,5,6,1]=>[3,2,1,1,1]=>64
[6,8,5,1,7,3,4,2]=>[3,2,2,1]=>70
[6,2,7,3,8,1,4,5]=>[4,3,1]=>70
[8,4,2,6,7,1,5,3]=>[3,2,2,1]=>70
[1,7,8,3,6,5,2,4]=>[3,2,2,1]=>70
[4,6,7,5,1,8,2,3]=>[4,3,1]=>70
[3,5,2,6,8,7,4,1]=>[4,2,1,1]=>90
[7,3,6,8,4,1,2,5]=>[3,3,1,1]=>56
[6,4,2,3,7,5,8,1]=>[4,2,1,1]=>90
[6,3,7,5,1,2,8,4]=>[3,3,2]=>42
[7,2,5,4,8,6,3,1]=>[3,2,1,1,1]=>64
[6,2,3,8,7,4,5,1]=>[4,2,1,1]=>90
[7,1,2,8,4,6,5,3]=>[4,2,1,1]=>90
[3,5,8,1,2,7,6,4]=>[3,3,1,1]=>56
[1,4,3,6,8,5,2,7]=>[4,3,1]=>70
[7,6,2,8,5,3,4,1]=>[3,2,1,1,1]=>64
[6,8,3,5,4,7,2,1]=>[3,2,1,1,1]=>64
[8,2,7,6,4,1,3,5]=>[3,2,1,1,1]=>64
[8,3,7,5,1,6,2,4]=>[3,3,1,1]=>56
[8,5,7,1,4,2,6,3]=>[3,2,2,1]=>70
[4,5,7,1,6,3,8,2]=>[4,2,1,1]=>90
[4,6,5,7,2,3,8,1]=>[4,2,1,1]=>90
[3,6,7,2,5,8,4,1]=>[4,2,1,1]=>90
[5,3,6,7,4,8,1,2]=>[4,2,2]=>56
[4,2,7,8,3,6,5,1]=>[3,3,1,1]=>56
[4,2,7,8,5,6,1,3]=>[3,3,2]=>42
[5,4,3,7,8,1,6,2]=>[3,2,2,1]=>70
[3,5,7,8,4,2,1,6]=>[4,2,1,1]=>90
[4,6,7,3,2,8,1,5]=>[4,2,1,1]=>90
[4,6,5,3,7,8,1,2]=>[4,2,1,1]=>90
[5,6,2,4,7,8,3,1]=>[4,2,1,1]=>90
[5,6,3,2,8,4,7,1]=>[3,3,1,1]=>56
[5,6,2,8,3,4,7,1]=>[4,3,1]=>70
[3,7,4,8,1,6,5,2]=>[3,2,2,1]=>70
[5,2,4,8,6,7,3,1]=>[4,2,1,1]=>90
[5,2,6,4,8,7,3,1]=>[3,3,1,1]=>56
[2,4,7,8,6,5,1,3]=>[4,2,1,1]=>90
[3,4,5,6,8,9,1,7,2]=>[6,2,1]=>105
[3,4,6,7,8,9,1,5,2]=>[6,2,1]=>105
[3,5,6,7,8,9,1,4,2]=>[6,2,1]=>105
[4,5,6,7,8,9,1,3,2]=>[6,2,1]=>105
[3,4,5,6,7,9,10,1,8,2]=>[7,2,1]=>160
[3,4,5,7,8,9,10,1,6,2]=>[7,2,1]=>160
[5,2,6,7,8,1,4,3]=>[4,2,2]=>56
[3,4,6,7,8,9,10,1,5,2]=>[7,2,1]=>160
[4,5,6,7,8,9,10,1,3,2]=>[7,2,1]=>160
[3,1,4,5,6,7,8,9,11,2,10]=>[8,3]=>110
[4,8,2,7,5,3,1,6]=>[3,2,1,1,1]=>64
[1,2,4,6,5,8,3,7]=>[5,2,1]=>64
[5,4,2,3,1,7,8,6]=>[4,2,1,1]=>90
[5,8,6,1,7,2,3,4]=>[4,3,1]=>70
[5,1,4,3,8,2,6,7]=>[4,2,1,1]=>90
[8,4,7,5,6,2,1,3]=>[3,2,1,1,1]=>64
[3,8,6,7,5,2,4,1]=>[3,2,1,1,1]=>64
[8,2,5,4,7,3,6,1]=>[3,2,1,1,1]=>64
[4,2,8,7,3,6,5,1]=>[3,2,1,1,1]=>64
[3,7,8,6,1,4,5,2]=>[3,3,1,1]=>56
[4,6,7,8,2,1,5,3]=>[4,2,2]=>56
[4,7,6,3,8,1,5,2]=>[3,2,2,1]=>70
[3,8,1,4,6,2,5,7]=>[4,3,1]=>70
[2,4,5,3,8,7,1,6]=>[4,2,2]=>56
[4,7,5,6,2,8,1,3]=>[4,2,1,1]=>90
[8,7,5,1,6,3,2,4]=>[3,2,1,1,1]=>64
[7,8,6,2,3,5,1,4]=>[3,2,2,1]=>70
[2,8,4,6,7,3,5,1]=>[4,2,1,1]=>90
[4,1,6,7,8,2,5,3]=>[4,3,1]=>70
[8,6,3,4,1,2,7,5]=>[3,3,1,1]=>56
[2,5,8,4,6,1,3,7]=>[4,2,2]=>56
[4,7,8,6,5,1,3,2]=>[3,2,1,1,1]=>64
[6,8,4,7,3,5,2,1]=>[2,2,2,1,1]=>28
[7,4,5,8,3,6,2,1]=>[3,2,1,1,1]=>64
[3,6,4,2,8,1,7,5]=>[3,2,2,1]=>70
[3,8,6,2,1,7,4,5]=>[3,3,1,1]=>56
[3,1,8,2,4,6,5,7]=>[5,2,1]=>64
[8,1,7,6,2,5,4,3]=>[3,1,1,1,1,1]=>21
[8,5,4,3,7,6,1,2]=>[2,2,2,1,1]=>28
[4,8,1,3,6,7,5,2]=>[4,2,1,1]=>90
[3,5,8,6,1,7,4,2]=>[4,2,1,1]=>90
[8,1,4,7,5,2,6,3]=>[4,2,1,1]=>90
[1,4,8,6,7,3,5,2]=>[4,2,1,1]=>90
[4,1,6,7,8,5,3,2]=>[4,2,1,1]=>90
[3,7,8,6,4,1,5,2]=>[3,2,2,1]=>70
[4,6,1,5,7,2,3,8]=>[4,3,1]=>70
[4,8,5,3,2,7,1,6]=>[3,2,1,1,1]=>64
[5,4,8,1,3,7,2,6]=>[3,2,2,1]=>70
[8,4,5,3,1,7,2,6]=>[3,3,1,1]=>56
[7,4,5,3,1,8,6,2]=>[3,2,2,1]=>70
[5,6,8,7,2,4,3,1]=>[3,2,1,1,1]=>64
[5,7,8,6,4,2,3,1]=>[3,2,1,1,1]=>64
[6,8,7,5,1,3,2,4]=>[3,2,1,1,1]=>64
[3,8,2,6,7,5,1,4]=>[3,2,2,1]=>70
[4,7,6,3,8,2,5,1]=>[3,2,1,1,1]=>64
[6,7,4,1,8,2,5,3]=>[3,3,2]=>42
[5,7,6,8,3,2,4,1]=>[3,2,1,1,1]=>64
[7,6,4,2,8,1,5,3]=>[2,2,2,1,1]=>28
[6,3,4,8,7,1,2,5]=>[3,3,2]=>42
[2,7,4,8,1,6,3,5]=>[3,3,2]=>42
[5,3,1,6,7,8,2,4]=>[4,3,1]=>70
[3,4,7,8,6,1,2,5]=>[4,3,1]=>70
[2,1,4,7,8,6,3,5]=>[4,3,1]=>70
[2,4,5,8,1,6,3,7]=>[5,2,1]=>64
[1,8,5,6,4,2,3,7]=>[4,2,1,1]=>90
[1,8,7,6,2,4,5,3]=>[4,1,1,1,1]=>35
[6,4,8,5,7,3,1,2]=>[3,2,2,1]=>70
[1,6,4,7,2,5,8,3]=>[4,2,2]=>56
[2,7,5,1,8,6,3,4]=>[3,3,2]=>42
[4,7,1,6,5,3,8,2]=>[3,2,1,1,1]=>64
[1,7,5,6,4,8,2,3]=>[4,2,1,1]=>90
[7,2,6,4,5,8,1,3]=>[4,2,1,1]=>90
[4,6,7,8,9,1,2,3,5]=>[5,4]=>42
[5,7,8,9,1,2,3,4,6]=>[5,4]=>42
[6,4,5,7,3,8,2,9,1,10]=>[6,1,1,1,1]=>126
[2,7,1,5,3,8,6,4]=>[3,3,2]=>42
[3,5,7,2,8,4,1,6]=>[4,3,1]=>70
[2,4,3,8,5,1,7,6]=>[4,2,2]=>56
[7,3,2,1,4,8,6,5]=>[3,2,2,1]=>70
[2,8,3,4,1,7,6,5]=>[4,2,1,1]=>90
[4,7,6,8,2,5,3,1]=>[3,2,1,1,1]=>64
[2,6,7,1,4,5,8,3]=>[4,3,1]=>70
[8,7,2,6,1,5,3,4]=>[3,2,1,1,1]=>64
[7,1,3,8,2,6,4,5]=>[4,2,2]=>56
[6,2,5,3,4,7,1,8]=>[5,1,1,1]=>35
[2,7,3,4,1,5,8,6]=>[5,2,1]=>64
[2,5,8,1,6,7,3,4]=>[4,3,1]=>70
[6,2,8,3,4,5,1,7]=>[5,2,1]=>64
[3,5,4,1,6,2,8,7]=>[4,3,1]=>70
[4,5,7,2,8,3,1,6]=>[4,3,1]=>70
[3,5,1,7,6,2,8,4]=>[4,3,1]=>70
[3,8,5,1,2,4,6,7]=>[5,2,1]=>64
[8,5,1,2,4,3,6,7]=>[5,1,1,1]=>35
[5,8,4,1,2,3,6,7]=>[5,2,1]=>64
[3,5,8,1,4,2,7,6]=>[3,3,2]=>42
[2,8,5,7,1,4,3,6]=>[3,3,1,1]=>56
[4,8,7,5,1,2,3,6]=>[4,2,1,1]=>90
[8,1,2,4,6,3,7,5]=>[5,2,1]=>64
[7,6,1,4,2,3,8,5]=>[4,2,1,1]=>90
[6,1,2,7,8,4,3,5]=>[4,3,1]=>70
[7,8,1,2,5,3,4,6]=>[5,2,1]=>64
[1,8,4,7,5,2,3,6]=>[4,2,1,1]=>90
[8,4,7,2,1,6,3,5]=>[3,2,2,1]=>70
[4,5,8,2,1,6,7,3]=>[4,2,2]=>56
[4,8,1,5,3,6,7,2]=>[4,2,1,1]=>90
[7,1,5,3,6,8,2,4]=>[4,2,1,1]=>90
[4,5,2,6,1,8,3,7]=>[4,3,1]=>70
[5,1,8,6,7,3,4,2]=>[3,3,1,1]=>56
[5,4,8,2,1,3,6,7]=>[4,2,1,1]=>90
[1,4,8,3,2,6,5,7]=>[4,2,2]=>56
[1,3,8,4,2,7,5,6]=>[5,2,1]=>64
[7,2,8,3,1,4,5,6]=>[5,2,1]=>64
[8,1,3,2,7,5,4,6]=>[4,2,1,1]=>90
[9,8,7,5,6,4,3,2,10,1]=>[3,1,1,1,1,1,1,1]=>36
[8,7,5,4,6,3,2,9,1]=>[3,1,1,1,1,1,1]=>28
[8,7,4,6,5,3,2,9,1]=>[3,1,1,1,1,1,1]=>28
[2,3,4,5,6,1,9,8,7]=>[6,2,1]=>105
[2,3,4,5,1,9,8,7,6]=>[5,2,1,1]=>189
[9,10,2,4,6,8,1,3,5,7]=>[4,4,2]=>252
[7,8,2,4,6,10,1,3,5,9]=>[4,4,2]=>252
[9,7,10,2,4,6,8,1,3,5]=>[4,3,2,1]=>768
[8,9,10,7,2,4,6,1,3,5]=>[3,3,3,1]=>210
[5,6,2,4,8,10,1,3,7,9]=>[4,4,2]=>252
[5,6,9,10,2,4,8,1,3,7]=>[4,3,3]=>210
[7,5,8,2,4,6,10,1,3,9]=>[4,3,2,1]=>768
[7,9,5,10,2,4,6,8,1,3]=>[4,3,2,1]=>768
[5,8,9,10,7,2,4,6,1,3]=>[4,3,2,1]=>768
[6,7,8,5,2,4,10,1,3,9]=>[4,3,2,1]=>768
[9,6,7,5,10,2,4,8,1,3]=>[3,3,2,1,1]=>450
[8,9,6,10,5,7,2,4,1,3]=>[3,2,2,2,1]=>288
[7,8,9,10,6,5,2,4,1,3]=>[4,2,2,1,1]=>567
[3,4,2,6,8,10,1,5,7,9]=>[5,4,1]=>288
[3,4,9,10,2,6,8,1,5,7]=>[4,3,3]=>210
[3,4,7,8,2,6,10,1,5,9]=>[5,3,2]=>450
[9,3,4,7,10,2,6,8,1,5]=>[4,3,2,1]=>768
[8,9,10,3,4,7,2,6,1,5]=>[3,3,2,2]=>252
[5,3,6,2,4,8,10,1,7,9]=>[4,4,1,1]=>300
[5,3,6,9,10,2,4,8,1,7]=>[4,3,2,1]=>768
[5,7,3,8,2,4,6,10,1,9]=>[4,4,1,1]=>300
[5,7,9,3,10,2,4,6,8,1]=>[4,4,1,1]=>300
[8,5,9,10,3,7,2,4,6,1]=>[3,3,2,1,1]=>450
[3,6,7,8,5,2,4,10,1,9]=>[5,3,1,1]=>567
[9,3,6,7,5,10,2,4,8,1]=>[4,3,1,1,1]=>525
[6,8,3,9,10,5,7,2,4,1]=>[4,3,2,1]=>768
[7,8,9,10,3,6,5,2,4,1]=>[4,2,2,1,1]=>567
[4,5,6,3,2,8,10,1,7,9]=>[5,3,1,1]=>567
[4,5,6,3,9,10,2,8,1,7]=>[5,2,2,1]=>525
[7,4,5,3,8,2,6,10,1,9]=>[4,3,1,1,1]=>525
[7,4,5,9,3,10,2,6,8,1]=>[4,3,1,1,1]=>525
[4,8,5,9,10,3,7,2,6,1]=>[4,2,2,1,1]=>567
[6,7,4,8,3,5,2,10,1,9]=>[4,3,1,1,1]=>525
[6,7,9,4,3,5,10,2,8,1]=>[4,3,1,1,1]=>525
[8,6,9,4,10,3,5,7,2,1]=>[3,3,1,1,1,1]=>225
[7,4,8,9,10,6,3,5,2,1]=>[4,2,2,1,1]=>567
[5,6,7,8,4,3,2,10,1,9]=>[5,2,1,1,1]=>448
[9,5,6,7,4,3,10,2,8,1]=>[4,2,1,1,1,1]=>350
[8,9,5,6,4,10,3,7,2,1]=>[3,3,1,1,1,1]=>225
[7,8,9,5,10,4,6,3,2,1]=>[4,2,1,1,1,1]=>350
[11,12,2,4,6,8,10,1,3,5,7,9]=>[5,5,2]=>1320
[9,10,2,4,6,8,12,1,3,5,7,11]=>[5,5,2]=>1320
[11,9,12,2,4,6,8,10,1,3,5,7]=>[5,4,2,1]=>5775
[10,11,12,9,2,4,6,8,1,3,5,7]=>[4,4,3,1]=>2970
[7,8,2,4,6,10,12,1,3,5,9,11]=>[5,5,2]=>1320
[7,8,11,12,2,4,6,10,1,3,5,9]=>[4,4,4]=>462
[9,7,10,2,4,6,8,12,1,3,5,11]=>[5,4,2,1]=>5775
[9,11,7,12,2,4,6,8,10,1,3,5]=>[5,3,3,1]=>4158
[7,10,11,12,9,2,4,6,8,1,3,5]=>[4,4,3,1]=>2970
[8,9,10,7,2,4,6,12,1,3,5,11]=>[4,4,3,1]=>2970
[11,8,9,7,12,2,4,6,10,1,3,5]=>[4,3,3,1,1]=>4158
[10,11,8,12,7,9,2,4,6,1,3,5]=>[3,3,3,2,1]=>2112
[9,10,11,12,8,7,2,4,6,1,3,5]=>[4,3,3,1,1]=>4158
[5,6,2,4,8,10,12,1,3,7,9,11]=>[5,5,2]=>1320
[5,6,11,12,2,4,8,10,1,3,7,9]=>[4,4,4]=>462
[5,6,9,10,2,4,8,12,1,3,7,11]=>[5,4,3]=>2112
[11,5,6,9,12,2,4,8,10,1,3,7]=>[4,4,3,1]=>2970
[10,11,12,5,6,9,2,4,8,1,3,7]=>[3,3,3,3]=>462
[7,5,8,2,4,6,10,12,1,3,9,11]=>[5,4,2,1]=>5775
[7,5,8,11,12,2,4,6,10,1,3,9]=>[4,4,3,1]=>2970
[7,9,5,10,2,4,6,8,12,1,3,11]=>[5,4,2,1]=>5775
[7,9,11,5,12,2,4,6,8,10,1,3]=>[5,4,2,1]=>5775
[10,7,11,12,5,9,2,4,6,8,1,3]=>[4,3,2,2,1]=>5775
[5,8,9,10,7,2,4,6,12,1,3,11]=>[5,4,2,1]=>5775
[11,5,8,9,7,12,2,4,6,10,1,3]=>[4,4,2,1,1]=>4455
[8,10,5,11,12,7,9,2,4,6,1,3]=>[4,3,3,2]=>2970
[9,10,11,12,5,8,7,2,4,6,1,3]=>[4,3,2,2,1]=>5775
[6,7,8,5,2,4,10,12,1,3,9,11]=>[5,4,2,1]=>5775
[6,7,8,5,11,12,2,4,10,1,3,9]=>[5,3,3,1]=>4158
[9,6,7,5,10,2,4,8,12,1,3,11]=>[4,4,2,1,1]=>4455
[9,6,7,11,5,12,2,4,8,10,1,3]=>[4,4,2,1,1]=>4455
[6,10,7,11,12,5,9,2,4,8,1,3]=>[4,3,2,2,1]=>5775
[8,9,6,10,5,7,2,4,12,1,3,11]=>[4,3,2,2,1]=>5775
[8,9,11,6,5,7,12,2,4,10,1,3]=>[4,3,2,2,1]=>5775
[10,8,11,6,12,5,7,9,2,4,1,3]=>[3,3,2,2,1,1]=>2673
[9,6,10,11,12,8,5,7,2,4,1,3]=>[4,2,2,2,2]=>1485
[7,8,9,10,6,5,2,4,12,1,3,11]=>[5,3,2,1,1]=>7700
[11,7,8,9,6,5,12,2,4,10,1,3]=>[4,3,2,1,1,1]=>5632
[10,11,7,8,6,12,5,9,2,4,1,3]=>[3,3,2,2,1,1]=>2673
[9,10,11,7,12,6,8,5,2,4,1,3]=>[4,2,2,2,1,1]=>3080
[8,9,10,11,12,7,6,5,2,4,1,3]=>[5,2,2,1,1,1]=>3696
[3,4,2,6,8,10,12,1,5,7,9,11]=>[6,5,1]=>1155
[3,4,11,12,2,6,8,10,1,5,7,9]=>[5,4,3]=>2112
[3,4,9,10,2,6,8,12,1,5,7,11]=>[5,4,3]=>2112
[11,3,4,9,12,2,6,8,10,1,5,7]=>[5,3,3,1]=>4158
[10,11,12,3,4,9,2,6,8,1,5,7]=>[4,3,3,2]=>2970
[3,4,7,8,2,6,10,12,1,5,9,11]=>[6,4,2]=>2673
[3,4,7,8,11,12,2,6,10,1,5,9]=>[6,3,3]=>1650
[9,3,4,7,10,2,6,8,12,1,5,11]=>[5,4,2,1]=>5775
[9,11,3,4,7,12,2,6,8,10,1,5]=>[5,3,2,2]=>4455
[3,10,11,12,4,7,9,2,6,8,1,5]=>[4,3,3,2]=>2970
[8,9,10,3,4,7,2,6,12,1,5,11]=>[4,4,2,2]=>2640
[11,8,9,3,4,7,12,2,6,10,1,5]=>[4,3,2,2,1]=>5775
[10,11,8,12,3,4,7,9,2,6,1,5]=>[4,3,2,2,1]=>5775
[9,10,11,12,8,3,4,7,2,6,1,5]=>[4,3,2,2,1]=>5775
[5,3,6,2,4,8,10,12,1,7,9,11]=>[5,5,1,1]=>1485
[5,3,6,11,12,2,4,8,10,1,7,9]=>[4,4,3,1]=>2970
[5,3,6,9,10,2,4,8,12,1,7,11]=>[5,4,2,1]=>5775
[5,11,3,6,9,12,2,4,8,10,1,7]=>[4,4,2,2]=>2640
[5,10,11,12,3,6,9,2,4,8,1,7]=>[4,3,3,2]=>2970
[5,7,3,8,2,4,6,10,12,1,9,11]=>[5,5,1,1]=>1485
[5,7,3,8,11,12,2,4,6,10,1,9]=>[5,4,2,1]=>5775
[5,7,9,3,10,2,4,6,8,12,1,11]=>[5,5,1,1]=>1485
[5,7,9,11,3,12,2,4,6,8,10,1]=>[5,5,1,1]=>1485
[10,5,7,11,12,3,9,2,4,6,8,1]=>[4,4,2,1,1]=>4455
[8,5,9,10,3,7,2,4,6,12,1,11]=>[4,4,2,1,1]=>4455
[8,11,5,9,3,7,12,2,4,6,10,1]=>[4,3,2,2,1]=>5775
[8,10,11,5,12,3,7,9,2,4,6,1]=>[4,3,3,1,1]=>4158
[5,9,10,11,12,8,3,7,2,4,6,1]=>[5,3,2,1,1]=>7700
[3,6,7,8,5,2,4,10,12,1,9,11]=>[6,4,1,1]=>3080
[3,6,7,8,5,11,12,2,4,10,1,9]=>[6,3,2,1]=>5632
[9,3,6,7,5,10,2,4,8,12,1,11]=>[5,4,1,1,1]=>3520
[9,3,6,7,11,5,12,2,4,8,10,1]=>[5,4,1,1,1]=>3520
[6,10,3,7,11,12,5,9,2,4,8,1]=>[4,3,3,1,1]=>4158
[6,8,3,9,10,5,7,2,4,12,1,11]=>[5,4,2,1]=>5775
[6,8,9,3,11,5,7,12,2,4,10,1]=>[5,4,2,1]=>5775
[10,6,8,3,11,12,5,7,9,2,4,1]=>[4,4,2,1,1]=>4455
[9,6,10,11,12,3,8,5,7,2,4,1]=>[4,3,2,2,1]=>5775
[7,8,9,10,3,6,5,2,4,12,1,11]=>[5,3,2,1,1]=>7700
[11,7,8,9,3,6,5,12,2,4,10,1]=>[4,3,2,1,1,1]=>5632
[10,11,7,8,3,6,12,5,9,2,4,1]=>[3,3,2,2,1,1]=>2673
[9,10,11,7,12,3,6,8,5,2,4,1]=>[4,3,2,1,1,1]=>5632
[8,9,10,11,12,7,3,6,5,2,4,1]=>[5,2,2,1,1,1]=>3696
[4,5,6,3,2,8,10,12,1,7,9,11]=>[6,4,1,1]=>3080
[4,5,6,3,11,12,2,8,10,1,7,9]=>[5,3,3,1]=>4158
[4,5,6,3,9,10,2,8,12,1,7,11]=>[6,3,2,1]=>5632
[4,5,6,11,3,9,12,2,8,10,1,7]=>[5,3,2,2]=>4455
[4,5,6,10,11,12,3,9,2,8,1,7]=>[6,2,2,2]=>1925
[7,4,5,3,8,2,6,10,12,1,9,11]=>[5,4,1,1,1]=>3520
[7,4,5,3,8,11,12,2,6,10,1,9]=>[5,3,2,1,1]=>7700
[7,4,5,9,3,10,2,6,8,12,1,11]=>[5,4,1,1,1]=>3520
[7,4,5,9,11,3,12,2,6,8,10,1]=>[5,4,1,1,1]=>3520
[7,10,4,5,11,12,3,9,2,6,8,1]=>[4,4,2,1,1]=>4455
[4,8,5,9,10,3,7,2,6,12,1,11]=>[5,3,2,1,1]=>7700
[4,8,11,5,9,3,7,12,2,6,10,1]=>[4,3,2,2,1]=>5775
[4,8,10,11,5,12,3,7,9,2,6,1]=>[5,3,2,1,1]=>7700
[4,5,9,10,11,12,8,3,7,2,6,1]=>[6,2,2,1,1]=>3564
[6,7,4,8,3,5,2,10,12,1,9,11]=>[5,4,1,1,1]=>3520
[6,7,4,8,3,5,11,12,2,10,1,9]=>[5,3,2,1,1]=>7700
[6,7,9,4,3,5,10,2,8,12,1,11]=>[5,4,1,1,1]=>3520
[6,7,9,4,11,3,5,12,2,8,10,1]=>[5,4,1,1,1]=>3520
[10,6,7,4,11,12,3,5,9,2,8,1]=>[4,3,2,1,1,1]=>5632
[8,6,9,4,10,3,5,7,2,12,1,11]=>[4,4,1,1,1,1]=>1925
[8,6,9,11,4,3,5,7,12,2,10,1]=>[4,4,1,1,1,1]=>1925
[8,10,6,11,4,12,3,5,7,9,2,1]=>[4,4,1,1,1,1]=>1925
[6,9,4,10,11,12,8,3,5,7,2,1]=>[5,3,2,1,1]=>7700
[7,4,8,9,10,6,3,5,2,12,1,11]=>[5,3,2,1,1]=>7700
[7,11,4,8,9,6,3,5,12,2,10,1]=>[4,3,2,1,1,1]=>5632
[7,8,10,4,11,6,12,3,5,9,2,1]=>[5,3,2,1,1]=>7700
[9,7,10,4,11,12,6,8,3,5,2,1]=>[4,3,2,1,1,1]=>5632
[4,8,9,10,11,12,7,6,3,5,2,1]=>[6,2,1,1,1,1]=>2100
[5,6,7,8,4,3,2,10,12,1,9,11]=>[6,3,1,1,1]=>3696
[5,6,7,8,4,3,11,12,2,10,1,9]=>[6,2,2,1,1]=>3564
[9,5,6,7,4,3,10,2,8,12,1,11]=>[5,3,1,1,1,1]=>3564
[9,5,6,7,4,11,3,12,2,8,10,1]=>[5,3,1,1,1,1]=>3564
[5,10,6,7,4,11,12,3,9,2,8,1]=>[5,2,2,1,1,1]=>3696
[8,9,5,6,4,10,3,7,2,12,1,11]=>[4,4,1,1,1,1]=>1925
[8,9,5,6,11,4,3,7,12,2,10,1]=>[4,4,1,1,1,1]=>1925
[10,8,5,6,11,4,12,3,7,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[9,5,10,6,11,12,4,8,3,7,2,1]=>[4,3,2,1,1,1]=>5632
[7,8,9,5,10,4,6,3,2,12,1,11]=>[5,3,1,1,1,1]=>3564
[7,8,9,11,5,4,6,3,12,2,10,1]=>[5,3,1,1,1,1]=>3564
[10,7,8,11,5,4,6,12,3,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[9,10,7,11,5,12,4,6,8,3,2,1]=>[4,3,1,1,1,1,1]=>2079
[8,9,5,10,11,12,7,4,6,3,2,1]=>[5,2,2,1,1,1]=>3696
[6,7,8,9,10,5,4,3,2,12,1,11]=>[6,2,1,1,1,1]=>2100
[11,6,7,8,9,5,4,3,12,2,10,1]=>[5,2,1,1,1,1,1]=>1728
[10,11,6,7,8,5,4,12,3,9,2,1]=>[4,3,1,1,1,1,1]=>2079
[9,10,11,6,7,5,12,4,8,3,2,1]=>[4,3,1,1,1,1,1]=>2079
[8,9,10,11,6,12,5,7,4,3,2,1]=>[5,2,1,1,1,1,1]=>1728
[7,6,1,8,2,5,4,3]=>[3,2,1,1,1]=>64
[8,4,1,6,7,3,5,2]=>[3,3,1,1]=>56
[5,4,2,8,1,6,3,7]=>[3,2,2,1]=>70
[8,7,2,6,4,5,3,1]=>[3,1,1,1,1,1]=>21
[7,2,8,4,3,6,1,5]=>[3,2,2,1]=>70
[1,7,5,4,8,6,2,3]=>[3,2,2,1]=>70
[4,8,6,3,5,2,1,7]=>[3,2,1,1,1]=>64
[5,7,3,2,8,6,4,1]=>[3,2,2,1]=>70
[4,5,1,6,8,2,7,3]=>[4,3,1]=>70
[1,2,4,5,6,8,10,9,3,7]=>[7,2,1]=>160
[1,2,3,5,7,8,10,6,9,4]=>[7,2,1]=>160
[1,2,4,5,7,8,10,3,9,6]=>[7,2,1]=>160
[1,2,4,6,7,5,10,8,3,9]=>[7,2,1]=>160
[1,3,4,2,7,8,10,5,9,6]=>[6,3,1]=>315
[1,3,4,6,7,2,10,8,5,9]=>[7,2,1]=>160
[1,2,3,5,6,9,8,10,7,4]=>[7,1,1,1]=>84
[1,2,4,5,6,9,8,10,3,7]=>[7,2,1]=>160
[1,2,3,5,7,9,6,10,8,4]=>[7,2,1]=>160
[1,2,4,5,7,9,3,10,8,6]=>[7,2,1]=>160
[1,2,4,6,5,9,7,10,3,8]=>[6,3,1]=>315
[1,3,4,2,7,9,5,10,8,6]=>[6,3,1]=>315
[1,3,4,6,2,9,7,10,5,8]=>[6,3,1]=>315
[1,2,3,5,8,7,9,6,10,4]=>[7,1,1,1]=>84
[1,2,4,5,8,7,9,3,10,6]=>[7,2,1]=>160
[1,2,4,6,8,5,9,3,10,7]=>[7,2,1]=>160
[1,2,4,7,6,8,5,9,3,10]=>[7,1,1,1]=>84
[1,3,4,2,8,7,9,5,10,6]=>[6,3,1]=>315
[1,3,4,6,8,2,9,5,10,7]=>[7,3]=>75
[1,3,4,7,6,8,2,9,5,10]=>[7,2,1]=>160
[1,2,3,6,5,9,7,10,8,4]=>[6,3,1]=>315
[1,2,4,6,3,9,7,10,8,5]=>[6,3,1]=>315
[1,2,5,4,6,9,7,10,3,8]=>[6,3,1]=>315
[1,3,2,6,4,9,7,10,8,5]=>[5,4,1]=>288
[1,3,5,2,6,9,7,10,4,8]=>[6,3,1]=>315
[1,2,3,6,8,5,9,7,10,4]=>[7,2,1]=>160
[1,2,4,6,8,3,9,7,10,5]=>[7,2,1]=>160
[1,2,5,4,8,6,9,3,10,7]=>[6,3,1]=>315
[1,2,5,7,4,8,6,9,3,10]=>[7,2,1]=>160
[1,3,2,6,8,4,9,7,10,5]=>[6,3,1]=>315
[1,3,5,2,8,6,9,4,10,7]=>[6,3,1]=>315
[1,3,5,7,2,8,6,9,4,10]=>[7,2,1]=>160
[1,4,3,5,8,2,9,6,10,7]=>[6,3,1]=>315
[1,4,3,7,5,8,2,9,6,10]=>[6,3,1]=>315
[2,1,3,6,4,9,7,10,8,5]=>[5,4,1]=>288
[2,1,5,3,6,9,7,10,4,8]=>[5,4,1]=>288
[2,1,3,6,8,4,9,7,10,5]=>[6,3,1]=>315
[2,1,5,3,8,6,9,4,10,7]=>[5,4,1]=>288
[2,1,5,7,3,8,6,9,4,10]=>[6,3,1]=>315
[2,4,1,5,8,3,9,6,10,7]=>[6,4]=>90
[2,4,1,7,5,8,3,9,6,10]=>[6,3,1]=>315
[1,6,3,7,2,4,8,5]=>[4,3,1]=>70
[8,9,7,6,5,4,3,1,2]=>[2,2,1,1,1,1,1]=>27
[8,6,7,5,4,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[8,7,9,6,5,4,3,1,2]=>[2,2,1,1,1,1,1]=>27
[9,7,8,6,5,4,3,1,2]=>[2,2,1,1,1,1,1]=>27
[4,3,1,6,7,2,5,8]=>[4,3,1]=>70
[5,2,1,4,8,6,7,3]=>[4,2,2]=>56
[4,5,2,1,3,7,6,8]=>[4,3,1]=>70
[8,2,7,4,1,6,5,3]=>[3,2,1,1,1]=>64
[3,2,8,4,1,6,5,7]=>[4,2,2]=>56
[7,1,8,4,2,3,6,5]=>[4,2,2]=>56
[3,6,8,1,5,7,4,2]=>[3,3,1,1]=>56
[2,8,3,1,6,7,4,5]=>[4,3,1]=>70
[4,5,6,8,2,1,7,3]=>[4,2,2]=>56
[4,5,6,8,1,3,7,2]=>[4,3,1]=>70
[4,5,8,3,2,1,7,6]=>[3,2,2,1]=>70
[4,5,1,3,2,6,7,8]=>[5,2,1]=>64
[4,7,3,2,1,6,5,8]=>[3,2,2,1]=>70
[4,7,8,3,5,1,6,2]=>[3,3,2]=>42
[4,7,1,3,5,6,2,8]=>[5,2,1]=>64
[4,8,3,2,1,6,7,5]=>[3,2,2,1]=>70
[5,2,8,1,4,6,7,3]=>[4,2,2]=>56
[5,6,3,7,8,1,4,2]=>[4,2,2]=>56
[5,7,1,4,3,6,2,8]=>[4,2,1,1]=>90
[6,2,3,7,1,5,4,8]=>[4,2,2]=>56
[6,2,8,1,5,4,7,3]=>[3,2,2,1]=>70
[6,1,3,4,5,2,7,8]=>[6,1,1]=>21
[7,1,3,4,5,6,2,8]=>[6,1,1]=>21
[7,2,5,1,3,6,4,8]=>[4,3,1]=>70
[6,5,2,7,8,4,3,1]=>[3,2,1,1,1]=>64
[7,5,3,6,4,2,1,8]=>[3,2,1,1,1]=>64
[1,3,6,7,5,2,4,8]=>[5,2,1]=>64
[1,5,2,6,8,7,3,4]=>[4,3,1]=>70
[3,2,1,5,6,7,8,9,4]=>[6,2,1]=>105
[3,2,6,1,4,7,8,9,5]=>[5,3,1]=>162
[4,3,2,1,6,7,8,9,5]=>[5,2,1,1]=>189
[3,2,7,8,1,4,5,9,6]=>[4,4,1]=>84
[4,7,2,5,1,3,8,9,6]=>[4,3,2]=>168
[4,3,2,7,1,5,8,9,6]=>[4,3,1,1]=>216
[5,4,3,2,1,7,8,9,6]=>[4,2,1,1,1]=>189
[4,3,2,8,9,1,5,6,7]=>[4,3,1,1]=>216
[8,5,6,3,4,1,2,9,7]=>[3,3,2,1]=>168
[5,3,8,2,6,1,4,9,7]=>[3,3,2,1]=>168
[5,4,3,2,8,1,6,9,7]=>[3,3,1,1,1]=>120
[6,5,4,3,2,1,8,9,7]=>[3,2,1,1,1,1]=>105
[6,9,4,7,2,5,1,3,8]=>[3,2,2,2]=>84
[6,4,3,9,2,7,1,5,8]=>[3,2,2,1,1]=>162
[6,5,4,3,2,9,1,7,8]=>[3,2,1,1,1,1]=>105
[5,6,1,2,3,7,8,9,10,4]=>[7,3]=>75
[2,5,1,3,6,7,8,9,10,4]=>[7,3]=>75
[3,2,1,5,6,7,8,9,10,4]=>[7,2,1]=>160
[6,7,8,1,2,3,4,9,10,5]=>[6,4]=>90
[2,6,7,1,3,4,8,9,10,5]=>[6,4]=>90
[6,3,4,1,2,7,8,9,10,5]=>[6,3,1]=>315
[3,2,6,1,4,7,8,9,10,5]=>[6,3,1]=>315
[4,3,2,1,6,7,8,9,10,5]=>[6,2,1,1]=>350
[2,7,8,9,1,3,4,5,10,6]=>[5,5]=>42
[7,3,4,8,1,2,5,9,10,6]=>[5,4,1]=>288
[3,2,7,8,1,4,5,9,10,6]=>[5,4,1]=>288
[4,7,2,5,1,3,8,9,10,6]=>[5,3,2]=>450
[4,3,2,7,1,5,8,9,10,6]=>[5,3,1,1]=>567
[5,4,3,2,1,7,8,9,10,6]=>[5,2,1,1,1]=>448
[8,3,4,9,10,1,2,5,6,7]=>[5,4,1]=>288
[8,9,4,5,6,1,2,3,10,7]=>[4,4,2]=>252
[4,3,2,8,9,1,5,6,10,7]=>[4,4,1,1]=>300
[8,5,6,3,4,1,2,9,10,7]=>[4,3,2,1]=>768
[5,3,8,2,6,1,4,9,10,7]=>[4,3,2,1]=>768
[5,4,3,2,8,1,6,9,10,7]=>[4,3,1,1,1]=>525
[6,5,4,3,2,1,8,9,10,7]=>[4,2,1,1,1,1]=>350
[5,9,10,2,6,7,1,3,4,8]=>[4,3,3]=>210
[9,5,6,3,4,10,1,2,7,8]=>[4,3,2,1]=>768
[5,3,9,2,6,10,1,4,7,8]=>[4,3,2,1]=>768
[5,4,3,2,9,10,1,6,7,8]=>[4,3,1,1,1]=>525
[6,9,4,7,2,5,1,3,10,8]=>[3,3,2,2]=>252
[6,4,3,9,2,7,1,5,10,8]=>[3,3,2,1,1]=>450
[6,5,4,3,2,9,1,7,10,8]=>[3,3,1,1,1,1]=>225
[7,6,5,4,3,2,1,9,10,8]=>[3,2,1,1,1,1,1]=>160
[10,7,8,5,6,3,4,1,2,9]=>[3,2,2,2,1]=>288
[7,5,10,3,8,2,6,1,4,9]=>[3,2,2,2,1]=>288
[7,5,4,3,10,2,8,1,6,9]=>[3,2,2,1,1,1]=>315
[7,6,5,4,3,2,10,1,8,9]=>[3,2,1,1,1,1,1]=>160
[4,2,3,7,6,1,8,5]=>[4,2,2]=>56
[4,2,6,3,1,5,7,8]=>[5,2,1]=>64
[2,1,8,7,4,3,6,5,10,9]=>[4,4,1,1]=>300
[6,5,2,1,4,3,12,11,8,7,10,9]=>[4,4,2,2]=>2640
[4,6,3,2,5,8,7,1]=>[3,3,1,1]=>56
[5,8,4,3,2,6,1,7]=>[3,2,1,1,1]=>64
[6,1,5,7,3,8,2,4]=>[4,2,1,1]=>90
[1,2,7,8,6,4,3,5]=>[4,2,1,1]=>90
[3,5,1,7,8,6,2,4]=>[4,3,1]=>70
[5,2,4,1,7,6,8,3]=>[4,2,2]=>56
[2,1,4,3,6,5,7,9,10,8]=>[6,4]=>90
[2,1,4,3,5,7,8,6,10,9]=>[6,4]=>90
[2,1,4,3,5,7,6,9,10,8]=>[6,4]=>90
[2,1,4,3,5,6,8,9,10,7]=>[7,3]=>75
[2,1,3,5,6,4,8,7,10,9]=>[6,4]=>90
[2,1,3,5,6,4,7,9,10,8]=>[7,3]=>75
[2,1,3,5,4,7,8,6,10,9]=>[6,4]=>90
[2,1,3,5,4,7,6,9,10,8]=>[6,4]=>90
[2,1,3,5,4,6,8,9,10,7]=>[7,3]=>75
[2,1,3,4,6,7,8,5,10,9]=>[7,3]=>75
[2,1,3,4,6,7,5,9,10,8]=>[7,3]=>75
[2,1,3,4,6,5,8,9,10,7]=>[7,3]=>75
[2,1,3,4,5,7,8,9,10,6]=>[8,2]=>35
[1,3,4,2,6,5,7,9,10,8]=>[7,3]=>75
[1,3,4,2,5,7,8,6,10,9]=>[7,3]=>75
[1,3,4,2,5,7,6,9,10,8]=>[7,3]=>75
[1,3,4,2,5,6,8,9,10,7]=>[8,2]=>35
[1,3,2,5,6,4,8,7,10,9]=>[6,4]=>90
[1,3,2,5,6,4,7,9,10,8]=>[7,3]=>75
[1,3,2,5,4,7,8,6,10,9]=>[6,4]=>90
[1,3,2,5,4,7,6,9,10,8]=>[6,4]=>90
[1,3,2,5,4,6,8,9,10,7]=>[7,3]=>75
[1,3,2,4,6,7,8,5,10,9]=>[7,3]=>75
[1,3,2,4,6,7,5,9,10,8]=>[7,3]=>75
[1,3,2,4,6,5,8,9,10,7]=>[7,3]=>75
[1,3,2,4,5,7,8,9,10,6]=>[8,2]=>35
[1,2,4,5,6,3,8,7,10,9]=>[7,3]=>75
[1,2,4,5,6,3,7,9,10,8]=>[8,2]=>35
[1,2,4,5,3,7,8,6,10,9]=>[7,3]=>75
[1,2,4,5,3,7,6,9,10,8]=>[7,3]=>75
[1,2,4,5,3,6,8,9,10,7]=>[8,2]=>35
[1,2,4,3,6,7,8,5,10,9]=>[7,3]=>75
[1,2,4,3,6,7,5,9,10,8]=>[7,3]=>75
[1,2,4,3,6,5,8,9,10,7]=>[7,3]=>75
[1,2,4,3,5,7,8,9,10,6]=>[8,2]=>35
[1,2,3,5,6,7,8,4,10,9]=>[8,2]=>35
[1,2,3,5,6,7,4,9,10,8]=>[8,2]=>35
[1,2,3,5,6,4,8,9,10,7]=>[8,2]=>35
[1,2,3,5,4,7,8,9,10,6]=>[8,2]=>35
[2,1,4,3,6,5,8,7,9,11,12,10]=>[7,5]=>297
[2,1,4,3,6,5,7,9,10,8,12,11]=>[7,5]=>297
[2,1,4,3,6,5,7,9,8,11,12,10]=>[7,5]=>297
[2,1,4,3,6,5,7,8,10,11,12,9]=>[8,4]=>275
[2,1,4,3,5,7,8,6,10,9,12,11]=>[7,5]=>297
[2,1,4,3,5,7,8,6,9,11,12,10]=>[8,4]=>275
[2,1,4,3,5,7,6,9,10,8,12,11]=>[7,5]=>297
[2,1,4,3,5,7,6,9,8,11,12,10]=>[7,5]=>297
[2,1,4,3,5,7,6,8,10,11,12,9]=>[8,4]=>275
[2,1,4,3,5,6,8,9,10,7,12,11]=>[8,4]=>275
[2,1,4,3,5,6,8,9,7,11,12,10]=>[8,4]=>275
[2,1,4,3,5,6,8,7,10,11,12,9]=>[8,4]=>275
[2,1,4,3,5,6,7,9,10,11,12,8]=>[9,3]=>154
[2,1,3,5,6,4,8,7,10,9,12,11]=>[7,5]=>297
[2,1,3,5,6,4,8,7,9,11,12,10]=>[8,4]=>275
[2,1,3,5,6,4,7,9,10,8,12,11]=>[8,4]=>275
[2,1,3,5,6,4,7,9,8,11,12,10]=>[8,4]=>275
[2,1,3,5,6,4,7,8,10,11,12,9]=>[9,3]=>154
[2,1,3,5,4,7,8,6,10,9,12,11]=>[7,5]=>297
[2,1,3,5,4,7,8,6,9,11,12,10]=>[8,4]=>275
[2,1,3,5,4,7,6,9,10,8,12,11]=>[7,5]=>297
[2,1,3,5,4,7,6,9,8,11,12,10]=>[7,5]=>297
[2,1,3,5,4,7,6,8,10,11,12,9]=>[8,4]=>275
[2,1,3,5,4,6,8,9,10,7,12,11]=>[8,4]=>275
[2,1,3,5,4,6,8,9,7,11,12,10]=>[8,4]=>275
[2,1,3,5,4,6,8,7,10,11,12,9]=>[8,4]=>275
[2,1,3,5,4,6,7,9,10,11,12,8]=>[9,3]=>154
[2,1,3,4,6,7,8,5,10,9,12,11]=>[8,4]=>275
[2,1,3,4,6,7,8,5,9,11,12,10]=>[9,3]=>154
[2,1,3,4,6,7,5,9,10,8,12,11]=>[8,4]=>275
[2,1,3,4,6,7,5,9,8,11,12,10]=>[8,4]=>275
[2,1,3,4,6,7,5,8,10,11,12,9]=>[9,3]=>154
[2,1,3,4,6,5,8,9,10,7,12,11]=>[8,4]=>275
[2,1,3,4,6,5,8,9,7,11,12,10]=>[8,4]=>275
[2,1,3,4,6,5,8,7,10,11,12,9]=>[8,4]=>275
[2,1,3,4,6,5,7,9,10,11,12,8]=>[9,3]=>154
[2,1,3,4,5,7,8,9,10,6,12,11]=>[9,3]=>154
[2,1,3,4,5,7,8,9,6,11,12,10]=>[9,3]=>154
[2,1,3,4,5,7,8,6,10,11,12,9]=>[9,3]=>154
[2,1,3,4,5,7,6,9,10,11,12,8]=>[9,3]=>154
[2,1,3,4,5,6,8,9,10,11,12,7]=>[10,2]=>54
[1,3,4,2,6,5,8,7,10,9,12,11]=>[7,5]=>297
[1,3,4,2,6,5,8,7,9,11,12,10]=>[8,4]=>275
[1,3,4,2,6,5,7,9,10,8,12,11]=>[8,4]=>275
[1,3,4,2,6,5,7,9,8,11,12,10]=>[8,4]=>275
[1,3,4,2,6,5,7,8,10,11,12,9]=>[9,3]=>154
[1,3,4,2,5,7,8,6,10,9,12,11]=>[8,4]=>275
[1,3,4,2,5,7,8,6,9,11,12,10]=>[9,3]=>154
[1,3,4,2,5,7,6,9,10,8,12,11]=>[8,4]=>275
[1,3,4,2,5,7,6,9,8,11,12,10]=>[8,4]=>275
[1,3,4,2,5,7,6,8,10,11,12,9]=>[9,3]=>154
[1,3,4,2,5,6,8,9,10,7,12,11]=>[9,3]=>154
[1,3,4,2,5,6,8,9,7,11,12,10]=>[9,3]=>154
[1,3,4,2,5,6,8,7,10,11,12,9]=>[9,3]=>154
[1,3,4,2,5,6,7,9,10,11,12,8]=>[10,2]=>54
[1,3,2,5,6,4,8,7,10,9,12,11]=>[7,5]=>297
[1,3,2,5,6,4,8,7,9,11,12,10]=>[8,4]=>275
[1,3,2,5,6,4,7,9,10,8,12,11]=>[8,4]=>275
[1,3,2,5,6,4,7,9,8,11,12,10]=>[8,4]=>275
[1,3,2,5,6,4,7,8,10,11,12,9]=>[9,3]=>154
[1,3,2,5,4,7,8,6,10,9,12,11]=>[7,5]=>297
[1,3,2,5,4,7,8,6,9,11,12,10]=>[8,4]=>275
[1,3,2,5,4,7,6,9,10,8,12,11]=>[7,5]=>297
[1,3,2,5,4,7,6,9,8,11,12,10]=>[7,5]=>297
[1,3,2,5,4,7,6,8,10,11,12,9]=>[8,4]=>275
[1,3,2,5,4,6,8,9,10,7,12,11]=>[8,4]=>275
[1,3,2,5,4,6,8,9,7,11,12,10]=>[8,4]=>275
[1,3,2,5,4,6,8,7,10,11,12,9]=>[8,4]=>275
[1,3,2,5,4,6,7,9,10,11,12,8]=>[9,3]=>154
[1,3,2,4,6,7,8,5,10,9,12,11]=>[8,4]=>275
[1,3,2,4,6,7,8,5,9,11,12,10]=>[9,3]=>154
[1,3,2,4,6,7,5,9,10,8,12,11]=>[8,4]=>275
[1,3,2,4,6,7,5,9,8,11,12,10]=>[8,4]=>275
[1,3,2,4,6,7,5,8,10,11,12,9]=>[9,3]=>154
[1,3,2,4,6,5,8,9,10,7,12,11]=>[8,4]=>275
[1,3,2,4,6,5,8,9,7,11,12,10]=>[8,4]=>275
[1,3,2,4,6,5,8,7,10,11,12,9]=>[8,4]=>275
[1,3,2,4,6,5,7,9,10,11,12,8]=>[9,3]=>154
[1,3,2,4,5,7,8,9,10,6,12,11]=>[9,3]=>154
[1,3,2,4,5,7,8,9,6,11,12,10]=>[9,3]=>154
[1,3,2,4,5,7,8,6,10,11,12,9]=>[9,3]=>154
[1,3,2,4,5,7,6,9,10,11,12,8]=>[9,3]=>154
[1,3,2,4,5,6,8,9,10,11,12,7]=>[10,2]=>54
[1,2,4,5,6,3,8,7,10,9,12,11]=>[8,4]=>275
[1,2,4,5,6,3,8,7,9,11,12,10]=>[9,3]=>154
[1,2,4,5,6,3,7,9,10,8,12,11]=>[9,3]=>154
[1,2,4,5,6,3,7,9,8,11,12,10]=>[9,3]=>154
[1,2,4,5,6,3,7,8,10,11,12,9]=>[10,2]=>54
[1,2,4,5,3,7,8,6,10,9,12,11]=>[8,4]=>275
[1,2,4,5,3,7,8,6,9,11,12,10]=>[9,3]=>154
[1,2,4,5,3,7,6,9,10,8,12,11]=>[8,4]=>275
[1,2,4,5,3,7,6,9,8,11,12,10]=>[8,4]=>275
[1,2,4,5,3,7,6,8,10,11,12,9]=>[9,3]=>154
[1,2,4,5,3,6,8,9,10,7,12,11]=>[9,3]=>154
[1,2,4,5,3,6,8,9,7,11,12,10]=>[9,3]=>154
[1,2,4,5,3,6,8,7,10,11,12,9]=>[9,3]=>154
[1,2,4,5,3,6,7,9,10,11,12,8]=>[10,2]=>54
[1,2,4,3,6,7,8,5,10,9,12,11]=>[8,4]=>275
[1,2,4,3,6,7,8,5,9,11,12,10]=>[9,3]=>154
[1,2,4,3,6,7,5,9,10,8,12,11]=>[8,4]=>275
[1,2,4,3,6,7,5,9,8,11,12,10]=>[8,4]=>275
[1,2,4,3,6,7,5,8,10,11,12,9]=>[9,3]=>154
[1,2,4,3,6,5,8,9,10,7,12,11]=>[8,4]=>275
[1,2,4,3,6,5,8,9,7,11,12,10]=>[8,4]=>275
[1,2,4,3,6,5,8,7,10,11,12,9]=>[8,4]=>275
[1,2,4,3,6,5,7,9,10,11,12,8]=>[9,3]=>154
[1,2,4,3,5,7,8,9,10,6,12,11]=>[9,3]=>154
[1,2,4,3,5,7,8,9,6,11,12,10]=>[9,3]=>154
[1,2,4,3,5,7,8,6,10,11,12,9]=>[9,3]=>154
[1,2,4,3,5,7,6,9,10,11,12,8]=>[9,3]=>154
[1,2,4,3,5,6,8,9,10,11,12,7]=>[10,2]=>54
[1,2,3,5,6,7,8,4,10,9,12,11]=>[9,3]=>154
[1,2,3,5,6,7,8,4,9,11,12,10]=>[10,2]=>54
[1,2,3,5,6,7,4,9,10,8,12,11]=>[9,3]=>154
[1,2,3,5,6,7,4,9,8,11,12,10]=>[9,3]=>154
[1,2,3,5,6,7,4,8,10,11,12,9]=>[10,2]=>54
[1,2,3,5,6,4,8,9,10,7,12,11]=>[9,3]=>154
[1,2,3,5,6,4,8,9,7,11,12,10]=>[9,3]=>154
[1,2,3,5,6,4,8,7,10,11,12,9]=>[9,3]=>154
[1,2,3,5,6,4,7,9,10,11,12,8]=>[10,2]=>54
[1,2,3,5,4,7,8,9,10,6,12,11]=>[9,3]=>154
[1,2,3,5,4,7,8,9,6,11,12,10]=>[9,3]=>154
[1,2,3,5,4,7,8,6,10,11,12,9]=>[9,3]=>154
[1,2,3,5,4,7,6,9,10,11,12,8]=>[9,3]=>154
[1,2,3,5,4,6,8,9,10,11,12,7]=>[10,2]=>54
[1,2,3,4,6,7,8,9,10,5,12,11]=>[10,2]=>54
[1,2,3,4,6,7,8,9,5,11,12,10]=>[10,2]=>54
[1,2,3,4,6,7,8,5,10,11,12,9]=>[10,2]=>54
[1,2,3,4,6,7,5,9,10,11,12,8]=>[10,2]=>54
[1,2,3,4,6,5,8,9,10,11,12,7]=>[10,2]=>54
[1,2,3,4,5,7,8,9,10,11,12,6]=>[11,1]=>11
[2,3,4,9,6,7,8,5,1]=>[6,1,1,1]=>56
[2,3,9,5,6,7,8,4,1]=>[6,1,1,1]=>56
[2,9,4,5,6,7,8,3,1]=>[6,1,1,1]=>56
[9,3,4,5,6,7,8,2,1]=>[6,1,1,1]=>56
[2,3,4,5,6,10,8,9,7,1]=>[7,1,1,1]=>84
[2,3,4,1,9,7,8,6,5]=>[5,2,1,1]=>189
[2,3,4,5,10,7,8,9,6,1]=>[7,1,1,1]=>84
[2,3,1,9,6,7,8,5,4]=>[5,2,1,1]=>189
[2,3,4,10,6,7,8,9,5,1]=>[7,1,1,1]=>84
[2,1,9,5,6,7,8,4,3]=>[5,2,1,1]=>189
[2,3,10,5,6,7,8,9,4,1]=>[7,1,1,1]=>84
[1,9,4,5,6,7,8,3,2]=>[6,1,1,1]=>56
[2,10,4,5,6,7,8,9,3,1]=>[7,1,1,1]=>84
[10,3,4,5,6,7,8,9,2,1]=>[7,1,1,1]=>84
[5,6,4,7,3,9,1,8,2]=>[4,2,2,1]=>216
[5,6,4,9,1,8,2,7,3]=>[3,3,2,1]=>168
[5,9,1,8,2,7,3,6,4]=>[4,2,1,1,1]=>189
[9,1,8,2,7,3,6,4,5]=>[5,1,1,1,1]=>70
[5,4,3,8,1,7,2,6]=>[3,2,2,1]=>70
[5,4,9,1,8,2,7,3,6]=>[4,2,2,1]=>216
[5,4,6,3,9,1,8,2,7]=>[3,3,2,1]=>168
[5,4,6,3,7,2,9,1,8]=>[4,2,1,1,1]=>189
[6,5,7,4,8,3,10,1,9,2]=>[4,2,2,1,1]=>567
[5,6,4,8,2,9,1,7,3]=>[4,2,2,1]=>216
[6,5,7,4,10,1,9,2,8,3]=>[3,3,2,2]=>252
[5,7,3,9,1,8,2,6,4]=>[3,3,2,1]=>168
[6,5,10,1,9,2,8,3,7,4]=>[4,2,2,1,1]=>567
[6,4,9,1,8,2,7,3,5]=>[4,2,2,1]=>216
[4,5,9,1,8,2,7,3,6]=>[4,3,1,1]=>216
[5,10,1,9,2,8,3,7,4,6]=>[5,2,1,1,1]=>448
[6,4,5,3,9,1,8,2,7]=>[3,3,2,1]=>168
[5,6,4,10,1,9,2,8,3,7]=>[4,3,2,1]=>768
[5,4,7,3,6,2,9,1,8]=>[3,3,1,1,1]=>120
[5,6,4,7,3,10,1,9,2,8]=>[4,3,2,1]=>768
[5,6,4,7,3,8,2,10,1,9]=>[5,2,1,1,1]=>448
[7,3,1,5,6,8,4,2]=>[4,2,1,1]=>90
[2,10,1,3,4,5,6,9,7,8]=>[7,2,1]=>160
[2,9,1,3,4,5,6,7,10,8]=>[7,3]=>75
[12,1,2,3,4,5,6,7,8,11,9,10]=>[10,1,1]=>55
[2,11,1,3,4,5,6,7,10,8,9]=>[8,2,1]=>231
[10,3,1,2,4,5,6,9,7,8]=>[7,2,1]=>160
[3,1,10,2,4,5,6,9,7,8]=>[7,2,1]=>160
[9,3,1,2,4,5,6,7,10,8]=>[7,2,1]=>160
[3,1,9,2,4,5,6,7,10,8]=>[7,3]=>75
[2,10,1,3,4,5,6,7,8,11,9]=>[8,3]=>110
[5,7,8,1,6,2,3,4]=>[4,3,1]=>70
[1,6,4,2,7,3,8,5]=>[4,3,1]=>70
[4,8,2,1,5,7,3,6]=>[3,3,2]=>42
[9,8,3,4,5,6,7,1,2]=>[5,2,1,1]=>189
[9,8,2,3,4,5,6,1,7]=>[6,1,1,1]=>56
[6,2,8,7,3,4,5,1]=>[4,2,1,1]=>90
[9,4,5,6,7,8,2,1,3]=>[5,2,1,1]=>189
[9,3,4,5,6,7,2,1,8]=>[6,1,1,1]=>56
[11,2,1,3,4,5,6,7,8,9,10]=>[9,1,1]=>45
[12,11,1,2,3,4,5,6,7,8,9,10]=>[10,1,1]=>55
[11,10,2,3,4,5,6,7,8,9,1]=>[8,1,1,1]=>120
[10,9,3,4,5,6,7,8,1,2]=>[6,2,1,1]=>350
[10,9,2,3,4,5,6,7,1,8]=>[7,1,1,1]=>84
[7,2,9,8,3,4,5,6,1]=>[5,2,1,1]=>189
[9,8,2,3,4,5,1,6,7]=>[6,1,1,1]=>56
[7,3,4,8,5,6,2,1]=>[4,2,1,1]=>90
[9,5,6,7,8,2,1,3,4]=>[4,3,1,1]=>216
[7,3,6,8,4,5,2,1]=>[3,2,1,1,1]=>64
[8,3,9,4,5,6,7,2,1]=>[5,2,1,1]=>189
[10,4,5,6,7,8,9,2,1,3]=>[6,2,1,1]=>350
[9,3,4,5,6,2,1,7,8]=>[6,1,1,1]=>56
[10,3,4,5,6,7,8,2,1,9]=>[7,1,1,1]=>84
[11,3,4,5,6,7,8,9,10,2,1]=>[8,1,1,1]=>120
[12,2,1,3,4,5,6,7,8,9,10,11]=>[10,1,1]=>55
[5,6,2,8,3,1,7,4]=>[3,3,2]=>42
[1,4,7,5,6,2,8,3]=>[5,2,1]=>64
[1,7,4,8,3,5,6,2]=>[4,2,1,1]=>90
[5,3,1,4,8,6,2,7]=>[4,2,2]=>56
[5,2,4,8,3,1,6,7]=>[4,2,1,1]=>90
[7,4,5,1,8,6,2,3]=>[3,3,2]=>42
[8,1,5,7,6,3,2,4]=>[3,2,1,1,1]=>64
[1,8,6,7,5,3,2,4]=>[3,2,1,1,1]=>64
[7,4,8,3,1,6,5,2]=>[2,2,2,2]=>14
[6,4,8,7,3,5,1,2]=>[2,2,2,2]=>14
[6,1,4,2,3,5,7,8]=>[6,1,1]=>21
[6,1,5,7,2,8,3,4]=>[4,3,1]=>70
[1,8,2,6,7,4,3,5]=>[4,2,1,1]=>90
[1,6,2,7,3,8,4,9,5]=>[5,4]=>42
[1,8,5,2,9,6,3,10,7,4]=>[4,3,3]=>210
[7,2,4,1,8,5,3,6]=>[4,2,2]=>56
[4,7,2,6,1,8,3,5]=>[3,3,2]=>42
[7,5,3,2,1,6,8,4]=>[3,2,1,1,1]=>64
[6,8,1,3,4,2,5,7]=>[5,2,1]=>64
[3,6,1,4,7,8,2,5]=>[4,3,1]=>70
[2,5,7,1,3,6,4,8]=>[4,3,1]=>70
[1,4,7,2,5,3,6,8]=>[5,2,1]=>64
[4,5,3,1,2,6,8,7]=>[4,3,1]=>70
[4,5,1,3,8,2,6,7]=>[4,3,1]=>70
[4,1,5,3,2,7,6,8]=>[4,3,1]=>70
[7,3,5,1,4,2,6,8]=>[4,2,1,1]=>90
[6,2,1,7,4,3,8,5]=>[3,3,2]=>42
[2,4,3,6,7,1,5,8]=>[5,2,1]=>64
[7,3,5,2,1,6,4,8]=>[4,2,1,1]=>90
[4,6,5,2,1,3,7,8]=>[4,2,1,1]=>90
[2,5,6,1,4,3,7,8]=>[5,2,1]=>64
[6,1,5,3,7,2,4,8]=>[4,2,1,1]=>90
[3,6,5,4,1,7,2,8]=>[4,2,1,1]=>90
[10,9,3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[8,7,6,4,5,3,2,1,10,9]=>[3,2,1,1,1,1,1]=>160
[10,9,8,6,5,4,7,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,11,1,2,3,4,5,6,7,8,10]=>[9,2]=>44
[6,7,1,9,2,3,4,5,8]=>[6,3]=>48
[6,1,8,9,2,3,4,5,7]=>[6,3]=>48
[8,1,9,10,2,3,4,5,6,7]=>[7,3]=>75
[6,8,7,5,4,2,1,3]=>[2,2,1,1,1,1]=>20
[5,6,1,8,4,3,7,2]=>[3,3,1,1]=>56
[1,8,2,6,7,5,4,3]=>[4,1,1,1,1]=>35
[2,7,5,1,6,8,3,4]=>[4,3,1]=>70
[3,8,6,1,2,4,5,7]=>[5,2,1]=>64
[1,8,5,3,2,7,4,6]=>[4,2,1,1]=>90
[1,8,4,7,2,3,5,6]=>[5,2,1]=>64
[3,2,8,1,7,5,4,6]=>[3,2,2,1]=>70
[3,4,5,2,1,6,7,8,9]=>[7,1,1]=>28
[7,1,5,6,2,3,4,8]=>[5,2,1]=>64
[6,5,1,7,2,3,4,8]=>[5,2,1]=>64
[1,6,8,2,7,3,4,5]=>[5,2,1]=>64
[1,6,8,7,3,4,2,5]=>[4,2,1,1]=>90
[7,4,1,5,6,8,3,2]=>[4,2,1,1]=>90
[4,1,2,6,7,8,5,3]=>[5,2,1]=>64
[3,4,5,8,9,1,2,6,7]=>[5,4]=>42
[3,4,7,8,9,1,2,5,6]=>[5,4]=>42
[3,6,7,8,9,1,2,4,5]=>[5,4]=>42
[3,4,5,6,1,7,2,8,9]=>[7,2]=>27
[3,4,5,1,6,2,7,8,9]=>[7,2]=>27
[3,4,5,6,7,10,1,2,8,9]=>[7,3]=>75
[3,4,1,5,9,2,6,7,8]=>[6,3]=>48
[3,4,5,6,9,10,1,2,7,8]=>[6,4]=>90
[3,4,5,8,9,10,1,2,6,7]=>[6,4]=>90
[1,3,7,8,9,2,4,5,6]=>[5,4]=>42
[3,4,7,8,9,10,1,2,5,6]=>[6,4]=>90
[2,6,7,8,9,1,3,4,5]=>[5,4]=>42
[3,6,7,8,9,10,1,2,4,5]=>[6,4]=>90
[6,3,7,1,8,2,4,5]=>[4,3,1]=>70
[2,1,4,3,6,5,10,7,9,8]=>[5,4,1]=>288
[2,1,4,3,8,5,7,6,10,9]=>[5,4,1]=>288
[2,1,4,3,10,9,7,5,6,8]=>[5,3,1,1]=>567
[2,1,4,3,10,5,6,8,9,7]=>[6,3,1]=>315
[2,1,6,3,5,4,8,7,10,9]=>[5,4,1]=>288
[2,1,6,3,5,4,10,7,9,8]=>[5,3,2]=>450
[2,1,8,7,5,3,4,6,10,9]=>[5,3,1,1]=>567
[2,1,10,7,5,9,4,3,6,8]=>[4,3,1,1,1]=>525
[2,1,10,8,5,3,6,4,9,7]=>[4,4,1,1]=>300
[2,1,8,3,4,6,7,5,10,9]=>[6,3,1]=>315
[2,1,10,9,4,6,7,3,5,8]=>[5,3,1,1]=>567
[2,1,10,3,9,6,4,8,5,7]=>[5,3,1,1]=>567
[2,1,10,3,4,5,7,8,9,6]=>[7,2,1]=>160
[4,1,3,2,6,5,8,7,10,9]=>[5,4,1]=>288
[4,1,3,2,6,5,10,7,9,8]=>[5,3,2]=>450
[4,1,3,2,8,5,7,6,10,9]=>[5,3,2]=>450
[4,1,3,2,10,9,7,5,6,8]=>[5,2,2,1]=>525
[4,1,3,2,10,5,6,8,9,7]=>[6,2,2]=>225
[6,5,3,1,2,4,10,7,9,8]=>[5,2,2,1]=>525
[8,5,3,7,2,1,4,6,10,9]=>[4,3,1,1,1]=>525
[10,5,3,7,2,9,4,1,6,8]=>[4,3,1,1,1]=>525
[10,5,3,8,2,1,6,4,9,7]=>[3,3,2,1,1]=>450
[8,6,3,1,4,2,7,5,10,9]=>[4,4,1,1]=>300
[10,6,3,9,4,2,7,1,5,8]=>[4,2,2,1,1]=>567
[10,6,3,1,9,2,4,8,5,7]=>[5,2,2,1]=>525
[10,7,3,1,4,5,2,8,9,6]=>[5,3,1,1]=>567
[6,1,2,4,5,3,8,7,10,9]=>[6,3,1]=>315
[6,1,2,4,5,3,10,7,9,8]=>[6,2,2]=>225
[8,7,2,4,5,1,3,6,10,9]=>[5,3,1,1]=>567
[10,7,2,4,5,9,3,1,6,8]=>[5,2,1,1,1]=>448
[10,8,2,4,5,1,6,3,9,7]=>[5,3,1,1]=>567
[8,1,7,4,2,6,3,5,10,9]=>[5,3,1,1]=>567
[10,9,7,4,2,6,3,1,5,8]=>[4,2,1,1,1,1]=>350
[10,1,8,4,9,6,2,3,5,7]=>[5,2,2,1]=>525
[10,1,8,4,2,5,7,3,9,6]=>[5,3,1,1]=>567
[8,1,2,3,5,6,7,4,10,9]=>[7,2,1]=>160
[10,9,2,3,5,6,7,1,4,8]=>[6,2,1,1]=>350
[10,1,9,3,5,6,2,8,4,7]=>[5,3,1,1]=>567
[10,1,2,9,5,3,7,8,4,6]=>[5,3,1,1]=>567
[2,1,4,3,6,5,8,7,12,9,11,10]=>[6,5,1]=>1155
[2,1,4,3,6,5,10,7,9,8,12,11]=>[6,5,1]=>1155
[2,1,4,3,6,5,12,11,9,7,8,10]=>[6,4,1,1]=>3080
[2,1,4,3,6,5,12,7,8,10,11,9]=>[7,4,1]=>1408
[2,1,4,3,8,5,7,6,10,9,12,11]=>[6,5,1]=>1155
[2,1,4,3,8,5,7,6,12,9,11,10]=>[6,4,2]=>2673
[2,1,4,3,10,9,7,5,6,8,12,11]=>[6,4,1,1]=>3080
[2,1,4,3,12,9,7,11,6,5,8,10]=>[5,4,1,1,1]=>3520
[2,1,4,3,12,10,7,5,8,6,11,9]=>[5,5,1,1]=>1485
[2,1,4,3,10,5,6,8,9,7,12,11]=>[7,4,1]=>1408
[2,1,4,3,12,11,6,8,9,5,7,10]=>[6,4,1,1]=>3080
[2,1,4,3,12,5,11,8,6,10,7,9]=>[6,4,1,1]=>3080
[2,1,4,3,12,5,6,7,9,10,11,8]=>[8,3,1]=>891
[2,1,6,3,5,4,8,7,10,9,12,11]=>[6,5,1]=>1155
[2,1,6,3,5,4,8,7,12,9,11,10]=>[6,4,2]=>2673
[2,1,6,3,5,4,10,7,9,8,12,11]=>[6,4,2]=>2673
[2,1,6,3,5,4,12,11,9,7,8,10]=>[6,3,2,1]=>5632
[2,1,6,3,5,4,12,7,8,10,11,9]=>[7,3,2]=>1925
[2,1,8,7,5,3,4,6,10,9,12,11]=>[6,4,1,1]=>3080
[2,1,8,7,5,3,4,6,12,9,11,10]=>[6,3,2,1]=>5632
[2,1,10,7,5,9,4,3,6,8,12,11]=>[5,4,1,1,1]=>3520
[2,1,12,7,5,9,4,11,6,3,8,10]=>[5,4,1,1,1]=>3520
[2,1,12,7,5,10,4,3,8,6,11,9]=>[4,4,2,1,1]=>4455
[2,1,10,8,5,3,6,4,9,7,12,11]=>[5,5,1,1]=>1485
[2,1,12,8,5,11,6,4,9,3,7,10]=>[5,3,2,1,1]=>7700
[2,1,12,8,5,3,11,4,6,10,7,9]=>[6,3,2,1]=>5632
[2,1,12,9,5,3,6,7,4,10,11,8]=>[6,4,1,1]=>3080
[2,1,8,3,4,6,7,5,10,9,12,11]=>[7,4,1]=>1408
[2,1,8,3,4,6,7,5,12,9,11,10]=>[7,3,2]=>1925
[2,1,10,9,4,6,7,3,5,8,12,11]=>[6,4,1,1]=>3080
[2,1,12,9,4,6,7,11,5,3,8,10]=>[6,3,1,1,1]=>3696
[2,1,12,10,4,6,7,3,8,5,11,9]=>[6,4,1,1]=>3080
[2,1,10,3,9,6,4,8,5,7,12,11]=>[6,4,1,1]=>3080
[2,1,12,11,9,6,4,8,5,3,7,10]=>[5,3,1,1,1,1]=>3564
[2,1,12,3,10,6,11,8,4,5,7,9]=>[6,3,2,1]=>5632
[2,1,12,3,10,6,4,7,9,5,11,8]=>[6,4,1,1]=>3080
[2,1,10,3,4,5,7,8,9,6,12,11]=>[8,3,1]=>891
[2,1,12,11,4,5,7,8,9,3,6,10]=>[7,3,1,1]=>2376
[2,1,12,3,11,5,7,8,4,10,6,9]=>[6,4,1,1]=>3080
[2,1,12,3,4,11,7,5,9,10,6,8]=>[6,4,1,1]=>3080
[2,1,12,3,4,5,6,8,9,10,11,7]=>[9,2,1]=>320
[4,1,3,2,6,5,8,7,10,9,12,11]=>[6,5,1]=>1155
[4,1,3,2,6,5,8,7,12,9,11,10]=>[6,4,2]=>2673
[4,1,3,2,6,5,10,7,9,8,12,11]=>[6,4,2]=>2673
[4,1,3,2,6,5,12,11,9,7,8,10]=>[6,3,2,1]=>5632
[4,1,3,2,6,5,12,7,8,10,11,9]=>[7,3,2]=>1925
[4,1,3,2,8,5,7,6,10,9,12,11]=>[6,4,2]=>2673
[4,1,3,2,8,5,7,6,12,9,11,10]=>[6,3,3]=>1650
[4,1,3,2,10,9,7,5,6,8,12,11]=>[6,3,2,1]=>5632
[4,1,3,2,12,9,7,11,6,5,8,10]=>[5,3,2,1,1]=>7700
[4,1,3,2,12,10,7,5,8,6,11,9]=>[5,4,2,1]=>5775
[4,1,3,2,10,5,6,8,9,7,12,11]=>[7,3,2]=>1925
[4,1,3,2,12,11,6,8,9,5,7,10]=>[6,3,2,1]=>5632
[4,1,3,2,12,5,11,8,6,10,7,9]=>[6,3,2,1]=>5632
[4,1,3,2,12,5,6,7,9,10,11,8]=>[8,2,2]=>616
[6,5,3,1,2,4,8,7,10,9,12,11]=>[6,4,1,1]=>3080
[6,5,3,1,2,4,8,7,12,9,11,10]=>[6,3,2,1]=>5632
[6,5,3,1,2,4,10,7,9,8,12,11]=>[6,3,2,1]=>5632
[6,5,3,1,2,4,12,11,9,7,8,10]=>[6,2,2,2]=>1925
[6,5,3,1,2,4,12,7,8,10,11,9]=>[7,2,2,1]=>2079
[8,5,3,7,2,1,4,6,10,9,12,11]=>[5,4,1,1,1]=>3520
[8,5,3,7,2,1,4,6,12,9,11,10]=>[5,3,2,1,1]=>7700
[10,5,3,7,2,9,4,1,6,8,12,11]=>[5,4,1,1,1]=>3520
[12,5,3,7,2,9,4,11,6,1,8,10]=>[5,4,1,1,1]=>3520
[12,5,3,7,2,10,4,1,8,6,11,9]=>[4,4,2,1,1]=>4455
[10,5,3,8,2,1,6,4,9,7,12,11]=>[4,4,2,1,1]=>4455
[12,5,3,8,2,11,6,4,9,1,7,10]=>[4,3,3,1,1]=>4158
[12,5,3,8,2,1,11,4,6,10,7,9]=>[5,3,2,1,1]=>7700
[12,5,3,9,2,1,6,7,4,10,11,8]=>[5,3,2,1,1]=>7700
[8,6,3,1,4,2,7,5,10,9,12,11]=>[5,5,1,1]=>1485
[8,6,3,1,4,2,7,5,12,9,11,10]=>[5,4,2,1]=>5775
[10,6,3,9,4,2,7,1,5,8,12,11]=>[5,3,2,1,1]=>7700
[12,6,3,9,4,2,7,11,5,1,8,10]=>[5,3,2,1,1]=>7700
[12,6,3,10,4,2,7,1,8,5,11,9]=>[5,3,2,1,1]=>7700
[10,6,3,1,9,2,4,8,5,7,12,11]=>[6,3,2,1]=>5632
[12,6,3,11,9,2,4,8,5,1,7,10]=>[5,2,2,1,1,1]=>3696
[12,6,3,1,10,2,11,8,4,5,7,9]=>[6,3,2,1]=>5632
[12,6,3,1,10,2,4,7,9,5,11,8]=>[6,3,2,1]=>5632
[10,7,3,1,4,5,2,8,9,6,12,11]=>[6,4,1,1]=>3080
[12,7,3,11,4,5,2,8,9,1,6,10]=>[6,2,2,1,1]=>3564
[12,7,3,1,11,5,2,8,4,10,6,9]=>[5,4,2,1]=>5775
[12,7,3,1,4,11,2,5,9,10,6,8]=>[5,4,2,1]=>5775
[12,8,3,1,4,5,6,2,9,10,11,7]=>[7,3,1,1]=>2376
[6,1,2,4,5,3,8,7,10,9,12,11]=>[7,4,1]=>1408
[6,1,2,4,5,3,8,7,12,9,11,10]=>[7,3,2]=>1925
[6,1,2,4,5,3,10,7,9,8,12,11]=>[7,3,2]=>1925
[6,1,2,4,5,3,12,11,9,7,8,10]=>[7,2,2,1]=>2079
[6,1,2,4,5,3,12,7,8,10,11,9]=>[8,2,2]=>616
[8,7,2,4,5,1,3,6,10,9,12,11]=>[6,4,1,1]=>3080
[8,7,2,4,5,1,3,6,12,9,11,10]=>[6,3,2,1]=>5632
[10,7,2,4,5,9,3,1,6,8,12,11]=>[6,3,1,1,1]=>3696
[12,7,2,4,5,9,3,11,6,1,8,10]=>[6,3,1,1,1]=>3696
[12,7,2,4,5,10,3,1,8,6,11,9]=>[5,3,2,1,1]=>7700
[10,8,2,4,5,1,6,3,9,7,12,11]=>[6,4,1,1]=>3080
[12,8,2,4,5,11,6,3,9,1,7,10]=>[6,2,2,1,1]=>3564
[12,8,2,4,5,1,11,3,6,10,7,9]=>[6,3,2,1]=>5632
[12,9,2,4,5,1,6,7,3,10,11,8]=>[7,3,1,1]=>2376
[8,1,7,4,2,6,3,5,10,9,12,11]=>[6,4,1,1]=>3080
[8,1,7,4,2,6,3,5,12,9,11,10]=>[6,3,2,1]=>5632
[10,9,7,4,2,6,3,1,5,8,12,11]=>[5,3,1,1,1,1]=>3564
[12,9,7,4,2,6,3,11,5,1,8,10]=>[5,3,1,1,1,1]=>3564
[12,10,7,4,2,6,3,1,8,5,11,9]=>[4,4,1,1,1,1]=>1925
[10,1,8,4,9,6,2,3,5,7,12,11]=>[6,3,2,1]=>5632
[12,11,8,4,9,6,2,3,5,1,7,10]=>[5,2,2,1,1,1]=>3696
[12,1,8,4,10,6,11,3,2,5,7,9]=>[5,3,2,1,1]=>7700
[12,1,9,4,10,6,2,7,3,5,11,8]=>[5,4,2,1]=>5775
[10,1,8,4,2,5,7,3,9,6,12,11]=>[6,4,1,1]=>3080
[12,11,8,4,2,5,7,3,9,1,6,10]=>[5,3,1,1,1,1]=>3564
[12,1,8,4,11,5,7,3,2,10,6,9]=>[5,3,2,1,1]=>7700
[12,1,9,4,2,11,7,5,3,10,6,8]=>[5,3,2,1,1]=>7700
[12,1,9,4,2,5,6,8,3,10,11,7]=>[7,3,1,1]=>2376
[8,1,2,3,5,6,7,4,10,9,12,11]=>[8,3,1]=>891
[8,1,2,3,5,6,7,4,12,9,11,10]=>[8,2,2]=>616
[10,9,2,3,5,6,7,1,4,8,12,11]=>[7,3,1,1]=>2376
[12,9,2,3,5,6,7,11,4,1,8,10]=>[7,2,1,1,1]=>1728
[12,10,2,3,5,6,7,1,8,4,11,9]=>[7,3,1,1]=>2376
[10,1,9,3,5,6,2,8,4,7,12,11]=>[6,4,1,1]=>3080
[12,11,9,3,5,6,2,8,4,1,7,10]=>[5,3,1,1,1,1]=>3564
[12,1,10,3,5,6,11,8,2,4,7,9]=>[6,3,2,1]=>5632
[12,1,10,3,5,6,2,7,9,4,11,8]=>[7,3,1,1]=>2376
[10,1,2,9,5,3,7,8,4,6,12,11]=>[6,4,1,1]=>3080
[12,11,2,9,5,3,7,8,4,1,6,10]=>[5,3,1,1,1,1]=>3564
[12,1,11,10,5,3,7,8,2,4,6,9]=>[5,3,1,1,1,1]=>3564
[12,1,2,10,5,11,7,3,9,4,6,8]=>[6,3,2,1]=>5632
[12,1,2,10,5,3,6,8,9,4,11,7]=>[7,3,1,1]=>2376
[10,1,2,3,4,6,7,8,9,5,12,11]=>[9,2,1]=>320
[12,11,2,3,4,6,7,8,9,1,5,10]=>[8,2,1,1]=>945
[12,1,11,3,4,6,7,8,2,10,5,9]=>[7,3,1,1]=>2376
[12,1,2,11,4,6,7,3,9,10,5,8]=>[7,3,1,1]=>2376
[12,1,2,3,11,6,4,8,9,10,5,7]=>[7,3,1,1]=>2376
[1,5,4,7,8,3,6,2]=>[4,2,1,1]=>90
[5,1,4,7,8,3,6,2]=>[4,2,1,1]=>90
[5,6,4,1,7,3,8,2]=>[4,2,1,1]=>90
[4,3,7,8,2,5,1,6]=>[3,3,1,1]=>56
[3,7,8,5,4,2,1,6]=>[3,2,1,1,1]=>64
[1,7,4,5,6,8,3,2]=>[5,1,1,1]=>35
[7,2,4,5,6,8,3,1]=>[5,1,1,1]=>35
[2,7,4,5,6,8,3,1]=>[5,1,1,1]=>35
[2,4,7,8,3,1,6,5]=>[4,2,2]=>56
[5,4,3,6,8,1,7,2]=>[3,2,2,1]=>70
[3,7,4,5,8,1,6,2]=>[4,2,2]=>56
[1,4,3,5,6,8,2,7]=>[5,2,1]=>64
[1,4,6,5,8,2,7,3]=>[4,2,2]=>56
[4,6,1,7,3,2,8,5]=>[4,3,1]=>70
[1,7,3,6,4,2,8,5]=>[4,2,1,1]=>90
[4,7,3,5,1,2,8,6]=>[3,3,2]=>42
[1,6,4,2,3,5,8,7]=>[5,2,1]=>64
[4,8,3,5,2,1,6,7]=>[4,2,1,1]=>90
[10,9,7,6,5,4,3,8,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[1,6,8,4,7,5,3,2]=>[3,2,1,1,1]=>64
[4,7,1,6,8,2,3,5]=>[4,3,1]=>70
[4,6,5,8,2,3,7,1]=>[3,3,1,1]=>56
[7,1,8,2,4,5,3,6]=>[5,2,1]=>64
[5,7,8,2,3,4,1,6]=>[4,3,1]=>70
[5,2,3,8,7,1,4,6]=>[4,2,2]=>56
[11,10,9,8,6,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[2,7,6,4,8,3,1,5]=>[3,2,1,1,1]=>64
[2,6,3,7,5,8,4,1]=>[4,2,1,1]=>90
[7,5,1,2,3,8,4,6]=>[5,2,1]=>64
[4,3,5,2,6,1,7,8,9]=>[6,1,1,1]=>56
[4,5,3,6,2,7,1,8,9]=>[6,1,1,1]=>56
[3,2,4,1,5,6,7,8,9,10]=>[8,1,1]=>36
[3,4,2,5,1,6,7,8,9,10]=>[8,1,1]=>36
[4,3,5,2,6,1,7,8,9,10]=>[7,1,1,1]=>84
[4,5,3,6,2,7,1,8,9,10]=>[7,1,1,1]=>84
[5,4,6,3,7,2,8,1,9,10]=>[6,1,1,1,1]=>126
[8,6,2,1,3,7,4,5]=>[4,2,1,1]=>90
[4,2,3,6,8,5,7,1]=>[4,3,1]=>70
[6,3,5,8,4,1,2,7]=>[3,3,1,1]=>56
[4,5,3,6,8,1,2,7]=>[4,3,1]=>70
[5,2,8,4,7,1,3,6]=>[3,3,2]=>42
[7,3,1,2,8,6,5,4]=>[3,2,2,1]=>70
[8,7,1,3,2,4,5,6]=>[5,1,1,1]=>35
[6,8,2,1,4,5,3,7]=>[4,2,2]=>56
[2,1,4,3,6,5,10,7,8,9]=>[6,4]=>90
[2,1,4,3,8,5,6,7,10,9]=>[6,4]=>90
[2,1,4,3,10,9,6,5,8,7]=>[4,4,1,1]=>300
[2,1,4,3,10,5,6,7,8,9]=>[7,3]=>75
[2,1,6,3,4,5,8,7,10,9]=>[6,4]=>90
[2,1,6,3,4,5,10,7,8,9]=>[7,3]=>75
[2,1,10,7,4,9,6,3,8,5]=>[4,3,2,1]=>768
[2,1,10,9,4,3,6,7,8,5]=>[5,3,1,1]=>567
[2,1,8,3,4,5,6,7,10,9]=>[7,3]=>75
[2,1,10,9,4,5,6,3,8,7]=>[5,3,1,1]=>567
[2,1,10,3,8,5,4,7,6,9]=>[5,3,1,1]=>567
[4,1,2,3,6,5,10,7,8,9]=>[7,3]=>75
[4,1,2,3,8,5,6,7,10,9]=>[7,3]=>75
[4,1,2,3,10,9,6,5,8,7]=>[5,3,1,1]=>567
[6,5,2,1,4,3,8,7,10,9]=>[4,4,1,1]=>300
[6,5,2,1,4,3,10,7,8,9]=>[5,3,1,1]=>567
[8,5,2,7,4,1,6,3,10,9]=>[4,3,2,1]=>768
[10,5,2,7,4,9,6,1,8,3]=>[4,3,2,1]=>768
[10,5,2,9,4,1,6,7,8,3]=>[5,2,2,1]=>525
[8,7,2,1,4,5,6,3,10,9]=>[5,3,1,1]=>567
[10,7,2,9,4,5,6,1,8,3]=>[5,2,2,1]=>525
[10,9,2,1,8,5,4,7,6,3]=>[3,3,1,1,1,1]=>225
[10,9,2,1,4,5,6,7,8,3]=>[6,2,1,1]=>350
[6,1,2,3,4,5,8,7,10,9]=>[7,3]=>75
[8,7,2,3,4,1,6,5,10,9]=>[5,3,1,1]=>567
[10,7,2,3,4,9,6,1,8,5]=>[5,2,2,1]=>525
[10,9,2,3,4,1,6,7,8,5]=>[6,2,1,1]=>350
[8,1,6,3,2,5,4,7,10,9]=>[5,3,1,1]=>567
[10,9,6,3,2,5,4,1,8,7]=>[3,3,1,1,1,1]=>225
[10,1,6,3,8,5,2,7,4,9]=>[5,2,2,1]=>525
[10,1,8,3,2,5,6,7,4,9]=>[6,2,1,1]=>350
[10,9,2,3,4,5,6,1,8,7]=>[6,2,1,1]=>350
[10,1,8,3,4,5,2,7,6,9]=>[6,2,1,1]=>350
[10,1,2,7,4,3,6,5,8,9]=>[6,2,1,1]=>350
[2,1,4,3,6,5,8,7,12,9,10,11]=>[7,5]=>297
[2,1,4,3,6,5,10,7,8,9,12,11]=>[7,5]=>297
[2,1,4,3,6,5,12,11,8,7,10,9]=>[5,5,1,1]=>1485
[2,1,4,3,6,5,12,7,8,9,10,11]=>[8,4]=>275
[2,1,4,3,8,5,6,7,10,9,12,11]=>[7,5]=>297
[2,1,4,3,8,5,6,7,12,9,10,11]=>[8,4]=>275
[2,1,4,3,10,9,6,5,8,7,12,11]=>[5,5,1,1]=>1485
[2,1,4,3,12,9,6,11,8,5,10,7]=>[5,4,2,1]=>5775
[2,1,4,3,12,11,6,5,8,9,10,7]=>[6,4,1,1]=>3080
[2,1,4,3,10,5,6,7,8,9,12,11]=>[8,4]=>275
[2,1,4,3,12,11,6,7,8,5,10,9]=>[6,4,1,1]=>3080
[2,1,4,3,12,5,10,7,6,9,8,11]=>[6,4,1,1]=>3080
[2,1,4,3,12,5,6,7,8,9,10,11]=>[9,3]=>154
[2,1,6,3,4,5,8,7,10,9,12,11]=>[7,5]=>297
[2,1,6,3,4,5,8,7,12,9,10,11]=>[8,4]=>275
[2,1,6,3,4,5,10,7,8,9,12,11]=>[8,4]=>275
[2,1,6,3,4,5,12,11,8,7,10,9]=>[6,4,1,1]=>3080
[2,1,6,3,4,5,12,7,8,9,10,11]=>[9,3]=>154
[2,1,8,7,4,3,6,5,10,9,12,11]=>[5,5,1,1]=>1485
[2,1,8,7,4,3,6,5,12,9,10,11]=>[6,4,1,1]=>3080
[2,1,10,7,4,9,6,3,8,5,12,11]=>[5,4,2,1]=>5775
[2,1,12,7,4,9,6,11,8,3,10,5]=>[5,4,2,1]=>5775
[2,1,12,7,4,11,6,3,8,9,10,5]=>[6,3,2,1]=>5632
[2,1,10,9,4,3,6,7,8,5,12,11]=>[6,4,1,1]=>3080
[2,1,12,9,4,11,6,7,8,3,10,5]=>[6,3,2,1]=>5632
[2,1,12,11,4,3,10,7,6,9,8,5]=>[4,4,1,1,1,1]=>1925
[2,1,12,11,4,3,6,7,8,9,10,5]=>[7,3,1,1]=>2376
[2,1,8,3,4,5,6,7,10,9,12,11]=>[8,4]=>275
[2,1,8,3,4,5,6,7,12,9,10,11]=>[9,3]=>154
[2,1,10,9,4,5,6,3,8,7,12,11]=>[6,4,1,1]=>3080
[2,1,12,9,4,5,6,11,8,3,10,7]=>[6,3,2,1]=>5632
[2,1,12,11,4,5,6,3,8,9,10,7]=>[7,3,1,1]=>2376
[2,1,10,3,8,5,4,7,6,9,12,11]=>[6,4,1,1]=>3080
[2,1,12,11,8,5,4,7,6,3,10,9]=>[4,4,1,1,1,1]=>1925
[2,1,12,3,8,5,10,7,4,9,6,11]=>[6,3,2,1]=>5632
[2,1,12,3,10,5,4,7,8,9,6,11]=>[7,3,1,1]=>2376
[2,1,10,3,4,5,6,7,8,9,12,11]=>[9,3]=>154
[2,1,12,11,4,5,6,7,8,3,10,9]=>[7,3,1,1]=>2376
[2,1,12,3,10,5,6,7,4,9,8,11]=>[7,3,1,1]=>2376
[2,1,12,3,4,9,6,5,8,7,10,11]=>[7,3,1,1]=>2376
[2,1,12,3,4,5,6,7,8,9,10,11]=>[10,2]=>54
[4,1,2,3,6,5,8,7,10,9,12,11]=>[7,5]=>297
[4,1,2,3,6,5,8,7,12,9,10,11]=>[8,4]=>275
[4,1,2,3,6,5,10,7,8,9,12,11]=>[8,4]=>275
[4,1,2,3,6,5,12,11,8,7,10,9]=>[6,4,1,1]=>3080
[4,1,2,3,6,5,12,7,8,9,10,11]=>[9,3]=>154
[4,1,2,3,8,5,6,7,10,9,12,11]=>[8,4]=>275
[4,1,2,3,8,5,6,7,12,9,10,11]=>[9,3]=>154
[4,1,2,3,10,9,6,5,8,7,12,11]=>[6,4,1,1]=>3080
[4,1,2,3,12,9,6,11,8,5,10,7]=>[6,3,2,1]=>5632
[4,1,2,3,12,11,6,5,8,9,10,7]=>[7,3,1,1]=>2376
[4,1,2,3,10,5,6,7,8,9,12,11]=>[9,3]=>154
[4,1,2,3,12,11,6,7,8,5,10,9]=>[7,3,1,1]=>2376
[4,1,2,3,12,5,10,7,6,9,8,11]=>[7,3,1,1]=>2376
[4,1,2,3,12,5,6,7,8,9,10,11]=>[10,2]=>54
[6,5,2,1,4,3,8,7,10,9,12,11]=>[5,5,1,1]=>1485
[6,5,2,1,4,3,8,7,12,9,10,11]=>[6,4,1,1]=>3080
[6,5,2,1,4,3,10,7,8,9,12,11]=>[6,4,1,1]=>3080
[6,5,2,1,4,3,12,7,8,9,10,11]=>[7,3,1,1]=>2376
[8,5,2,7,4,1,6,3,10,9,12,11]=>[5,4,2,1]=>5775
[8,5,2,7,4,1,6,3,12,9,10,11]=>[6,3,2,1]=>5632
[10,5,2,7,4,9,6,1,8,3,12,11]=>[5,4,2,1]=>5775
[12,5,2,7,4,9,6,11,8,1,10,3]=>[5,4,2,1]=>5775
[12,5,2,7,4,11,6,1,8,9,10,3]=>[6,3,2,1]=>5632
[10,5,2,9,4,1,6,7,8,3,12,11]=>[6,3,2,1]=>5632
[12,5,2,9,4,11,6,7,8,1,10,3]=>[6,3,2,1]=>5632
[12,5,2,11,4,1,10,7,6,9,8,3]=>[4,3,2,1,1,1]=>5632
[12,5,2,11,4,1,6,7,8,9,10,3]=>[7,2,2,1]=>2079
[8,7,2,1,4,5,6,3,10,9,12,11]=>[6,4,1,1]=>3080
[8,7,2,1,4,5,6,3,12,9,10,11]=>[7,3,1,1]=>2376
[10,7,2,9,4,5,6,1,8,3,12,11]=>[6,3,2,1]=>5632
[12,7,2,9,4,5,6,11,8,1,10,3]=>[6,3,2,1]=>5632
[12,7,2,11,4,5,6,1,8,9,10,3]=>[7,2,2,1]=>2079
[10,9,2,1,8,5,4,7,6,3,12,11]=>[4,4,1,1,1,1]=>1925
[12,9,2,11,8,5,4,7,6,1,10,3]=>[4,2,2,2,1,1]=>3080
[12,11,2,1,8,5,10,7,4,9,6,3]=>[4,3,2,1,1,1]=>5632
[12,11,2,1,10,5,4,7,8,9,6,3]=>[5,3,1,1,1,1]=>3564
[10,9,2,1,4,5,6,7,8,3,12,11]=>[7,3,1,1]=>2376
[12,9,2,11,4,5,6,7,8,1,10,3]=>[7,2,2,1]=>2079
[12,11,2,1,10,5,6,7,4,9,8,3]=>[5,3,1,1,1,1]=>3564
[12,11,2,1,4,9,6,5,8,7,10,3]=>[5,3,1,1,1,1]=>3564
[12,11,2,1,4,5,6,7,8,9,10,3]=>[8,2,1,1]=>945
[6,1,2,3,4,5,8,7,10,9,12,11]=>[8,4]=>275
[6,1,2,3,4,5,8,7,12,9,10,11]=>[9,3]=>154
[6,1,2,3,4,5,10,7,8,9,12,11]=>[9,3]=>154
[6,1,2,3,4,5,12,11,8,7,10,9]=>[7,3,1,1]=>2376
[6,1,2,3,4,5,12,7,8,9,10,11]=>[10,2]=>54
[8,7,2,3,4,1,6,5,10,9,12,11]=>[6,4,1,1]=>3080
[8,7,2,3,4,1,6,5,12,9,10,11]=>[7,3,1,1]=>2376
[10,7,2,3,4,9,6,1,8,5,12,11]=>[6,3,2,1]=>5632
[12,7,2,3,4,9,6,11,8,1,10,5]=>[6,3,2,1]=>5632
[12,7,2,3,4,11,6,1,8,9,10,5]=>[7,2,2,1]=>2079
[10,9,2,3,4,1,6,7,8,5,12,11]=>[7,3,1,1]=>2376
[12,9,2,3,4,11,6,7,8,1,10,5]=>[7,2,2,1]=>2079
[12,11,2,3,4,1,10,7,6,9,8,5]=>[5,3,1,1,1,1]=>3564
[12,11,2,3,4,1,6,7,8,9,10,5]=>[8,2,1,1]=>945
[8,1,6,3,2,5,4,7,10,9,12,11]=>[6,4,1,1]=>3080
[8,1,6,3,2,5,4,7,12,9,10,11]=>[7,3,1,1]=>2376
[10,9,6,3,2,5,4,1,8,7,12,11]=>[4,4,1,1,1,1]=>1925
[12,9,6,3,2,5,4,11,8,1,10,7]=>[4,3,2,1,1,1]=>5632
[12,11,6,3,2,5,4,1,8,9,10,7]=>[5,3,1,1,1,1]=>3564
[10,1,6,3,8,5,2,7,4,9,12,11]=>[6,3,2,1]=>5632
[12,11,6,3,8,5,2,7,4,1,10,9]=>[4,3,2,1,1,1]=>5632
[12,1,6,3,8,5,10,7,2,9,4,11]=>[6,3,2,1]=>5632
[12,1,6,3,10,5,2,7,8,9,4,11]=>[7,2,2,1]=>2079
[10,1,8,3,2,5,6,7,4,9,12,11]=>[7,3,1,1]=>2376
[12,11,8,3,2,5,6,7,4,1,10,9]=>[5,3,1,1,1,1]=>3564
[12,1,8,3,10,5,6,7,2,9,4,11]=>[7,2,2,1]=>2079
[12,1,10,3,2,9,6,5,8,7,4,11]=>[5,3,1,1,1,1]=>3564
[12,1,10,3,2,5,6,7,8,9,4,11]=>[8,2,1,1]=>945
[8,1,2,3,4,5,6,7,10,9,12,11]=>[9,3]=>154
[8,1,2,3,4,5,6,7,12,9,10,11]=>[10,2]=>54
[10,9,2,3,4,5,6,1,8,7,12,11]=>[7,3,1,1]=>2376
[12,9,2,3,4,5,6,11,8,1,10,7]=>[7,2,2,1]=>2079
[12,11,2,3,4,5,6,1,8,9,10,7]=>[8,2,1,1]=>945
[10,1,8,3,4,5,2,7,6,9,12,11]=>[7,3,1,1]=>2376
[12,11,8,3,4,5,2,7,6,1,10,9]=>[5,3,1,1,1,1]=>3564
[12,1,8,3,4,5,10,7,2,9,6,11]=>[7,2,2,1]=>2079
[12,1,10,3,4,5,2,7,8,9,6,11]=>[8,2,1,1]=>945
[10,1,2,7,4,3,6,5,8,9,12,11]=>[7,3,1,1]=>2376
[12,11,2,7,4,3,6,5,8,1,10,9]=>[5,3,1,1,1,1]=>3564
[12,1,10,7,4,3,6,5,2,9,8,11]=>[5,3,1,1,1,1]=>3564
[12,1,2,7,4,9,6,3,8,5,10,11]=>[7,2,2,1]=>2079
[12,1,2,9,4,3,6,7,8,5,10,11]=>[8,2,1,1]=>945
[10,1,2,3,4,5,6,7,8,9,12,11]=>[10,2]=>54
[12,11,2,3,4,5,6,7,8,1,10,9]=>[8,2,1,1]=>945
[12,1,10,3,4,5,6,7,2,9,8,11]=>[8,2,1,1]=>945
[12,1,2,9,4,5,6,3,8,7,10,11]=>[8,2,1,1]=>945
[12,1,2,3,8,5,4,7,6,9,10,11]=>[8,2,1,1]=>945
[12,1,2,3,4,5,6,7,8,9,10,11]=>[11,1]=>11
[1,5,4,8,7,3,2,6]=>[3,2,2,1]=>70
[4,3,1,2,6,5,7,8]=>[5,2,1]=>64
[7,5,8,1,2,4,6,3]=>[4,2,1,1]=>90
[6,1,5,2,8,7,4,3]=>[3,2,2,1]=>70
[1,4,7,2,6,5,8,3]=>[4,2,1,1]=>90
[1,5,7,2,6,4,8,3]=>[4,2,1,1]=>90
[7,2,4,6,1,8,3,5]=>[4,3,1]=>70
[1,2,7,8,3,5,4,6]=>[5,2,1]=>64
[1,7,6,2,8,5,4,3]=>[3,2,1,1,1]=>64
[1,2,7,8,3,4,6,5]=>[5,2,1]=>64
[1,7,6,8,3,4,2,5]=>[4,2,1,1]=>90
[3,4,1,7,8,6,5,2]=>[4,2,1,1]=>90
[2,4,8,6,5,7,1,3]=>[4,2,1,1]=>90
[5,1,3,4,8,2,7,6]=>[4,2,2]=>56
[8,7,3,6,1,4,2,5]=>[3,2,1,1,1]=>64
[6,5,1,8,3,4,7,2]=>[4,2,1,1]=>90
[8,2,1,5,6,4,7,3]=>[4,2,1,1]=>90
[7,5,6,1,3,4,8,2]=>[4,2,1,1]=>90
[5,7,2,4,6,1,8,3]=>[4,2,2]=>56
[2,1,5,6,3,8,7,4]=>[4,3,1]=>70
[3,2,7,5,8,6,4,1]=>[3,3,1,1]=>56
[2,4,5,3,8,1,7,6]=>[4,2,2]=>56
[7,2,5,4,3,8,6,1]=>[3,2,1,1,1]=>64
[8,5,3,1,2,6,7,4]=>[4,2,1,1]=>90
[7,2,5,1,3,6,8,4]=>[4,3,1]=>70
[1,8,7,3,5,2,6,4]=>[4,2,1,1]=>90
[2,4,8,3,6,5,7,1]=>[4,2,1,1]=>90
[3,1,8,2,6,5,7,4]=>[4,2,1,1]=>90
[4,6,7,8,5,2,1,3]=>[4,2,1,1]=>90
[4,7,2,1,8,6,5,3]=>[3,2,2,1]=>70
[5,6,2,8,4,1,7,3]=>[3,3,2]=>42
[5,7,2,4,8,6,1,3]=>[3,3,2]=>42
[6,7,2,4,8,5,1,3]=>[3,3,2]=>42
[6,7,3,2,8,5,1,4]=>[3,2,2,1]=>70
[7,2,3,1,8,6,5,4]=>[3,2,2,1]=>70
[7,2,8,3,5,6,1,4]=>[4,2,2]=>56
[7,2,3,8,4,6,1,5]=>[4,2,2]=>56
[1,7,3,4,8,5,2,6]=>[5,2,1]=>64
[1,7,3,8,5,4,2,6]=>[4,2,1,1]=>90
[7,2,8,4,5,3,1,6]=>[4,2,1,1]=>90
[2,8,6,4,3,1,7,5]=>[3,2,1,1,1]=>64
[1,7,3,4,8,2,5,6]=>[5,2,1]=>64
[1,5,8,3,4,6,2,7]=>[5,2,1]=>64
[1,3,8,4,2,5,7,6]=>[5,2,1]=>64
[1,4,7,6,2,3,8,5]=>[4,3,1]=>70
[1,8,4,6,7,2,3,5]=>[4,3,1]=>70
[1,4,2,3,7,8,6,5]=>[5,2,1]=>64
[5,7,1,6,4,8,3,2]=>[3,2,1,1,1]=>64
[1,2,9,7,5,3,10,8,6,4]=>[4,2,2,2]=>300
[7,4,5,8,1,3,6,2]=>[3,3,1,1]=>56
[1,4,3,6,2,5,8,7]=>[4,3,1]=>70
[1,3,6,5,8,2,4,7]=>[4,3,1]=>70
[1,4,6,3,2,8,5,7]=>[4,3,1]=>70
[6,8,4,1,5,7,2,3]=>[3,3,2]=>42
[5,2,6,7,4,1,8,3]=>[4,2,2]=>56
[8,5,6,4,1,7,3,2]=>[3,2,1,1,1]=>64
[7,8,3,1,6,4,5,2]=>[3,2,2,1]=>70
[5,8,2,6,3,1,7,4]=>[3,3,1,1]=>56
[4,5,8,1,6,3,7,2]=>[4,2,1,1]=>90
[8,1,4,6,2,5,7,3]=>[4,2,1,1]=>90
[4,5,8,1,6,2,7,3]=>[4,3,1]=>70
[5,2,6,8,1,4,3,7]=>[3,3,2]=>42
[6,7,3,8,2,1,4,5]=>[3,3,1,1]=>56
[2,4,1,5,6,7,8,10,3,9]=>[7,3]=>75
[2,1,4,8,5,3,7,6]=>[4,3,1]=>70
[2,7,3,8,4,1,6,5]=>[4,2,2]=>56
[2,6,3,1,5,4,8,7]=>[4,3,1]=>70
[1,5,8,3,4,7,2,6]=>[4,2,2]=>56
[5,3,8,1,4,6,2,7]=>[4,2,2]=>56
[4,5,8,1,3,6,2,7]=>[4,3,1]=>70
[7,4,6,5,2,8,3,1]=>[3,2,1,1,1]=>64
[4,1,3,8,5,7,6,2]=>[4,2,1,1]=>90
[4,1,3,7,2,8,6,5]=>[4,2,2]=>56
[4,6,3,1,7,2,8,5]=>[4,3,1]=>70
[7,2,6,3,1,8,5,4]=>[3,2,2,1]=>70
[4,8,7,2,5,3,1,6]=>[3,2,1,1,1]=>64
[1,6,3,2,8,7,4,5]=>[4,2,2]=>56
[2,8,1,7,5,4,6,3]=>[3,2,1,1,1]=>64
[6,8,3,1,5,7,2,4]=>[3,3,2]=>42
[8,7,3,1,2,5,6,4]=>[4,2,1,1]=>90
[1,3,5,7,2,8,4,9,6]=>[6,3]=>48
[1,3,5,6,2,7,4,9,8]=>[6,3]=>48
[1,3,4,5,2,7,6,9,8]=>[6,3]=>48
[3,5,7,1,2,4,6,9,8]=>[5,4]=>42
[1,3,5,7,2,9,4,6,8,10]=>[6,4]=>90
[3,5,7,8,1,9,2,4,6]=>[5,4]=>42
[1,3,5,7,2,9,4,10,6,8]=>[6,4]=>90
[3,5,6,7,1,8,2,9,4]=>[6,3]=>48
[1,3,5,7,2,8,4,9,6,10]=>[7,3]=>75
[1,3,5,6,2,7,4,9,8,10]=>[7,3]=>75
[1,3,4,5,2,7,6,9,8,10]=>[7,3]=>75
[5,4,3,6,1,7,8,2]=>[4,2,1,1]=>90
[3,2,7,8,5,6,1,4]=>[3,3,2]=>42
[4,8,3,2,1,7,5,6]=>[3,2,2,1]=>70
[1,9,7,6,5,4,3,2,8]=>[3,1,1,1,1,1,1]=>28
[1,3,7,8,4,6,2,5]=>[4,2,2]=>56
[4,8,7,3,6,1,2,5]=>[3,2,2,1]=>70
[5,6,4,8,7,2,1,3]=>[3,2,2,1]=>70
[4,8,3,7,6,1,2,5]=>[3,2,2,1]=>70
[2,8,4,7,1,3,6,5]=>[3,3,1,1]=>56
[8,9,2,3,4,5,6,1,7]=>[6,2,1]=>105
[7,8,9,2,3,4,5,1,6]=>[5,3,1]=>162
[6,7,8,9,2,3,4,1,5]=>[4,4,1]=>84
[5,6,7,8,9,2,3,1,4]=>[5,3,1]=>162
[9,10,2,3,4,5,6,7,1,8]=>[7,2,1]=>160
[8,9,10,2,3,4,5,6,1,7]=>[6,3,1]=>315
[7,8,9,2,3,4,1,5,6]=>[5,3,1]=>162
[7,8,9,10,2,3,4,5,1,6]=>[5,4,1]=>288
[6,7,8,9,2,3,1,4,5]=>[4,4,1]=>84
[5,6,7,8,9,10,2,3,1,4]=>[6,3,1]=>315
[4,5,6,7,8,1,9,2,3]=>[6,3]=>48
[4,5,6,7,8,9,10,2,1,3]=>[7,2,1]=>160
[6,8,3,4,5,2,1,7]=>[4,2,1,1]=>90
[3,7,1,4,5,6,2,8]=>[5,2,1]=>64
[7,9,3,4,5,6,2,1,8]=>[5,2,1,1]=>189
[3,9,2,1,5,6,7,8,4]=>[5,2,2]=>120
[3,6,1,4,5,2,7,8]=>[5,2,1]=>64
[3,8,1,4,5,6,7,2,9]=>[6,2,1]=>105
[8,10,3,4,5,6,7,2,1,9]=>[6,2,1,1]=>350
[6,9,3,4,5,2,7,1,8]=>[5,2,1,1]=>189
[3,8,2,4,5,1,7,6]=>[4,2,2]=>56
[3,9,2,4,1,6,7,8,5]=>[5,2,2]=>120
[3,7,2,1,5,6,4,8]=>[4,2,2]=>56
[3,6,8,1,5,4,7,2]=>[3,3,1,1]=>56
[3,8,9,1,5,6,7,4,2]=>[4,3,1,1]=>216
[3,10,2,1,5,6,7,8,9,4]=>[6,2,2]=>225
[3,7,1,4,5,6,2,8,9]=>[6,2,1]=>105
[3,9,1,4,5,6,7,8,2,10]=>[7,2,1]=>160
[1,7,4,6,3,5,2,8]=>[4,2,1,1]=>90
[1,3,6,5,7,2,4,8]=>[5,2,1]=>64
[1,7,2,5,6,4,3,8]=>[5,1,1,1]=>35
[1,6,8,5,4,3,7,2]=>[3,2,1,1,1]=>64
[2,5,7,8,4,3,1,6]=>[4,2,1,1]=>90
[6,8,5,3,2,4,1,7]=>[3,2,1,1,1]=>64
[1,6,8,5,3,2,7,4]=>[3,2,2,1]=>70
[4,6,1,8,7,5,3,2]=>[3,2,1,1,1]=>64
[1,3,7,6,8,5,2,4]=>[4,2,1,1]=>90
[4,1,7,8,6,5,2,3]=>[3,3,1,1]=>56
[4,7,6,1,2,3,8,5]=>[4,3,1]=>70
[4,5,2,6,7,8,1,3]=>[5,2,1]=>64
[2,8,7,6,5,4,3,1,9]=>[3,1,1,1,1,1,1]=>28
[2,1,4,9,8,7,6,5,3]=>[3,2,1,1,1,1]=>105
[1,7,6,2,3,8,5,4]=>[4,2,1,1]=>90
[1,5,4,3,8,6,2,7]=>[4,2,1,1]=>90
[1,3,7,5,8,4,6,2]=>[4,2,1,1]=>90
[5,8,1,2,7,6,4,3]=>[3,2,1,1,1]=>64
[1,6,7,4,5,3,2,8]=>[4,2,1,1]=>90
[1,4,2,6,7,5,3,8]=>[5,2,1]=>64
[1,8,2,4,6,5,3,7]=>[5,1,1,1]=>35
[1,4,8,7,2,3,6,5]=>[4,2,1,1]=>90
[4,1,3,6,5,8,2,7]=>[4,3,1]=>70
[4,3,7,1,5,8,2,6]=>[3,3,2]=>42
[1,8,6,5,2,7,4,3]=>[3,2,1,1,1]=>64
[6,4,1,8,3,7,5,2]=>[3,2,2,1]=>70
[4,5,8,7,3,6,2,1]=>[3,2,1,1,1]=>64
[3,5,4,1,7,8,6,2]=>[4,2,2]=>56
[6,8,7,2,1,5,4,3]=>[2,2,2,1,1]=>28
[8,1,6,3,7,5,4,2]=>[3,2,1,1,1]=>64
[8,5,1,3,7,6,4,2]=>[3,2,1,1,1]=>64
[8,3,6,5,4,2,1,7]=>[3,1,1,1,1,1]=>21
[6,1,3,5,7,2,8,4]=>[5,2,1]=>64
[1,6,7,5,8,4,2,3]=>[4,2,1,1]=>90
[7,4,1,6,5,2,8,3]=>[3,3,1,1]=>56
[7,4,2,8,6,5,3,1]=>[2,2,2,1,1]=>28
[6,8,4,7,3,2,5,1]=>[2,2,2,1,1]=>28
[5,8,7,3,2,1,6,4]=>[2,2,2,1,1]=>28
[5,8,7,2,6,4,3,1]=>[2,2,1,1,1,1]=>20
[6,8,7,3,5,1,4,2]=>[2,2,2,1,1]=>28
[7,2,5,6,8,3,4,1]=>[4,2,1,1]=>90
[1,6,5,7,8,3,2,4]=>[4,2,1,1]=>90
[8,6,7,2,3,5,4,1]=>[3,2,1,1,1]=>64
[5,4,8,6,7,3,1,2]=>[3,2,2,1]=>70
[4,2,7,3,1,6,8,5]=>[4,2,2]=>56
[7,3,6,4,2,1,8,5]=>[3,2,1,1,1]=>64
[4,8,5,2,7,3,1,6]=>[3,3,1,1]=>56
[6,4,3,1,8,5,2,7]=>[3,2,2,1]=>70
[7,4,3,1,5,8,6,2]=>[3,2,2,1]=>70
[7,4,8,6,5,3,1,2]=>[2,2,2,1,1]=>28
[4,8,5,2,6,7,3,1]=>[4,2,1,1]=>90
[7,3,2,1,8,5,6,4]=>[3,2,2,1]=>70
[7,8,1,9,2,3,4,5,6]=>[6,3]=>48
[6,7,8,1,9,2,3,4,5]=>[5,4]=>42
[5,6,7,8,1,9,2,3,4]=>[5,4]=>42
[9,1,2,3,4,5,7,6,8]=>[7,1,1]=>28
[2,1,3,4,5,9,6,7,8]=>[7,2]=>27
[5,1,3,8,2,7,4,6]=>[4,2,2]=>56
[8,1,6,3,2,4,7,5]=>[4,2,1,1]=>90
[8,7,2,4,3,1,5,6]=>[4,1,1,1,1]=>35
[2,1,4,3,10,5,7,6,9,8]=>[5,4,1]=>288
[2,1,4,3,9,6,10,5,8,7]=>[4,4,2]=>252
[2,1,8,3,5,4,7,6,10,9]=>[5,4,1]=>288
[2,1,10,3,5,4,7,6,9,8]=>[5,4,1]=>288
[2,1,9,6,10,3,5,4,8,7]=>[4,3,2,1]=>768
[2,1,7,4,8,3,6,5,10,9]=>[4,4,2]=>252
[2,1,7,4,10,3,6,5,9,8]=>[4,4,2]=>252
[2,1,10,3,6,5,9,4,8,7]=>[4,3,2,1]=>768
[2,1,9,4,8,5,10,3,7,6]=>[4,3,2,1]=>768
[4,1,3,2,10,5,7,6,9,8]=>[5,3,2]=>450
[4,1,3,2,9,6,10,5,8,7]=>[4,3,3]=>210
[6,1,3,2,5,4,8,7,10,9]=>[5,4,1]=>288
[6,1,3,2,5,4,10,7,9,8]=>[5,3,2]=>450
[8,1,3,2,5,4,7,6,10,9]=>[5,4,1]=>288
[9,6,10,1,3,2,5,4,8,7]=>[4,3,2,1]=>768
[7,4,8,1,3,2,6,5,10,9]=>[4,3,2,1]=>768
[7,4,10,1,3,2,6,5,9,8]=>[4,3,2,1]=>768
[10,1,3,2,6,5,9,4,8,7]=>[4,3,2,1]=>768
[9,4,8,5,10,1,3,2,7,6]=>[3,3,2,1,1]=>450
[5,2,6,1,4,3,8,7,10,9]=>[4,4,2]=>252
[5,2,6,1,4,3,10,7,9,8]=>[4,3,3]=>210
[5,2,8,1,4,3,7,6,10,9]=>[4,4,2]=>252
[5,2,10,1,4,3,7,6,9,8]=>[4,4,2]=>252
[5,2,9,6,10,1,4,3,8,7]=>[3,3,3,1]=>210
[8,1,4,3,7,2,6,5,10,9]=>[4,3,2,1]=>768
[10,1,4,3,7,2,6,5,9,8]=>[4,3,2,1]=>768
[9,2,6,5,10,1,4,3,8,7]=>[3,3,2,1,1]=>450
[10,1,4,3,8,5,9,2,7,6]=>[4,3,2,1]=>768
[7,2,6,3,8,1,5,4,10,9]=>[4,3,2,1]=>768
[7,2,6,3,10,1,5,4,9,8]=>[4,3,2,1]=>768
[10,1,5,4,9,2,6,3,8,7]=>[4,3,2,1]=>768
[8,3,10,1,5,4,9,2,7,6]=>[3,3,2,2]=>252
[8,3,9,2,7,4,10,1,6,5]=>[3,3,2,2]=>252
[2,1,4,3,6,5,12,7,9,8,11,10]=>[6,5,1]=>1155
[2,1,4,3,6,5,11,8,12,7,10,9]=>[5,5,2]=>1320
[2,1,4,3,10,5,7,6,9,8,12,11]=>[6,5,1]=>1155
[2,1,4,3,12,5,7,6,9,8,11,10]=>[6,5,1]=>1155
[2,1,4,3,11,8,12,5,7,6,10,9]=>[5,4,2,1]=>5775
[2,1,4,3,9,6,10,5,8,7,12,11]=>[5,5,2]=>1320
[2,1,4,3,9,6,12,5,8,7,11,10]=>[5,5,2]=>1320
[2,1,4,3,12,5,8,7,11,6,10,9]=>[5,4,2,1]=>5775
[2,1,4,3,11,6,10,7,12,5,9,8]=>[5,4,2,1]=>5775
[2,1,6,3,5,4,12,7,9,8,11,10]=>[6,4,2]=>2673
[2,1,6,3,5,4,11,8,12,7,10,9]=>[5,4,3]=>2112
[2,1,8,3,5,4,7,6,10,9,12,11]=>[6,5,1]=>1155
[2,1,8,3,5,4,7,6,12,9,11,10]=>[6,4,2]=>2673
[2,1,10,3,5,4,7,6,9,8,12,11]=>[6,5,1]=>1155
[2,1,12,3,5,4,7,6,9,8,11,10]=>[6,5,1]=>1155
[2,1,11,8,12,3,5,4,7,6,10,9]=>[5,4,2,1]=>5775
[2,1,9,6,10,3,5,4,8,7,12,11]=>[5,4,2,1]=>5775
[2,1,9,6,12,3,5,4,8,7,11,10]=>[5,4,2,1]=>5775
[2,1,12,3,5,4,8,7,11,6,10,9]=>[5,4,2,1]=>5775
[2,1,11,6,10,7,12,3,5,4,9,8]=>[4,4,2,1,1]=>4455
[2,1,7,4,8,3,6,5,10,9,12,11]=>[5,5,2]=>1320
[2,1,7,4,8,3,6,5,12,9,11,10]=>[5,4,3]=>2112
[2,1,7,4,10,3,6,5,9,8,12,11]=>[5,5,2]=>1320
[2,1,7,4,12,3,6,5,9,8,11,10]=>[5,5,2]=>1320
[2,1,7,4,11,8,12,3,6,5,10,9]=>[4,4,3,1]=>2970
[2,1,10,3,6,5,9,4,8,7,12,11]=>[5,4,2,1]=>5775
[2,1,12,3,6,5,9,4,8,7,11,10]=>[5,4,2,1]=>5775
[2,1,11,4,8,7,12,3,6,5,10,9]=>[4,4,2,1,1]=>4455
[2,1,12,3,6,5,10,7,11,4,9,8]=>[5,4,2,1]=>5775
[2,1,9,4,8,5,10,3,7,6,12,11]=>[5,4,2,1]=>5775
[2,1,9,4,8,5,12,3,7,6,11,10]=>[5,4,2,1]=>5775
[2,1,12,3,7,6,11,4,8,5,10,9]=>[5,4,2,1]=>5775
[2,1,10,5,12,3,7,6,11,4,9,8]=>[4,4,2,2]=>2640
[2,1,10,5,11,4,9,6,12,3,8,7]=>[4,4,2,2]=>2640
[4,1,3,2,6,5,12,7,9,8,11,10]=>[6,4,2]=>2673
[4,1,3,2,6,5,11,8,12,7,10,9]=>[5,4,3]=>2112
[4,1,3,2,10,5,7,6,9,8,12,11]=>[6,4,2]=>2673
[4,1,3,2,12,5,7,6,9,8,11,10]=>[6,4,2]=>2673
[4,1,3,2,11,8,12,5,7,6,10,9]=>[5,3,3,1]=>4158
[4,1,3,2,9,6,10,5,8,7,12,11]=>[5,4,3]=>2112
[4,1,3,2,9,6,12,5,8,7,11,10]=>[5,4,3]=>2112
[4,1,3,2,12,5,8,7,11,6,10,9]=>[5,3,3,1]=>4158
[4,1,3,2,11,6,10,7,12,5,9,8]=>[5,3,3,1]=>4158
[6,1,3,2,5,4,8,7,10,9,12,11]=>[6,5,1]=>1155
[6,1,3,2,5,4,8,7,12,9,11,10]=>[6,4,2]=>2673
[6,1,3,2,5,4,10,7,9,8,12,11]=>[6,4,2]=>2673
[6,1,3,2,5,4,12,7,9,8,11,10]=>[6,4,2]=>2673
[6,1,3,2,5,4,11,8,12,7,10,9]=>[5,4,3]=>2112
[8,1,3,2,5,4,7,6,10,9,12,11]=>[6,5,1]=>1155
[8,1,3,2,5,4,7,6,12,9,11,10]=>[6,4,2]=>2673
[10,1,3,2,5,4,7,6,9,8,12,11]=>[6,5,1]=>1155
[11,8,12,1,3,2,5,4,7,6,10,9]=>[5,4,2,1]=>5775
[9,6,10,1,3,2,5,4,8,7,12,11]=>[5,4,2,1]=>5775
[9,6,12,1,3,2,5,4,8,7,11,10]=>[5,4,2,1]=>5775
[12,1,3,2,5,4,8,7,11,6,10,9]=>[5,4,2,1]=>5775
[11,6,10,7,12,1,3,2,5,4,9,8]=>[4,3,3,1,1]=>4158
[7,4,8,1,3,2,6,5,10,9,12,11]=>[5,4,2,1]=>5775
[7,4,8,1,3,2,6,5,12,9,11,10]=>[5,3,3,1]=>4158
[7,4,10,1,3,2,6,5,9,8,12,11]=>[5,4,2,1]=>5775
[7,4,12,1,3,2,6,5,9,8,11,10]=>[5,4,2,1]=>5775
[7,4,11,8,12,1,3,2,6,5,10,9]=>[4,3,3,2]=>2970
[10,1,3,2,6,5,9,4,8,7,12,11]=>[5,4,2,1]=>5775
[12,1,3,2,6,5,9,4,8,7,11,10]=>[5,4,2,1]=>5775
[11,4,8,7,12,1,3,2,6,5,10,9]=>[4,3,3,1,1]=>4158
[12,1,3,2,6,5,10,7,11,4,9,8]=>[5,4,2,1]=>5775
[9,4,8,5,10,1,3,2,7,6,12,11]=>[4,4,2,1,1]=>4455
[9,4,8,5,12,1,3,2,7,6,11,10]=>[4,4,2,1,1]=>4455
[12,1,3,2,7,6,11,4,8,5,10,9]=>[5,4,2,1]=>5775
[10,5,12,1,3,2,7,6,11,4,9,8]=>[4,3,3,2]=>2970
[10,5,11,4,9,6,12,1,3,2,8,7]=>[3,3,3,2,1]=>2112
[5,2,6,1,4,3,8,7,10,9,12,11]=>[5,5,2]=>1320
[5,2,6,1,4,3,8,7,12,9,11,10]=>[5,4,3]=>2112
[5,2,6,1,4,3,10,7,9,8,12,11]=>[5,4,3]=>2112
[5,2,6,1,4,3,12,7,9,8,11,10]=>[5,4,3]=>2112
[5,2,6,1,4,3,11,8,12,7,10,9]=>[4,4,4]=>462
[5,2,8,1,4,3,7,6,10,9,12,11]=>[5,5,2]=>1320
[5,2,8,1,4,3,7,6,12,9,11,10]=>[5,4,3]=>2112
[5,2,10,1,4,3,7,6,9,8,12,11]=>[5,5,2]=>1320
[5,2,12,1,4,3,7,6,9,8,11,10]=>[5,5,2]=>1320
[5,2,11,8,12,1,4,3,7,6,10,9]=>[4,4,3,1]=>2970
[5,2,9,6,10,1,4,3,8,7,12,11]=>[4,4,3,1]=>2970
[5,2,9,6,12,1,4,3,8,7,11,10]=>[4,4,3,1]=>2970
[5,2,12,1,4,3,8,7,11,6,10,9]=>[4,4,3,1]=>2970
[5,2,11,6,10,7,12,1,4,3,9,8]=>[4,3,3,1,1]=>4158
[8,1,4,3,7,2,6,5,10,9,12,11]=>[5,4,2,1]=>5775
[8,1,4,3,7,2,6,5,12,9,11,10]=>[5,3,3,1]=>4158
[10,1,4,3,7,2,6,5,9,8,12,11]=>[5,4,2,1]=>5775
[12,1,4,3,7,2,6,5,9,8,11,10]=>[5,4,2,1]=>5775
[11,8,12,1,4,3,7,2,6,5,10,9]=>[4,3,2,2,1]=>5775
[9,2,6,5,10,1,4,3,8,7,12,11]=>[4,4,2,1,1]=>4455
[9,2,6,5,12,1,4,3,8,7,11,10]=>[4,4,2,1,1]=>4455
[12,1,4,3,8,7,11,2,6,5,10,9]=>[4,3,3,1,1]=>4158
[11,2,6,5,10,7,12,1,4,3,9,8]=>[4,3,3,1,1]=>4158
[10,1,4,3,8,5,9,2,7,6,12,11]=>[5,4,2,1]=>5775
[12,1,4,3,8,5,9,2,7,6,11,10]=>[5,4,2,1]=>5775
[11,2,7,6,12,1,4,3,8,5,10,9]=>[4,4,2,1,1]=>4455
[10,5,11,2,7,6,12,1,4,3,9,8]=>[3,3,3,2,1]=>2112
[10,5,12,1,4,3,9,6,11,2,8,7]=>[4,3,2,2,1]=>5775
[7,2,6,3,8,1,5,4,10,9,12,11]=>[5,4,2,1]=>5775
[7,2,6,3,8,1,5,4,12,9,11,10]=>[5,3,3,1]=>4158
[7,2,6,3,10,1,5,4,9,8,12,11]=>[5,4,2,1]=>5775
[7,2,6,3,12,1,5,4,9,8,11,10]=>[5,4,2,1]=>5775
[7,2,6,3,11,8,12,1,5,4,10,9]=>[4,3,3,2]=>2970
[10,1,5,4,9,2,6,3,8,7,12,11]=>[5,4,2,1]=>5775
[12,1,5,4,9,2,6,3,8,7,11,10]=>[5,4,2,1]=>5775
[11,2,6,3,8,7,12,1,5,4,10,9]=>[4,3,3,1,1]=>4158
[12,1,5,4,10,7,11,2,6,3,9,8]=>[4,3,3,1,1]=>4158
[8,3,10,1,5,4,9,2,7,6,12,11]=>[4,4,2,2]=>2640
[8,3,12,1,5,4,9,2,7,6,11,10]=>[4,4,2,2]=>2640
[8,3,11,2,7,6,12,1,5,4,10,9]=>[3,3,3,2,1]=>2112
[11,2,7,6,12,1,5,4,10,3,9,8]=>[3,3,2,2,1,1]=>2673
[12,1,5,4,10,3,9,6,11,2,8,7]=>[4,3,2,2,1]=>5775
[8,3,9,2,7,4,10,1,6,5,12,11]=>[4,4,2,2]=>2640
[8,3,9,2,7,4,12,1,6,5,11,10]=>[4,3,3,2]=>2970
[8,3,12,1,6,5,11,2,7,4,10,9]=>[4,4,2,2]=>2640
[12,1,6,5,11,2,7,4,10,3,9,8]=>[4,3,2,2,1]=>5775
[10,3,9,4,12,1,6,5,11,2,8,7]=>[4,3,2,2,1]=>5775
[10,3,9,4,11,2,8,5,12,1,7,6]=>[4,3,2,2,1]=>5775
[4,7,6,1,3,2,8,5]=>[3,3,1,1]=>56
[7,2,6,5,4,3,1,9,8]=>[3,2,1,1,1,1]=>105
[3,2,1,9,5,8,7,6,4]=>[3,2,2,1,1]=>162
[6,3,5,4,2,1,9,8,7]=>[3,2,2,1,1]=>162
[4,3,2,1,9,7,8,6,5]=>[3,2,2,2]=>84
[7,6,3,1,8,5,2,4]=>[3,2,2,1]=>70
[7,2,5,8,6,1,3,4]=>[3,3,2]=>42
[4,1,3,6,2,5,8,7]=>[4,3,1]=>70
[7,1,4,6,3,2,5,8]=>[4,2,1,1]=>90
[7,4,5,8,6,2,3,1]=>[3,2,2,1]=>70
[6,7,2,3,8,4,1,5]=>[4,3,1]=>70
[1,2,3,4,5,6,8,9,7,10]=>[9,1]=>9
[3,1,6,7,5,2,8,4]=>[4,3,1]=>70
[4,1,6,2,3,8,7,5]=>[4,3,1]=>70
[4,1,7,6,5,2,8,3]=>[3,3,1,1]=>56
[8,4,1,5,6,2,7,3]=>[4,3,1]=>70
[2,8,4,7,3,5,6,1]=>[4,2,1,1]=>90
[1,5,4,8,3,2,6,7]=>[4,2,1,1]=>90
[1,5,7,6,3,8,2,4]=>[4,2,1,1]=>90
[2,6,3,1,7,8,4,5]=>[4,3,1]=>70
[2,1,7,8,3,5,4,6]=>[4,3,1]=>70
[1,5,8,6,7,4,2,3]=>[4,2,1,1]=>90
[8,7,1,3,5,2,6,4]=>[4,2,1,1]=>90
[3,7,8,2,5,4,1,6]=>[3,3,1,1]=>56
[4,7,6,5,8,1,3,2]=>[3,2,1,1,1]=>64
[4,7,8,6,2,1,5,3]=>[3,2,2,1]=>70
[4,8,6,3,2,1,7,5]=>[3,2,1,1,1]=>64
[5,1,4,7,6,8,3,2]=>[4,2,1,1]=>90
[5,6,4,7,1,8,3,2]=>[4,2,1,1]=>90
[5,3,7,4,6,1,8,2]=>[4,2,2]=>56
[4,1,5,7,8,6,3,2]=>[4,2,1,1]=>90
[3,6,7,1,5,4,8,2]=>[4,2,1,1]=>90
[3,6,4,7,5,8,2,1]=>[4,2,1,1]=>90
[9,1,2,3,4,8,6,5,7]=>[6,1,1,1]=>56
[9,1,2,3,8,5,6,4,7]=>[6,1,1,1]=>56
[8,1,2,9,4,5,6,3,7]=>[6,2,1]=>105
[9,1,8,3,4,5,6,2,7]=>[6,1,1,1]=>56
[7,1,2,3,4,9,5,8,6]=>[6,2,1]=>105
[10,1,2,3,4,5,9,7,6,8]=>[7,1,1,1]=>84
[6,1,2,3,8,4,5,9,7]=>[6,3]=>48
[10,1,2,3,4,9,6,7,5,8]=>[7,1,1,1]=>84
[5,1,2,8,3,4,6,9,7]=>[6,3]=>48
[9,1,2,3,10,5,6,7,4,8]=>[7,2,1]=>160
[4,1,9,2,3,5,6,8,7]=>[6,2,1]=>105
[10,1,2,9,4,5,6,7,3,8]=>[7,1,1,1]=>84
[3,8,1,2,4,5,6,9,7]=>[6,3]=>48
[10,1,9,3,4,5,6,7,2,8]=>[7,1,1,1]=>84
[8,2,1,3,4,5,6,9,7]=>[6,2,1]=>105
[8,1,2,3,4,5,10,6,9,7]=>[7,2,1]=>160
[11,1,2,3,4,5,6,10,8,7,9]=>[8,1,1,1]=>120
[9,1,2,3,8,5,4,7,6]=>[5,2,1,1]=>189
[7,1,2,3,4,9,5,6,10,8]=>[7,3]=>75
[11,1,2,3,4,5,10,7,8,6,9]=>[8,1,1,1]=>120
[6,1,2,3,9,4,7,8,5]=>[6,2,1]=>105
[6,1,2,3,9,4,5,7,10,8]=>[7,3]=>75
[10,1,2,3,4,11,6,7,8,5,9]=>[8,2,1]=>231
[5,1,2,8,3,6,4,9,7]=>[5,3,1]=>162
[5,1,2,10,3,4,6,7,9,8]=>[7,2,1]=>160
[11,1,2,3,10,5,6,7,8,4,9]=>[8,1,1,1]=>120
[9,8,2,1,4,5,6,7,3]=>[5,2,1,1]=>189
[8,1,7,3,2,4,5,6]=>[5,1,1,1]=>35
[4,1,8,2,5,3,6,9,7]=>[5,3,1]=>162
[4,1,9,2,3,5,6,7,10,8]=>[7,3]=>75
[11,1,2,10,4,5,6,7,8,3,9]=>[8,1,1,1]=>120
[3,9,1,4,2,5,6,8,7]=>[5,3,1]=>162
[3,9,1,2,4,5,6,7,10,8]=>[7,3]=>75
[10,1,11,3,4,5,6,7,8,2,9]=>[8,2,1]=>231
[8,2,3,1,4,5,6,9,7]=>[6,2,1]=>105
[10,2,1,3,4,5,6,7,9,8]=>[7,2,1]=>160
[11,10,2,3,4,5,6,7,8,1,9]=>[8,1,1,1]=>120
[6,4,7,1,5,2,8,3]=>[3,3,2]=>42
[1,6,5,2,8,7,4,3]=>[3,2,2,1]=>70
[2,3,4,5,7,8,1,9,6]=>[7,2]=>27
[1,3,4,5,2,6,7,8,9]=>[8,1]=>8
[1,2,3,4,5,7,8,6,9,10]=>[9,1]=>9
[2,3,4,5,7,9,1,6,8]=>[6,3]=>48
[1,2,3,4,5,7,8,9,6,10]=>[9,1]=>9
[2,3,4,5,1,6,7,9,8]=>[7,2]=>27
[4,5,6,1,7,8,9,2,3]=>[6,3]=>48
[2,1,4,5,3,6,7,8,9]=>[7,2]=>27
[2,4,5,6,1,7,8,9,10,3]=>[8,2]=>35
[1,3,2,5,4,6,7,8,9]=>[7,2]=>27
[2,3,5,6,1,7,8,9,10,4]=>[8,2]=>35
[3,2,5,8,6,1,7,4]=>[4,2,2]=>56
[4,5,1,7,2,8,6,3]=>[4,3,1]=>70
[6,4,7,2,5,3,1,8]=>[3,2,2,1]=>70
[7,1,4,3,6,8,2,5]=>[4,2,1,1]=>90
[4,1,6,2,8,3,5,7,9]=>[6,3]=>48
[4,1,6,2,8,3,9,5,7]=>[5,4]=>42
[4,1,6,2,7,3,8,5,9]=>[5,4]=>42
[4,8,7,3,5,1,6,2]=>[3,2,2,1]=>70
[5,3,8,7,1,6,2,4]=>[3,2,2,1]=>70
[5,2,6,7,4,3,1,8]=>[4,2,1,1]=>90
[8,5,1,6,4,3,2,7]=>[3,2,1,1,1]=>64
[8,6,3,5,2,7,1,4]=>[3,2,1,1,1]=>64
[8,4,6,2,1,5,7,3]=>[3,2,2,1]=>70
[8,5,2,1,6,4,7,3]=>[3,2,2,1]=>70
[1,7,2,8,5,4,6,3]=>[4,2,1,1]=>90
[6,7,1,4,8,5,3,2]=>[3,3,1,1]=>56
[7,3,2,8,5,1,4,6]=>[3,2,2,1]=>70
[4,1,7,3,2,8,5,6]=>[4,3,1]=>70
[8,3,5,2,4,7,1,6]=>[3,3,1,1]=>56
[4,3,7,8,6,1,5,2]=>[3,2,2,1]=>70
[1,2,6,3,7,8,5,4]=>[5,2,1]=>64
[6,1,3,7,8,5,4,2]=>[4,2,1,1]=>90
[8,7,9,1,4,5,6,2,3]=>[4,2,2,1]=>216
[7,6,9,1,4,5,2,8,3]=>[4,2,2,1]=>216
[9,8,10,1,4,5,6,7,2,3]=>[5,2,2,1]=>525
[11,10,2,1,4,5,6,7,8,9,3]=>[7,2,1,1]=>594
[2,6,4,7,5,3,1,8]=>[4,2,1,1]=>90
[4,5,1,8,6,2,7,3]=>[4,3,1]=>70
[5,6,1,8,7,2,3,4]=>[4,3,1]=>70
[4,5,1,6,8,7,3,2]=>[4,2,1,1]=>90
[3,9,2,4,5,6,7,8,1]=>[6,2,1]=>105
[3,8,6,1,5,2,4,7]=>[4,2,1,1]=>90
[3,2,8,1,5,6,4,7]=>[4,2,2]=>56
[5,8,7,3,2,1,4,6]=>[3,2,1,1,1]=>64
[3,4,7,6,8,2,1,5]=>[4,2,1,1]=>90
[2,8,1,3,7,5,6,4]=>[4,2,1,1]=>90
[1,8,7,2,5,6,4,3]=>[4,1,1,1,1]=>35
[3,4,7,1,5,8,2,6]=>[4,3,1]=>70
[4,2,7,1,5,8,3,6]=>[3,3,2]=>42
[1,3,5,2,4,6,7,8,9]=>[7,2]=>27
[4,1,2,3,5,6,8,7,9]=>[7,2]=>27
[1,2,4,7,3,5,6,8,9]=>[7,2]=>27
[5,1,2,3,4,7,6,8,9]=>[7,2]=>27
[1,4,7,5,2,3,6,8]=>[5,2,1]=>64
[2,5,7,6,8,3,4,1]=>[4,2,1,1]=>90
[3,1,6,7,2,8,5,4]=>[4,3,1]=>70
[1,5,3,6,8,4,7,2]=>[4,3,1]=>70
[6,5,1,3,8,4,7,2]=>[4,2,1,1]=>90
[1,7,4,8,5,3,2,6]=>[4,2,1,1]=>90
[7,3,1,6,8,4,5,2]=>[3,3,1,1]=>56
[8,5,1,4,6,7,3,2]=>[4,1,1,1,1]=>35
[3,4,7,5,6,8,2,1]=>[5,1,1,1]=>35
[3,4,7,8,5,2,6,1]=>[4,2,1,1]=>90
[4,8,1,7,5,6,3,2]=>[3,2,1,1,1]=>64
[1,8,7,5,2,6,3,4]=>[4,2,1,1]=>90
[1,7,6,3,4,5,8,2]=>[5,1,1,1]=>35
[1,8,7,4,5,6,2,3]=>[4,2,1,1]=>90
[1,8,7,3,6,4,2,5]=>[4,1,1,1,1]=>35
[1,4,7,5,8,2,6,3]=>[4,2,2]=>56
[1,4,7,2,3,6,5,8]=>[5,2,1]=>64
[1,7,2,5,6,3,4,8]=>[5,2,1]=>64
[1,2,6,5,8,3,4,7]=>[5,2,1]=>64
[1,5,8,2,6,3,4,7]=>[5,2,1]=>64
[6,8,3,2,7,5,1,4]=>[2,2,2,2]=>14
[4,1,5,7,2,6,3,8]=>[4,3,1]=>70
[5,7,2,1,3,6,4,8]=>[4,2,2]=>56
[10,11,8,1,2,3,4,5,6,7,9]=>[8,2,1]=>231
[7,1,10,9,2,3,4,5,6,8]=>[7,2,1]=>160
[6,7,9,1,2,3,4,5,10,8]=>[6,4]=>90
[2,8,1,9,10,3,4,5,6,7]=>[6,4]=>90
[8,7,1,10,2,3,4,5,6,9]=>[7,2,1]=>160
[3,5,6,7,2,4,1,8]=>[5,2,1]=>64
[6,4,7,5,2,3,1,8]=>[3,2,2,1]=>70
[1,5,6,4,8,3,2,7]=>[4,2,1,1]=>90
[2,1,5,6,4,8,3,7]=>[4,3,1]=>70
[5,1,4,7,8,6,2,3]=>[4,2,2]=>56
[1,6,7,2,8,5,4,3]=>[4,2,1,1]=>90
[5,3,2,1,7,8,6,4]=>[3,2,2,1]=>70
[7,4,3,8,6,1,5,2]=>[2,2,2,2]=>14
[4,3,7,1,5,8,6,2]=>[3,3,2]=>42
[8,2,4,5,3,1,7,6]=>[4,2,1,1]=>90
[1,4,3,2,7,5,8,6]=>[4,3,1]=>70
[1,5,2,8,6,3,10,9,7,4]=>[4,3,2,1]=>768
[4,1,5,2,8,6,3,10,9,7]=>[4,4,2]=>252
[1,7,5,2,8,6,3,10,9,4]=>[4,3,3]=>210
[4,1,7,5,2,8,3,10,9,6]=>[4,4,2]=>252
[6,4,1,7,5,2,8,3,10,9]=>[4,4,2]=>252
[3,4,1,7,2,8,5,10,9,6]=>[5,4,1]=>288
[3,6,4,1,7,2,8,5,10,9]=>[5,4,1]=>288
[1,5,2,9,8,6,3,10,7,4]=>[4,3,2,1]=>768
[4,1,5,2,9,8,6,3,10,7]=>[4,4,1,1]=>300
[1,7,5,2,9,6,3,10,8,4]=>[4,3,3]=>210
[4,1,7,5,2,9,3,10,8,6]=>[4,4,2]=>252
[4,1,9,6,5,2,7,3,10,8]=>[4,4,1,1]=>300
[3,4,1,7,2,9,5,10,8,6]=>[5,4,1]=>288
[3,6,1,9,4,2,7,5,10,8]=>[4,4,2]=>252
[1,8,7,5,2,9,6,3,10,4]=>[4,3,2,1]=>768
[4,1,8,7,5,2,9,3,10,6]=>[4,4,1,1]=>300
[6,4,1,8,5,2,9,3,10,7]=>[4,4,2]=>252
[7,6,4,1,8,5,2,9,3,10]=>[4,3,2,1]=>768
[3,4,1,8,7,2,9,5,10,6]=>[5,4,1]=>288
[3,6,4,1,8,2,9,5,10,7]=>[5,4,1]=>288
[3,7,6,4,1,8,2,9,5,10]=>[5,3,1,1]=>567
[1,9,6,5,2,7,3,10,8,4]=>[4,3,2,1]=>768
[6,1,9,4,2,7,3,10,8,5]=>[4,3,3]=>210
[5,4,1,9,6,2,7,3,10,8]=>[4,4,2]=>252
[9,3,1,6,2,7,4,10,8,5]=>[4,4,2]=>252
[9,5,3,1,6,2,7,4,10,8]=>[4,4,1,1]=>300
[6,1,8,5,2,9,7,3,10,4]=>[4,4,2]=>252
[6,4,1,8,2,9,7,3,10,5]=>[4,4,2]=>252
[8,5,4,1,6,2,9,3,10,7]=>[4,4,1,1]=>300
[5,7,4,1,8,6,2,9,3,10]=>[5,3,2]=>450
[3,6,1,8,2,9,7,4,10,5]=>[5,4,1]=>288
[5,8,3,1,6,2,9,4,10,7]=>[4,4,2]=>252
[5,3,7,1,8,6,2,9,4,10]=>[5,3,2]=>450
[4,3,8,1,9,5,2,6,10,7]=>[4,4,2]=>252
[7,4,3,5,1,8,2,9,6,10]=>[5,3,1,1]=>567
[9,6,2,1,3,7,4,10,8,5]=>[4,3,2,1]=>768
[5,9,2,1,6,3,7,4,10,8]=>[4,4,2]=>252
[6,8,2,1,3,9,7,4,10,5]=>[4,4,2]=>252
[8,2,5,1,6,3,9,4,10,7]=>[5,4,1]=>288
[2,5,7,1,8,6,3,9,4,10]=>[6,3,1]=>315
[2,4,8,1,9,5,3,6,10,7]=>[5,4,1]=>288
[4,8,7,2,6,1,3,5]=>[3,2,2,1]=>70
[4,5,8,2,1,7,3,6]=>[3,3,2]=>42
[6,8,4,1,7,3,2,5]=>[3,2,2,1]=>70
[7,6,2,8,4,5,3,1]=>[3,2,1,1,1]=>64
[5,8,2,1,3,6,4,7]=>[4,2,2]=>56
[7,6,4,3,5,2,1,9,8]=>[3,2,1,1,1,1]=>105
[7,6,3,5,4,2,1,9,8]=>[3,2,1,1,1,1]=>105
[8,5,1,7,3,4,6,2]=>[4,2,1,1]=>90
[5,7,6,3,4,1,8,2]=>[3,2,2,1]=>70
[7,8,9,10,1,5,6,3,4,2]=>[4,3,2,1]=>768
[7,1,2,6,4,3,5,8]=>[5,1,1,1]=>35
[7,1,2,6,5,3,4,8]=>[5,1,1,1]=>35
[4,7,8,6,2,3,5,1]=>[3,3,1,1]=>56
[7,1,2,4,8,6,5,3]=>[4,2,1,1]=>90
[2,7,5,6,4,8,1,3]=>[4,2,1,1]=>90
[2,8,3,6,5,7,1,4]=>[4,2,1,1]=>90
[9,8,4,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[9,8,3,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1]=>8
[9,3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1]=>8
[9,2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]=>8
[10,9,8,5,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,4,6,5,7,3,2,1]=>[3,1,1,1,1,1,1]=>28
[10,9,8,4,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,8,3,6,5,4,7,2,1]=>[3,1,1,1,1,1,1]=>28
[10,9,4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[9,3,7,6,5,4,8,2,1]=>[3,1,1,1,1,1,1]=>28
[9,2,7,6,5,4,3,8,1]=>[3,1,1,1,1,1,1]=>28
[10,3,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[10,2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]=>9
[7,4,3,1,6,5,2,8]=>[3,2,2,1]=>70
[3,5,1,2,6,8,7,4]=>[4,3,1]=>70
[3,1,2,4,8,7,5,6]=>[5,2,1]=>64
[5,4,1,2,3,7,8,6]=>[5,2,1]=>64
[1,6,7,2,5,8,3,4]=>[4,3,1]=>70
[7,8,5,6,2,4,3,1]=>[2,2,2,1,1]=>28
[5,3,8,6,2,4,1,7]=>[3,2,2,1]=>70
[2,7,4,6,3,8,1,5]=>[4,2,1,1]=>90
[5,4,7,8,6,2,1,3]=>[3,2,2,1]=>70
[2,7,4,8,3,1,5,6]=>[4,2,1,1]=>90
[8,2,1,3,7,4,6,5]=>[4,2,1,1]=>90
[6,5,8,2,3,4,7,1]=>[4,2,1,1]=>90
[7,8,2,3,6,4,5,1]=>[4,2,1,1]=>90
[8,1,2,7,5,3,4,6]=>[5,1,1,1]=>35
[4,2,8,1,3,7,5,6]=>[4,2,2]=>56
[7,5,1,8,2,3,4,6]=>[5,2,1]=>64
[8,2,4,1,3,7,5,6]=>[4,3,1]=>70
[8,1,6,2,3,7,4,5]=>[5,2,1]=>64
[7,1,8,2,3,6,4,5]=>[5,2,1]=>64
[4,2,6,7,5,1,8,3]=>[4,2,2]=>56
[4,7,2,5,3,8,1,6]=>[3,3,1,1]=>56
[3,5,7,4,2,8,1,6]=>[4,2,1,1]=>90
[2,4,7,6,3,8,1,5]=>[4,2,1,1]=>90
[4,6,8,5,1,2,3,7]=>[4,3,1]=>70
[4,6,5,7,1,2,3,8]=>[4,3,1]=>70
[4,6,5,7,1,3,8,2]=>[4,2,1,1]=>90
[3,4,7,6,1,8,2,5]=>[4,3,1]=>70
[8,5,2,1,6,3,4,7]=>[4,2,1,1]=>90
[7,1,8,5,3,2,4,6]=>[4,2,1,1]=>90
[9,10,2,1,6,4,3,5,7,8]=>[5,2,2,1]=>525
[7,10,2,1,8,4,3,5,6,9]=>[5,2,2,1]=>525
[2,9,1,10,7,4,3,5,6,8]=>[5,3,1,1]=>567
[2,8,1,9,4,3,10,5,6,7]=>[5,4,1]=>288
[10,8,5,2,1,6,3,4,7,9]=>[5,2,1,1,1]=>448
[9,5,2,1,10,6,3,4,7,8]=>[5,2,2,1]=>525
[10,7,2,1,8,5,3,4,6,9]=>[5,2,2,1]=>525
[9,2,1,10,7,5,3,4,6,8]=>[5,2,2,1]=>525
[2,8,1,9,3,10,5,4,6,7]=>[5,4,1]=>288
[10,6,2,1,7,3,8,4,5,9]=>[5,3,1,1]=>567
[9,2,1,10,6,3,7,4,5,8]=>[5,3,2]=>450
[8,2,1,9,3,10,6,4,5,7]=>[5,3,2]=>450
[7,2,1,8,3,9,4,10,5,6]=>[5,4,1]=>288
[10,8,6,3,1,4,2,5,7,9]=>[5,2,1,1,1]=>448
[3,9,1,10,6,4,2,5,7,8]=>[5,3,1,1]=>567
[10,7,3,1,8,4,2,5,6,9]=>[5,2,2,1]=>525
[9,3,1,10,7,4,2,5,6,8]=>[5,2,2,1]=>525
[8,3,1,9,4,2,10,5,6,7]=>[5,3,2]=>450
[10,8,5,1,6,3,2,4,7,9]=>[5,2,1,1,1]=>448
[9,5,1,10,6,3,2,4,7,8]=>[5,2,2,1]=>525
[10,7,1,8,5,3,2,4,6,9]=>[5,2,1,1,1]=>448
[9,1,10,7,5,3,2,4,6,8]=>[5,2,1,1,1]=>448
[8,3,1,9,2,10,5,4,6,7]=>[5,3,2]=>450
[10,6,1,7,3,2,8,4,5,9]=>[5,3,1,1]=>567
[9,1,10,6,3,2,7,4,5,8]=>[5,2,2,1]=>525
[8,1,9,3,2,10,6,4,5,7]=>[5,3,2]=>450
[7,1,8,3,2,9,4,10,5,6]=>[5,4,1]=>288
[10,8,4,1,5,2,6,3,7,9]=>[5,3,1,1]=>567
[9,4,1,10,5,2,6,3,7,8]=>[5,3,2]=>450
[10,7,1,8,4,2,5,3,6,9]=>[5,2,2,1]=>525
[9,1,10,7,4,2,5,3,6,8]=>[5,2,2,1]=>525
[8,1,9,4,2,10,5,3,6,7]=>[5,3,2]=>450
[10,6,1,7,2,8,4,3,5,9]=>[5,3,1,1]=>567
[9,1,10,6,2,7,4,3,5,8]=>[5,2,2,1]=>525
[8,1,9,2,10,6,4,3,5,7]=>[5,3,1,1]=>567
[7,1,8,2,9,4,3,10,5,6]=>[5,4,1]=>288
[10,5,1,6,2,7,3,8,4,9]=>[5,4,1]=>288
[9,1,10,5,2,6,3,7,4,8]=>[5,3,2]=>450
[8,1,9,2,10,5,3,6,4,7]=>[5,3,2]=>450
[7,1,8,2,9,3,10,5,4,6]=>[5,4,1]=>288
[11,12,8,2,1,6,4,3,5,7,9,10]=>[6,2,2,1,1]=>3564
[12,2,9,1,10,6,4,3,5,7,8,11]=>[6,3,1,1,1]=>3696
[11,12,2,1,9,6,4,3,5,7,8,10]=>[6,2,2,1,1]=>3564
[10,2,4,1,11,3,12,6,5,7,8,9]=>[6,4,2]=>2673
[7,12,10,2,1,8,4,3,5,6,9,11]=>[6,2,2,1,1]=>3564
[2,11,7,1,12,8,4,3,5,6,9,10]=>[6,3,2,1]=>5632
[9,12,2,1,10,7,4,3,5,6,8,11]=>[6,2,2,1,1]=>3564
[2,11,1,12,9,7,4,3,5,6,8,10]=>[6,3,1,1,1]=>3696
[10,11,2,1,4,3,12,7,5,6,8,9]=>[6,3,3]=>1650
[8,12,2,1,9,4,3,10,5,6,7,11]=>[6,3,2,1]=>5632
[2,11,1,12,8,4,3,9,5,6,7,10]=>[6,3,2,1]=>5632
[2,10,1,11,4,3,12,8,5,6,7,9]=>[6,4,2]=>2673
[2,9,1,10,4,3,11,5,12,6,7,8]=>[6,5,1]=>1155
[12,10,8,5,2,1,6,3,4,7,9,11]=>[6,2,1,1,1,1]=>2100
[5,11,2,1,12,8,6,3,4,7,9,10]=>[6,3,2,1]=>5632
[12,9,5,2,1,10,6,3,4,7,8,11]=>[6,2,2,1,1]=>3564
[11,5,2,1,12,9,6,3,4,7,8,10]=>[6,2,2,2]=>1925
[10,11,2,1,5,3,12,6,4,7,8,9]=>[6,3,3]=>1650
[12,10,7,2,1,8,5,3,4,6,9,11]=>[6,2,2,1,1]=>3564
[11,7,2,1,12,8,5,3,4,6,9,10]=>[6,2,2,2]=>1925
[12,9,2,1,10,7,5,3,4,6,8,11]=>[6,2,2,1,1]=>3564
[11,2,1,12,9,7,5,3,4,6,8,10]=>[6,2,2,1,1]=>3564
[10,11,2,1,3,12,7,5,4,6,8,9]=>[6,3,2,1]=>5632
[8,9,2,1,12,3,10,5,4,6,7,11]=>[6,3,2,1]=>5632
[11,8,2,1,12,3,9,5,4,6,7,10]=>[6,2,2,2]=>1925
[2,10,1,11,3,12,8,5,4,6,7,9]=>[6,4,1,1]=>3080
[2,9,1,10,3,11,5,4,12,6,7,8]=>[6,5,1]=>1155
[12,10,6,2,1,7,3,8,4,5,9,11]=>[6,3,1,1,1]=>3696
[11,6,2,1,12,7,3,8,4,5,9,10]=>[6,3,2,1]=>5632
[12,9,2,1,10,6,3,7,4,5,8,11]=>[6,3,2,1]=>5632
[11,2,1,12,9,6,3,7,4,5,8,10]=>[6,3,2,1]=>5632
[10,2,1,11,6,3,12,7,4,5,8,9]=>[6,3,3]=>1650
[12,8,2,1,9,3,10,6,4,5,7,11]=>[6,3,2,1]=>5632
[11,2,1,12,8,3,9,6,4,5,7,10]=>[6,3,2,1]=>5632
[10,2,1,11,3,12,8,6,4,5,7,9]=>[6,3,2,1]=>5632
[2,9,1,10,3,11,4,12,6,5,7,8]=>[6,5,1]=>1155
[12,7,2,1,8,3,9,4,10,5,6,11]=>[6,4,1,1]=>3080
[11,2,1,12,7,3,8,4,9,5,6,10]=>[6,4,2]=>2673
[10,2,1,11,3,12,7,4,8,5,6,9]=>[6,3,3]=>1650
[9,2,1,10,3,11,4,12,7,5,6,8]=>[6,4,2]=>2673
[8,2,1,9,3,10,4,11,5,12,6,7]=>[6,5,1]=>1155
[12,10,8,6,3,1,4,2,5,7,9,11]=>[6,2,1,1,1,1]=>2100
[11,12,3,1,8,6,4,2,5,7,9,10]=>[6,2,2,1,1]=>3564
[9,12,3,1,10,6,4,2,5,7,8,11]=>[6,2,2,1,1]=>3564
[3,11,1,12,9,6,4,2,5,7,8,10]=>[6,3,1,1,1]=>3696
[3,10,4,1,11,2,12,6,5,7,8,9]=>[6,4,2]=>2673
[12,10,7,3,1,8,4,2,5,6,9,11]=>[6,2,2,1,1]=>3564
[11,7,3,1,12,8,4,2,5,6,9,10]=>[6,2,2,2]=>1925
[12,9,3,1,10,7,4,2,5,6,8,11]=>[6,2,2,1,1]=>3564
[11,3,1,12,9,7,4,2,5,6,8,10]=>[6,2,2,1,1]=>3564
[3,10,1,11,4,2,12,7,5,6,8,9]=>[6,4,2]=>2673
[12,8,3,1,9,4,2,10,5,6,7,11]=>[6,3,2,1]=>5632
[11,3,1,12,8,4,2,9,5,6,7,10]=>[6,3,2,1]=>5632
[10,3,1,11,4,2,12,8,5,6,7,9]=>[6,3,3]=>1650
[9,3,1,10,4,2,11,5,12,6,7,8]=>[6,4,2]=>2673
[12,10,8,5,1,6,3,2,4,7,9,11]=>[6,2,1,1,1,1]=>2100
[5,11,1,12,8,6,3,2,4,7,9,10]=>[6,3,1,1,1]=>3696
[12,9,5,1,10,6,3,2,4,7,8,11]=>[6,2,2,1,1]=>3564
[11,5,1,12,9,6,3,2,4,7,8,10]=>[6,2,2,1,1]=>3564
[3,10,1,11,5,2,12,6,4,7,8,9]=>[6,4,2]=>2673
[12,10,7,1,8,5,3,2,4,6,9,11]=>[6,2,1,1,1,1]=>2100
[11,7,1,12,8,5,3,2,4,6,9,10]=>[6,2,2,1,1]=>3564
[12,9,1,10,7,5,3,2,4,6,8,11]=>[6,2,1,1,1,1]=>2100
[11,1,12,9,7,5,3,2,4,6,8,10]=>[6,2,1,1,1,1]=>2100
[3,10,1,11,2,12,7,5,4,6,8,9]=>[6,4,1,1]=>3080
[8,9,1,12,3,2,10,5,4,6,7,11]=>[6,3,2,1]=>5632
[11,8,1,12,3,2,9,5,4,6,7,10]=>[6,2,2,2]=>1925
[10,3,1,11,2,12,8,5,4,6,7,9]=>[6,3,2,1]=>5632
[9,3,1,10,2,11,5,4,12,6,7,8]=>[6,4,2]=>2673
[12,10,6,1,7,3,2,8,4,5,9,11]=>[6,3,1,1,1]=>3696
[11,6,1,12,7,3,2,8,4,5,9,10]=>[6,3,2,1]=>5632
[12,9,1,10,6,3,2,7,4,5,8,11]=>[6,2,2,1,1]=>3564
[11,1,12,9,6,3,2,7,4,5,8,10]=>[6,2,2,1,1]=>3564
[10,1,11,6,3,2,12,7,4,5,8,9]=>[6,3,2,1]=>5632
[12,8,1,9,3,2,10,6,4,5,7,11]=>[6,3,2,1]=>5632
[11,1,12,8,3,2,9,6,4,5,7,10]=>[6,2,2,2]=>1925
[10,1,11,3,2,12,8,6,4,5,7,9]=>[6,3,2,1]=>5632
[9,3,1,10,2,11,4,12,6,5,7,8]=>[6,4,2]=>2673
[12,7,1,8,3,2,9,4,10,5,6,11]=>[6,4,1,1]=>3080
[11,1,12,7,3,2,8,4,9,5,6,10]=>[6,3,2,1]=>5632
[10,1,11,3,2,12,7,4,8,5,6,9]=>[6,3,3]=>1650
[9,1,10,3,2,11,4,12,7,5,6,8]=>[6,4,2]=>2673
[8,1,9,3,2,10,4,11,5,12,6,7]=>[6,5,1]=>1155
[12,10,8,4,1,5,2,6,3,7,9,11]=>[6,3,1,1,1]=>3696
[4,11,1,12,8,5,2,6,3,7,9,10]=>[6,3,2,1]=>5632
[12,9,4,1,10,5,2,6,3,7,8,11]=>[6,3,2,1]=>5632
[11,4,1,12,9,5,2,6,3,7,8,10]=>[6,3,2,1]=>5632
[10,4,1,11,5,2,12,6,3,7,8,9]=>[6,3,3]=>1650
[12,10,7,1,8,4,2,5,3,6,9,11]=>[6,2,2,1,1]=>3564
[11,7,1,12,8,4,2,5,3,6,9,10]=>[6,2,2,2]=>1925
[12,9,1,10,7,4,2,5,3,6,8,11]=>[6,2,2,1,1]=>3564
[11,1,12,9,7,4,2,5,3,6,8,10]=>[6,2,2,1,1]=>3564
[10,4,1,11,2,12,7,5,3,6,8,9]=>[6,3,2,1]=>5632
[12,8,1,9,4,2,10,5,3,6,7,11]=>[6,3,2,1]=>5632
[11,1,12,8,4,2,9,5,3,6,7,10]=>[6,2,2,2]=>1925
[10,1,11,4,2,12,8,5,3,6,7,9]=>[6,3,2,1]=>5632
[9,1,10,4,2,11,5,3,12,6,7,8]=>[6,4,2]=>2673
[12,10,6,1,7,2,8,4,3,5,9,11]=>[6,3,1,1,1]=>3696
[11,6,1,12,7,2,8,4,3,5,9,10]=>[6,3,2,1]=>5632
[12,9,1,10,6,2,7,4,3,5,8,11]=>[6,2,2,1,1]=>3564
[11,1,12,9,6,2,7,4,3,5,8,10]=>[6,2,2,1,1]=>3564
[10,1,11,6,2,12,7,4,3,5,8,9]=>[6,3,2,1]=>5632
[12,8,1,9,2,10,6,4,3,5,7,11]=>[6,3,1,1,1]=>3696
[11,1,12,8,2,9,6,4,3,5,7,10]=>[6,2,2,1,1]=>3564
[10,1,11,2,12,8,6,4,3,5,7,9]=>[6,3,1,1,1]=>3696
[9,1,10,4,2,11,3,12,6,5,7,8]=>[6,4,2]=>2673
[12,7,1,8,2,9,4,3,10,5,6,11]=>[6,4,1,1]=>3080
[11,1,12,7,2,8,4,3,9,5,6,10]=>[6,3,2,1]=>5632
[10,1,11,2,12,7,4,3,8,5,6,9]=>[6,3,2,1]=>5632
[9,1,10,2,11,4,3,12,7,5,6,8]=>[6,4,2]=>2673
[8,1,9,2,10,4,3,11,5,12,6,7]=>[6,5,1]=>1155
[12,10,5,1,6,2,7,3,8,4,9,11]=>[6,4,1,1]=>3080
[11,5,1,12,6,2,7,3,8,4,9,10]=>[6,4,2]=>2673
[12,9,1,10,5,2,6,3,7,4,8,11]=>[6,3,2,1]=>5632
[11,1,12,9,5,2,6,3,7,4,8,10]=>[6,3,2,1]=>5632
[10,1,11,5,2,12,6,3,7,4,8,9]=>[6,3,3]=>1650
[12,8,1,9,2,10,5,3,6,4,7,11]=>[6,3,2,1]=>5632
[11,1,12,8,2,9,5,3,6,4,7,10]=>[6,2,2,2]=>1925
[10,1,11,2,12,8,5,3,6,4,7,9]=>[6,3,2,1]=>5632
[9,1,10,2,11,5,3,12,6,4,7,8]=>[6,4,2]=>2673
[12,7,1,8,2,9,3,10,5,4,6,11]=>[6,4,1,1]=>3080
[11,1,12,7,2,8,3,9,5,4,6,10]=>[6,3,2,1]=>5632
[10,1,11,2,12,7,3,8,5,4,6,9]=>[6,3,2,1]=>5632
[9,1,10,2,11,3,12,7,5,4,6,8]=>[6,4,1,1]=>3080
[8,1,9,2,10,3,11,5,4,12,6,7]=>[6,5,1]=>1155
[12,6,1,7,2,8,3,9,4,10,5,11]=>[6,5,1]=>1155
[11,1,12,6,2,7,3,8,4,9,5,10]=>[6,4,2]=>2673
[10,1,11,2,12,6,3,7,4,8,5,9]=>[6,3,3]=>1650
[9,1,10,2,11,3,12,6,4,7,5,8]=>[6,4,2]=>2673
[8,1,9,2,10,3,11,4,12,6,5,7]=>[6,5,1]=>1155
[8,2,7,5,4,1,6,3]=>[3,2,1,1,1]=>64
[6,8,7,4,5,3,2,1]=>[2,2,1,1,1,1]=>20
[5,2,6,7,4,8,3,1]=>[4,2,1,1]=>90
[6,5,8,1,7,3,2,4]=>[3,2,2,1]=>70
[6,4,8,1,5,2,3,7]=>[4,2,2]=>56
[7,2,4,1,6,3,5,8]=>[4,3,1]=>70
[2,6,1,5,3,4,8,7]=>[4,3,1]=>70
[3,8,7,5,4,2,6,1]=>[3,1,1,1,1,1]=>21
[5,7,8,2,3,6,4,1]=>[3,3,1,1]=>56
[2,8,7,3,1,4,5,6]=>[5,1,1,1]=>35
[5,6,1,2,4,7,8,3]=>[5,2,1]=>64
[10,2,3,1,4,5,6,7,8,9]=>[8,1,1]=>36
[9,2,3,4,1,5,6,7,8]=>[7,1,1]=>28
[9,8,4,5,7,6,3,2,1]=>[3,1,1,1,1,1,1]=>28
[9,8,5,4,6,7,3,2,1]=>[3,1,1,1,1,1,1]=>28
[10,9,8,6,5,7,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[11,10,9,8,5,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[10,9,8,4,5,7,6,3,2,1]=>[3,1,1,1,1,1,1,1]=>36
[9,8,4,5,3,7,6,2,1]=>[3,2,1,1,1,1]=>105
[9,8,3,5,7,6,4,2,1]=>[3,1,1,1,1,1,1]=>28
[9,8,5,4,6,3,7,2,1]=>[3,1,1,1,1,1,1]=>28
[9,8,4,3,6,7,5,2,1]=>[3,2,1,1,1,1]=>105
[10,9,8,5,4,6,7,3,2,1]=>[3,1,1,1,1,1,1,1]=>36
[11,10,9,8,6,5,7,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[3,8,6,7,5,4,2,1]=>[3,1,1,1,1,1]=>21
[7,8,5,1,4,6,2,3]=>[3,2,2,1]=>70
[8,2,7,5,4,6,1,3]=>[3,2,1,1,1]=>64
[8,4,7,6,3,1,2,5]=>[3,2,1,1,1]=>64
[4,6,7,1,3,2,8,5]=>[4,3,1]=>70
[6,4,7,5,3,2,8,1]=>[3,2,1,1,1]=>64
[8,4,6,3,1,5,7,2]=>[3,2,2,1]=>70
[7,3,1,4,5,6,8,2]=>[5,2,1]=>64
[2,5,3,8,6,4,1,7]=>[4,2,1,1]=>90
[5,8,4,1,3,2,7,6]=>[3,2,2,1]=>70
[5,3,4,7,6,1,8,2]=>[4,2,2]=>56
[4,5,2,1,6,3,8,7]=>[4,3,1]=>70
[4,5,2,1,6,7,3,8]=>[5,2,1]=>64
[5,3,8,6,2,4,7,1]=>[3,2,2,1]=>70
[2,5,1,6,4,3,8,7]=>[4,3,1]=>70
[3,6,2,8,5,7,1,4]=>[3,3,2]=>42
[4,6,8,1,5,7,2,3]=>[3,3,2]=>42
[4,1,2,5,7,6,3,8]=>[5,2,1]=>64
[4,6,5,8,1,7,3,2]=>[3,2,2,1]=>70
[2,1,3,6,4,8,7,5]=>[4,3,1]=>70
[4,8,1,2,7,5,6,3]=>[4,2,1,1]=>90
[1,6,4,3,8,7,5,2]=>[3,2,2,1]=>70
[2,5,1,8,6,4,7,3]=>[4,2,1,1]=>90
[3,8,7,2,6,1,4,5]=>[3,2,2,1]=>70
[2,5,1,8,3,6,4,7]=>[4,3,1]=>70
[5,8,4,7,3,2,1,6]=>[2,2,2,1,1]=>28
[4,3,8,6,1,2,5,7]=>[4,2,2]=>56
[4,8,6,5,7,1,3,2]=>[3,2,1,1,1]=>64
[7,2,3,5,6,8,4,1]=>[5,1,1,1]=>35
[5,8,1,3,4,7,2,6]=>[4,2,2]=>56
[8,7,5,6,4,1,3,2]=>[2,2,1,1,1,1]=>20
[7,2,4,5,3,1,6,8]=>[5,1,1,1]=>35
[7,6,3,1,4,5,8,2]=>[4,2,1,1]=>90
[5,4,1,7,8,6,2,3]=>[3,3,2]=>42
[5,3,4,7,8,1,6,2]=>[4,2,2]=>56
[4,3,7,6,5,1,8,2]=>[3,2,2,1]=>70
[5,1,4,8,2,3,7,6]=>[4,2,2]=>56
[3,2,8,5,4,1,6,7]=>[4,2,1,1]=>90
[7,8,9,1,3,4,5,6,2]=>[5,3,1]=>162
[6,1,2,9,3,4,5,7,8]=>[7,2]=>27
[4,1,2,3,5,9,6,7,8]=>[7,2]=>27
[3,1,2,4,5,6,9,7,8]=>[7,2]=>27
[1,2,8,3,4,6,5,7]=>[6,1,1]=>21
[8,1,2,7,3,5,4,6]=>[5,1,1,1]=>35
[5,7,1,2,6,3,4,8]=>[5,2,1]=>64
[1,2,7,5,6,3,4,8]=>[5,2,1]=>64
[5,1,4,7,2,3,6,8]=>[5,2,1]=>64
[4,8,1,2,3,6,5,7]=>[5,2,1]=>64
[1,3,4,2,5,6,7,8,9]=>[8,1]=>8
[1,2,4,5,6,3,7,8,9]=>[8,1]=>8
[1,2,3,5,6,7,8,4,9]=>[8,1]=>8
[2,1,5,3,6,7,4,8,9]=>[6,3]=>48
[1,3,5,6,4,2,7,8,9]=>[7,1,1]=>28
[3,5,2,1,6,4,7,8,9]=>[6,2,1]=>105
[2,1,3,6,4,7,8,9,5]=>[6,3]=>48
[1,3,4,6,7,2,8,5,9]=>[7,2]=>27
[3,2,6,1,4,7,8,5,9]=>[5,3,1]=>162
[2,4,6,1,7,5,3,8,9]=>[6,2,1]=>105
[4,6,3,2,1,7,5,8,9]=>[5,2,1,1]=>189
[2,4,1,7,5,8,3,9,6]=>[5,3,1]=>162
[4,3,7,2,1,5,8,9,6]=>[4,3,1,1]=>216
[1,3,5,7,8,6,4,2,9]=>[6,1,1,1]=>56
[3,5,7,2,1,8,6,4,9]=>[5,2,2]=>120
[5,7,4,3,2,1,8,6,9]=>[4,2,1,1,1]=>189
[2,4,6,8,1,9,7,5,3]=>[5,2,1,1]=>189
[4,6,8,3,2,1,9,7,5]=>[4,2,2,1]=>216
[6,8,5,4,3,2,1,9,7]=>[3,2,1,1,1,1]=>105
[1,3,4,2,5,6,7,8,9,10]=>[9,1]=>9
[1,2,4,5,6,3,7,8,9,10]=>[9,1]=>9
[1,2,3,5,6,7,8,4,9,10]=>[9,1]=>9
[2,1,5,3,6,7,4,8,9,10]=>[7,3]=>75
[1,3,5,6,4,2,7,8,9,10]=>[8,1,1]=>36
[3,5,2,1,6,4,7,8,9,10]=>[7,2,1]=>160
[2,1,3,6,4,7,8,9,5,10]=>[7,3]=>75
[1,3,4,6,7,2,8,5,9,10]=>[8,2]=>35
[3,2,6,1,4,7,8,5,9,10]=>[6,3,1]=>315
[2,4,6,1,7,5,3,8,9,10]=>[7,2,1]=>160
[4,6,3,2,1,7,5,8,9,10]=>[6,2,1,1]=>350
[1,3,4,2,7,8,5,9,10,6]=>[7,3]=>75
[3,2,1,7,4,5,8,9,10,6]=>[6,3,1]=>315
[1,2,4,5,7,8,9,6,3,10]=>[8,1,1]=>36
[4,3,7,2,1,5,8,9,6,10]=>[5,3,1,1]=>567
[1,3,5,7,8,6,4,2,9,10]=>[7,1,1,1]=>84
[3,5,7,2,1,8,6,4,9,10]=>[6,2,2]=>225
[5,7,4,3,2,1,8,6,9,10]=>[5,2,1,1,1]=>448
[2,1,5,3,8,6,9,10,7,4]=>[5,4,1]=>288
[1,3,5,6,8,9,4,2,10,7]=>[7,2,1]=>160
[3,5,2,8,1,6,9,4,10,7]=>[5,3,2]=>450
[5,4,8,3,2,1,6,9,10,7]=>[4,3,1,1,1]=>525
[2,4,6,8,1,9,7,5,3,10]=>[6,2,1,1]=>350
[4,6,8,3,2,1,9,7,5,10]=>[5,2,2,1]=>525
[6,8,5,4,3,2,1,9,7,10]=>[4,2,1,1,1,1]=>350
[3,5,7,9,2,1,10,8,6,4]=>[5,2,2,1]=>525
[5,7,9,4,3,2,1,10,8,6]=>[4,2,2,1,1]=>567
[7,9,6,5,4,3,2,1,10,8]=>[3,2,1,1,1,1,1]=>160
[4,5,6,3,7,2,8,1,9]=>[6,1,1,1]=>56
[1,5,6,7,4,8,3,9,2]=>[6,1,1,1]=>56
[5,4,1,6,2,7,8,3]=>[4,3,1]=>70
[7,1,3,5,4,2,8,6]=>[4,2,1,1]=>90
[7,6,8,2,4,5,3,1]=>[3,2,1,1,1]=>64
[4,2,8,6,5,1,3,7]=>[3,2,2,1]=>70
[3,8,5,4,7,1,2,6]=>[3,3,1,1]=>56
[1,4,8,3,6,2,7,5]=>[4,2,2]=>56
[6,3,2,4,8,7,1,5]=>[3,2,2,1]=>70
[8,3,2,7,4,1,5,6]=>[4,2,1,1]=>90
[7,3,2,6,5,8,1,4]=>[3,2,2,1]=>70
[3,6,2,5,7,4,8,1]=>[4,2,1,1]=>90
[2,7,1,5,8,6,4,3]=>[3,3,1,1]=>56
[7,2,4,1,6,8,5,3]=>[4,2,1,1]=>90
[6,4,7,2,3,8,5,1]=>[3,3,1,1]=>56
[6,1,8,5,7,4,2,3]=>[3,2,2,1]=>70
[7,1,4,3,6,5,8,2]=>[4,2,1,1]=>90
[7,1,5,6,3,4,8,2]=>[4,2,1,1]=>90
[6,1,8,5,4,7,3,2]=>[3,2,1,1,1]=>64
[7,6,1,5,4,2,8,3]=>[3,2,1,1,1]=>64
[5,1,6,8,7,2,4,3]=>[3,3,1,1]=>56
[4,6,7,5,3,1,8,2]=>[4,2,1,1]=>90
[5,3,2,6,8,7,4,1]=>[3,2,2,1]=>70
[5,4,6,2,8,7,3,1]=>[3,2,2,1]=>70
[4,5,8,6,7,2,3,1]=>[4,2,1,1]=>90
[4,5,7,6,1,2,8,3]=>[4,3,1]=>70
[4,6,5,7,2,1,8,3]=>[4,2,1,1]=>90
[2,3,7,5,6,1,10,9,4,8]=>[5,3,2]=>450
[2,3,4,10,6,9,8,5,1,7]=>[5,2,1,1,1]=>448
[2,3,6,5,9,10,8,4,1,7]=>[5,2,2,1]=>525
[2,3,9,5,8,7,4,1,10,6]=>[5,2,1,1,1]=>448
[2,5,4,9,6,10,8,3,1,7]=>[4,3,2,1]=>768
[2,5,4,8,9,7,3,1,10,6]=>[5,2,2,1]=>525
[2,3,4,10,6,7,1,9,8,5]=>[6,2,1,1]=>350
[2,3,7,5,6,1,10,9,8,4]=>[5,2,2,1]=>525
[2,3,4,10,6,8,9,1,7,5]=>[6,2,1,1]=>350
[2,3,6,5,8,10,9,1,7,4]=>[5,2,2,1]=>525
[2,3,8,5,7,9,1,10,6,4]=>[6,2,1,1]=>350
[2,5,4,8,6,10,9,1,7,3]=>[4,3,2,1]=>768
[2,5,4,7,8,9,1,10,6,3]=>[6,2,2]=>225
[2,3,4,10,6,9,8,7,5,1]=>[5,1,1,1,1,1]=>126
[2,3,6,5,9,10,8,7,4,1]=>[5,2,1,1,1]=>448
[2,3,7,5,9,8,10,6,4,1]=>[5,2,1,1,1]=>448
[2,3,9,5,8,7,6,4,1,10]=>[5,1,1,1,1,1]=>126
[2,5,4,9,6,10,8,7,3,1]=>[4,3,1,1,1]=>525
[2,5,4,9,7,8,10,6,3,1]=>[5,2,1,1,1]=>448
[2,5,4,8,9,7,6,3,1,10]=>[5,2,1,1,1]=>448
[2,3,4,10,7,9,8,1,6,5]=>[5,2,1,1,1]=>448
[2,3,5,7,10,9,8,1,6,4]=>[5,2,1,1,1]=>448
[2,3,8,6,9,7,1,10,5,4]=>[5,2,2,1]=>525
[2,4,7,5,10,9,8,1,6,3]=>[4,2,2,1,1]=>567
[2,4,6,8,9,7,1,10,5,3]=>[6,2,1,1]=>350
[2,3,4,10,7,8,9,6,5,1]=>[6,1,1,1,1]=>126
[2,3,5,7,10,8,9,6,4,1]=>[6,1,1,1,1]=>126
[2,3,7,6,8,9,10,5,4,1]=>[6,1,1,1,1]=>126
[2,3,9,6,7,8,5,4,1,10]=>[6,1,1,1,1]=>126
[2,4,7,5,10,8,9,6,3,1]=>[5,2,1,1,1]=>448
[2,4,6,7,8,9,10,5,3,1]=>[7,1,1,1]=>84
[2,4,6,9,7,8,5,3,1,10]=>[6,1,1,1,1]=>126
[2,6,5,8,9,7,10,4,3,1]=>[5,2,1,1,1]=>448
[2,6,5,7,8,9,4,3,1,10]=>[6,1,1,1,1]=>126
[3,7,4,5,10,9,8,1,6,2]=>[4,2,2,1,1]=>567
[3,6,4,8,9,7,1,10,5,2]=>[5,2,2,1]=>525
[3,7,4,5,10,8,9,6,2,1]=>[5,2,1,1,1]=>448
[3,6,4,7,8,9,10,5,2,1]=>[6,2,1,1]=>350
[3,6,4,9,7,8,5,2,1,10]=>[5,2,1,1,1]=>448
[3,5,6,8,9,7,10,4,2,1]=>[6,1,1,1,1]=>126
[3,5,6,7,8,9,4,2,1,10]=>[7,1,1,1]=>84
[7,4,8,6,3,5,1,2]=>[2,2,2,2]=>14
[7,2,4,3,6,1,8,5]=>[4,2,1,1]=>90
[2,3,4,7,8,6,1,5]=>[5,2,1]=>64
[6,3,7,1,4,2,8,5]=>[3,3,2]=>42
[8,5,7,6,2,3,4,1]=>[3,2,1,1,1]=>64
[3,5,6,7,8,9,2,4,1]=>[6,2,1]=>105
[3,4,6,7,8,2,5,1]=>[5,2,1]=>64
[2,4,6,7,8,9,1,3,5]=>[6,3]=>48
[2,5,6,7,3,8,1,4]=>[5,2,1]=>64
[2,5,6,7,8,9,3,1,4]=>[6,2,1]=>105
[5,8,4,6,2,1,7,3]=>[3,2,2,1]=>70
[1,6,8,3,4,2,7,5]=>[4,2,2]=>56
[4,1,7,6,2,8,3,5]=>[4,3,1]=>70
[4,1,8,2,7,5,3,6]=>[4,2,1,1]=>90
[4,1,7,2,8,5,3,6]=>[4,3,1]=>70
[2,5,6,3,7,4,8,1]=>[5,2,1]=>64
[2,6,5,3,8,4,7,1]=>[4,2,1,1]=>90
[2,6,5,3,7,4,8,1]=>[4,2,1,1]=>90
[7,1,6,3,5,4,8,2]=>[4,1,1,1,1]=>35
[5,7,3,2,8,4,1,6]=>[3,3,1,1]=>56
[2,8,6,1,7,5,3,4]=>[3,3,1,1]=>56
[8,1,5,2,7,4,3,6]=>[4,2,1,1]=>90
[7,1,4,2,8,5,3,6]=>[4,2,2]=>56
[2,6,8,1,7,5,3,4]=>[3,3,1,1]=>56
[1,4,6,5,3,8,2,7]=>[4,2,1,1]=>90
[2,4,5,8,7,1,3,6]=>[4,3,1]=>70
[3,1,6,8,7,5,4,2]=>[3,2,1,1,1]=>64
[3,1,8,7,5,6,4,2]=>[3,2,1,1,1]=>64
[5,1,8,7,6,3,4,2]=>[3,2,1,1,1]=>64
[8,2,7,5,3,6,4,1]=>[3,2,1,1,1]=>64
[8,7,2,3,1,5,6,4]=>[4,2,1,1]=>90
[2,8,5,7,6,1,3,4]=>[3,3,1,1]=>56
[1,8,7,2,6,4,5,3]=>[4,1,1,1,1]=>35
[8,7,2,1,6,4,5,3]=>[3,2,1,1,1]=>64
[1,8,4,7,6,2,5,3]=>[3,2,1,1,1]=>64
[8,7,1,6,4,3,5,2]=>[3,1,1,1,1,1]=>21
[8,4,1,7,3,6,5,2]=>[3,2,1,1,1]=>64
[5,4,6,3,8,1,7,2,9]=>[4,2,2,1]=>216
[1,6,5,7,4,9,2,8,3]=>[4,2,2,1]=>216
[5,6,4,7,3,9,1,8,2,10]=>[5,2,2,1]=>525
[5,4,8,1,7,2,6,3,9]=>[4,2,2,1]=>216
[5,4,8,1,6,3,7,2,9]=>[4,2,2,1]=>216
[1,6,5,9,2,8,3,7,4]=>[4,2,2,1]=>216
[1,6,5,9,2,7,4,8,3]=>[4,2,2,1]=>216
[1,6,7,5,8,4,10,2,9,3]=>[5,2,2,1]=>525
[4,5,6,7,8,9,1,10,2,3]=>[7,3]=>75
[2,5,6,7,8,1,9,3,4]=>[6,3]=>48
[4,5,6,7,1,2,8,3,9]=>[6,3]=>48
[1,3,6,7,8,9,2,4,5]=>[6,3]=>48
[3,5,6,7,8,1,2,9,4]=>[6,3]=>48
[3,2,5,4,7,6,8,10,9,1]=>[5,4,1]=>288
[3,2,5,4,6,9,7,8,10,1]=>[6,3,1]=>315
[3,2,5,4,6,8,7,10,9,1]=>[5,4,1]=>288
[3,2,5,4,6,7,10,8,9,1]=>[6,3,1]=>315
[3,2,4,7,5,6,9,8,10,1]=>[6,3,1]=>315
[3,2,4,7,5,6,8,10,9,1]=>[6,3,1]=>315
[3,2,4,6,5,9,7,8,10,1]=>[6,3,1]=>315
[3,2,4,6,5,8,7,10,9,1]=>[5,4,1]=>288
[3,2,4,6,5,7,10,8,9,1]=>[6,3,1]=>315
[3,2,4,5,9,6,7,8,10,1]=>[7,2,1]=>160
[3,2,4,5,8,6,7,10,9,1]=>[6,3,1]=>315
[3,2,4,5,7,6,10,8,9,1]=>[6,3,1]=>315
[3,2,4,5,6,10,7,8,9,1]=>[7,2,1]=>160
[2,5,3,4,7,6,9,8,10,1]=>[6,3,1]=>315
[2,5,3,4,7,6,8,10,9,1]=>[6,3,1]=>315
[2,5,3,4,6,9,7,8,10,1]=>[7,2,1]=>160
[2,5,3,4,6,8,7,10,9,1]=>[6,3,1]=>315
[2,5,3,4,6,7,10,8,9,1]=>[7,2,1]=>160
[2,4,3,7,5,6,9,8,10,1]=>[6,3,1]=>315
[2,4,3,7,5,6,8,10,9,1]=>[6,3,1]=>315
[2,4,3,6,5,9,7,8,10,1]=>[6,3,1]=>315
[2,4,3,6,5,7,10,8,9,1]=>[6,3,1]=>315
[2,4,3,5,9,6,7,8,10,1]=>[7,2,1]=>160
[2,4,3,5,8,6,7,10,9,1]=>[6,3,1]=>315
[2,4,3,5,7,6,10,8,9,1]=>[6,3,1]=>315
[2,4,3,5,6,10,7,8,9,1]=>[7,2,1]=>160
[2,3,7,4,5,6,9,8,10,1]=>[7,2,1]=>160
[2,3,7,4,5,6,8,10,9,1]=>[7,2,1]=>160
[2,3,6,4,5,9,7,8,10,1]=>[7,2,1]=>160
[2,3,6,4,5,8,7,10,9,1]=>[6,3,1]=>315
[2,3,6,4,5,7,10,8,9,1]=>[7,2,1]=>160
[2,3,5,4,9,6,7,8,10,1]=>[7,2,1]=>160
[2,3,5,4,8,6,7,10,9,1]=>[6,3,1]=>315
[2,3,5,4,7,6,10,8,9,1]=>[6,3,1]=>315
[2,3,5,4,6,10,7,8,9,1]=>[7,2,1]=>160
[2,3,4,9,5,6,7,8,10,1]=>[8,1,1]=>36
[2,3,4,8,5,6,7,10,9,1]=>[7,2,1]=>160
[2,3,4,7,5,6,10,8,9,1]=>[7,2,1]=>160
[2,3,4,6,5,10,7,8,9,1]=>[7,2,1]=>160
[3,2,5,4,7,6,9,8,10,12,11,1]=>[6,5,1]=>1155
[3,2,5,4,7,6,8,11,9,10,12,1]=>[7,4,1]=>1408
[3,2,5,4,7,6,8,10,9,12,11,1]=>[6,5,1]=>1155
[3,2,5,4,7,6,8,9,12,10,11,1]=>[7,4,1]=>1408
[3,2,5,4,6,9,7,8,11,10,12,1]=>[7,4,1]=>1408
[3,2,5,4,6,9,7,8,10,12,11,1]=>[7,4,1]=>1408
[3,2,5,4,6,8,7,11,9,10,12,1]=>[7,4,1]=>1408
[3,2,5,4,6,8,7,10,9,12,11,1]=>[6,5,1]=>1155
[3,2,5,4,6,8,7,9,12,10,11,1]=>[7,4,1]=>1408
[3,2,5,4,6,7,11,8,9,10,12,1]=>[8,3,1]=>891
[3,2,5,4,6,7,10,8,9,12,11,1]=>[7,4,1]=>1408
[3,2,5,4,6,7,9,8,12,10,11,1]=>[7,4,1]=>1408
[3,2,5,4,6,7,8,12,9,10,11,1]=>[8,3,1]=>891
[3,2,4,7,5,6,9,8,11,10,12,1]=>[7,4,1]=>1408
[3,2,4,7,5,6,9,8,10,12,11,1]=>[7,4,1]=>1408
[3,2,4,7,5,6,8,11,9,10,12,1]=>[8,3,1]=>891
[3,2,4,7,5,6,8,10,9,12,11,1]=>[7,4,1]=>1408
[3,2,4,7,5,6,8,9,12,10,11,1]=>[8,3,1]=>891
[3,2,4,6,5,9,7,8,11,10,12,1]=>[7,4,1]=>1408
[3,2,4,6,5,9,7,8,10,12,11,1]=>[7,4,1]=>1408
[3,2,4,6,5,8,7,11,9,10,12,1]=>[7,4,1]=>1408
[3,2,4,6,5,8,7,10,9,12,11,1]=>[6,5,1]=>1155
[3,2,4,6,5,8,7,9,12,10,11,1]=>[7,4,1]=>1408
[3,2,4,6,5,7,11,8,9,10,12,1]=>[8,3,1]=>891
[3,2,4,6,5,7,10,8,9,12,11,1]=>[7,4,1]=>1408
[3,2,4,6,5,7,9,8,12,10,11,1]=>[7,4,1]=>1408
[3,2,4,6,5,7,8,12,9,10,11,1]=>[8,3,1]=>891
[3,2,4,5,9,6,7,8,11,10,12,1]=>[8,3,1]=>891
[3,2,4,5,9,6,7,8,10,12,11,1]=>[8,3,1]=>891
[3,2,4,5,8,6,7,11,9,10,12,1]=>[8,3,1]=>891
[3,2,4,5,8,6,7,10,9,12,11,1]=>[7,4,1]=>1408
[3,2,4,5,8,6,7,9,12,10,11,1]=>[8,3,1]=>891
[3,2,4,5,7,6,11,8,9,10,12,1]=>[8,3,1]=>891
[3,2,4,5,7,6,10,8,9,12,11,1]=>[7,4,1]=>1408
[3,2,4,5,7,6,9,8,12,10,11,1]=>[7,4,1]=>1408
[3,2,4,5,7,6,8,12,9,10,11,1]=>[8,3,1]=>891
[3,2,4,5,6,11,7,8,9,10,12,1]=>[9,2,1]=>320
[3,2,4,5,6,10,7,8,9,12,11,1]=>[8,3,1]=>891
[3,2,4,5,6,9,7,8,12,10,11,1]=>[8,3,1]=>891
[3,2,4,5,6,8,7,12,9,10,11,1]=>[8,3,1]=>891
[3,2,4,5,6,7,12,8,9,10,11,1]=>[9,2,1]=>320
[2,5,3,4,7,6,9,8,11,10,12,1]=>[7,4,1]=>1408
[2,5,3,4,7,6,9,8,10,12,11,1]=>[7,4,1]=>1408
[2,5,3,4,7,6,8,11,9,10,12,1]=>[8,3,1]=>891
[2,5,3,4,7,6,8,10,9,12,11,1]=>[7,4,1]=>1408
[2,5,3,4,7,6,8,9,12,10,11,1]=>[8,3,1]=>891
[2,5,3,4,6,9,7,8,11,10,12,1]=>[8,3,1]=>891
[2,5,3,4,6,9,7,8,10,12,11,1]=>[8,3,1]=>891
[2,5,3,4,6,8,7,11,9,10,12,1]=>[8,3,1]=>891
[2,5,3,4,6,8,7,10,9,12,11,1]=>[7,4,1]=>1408
[2,5,3,4,6,8,7,9,12,10,11,1]=>[8,3,1]=>891
[2,5,3,4,6,7,11,8,9,10,12,1]=>[9,2,1]=>320
[2,5,3,4,6,7,10,8,9,12,11,1]=>[8,3,1]=>891
[2,5,3,4,6,7,9,8,12,10,11,1]=>[8,3,1]=>891
[2,5,3,4,6,7,8,12,9,10,11,1]=>[9,2,1]=>320
[2,4,3,7,5,6,9,8,11,10,12,1]=>[7,4,1]=>1408
[2,4,3,7,5,6,9,8,10,12,11,1]=>[7,4,1]=>1408
[2,4,3,7,5,6,8,11,9,10,12,1]=>[8,3,1]=>891
[2,4,3,7,5,6,8,10,9,12,11,1]=>[7,4,1]=>1408
[2,4,3,7,5,6,8,9,12,10,11,1]=>[8,3,1]=>891
[2,4,3,6,5,9,7,8,11,10,12,1]=>[7,4,1]=>1408
[2,4,3,6,5,9,7,8,10,12,11,1]=>[7,4,1]=>1408
[2,4,3,6,5,8,7,11,9,10,12,1]=>[7,4,1]=>1408
[2,4,3,6,5,8,7,9,12,10,11,1]=>[7,4,1]=>1408
[2,4,3,6,5,7,11,8,9,10,12,1]=>[8,3,1]=>891
[2,4,3,6,5,7,10,8,9,12,11,1]=>[7,4,1]=>1408
[2,4,3,6,5,7,9,8,12,10,11,1]=>[7,4,1]=>1408
[2,4,3,6,5,7,8,12,9,10,11,1]=>[8,3,1]=>891
[2,4,3,5,9,6,7,8,11,10,12,1]=>[8,3,1]=>891
[2,4,3,5,9,6,7,8,10,12,11,1]=>[8,3,1]=>891
[2,4,3,5,8,6,7,11,9,10,12,1]=>[8,3,1]=>891
[2,4,3,5,8,6,7,10,9,12,11,1]=>[7,4,1]=>1408
[2,4,3,5,8,6,7,9,12,10,11,1]=>[8,3,1]=>891
[2,4,3,5,7,6,11,8,9,10,12,1]=>[8,3,1]=>891
[2,4,3,5,7,6,10,8,9,12,11,1]=>[7,4,1]=>1408
[2,4,3,5,7,6,9,8,12,10,11,1]=>[7,4,1]=>1408
[2,4,3,5,7,6,8,12,9,10,11,1]=>[8,3,1]=>891
[2,4,3,5,6,11,7,8,9,10,12,1]=>[9,2,1]=>320
[2,4,3,5,6,10,7,8,9,12,11,1]=>[8,3,1]=>891
[2,4,3,5,6,9,7,8,12,10,11,1]=>[8,3,1]=>891
[2,4,3,5,6,8,7,12,9,10,11,1]=>[8,3,1]=>891
[2,4,3,5,6,7,12,8,9,10,11,1]=>[9,2,1]=>320
[2,3,7,4,5,6,9,8,11,10,12,1]=>[8,3,1]=>891
[2,3,7,4,5,6,9,8,10,12,11,1]=>[8,3,1]=>891
[2,3,7,4,5,6,8,11,9,10,12,1]=>[9,2,1]=>320
[2,3,7,4,5,6,8,10,9,12,11,1]=>[8,3,1]=>891
[2,3,7,4,5,6,8,9,12,10,11,1]=>[9,2,1]=>320
[2,3,6,4,5,9,7,8,11,10,12,1]=>[8,3,1]=>891
[2,3,6,4,5,9,7,8,10,12,11,1]=>[8,3,1]=>891
[2,3,6,4,5,8,7,11,9,10,12,1]=>[8,3,1]=>891
[2,3,6,4,5,8,7,10,9,12,11,1]=>[7,4,1]=>1408
[2,3,6,4,5,8,7,9,12,10,11,1]=>[8,3,1]=>891
[2,3,6,4,5,7,11,8,9,10,12,1]=>[9,2,1]=>320
[2,3,6,4,5,7,10,8,9,12,11,1]=>[8,3,1]=>891
[2,3,6,4,5,7,9,8,12,10,11,1]=>[8,3,1]=>891
[2,3,6,4,5,7,8,12,9,10,11,1]=>[9,2,1]=>320
[2,3,5,4,9,6,7,8,11,10,12,1]=>[8,3,1]=>891
[2,3,5,4,9,6,7,8,10,12,11,1]=>[8,3,1]=>891
[2,3,5,4,8,6,7,11,9,10,12,1]=>[8,3,1]=>891
[2,3,5,4,8,6,7,10,9,12,11,1]=>[7,4,1]=>1408
[2,3,5,4,8,6,7,9,12,10,11,1]=>[8,3,1]=>891
[2,3,5,4,7,6,11,8,9,10,12,1]=>[8,3,1]=>891
[2,3,5,4,7,6,10,8,9,12,11,1]=>[7,4,1]=>1408
[2,3,5,4,7,6,9,8,12,10,11,1]=>[7,4,1]=>1408
[2,3,5,4,7,6,8,12,9,10,11,1]=>[8,3,1]=>891
[2,3,5,4,6,11,7,8,9,10,12,1]=>[9,2,1]=>320
[2,3,5,4,6,10,7,8,9,12,11,1]=>[8,3,1]=>891
[2,3,5,4,6,9,7,8,12,10,11,1]=>[8,3,1]=>891
[2,3,5,4,6,8,7,12,9,10,11,1]=>[8,3,1]=>891
[2,3,5,4,6,7,12,8,9,10,11,1]=>[9,2,1]=>320
[2,3,4,9,5,6,7,8,11,10,12,1]=>[9,2,1]=>320
[2,3,4,9,5,6,7,8,10,12,11,1]=>[9,2,1]=>320
[2,3,4,8,5,6,7,11,9,10,12,1]=>[9,2,1]=>320
[2,3,4,8,5,6,7,10,9,12,11,1]=>[8,3,1]=>891
[2,3,4,8,5,6,7,9,12,10,11,1]=>[9,2,1]=>320
[2,3,4,7,5,6,11,8,9,10,12,1]=>[9,2,1]=>320
[2,3,4,7,5,6,10,8,9,12,11,1]=>[8,3,1]=>891
[2,3,4,7,5,6,9,8,12,10,11,1]=>[8,3,1]=>891
[2,3,4,7,5,6,8,12,9,10,11,1]=>[9,2,1]=>320
[2,3,4,6,5,11,7,8,9,10,12,1]=>[9,2,1]=>320
[2,3,4,6,5,10,7,8,9,12,11,1]=>[8,3,1]=>891
[2,3,4,6,5,9,7,8,12,10,11,1]=>[8,3,1]=>891
[2,3,4,6,5,8,7,12,9,10,11,1]=>[8,3,1]=>891
[2,3,4,6,5,7,12,8,9,10,11,1]=>[9,2,1]=>320
[2,3,4,5,11,6,7,8,9,10,12,1]=>[10,1,1]=>55
[2,3,4,5,10,6,7,8,9,12,11,1]=>[9,2,1]=>320
[2,3,4,5,9,6,7,8,12,10,11,1]=>[9,2,1]=>320
[2,3,4,5,8,6,7,12,9,10,11,1]=>[9,2,1]=>320
[2,3,4,5,7,6,12,8,9,10,11,1]=>[9,2,1]=>320
[4,5,1,8,7,3,6,2]=>[3,3,1,1]=>56
[3,6,4,7,5,2,1,8]=>[4,2,1,1]=>90
[5,7,4,1,2,6,8,3]=>[4,2,2]=>56
[2,8,6,7,5,3,1,4]=>[3,2,1,1,1]=>64
[4,8,3,2,6,1,7,5]=>[3,2,2,1]=>70
[1,4,8,7,6,2,5,3]=>[3,2,1,1,1]=>64
[7,2,4,1,5,3,8,6]=>[4,3,1]=>70
[8,5,3,4,1,7,2,6]=>[3,3,1,1]=>56
[2,8,5,4,3,6,1,7]=>[4,1,1,1,1]=>35
[8,6,5,3,1,2,7,4]=>[3,2,1,1,1]=>64
[7,4,6,5,3,2,8,1]=>[3,1,1,1,1,1]=>21
[5,6,7,2,3,8,4,1]=>[4,3,1]=>70
[8,4,2,6,5,7,3,1]=>[3,2,1,1,1]=>64
[1,7,4,2,8,5,6,3]=>[4,2,2]=>56
[3,2,1,7,4,6,8,5]=>[4,2,2]=>56
[6,2,5,7,1,4,3,8]=>[4,2,1,1]=>90
[4,8,5,3,1,2,6,7]=>[4,2,1,1]=>90
[8,5,2,4,6,1,3,7]=>[4,2,1,1]=>90
[1,5,3,4,7,2,6,8]=>[5,2,1]=>64
[8,4,6,1,5,7,3,2]=>[3,2,1,1,1]=>64
[6,4,7,2,1,3,8,5]=>[3,3,1,1]=>56
[6,7,3,1,2,4,8,5]=>[4,3,1]=>70
[3,1,8,7,6,2,5,4]=>[3,2,1,1,1]=>64
[1,3,8,6,7,2,5,4]=>[4,2,1,1]=>90
[5,2,3,6,1,8,4,7]=>[4,3,1]=>70
[3,2,6,4,7,1,5,8]=>[4,3,1]=>70
[3,6,2,5,7,8,4,1]=>[4,2,1,1]=>90
[2,7,4,6,8,3,5,1]=>[4,2,1,1]=>90
[3,7,6,8,1,5,4,2]=>[3,2,1,1,1]=>64
[1,5,7,6,8,4,2,3]=>[4,2,1,1]=>90
[2,7,4,6,8,5,3,1]=>[4,1,1,1,1]=>35
[3,7,6,8,5,1,4,2]=>[3,2,1,1,1]=>64
[7,1,3,8,6,2,4,5]=>[4,2,2]=>56
[2,7,1,8,6,5,3,4]=>[3,3,1,1]=>56
[2,3,4,5,7,6,8,9,1]=>[7,1,1]=>28
[2,3,4,5,8,7,6,9,1]=>[6,1,1,1]=>56
[5,3,4,7,6,2,1,8]=>[4,2,1,1]=>90
[4,1,8,5,7,2,6,3]=>[3,3,1,1]=>56
[4,1,8,2,7,5,6,3]=>[4,2,1,1]=>90
[7,6,8,2,4,3,5,1]=>[3,2,1,1,1]=>64
[7,4,5,3,8,1,6,2]=>[3,2,2,1]=>70
[7,3,6,1,4,2,8,5]=>[3,3,1,1]=>56
[8,7,2,6,4,5,1,3]=>[3,2,1,1,1]=>64
[1,2,3,4,7,9,5,6,8]=>[7,2]=>27
[1,2,3,4,6,7,9,5,8]=>[7,2]=>27
[1,2,3,4,8,5,6,9,7]=>[7,2]=>27
[1,2,3,4,7,8,5,9,6]=>[7,2]=>27
[7,3,2,5,1,6,8,4]=>[4,2,1,1]=>90
[3,5,1,7,6,4,8,2]=>[4,2,1,1]=>90
[8,7,4,2,1,6,5,3]=>[2,2,2,1,1]=>28
[5,4,7,6,2,1,8,3]=>[3,2,2,1]=>70
[3,5,2,8,7,1,6,4]=>[3,2,2,1]=>70
[3,7,6,5,4,1,8,2]=>[3,2,1,1,1]=>64
[4,6,5,3,1,8,7,2]=>[3,2,2,1]=>70
[4,5,2,6,7,3,8,1]=>[5,2,1]=>64
[9,3,10,1,2,4,5,6,7,8]=>[7,2,1]=>160
[10,3,1,9,2,4,5,6,7,8]=>[7,2,1]=>160
[3,1,4,10,2,5,6,7,8,9]=>[7,3]=>75
[8,6,7,4,3,1,5,2]=>[2,2,2,1,1]=>28
[4,7,1,8,5,3,2,6]=>[3,3,1,1]=>56
[8,6,7,1,4,3,5,2]=>[3,2,1,1,1]=>64
[8,6,7,2,1,3,5,4]=>[3,2,2,1]=>70
[8,5,6,1,7,4,2,3]=>[3,3,1,1]=>56
[6,4,1,2,5,7,8,3]=>[5,2,1]=>64
[6,1,5,4,2,7,3,8]=>[4,2,1,1]=>90
[6,4,2,3,1,7,5,8]=>[4,2,1,1]=>90
[3,4,6,1,8,2,7,5]=>[4,3,1]=>70
[5,3,1,4,7,6,2,8]=>[4,2,2]=>56
[6,4,5,2,7,1,3,8]=>[4,2,1,1]=>90
[7,4,3,5,1,6,2,8]=>[4,2,1,1]=>90
[7,5,3,6,2,1,4,8]=>[3,2,1,1,1]=>64
[6,4,3,7,1,8,2,5]=>[3,3,1,1]=>56
[3,1,2,7,6,4,5,8]=>[5,2,1]=>64
[5,1,2,7,6,3,4,8]=>[5,2,1]=>64
[5,6,1,7,2,4,3,8]=>[4,3,1]=>70
[3,5,6,8,1,2,7,4]=>[4,3,1]=>70
[2,6,5,7,1,3,4,8]=>[4,3,1]=>70
[2,3,7,1,5,6,4,8]=>[5,2,1]=>64
[2,6,5,3,4,1,7,8]=>[5,1,1,1]=>35
[2,6,1,3,5,4,7,8]=>[5,2,1]=>64
[4,6,1,5,2,8,7,3]=>[3,3,2]=>42
[6,1,5,4,2,7,8,3]=>[4,2,1,1]=>90
[4,6,1,5,2,7,8,3]=>[4,3,1]=>70
[2,8,6,5,1,3,7,4]=>[3,3,1,1]=>56
[5,1,8,6,2,7,4,3]=>[3,3,1,1]=>56
[3,6,8,2,7,5,1,4]=>[3,2,2,1]=>70
[5,6,4,1,7,2,8,3]=>[4,3,1]=>70
[8,1,6,3,4,2,5,7]=>[5,1,1,1]=>35
[7,4,2,3,1,6,8,5]=>[4,2,1,1]=>90
[8,9,1,2,3,4,5,6,10,11,7]=>[8,3]=>110
[10,7,1,2,3,4,8,9,5,6]=>[6,3,1]=>315
[1,6,4,5,7,3,2,8]=>[5,1,1,1]=>35
[1,6,4,5,7,2,8,3]=>[5,2,1]=>64
[1,7,5,6,4,8,3,2]=>[4,1,1,1,1]=>35
[1,5,6,7,3,2,4,8]=>[5,2,1]=>64
[8,2,4,3,1,7,5,6]=>[4,2,1,1]=>90
[8,2,1,4,3,7,5,6]=>[4,3,1]=>70
[7,6,8,2,1,5,3,4]=>[3,2,2,1]=>70
[8,6,2,5,1,3,7,4]=>[3,3,1,1]=>56
[5,7,2,6,4,1,8,3]=>[3,2,2,1]=>70
[4,5,6,1,3,8,2,7]=>[4,3,1]=>70
[6,3,5,7,4,2,8,1]=>[4,1,1,1,1]=>35
[7,6,4,8,5,3,1,2]=>[2,2,2,1,1]=>28
[8,2,1,6,4,7,3,5]=>[3,3,1,1]=>56
[1,3,8,6,5,2,7,4]=>[4,2,1,1]=>90
[2,7,3,8,5,6,4,1]=>[4,2,1,1]=>90
[1,2,8,5,7,4,6,3]=>[4,2,1,1]=>90
[1,6,8,5,4,7,2,3]=>[3,2,2,1]=>70
[5,7,1,8,3,2,6,4]=>[3,3,2]=>42
[8,2,5,4,3,7,1,6]=>[3,2,1,1,1]=>64
[5,8,4,3,7,6,2,1]=>[2,2,2,1,1]=>28
[8,1,5,3,4,7,2,6]=>[4,2,1,1]=>90
[6,1,8,7,4,5,3,2]=>[3,2,1,1,1]=>64
[1,5,8,6,4,3,7,2]=>[4,1,1,1,1]=>35
[5,8,6,4,2,1,7,3]=>[3,2,1,1,1]=>64
[2,6,1,8,4,7,5,3]=>[3,3,1,1]=>56
[5,3,8,6,1,2,7,4]=>[3,3,2]=>42
[5,8,1,4,6,2,7,3]=>[4,2,2]=>56
[3,7,6,2,1,4,8,5]=>[3,3,1,1]=>56
[4,6,2,3,7,1,8,5]=>[4,3,1]=>70
[6,8,7,5,1,3,4,2]=>[3,2,1,1,1]=>64
[6,4,3,2,7,8,5,1]=>[3,2,1,1,1]=>64
[2,7,6,1,5,3,8,4]=>[3,3,1,1]=>56
[7,8,6,4,2,5,3,1]=>[2,2,2,1,1]=>28
[6,4,5,8,7,1,3,2]=>[3,2,2,1]=>70
[6,4,1,7,8,3,2,5]=>[3,3,1,1]=>56
[2,3,4,5,8,6,7,9,1]=>[7,1,1]=>28
[2,3,4,5,9,6,8,7,1]=>[6,1,1,1]=>56
[9,3,4,5,2,6,7,8,1]=>[6,1,1,1]=>56
[6,2,3,4,5,7,8,9,10,1]=>[8,1,1]=>36
[2,6,3,4,5,7,8,9,10,1]=>[8,1,1]=>36
[2,3,6,4,5,7,8,9,10,1]=>[8,1,1]=>36
[2,6,4,5,7,1,8,3]=>[5,2,1]=>64
[3,7,4,6,1,5,8,2]=>[4,2,1,1]=>90
[3,4,6,5,2,8,1,7]=>[4,2,1,1]=>90
[4,6,7,5,8,2,1,3]=>[4,2,1,1]=>90
[2,5,7,6,4,1,8,3]=>[4,2,1,1]=>90
[5,1,4,6,2,7,8,3]=>[5,2,1]=>64
[1,2,5,3,7,8,6,4]=>[5,2,1]=>64
[4,8,3,5,1,2,7,6]=>[3,3,2]=>42
[6,1,3,7,2,8,4,5]=>[4,3,1]=>70
[3,8,5,4,1,7,2,6]=>[3,3,1,1]=>56
[3,1,5,8,2,6,7,4]=>[4,3,1]=>70
[2,8,5,3,1,7,4,6]=>[4,2,1,1]=>90
[6,5,2,3,7,1,8,4]=>[4,2,1,1]=>90
[7,2,1,6,4,8,3,5]=>[3,3,1,1]=>56
[2,1,3,7,5,8,4,6]=>[4,3,1]=>70
[6,2,4,5,7,1,8,3]=>[5,2,1]=>64
[2,3,8,7,1,4,6,5]=>[4,2,1,1]=>90
[4,2,7,5,6,8,1,3]=>[4,2,2]=>56
[2,1,3,4,5,8,6,7,9]=>[7,2]=>27
[6,8,2,5,4,7,3,1]=>[3,2,1,1,1]=>64
[9,2,3,4,5,1,6,7,8]=>[7,1,1]=>28
[7,2,3,4,5,6,9,1,8]=>[6,2,1]=>105
[10,2,3,4,5,6,7,1,8,9]=>[8,1,1]=>36
[6,2,3,4,5,9,1,7,8]=>[6,2,1]=>105
[10,2,3,4,5,6,1,7,8,9]=>[8,1,1]=>36
[5,2,3,4,9,1,6,7,8]=>[6,2,1]=>105
[10,2,3,4,5,1,6,7,8,9]=>[8,1,1]=>36
[4,2,3,9,1,5,6,7,8]=>[6,2,1]=>105
[10,2,3,4,1,5,6,7,8,9]=>[8,1,1]=>36
[3,2,9,1,4,5,6,7,8]=>[6,2,1]=>105
[2,8,1,3,4,5,6,10,7,9]=>[7,3]=>75
[10,7,1,2,3,4,5,9,6,8]=>[7,2,1]=>160
[5,3,2,7,6,1,8,4]=>[3,2,2,1]=>70
[5,6,4,2,8,7,1,3]=>[3,2,2,1]=>70
[5,7,4,2,6,1,8,3]=>[3,2,2,1]=>70
[5,4,7,1,6,2,8,3]=>[3,3,2]=>42
[4,5,8,7,6,2,1,3]=>[3,2,1,1,1]=>64
[6,4,7,1,2,3,8,5]=>[4,3,1]=>70
[4,5,6,8,2,9,3,10,7,1]=>[6,3,1]=>315
[10,4,5,6,9,3,8,2,7,1]=>[4,2,2,1,1]=>567
[4,5,10,6,9,3,8,2,7,1]=>[4,2,2,1,1]=>567
[4,5,8,2,6,10,9,3,7,1]=>[4,3,2,1]=>768
[10,6,9,5,4,3,8,2,7,1]=>[2,2,2,1,1,1,1]=>75
[8,2,6,10,9,5,4,3,7,1]=>[3,2,2,1,1,1]=>315
[8,2,10,4,5,6,7,1,9,3]=>[6,2,2]=>225
[4,5,6,8,2,10,7,1,9,3]=>[5,3,2]=>450
[10,4,5,6,8,2,7,1,9,3]=>[5,2,2,1]=>525
[4,5,10,6,8,2,7,1,9,3]=>[5,2,2,1]=>525
[4,5,10,8,2,6,7,1,9,3]=>[5,2,2,1]=>525
[10,6,8,2,7,1,9,5,4,3]=>[3,2,2,1,1,1]=>315
[10,8,2,6,7,1,9,5,4,3]=>[4,2,1,1,1,1]=>350
[8,2,7,1,9,3,10,4,5,6]=>[5,4,1]=>288
[4,5,8,2,7,1,9,3,10,6]=>[5,3,2]=>450
[4,5,9,3,10,7,1,8,2,6]=>[4,3,3]=>210
[4,5,7,1,9,3,8,2,6,10]=>[5,3,2]=>450
[8,2,7,1,9,5,4,3,10,6]=>[4,3,1,1,1]=>525
[9,5,4,3,10,7,1,8,2,6]=>[3,3,2,1,1]=>450
[7,1,9,5,4,3,8,2,6,10]=>[4,2,2,1,1]=>567
[8,2,6,10,4,5,7,1,9,3]=>[5,2,2,1]=>525
[4,8,2,6,10,5,7,1,9,3]=>[4,3,2,1]=>768
[4,10,8,2,5,6,7,1,9,3]=>[5,2,2,1]=>525
[8,2,6,10,5,7,1,9,4,3]=>[4,2,2,1,1]=>567
[10,8,2,5,6,7,1,9,4,3]=>[5,2,1,1,1]=>448
[9,3,10,4,5,7,1,8,2,6]=>[5,3,2]=>450
[4,9,3,10,5,7,1,8,2,6]=>[4,3,3]=>210
[4,9,3,10,7,1,8,2,5,6]=>[4,3,3]=>210
[4,7,1,9,3,8,2,5,6,10]=>[5,3,2]=>450
[9,4,3,10,5,7,1,8,2,6]=>[4,3,2,1]=>768
[9,4,3,10,7,1,8,2,5,6]=>[4,3,2,1]=>768
[7,1,9,4,3,8,2,5,6,10]=>[5,2,2,1]=>525
[5,10,7,1,8,2,4,3,9,6]=>[4,4,1,1]=>300
[5,7,1,8,2,4,3,9,6,10]=>[5,4,1]=>288
[10,5,7,1,9,4,2,6,8,3]=>[4,3,2,1]=>768
[9,4,2,5,6,7,1,10,8,3]=>[5,2,2,1]=>525
[10,5,7,1,8,3,9,4,2,6]=>[4,4,1,1]=>300
[10,7,1,8,3,9,4,2,5,6]=>[5,3,1,1]=>567
[7,1,8,3,9,4,2,5,6,10]=>[6,3,1]=>315
[4,2,5,10,7,1,8,3,9,6]=>[5,3,2]=>450
[4,2,5,7,1,8,3,9,6,10]=>[6,3,1]=>315
[1,8,7,2,3,4,6,5]=>[5,1,1,1]=>35
[1,8,3,7,6,2,5,4]=>[3,2,1,1,1]=>64
[1,3,8,2,5,6,4,7]=>[5,2,1]=>64
[1,3,2,7,4,6,8,5]=>[5,2,1]=>64
[1,3,8,4,6,2,7,5]=>[5,2,1]=>64
[8,2,3,6,7,4,5,1]=>[4,2,1,1]=>90
[2,5,7,6,3,8,4,1]=>[4,2,1,1]=>90
[4,5,6,7,8,9,1,2,10,3]=>[7,3]=>75
[4,5,6,7,8,1,3,9,2]=>[6,2,1]=>105
[1,7,8,4,2,6,3,5]=>[4,2,2]=>56
[6,2,1,5,3,7,8,4]=>[4,3,1]=>70
[6,2,5,1,3,8,7,4]=>[3,3,2]=>42
[6,2,8,5,1,3,7,4]=>[3,3,2]=>42
[10,9,7,3,6,1,2,4,8,5]=>[4,3,1,1,1]=>525
[9,7,3,6,1,2,4,10,8,5]=>[4,3,2,1]=>768
[7,3,10,9,6,1,2,4,8,5]=>[4,3,2,1]=>768
[7,3,9,6,1,2,4,10,8,5]=>[4,3,3]=>210
[9,6,1,2,4,10,7,3,8,5]=>[5,2,2,1]=>525
[8,4,10,9,7,3,6,1,2,5]=>[3,2,2,2,1]=>288
[10,8,4,9,7,3,6,1,2,5]=>[3,2,2,2,1]=>288
[7,3,8,4,10,9,6,1,2,5]=>[3,3,3,1]=>210
[7,3,10,8,4,9,6,1,2,5]=>[3,3,3,1]=>210
[10,7,3,8,4,9,6,1,2,5]=>[3,3,3,1]=>210
[6,1,2,7,3,8,4,10,9,5]=>[5,4,1]=>288
[6,1,2,7,3,10,8,4,9,5]=>[5,4,1]=>288
[6,1,2,10,7,3,8,4,9,5]=>[5,4,1]=>288
[10,6,1,2,7,3,8,4,9,5]=>[5,4,1]=>288
[6,1,3,10,9,7,2,4,8,5]=>[4,3,2,1]=>768
[6,1,3,9,7,2,4,10,8,5]=>[4,3,3]=>210
[10,9,6,1,3,7,2,4,8,5]=>[4,3,1,1,1]=>525
[9,6,1,3,7,2,4,10,8,5]=>[4,3,2,1]=>768
[10,7,2,4,9,6,1,3,8,5]=>[4,3,2,1]=>768
[6,1,3,8,4,10,9,7,2,5]=>[4,3,2,1]=>768
[6,1,3,10,8,4,9,7,2,5]=>[4,3,2,1]=>768
[8,4,10,9,6,1,3,7,2,5]=>[3,3,2,1,1]=>450
[10,8,4,9,6,1,3,7,2,5]=>[3,3,2,1,1]=>450
[9,6,1,3,8,4,10,7,2,5]=>[4,3,2,1]=>768
[7,2,6,1,3,8,4,10,9,5]=>[4,4,2]=>252
[7,2,6,1,3,10,8,4,9,5]=>[4,4,2]=>252
[10,7,2,6,1,3,8,4,9,5]=>[4,4,1,1]=>300
[7,2,10,6,1,3,8,4,9,5]=>[4,4,2]=>252
[8,3,6,1,4,10,9,7,2,5]=>[3,3,2,2]=>252
[10,8,3,6,1,4,9,7,2,5]=>[3,3,2,1,1]=>450
[10,9,6,1,4,8,3,7,2,5]=>[3,2,2,1,1,1]=>315
[9,6,1,4,10,8,3,7,2,5]=>[3,2,2,2,1]=>288
[8,3,9,6,1,4,10,7,2,5]=>[3,3,3,1]=>210
[8,3,7,2,6,1,4,10,9,5]=>[3,3,3,1]=>210
[10,8,3,7,2,6,1,4,9,5]=>[3,3,2,1,1]=>450
[8,3,10,7,2,6,1,4,9,5]=>[3,3,2,2]=>252
[7,2,8,3,10,6,1,4,9,5]=>[4,3,3]=>210
[9,4,10,8,3,7,2,6,1,5]=>[2,2,2,2,2]=>42
[8,3,9,4,10,7,2,6,1,5]=>[3,3,2,2]=>252
[7,2,8,3,9,4,10,6,1,5]=>[4,4,2]=>252
[12,11,9,5,10,7,1,2,4,8,3,6]=>[4,3,2,1,1,1]=>5632
[11,9,5,12,10,7,1,2,4,8,3,6]=>[4,3,2,2,1]=>5775
[10,7,1,2,4,9,5,12,11,8,3,6]=>[5,3,2,2]=>4455
[12,10,7,1,2,4,9,5,11,8,3,6]=>[5,3,2,1,1]=>7700
[10,7,1,2,4,12,9,5,11,8,3,6]=>[5,3,2,2]=>4455
[8,3,7,1,2,4,12,11,9,5,10,6]=>[5,4,2,1]=>5775
[8,3,7,1,2,4,11,9,5,12,10,6]=>[5,4,3]=>2112
[12,11,8,3,7,1,2,4,9,5,10,6]=>[5,4,1,1,1]=>3520
[11,8,3,7,1,2,4,9,5,12,10,6]=>[5,4,2,1]=>5775
[12,9,5,11,8,3,7,1,2,4,10,6]=>[4,3,2,2,1]=>5775
[8,3,12,11,7,1,2,4,9,5,10,6]=>[5,4,2,1]=>5775
[8,3,11,7,1,2,4,9,5,12,10,6]=>[5,4,3]=>2112
[8,3,12,9,5,11,7,1,2,4,10,6]=>[4,4,3,1]=>2970
[12,8,3,9,5,11,7,1,2,4,10,6]=>[4,4,3,1]=>2970
[10,7,1,2,5,12,11,9,4,8,3,6]=>[4,2,2,2,2]=>1485
[12,10,7,1,2,5,11,9,4,8,3,6]=>[4,2,2,2,1,1]=>3080
[9,4,10,7,1,2,5,12,11,8,3,6]=>[4,3,3,2]=>2970
[9,4,12,10,7,1,2,5,11,8,3,6]=>[4,3,3,1,1]=>4158
[12,9,4,10,7,1,2,5,11,8,3,6]=>[4,3,3,1,1]=>4158
[12,11,9,4,8,3,7,1,2,5,10,6]=>[4,3,2,1,1,1]=>5632
[11,9,4,8,3,7,1,2,5,12,10,6]=>[4,3,3,1,1]=>4158
[9,4,12,11,8,3,7,1,2,5,10,6]=>[4,3,2,2,1]=>5775
[9,4,11,8,3,7,1,2,5,12,10,6]=>[4,3,3,2]=>2970
[11,8,3,7,1,2,5,12,9,4,10,6]=>[5,3,2,1,1]=>7700
[8,3,9,4,12,11,7,1,2,5,10,6]=>[4,4,3,1]=>2970
[8,3,9,4,11,7,1,2,5,12,10,6]=>[4,4,4]=>462
[8,3,11,7,1,2,5,12,9,4,10,6]=>[5,3,3,1]=>4158
[11,7,1,2,5,12,8,3,9,4,10,6]=>[6,3,2,1]=>5632
[10,5,12,11,9,4,8,3,7,1,2,6]=>[3,2,2,2,2,1]=>1155
[12,10,5,11,9,4,8,3,7,1,2,6]=>[3,2,2,2,2,1]=>1155
[9,4,10,5,12,11,8,3,7,1,2,6]=>[3,3,3,2,1]=>2112
[9,4,12,10,5,11,8,3,7,1,2,6]=>[3,3,3,2,1]=>2112
[12,9,4,10,5,11,8,3,7,1,2,6]=>[3,3,3,2,1]=>2112
[8,3,9,4,10,5,12,11,7,1,2,6]=>[4,4,3,1]=>2970
[8,3,9,4,12,10,5,11,7,1,2,6]=>[4,4,3,1]=>2970
[8,3,12,9,4,10,5,11,7,1,2,6]=>[4,4,3,1]=>2970
[12,8,3,9,4,10,5,11,7,1,2,6]=>[4,4,3,1]=>2970
[7,1,2,8,3,9,4,10,5,12,11,6]=>[6,5,1]=>1155
[7,1,2,8,3,9,4,12,10,5,11,6]=>[6,5,1]=>1155
[7,1,2,8,3,12,9,4,10,5,11,6]=>[6,5,1]=>1155
[7,1,2,12,8,3,9,4,10,5,11,6]=>[6,5,1]=>1155
[12,7,1,2,8,3,9,4,10,5,11,6]=>[6,5,1]=>1155
[8,2,4,12,11,9,5,10,7,1,3,6]=>[4,3,3,1,1]=>4158
[8,2,4,11,9,5,12,10,7,1,3,6]=>[4,3,3,2]=>2970
[12,11,8,2,4,9,5,10,7,1,3,6]=>[4,3,3,1,1]=>4158
[11,8,2,4,9,5,12,10,7,1,3,6]=>[4,3,3,2]=>2970
[12,9,5,11,8,2,4,10,7,1,3,6]=>[3,3,3,2,1]=>2112
[7,1,3,8,2,4,12,11,9,5,10,6]=>[5,4,2,1]=>5775
[7,1,3,8,2,4,11,9,5,12,10,6]=>[5,4,3]=>2112
[7,1,3,12,11,8,2,4,9,5,10,6]=>[5,4,2,1]=>5775
[7,1,3,11,8,2,4,9,5,12,10,6]=>[5,4,3]=>2112
[7,1,3,12,9,5,11,8,2,4,10,6]=>[5,3,3,1]=>4158
[12,11,7,1,3,8,2,4,9,5,10,6]=>[5,4,1,1,1]=>3520
[11,7,1,3,8,2,4,9,5,12,10,6]=>[5,4,2,1]=>5775
[12,9,5,11,7,1,3,8,2,4,10,6]=>[4,4,2,1,1]=>4455
[11,7,1,3,9,5,12,8,2,4,10,6]=>[5,3,3,1]=>4158
[12,11,9,4,8,2,5,10,7,1,3,6]=>[3,3,3,1,1,1]=>1650
[11,9,4,8,2,5,12,10,7,1,3,6]=>[3,3,3,2,1]=>2112
[9,4,12,11,8,2,5,10,7,1,3,6]=>[3,3,3,2,1]=>2112
[9,4,11,8,2,5,12,10,7,1,3,6]=>[3,3,3,3]=>462
[11,8,2,5,12,9,4,10,7,1,3,6]=>[4,3,2,2,1]=>5775
[7,1,3,12,11,9,4,8,2,5,10,6]=>[5,3,2,1,1]=>7700
[7,1,3,11,9,4,8,2,5,12,10,6]=>[5,3,3,1]=>4158
[7,1,3,9,4,12,11,8,2,5,10,6]=>[5,3,3,1]=>4158
[7,1,3,9,4,11,8,2,5,12,10,6]=>[5,4,3]=>2112
[7,1,3,11,8,2,5,12,9,4,10,6]=>[5,3,3,1]=>4158
[9,4,12,11,7,1,3,8,2,5,10,6]=>[4,4,2,1,1]=>4455
[9,4,11,7,1,3,8,2,5,12,10,6]=>[4,4,3,1]=>2970
[11,7,1,3,8,2,5,12,9,4,10,6]=>[5,3,3,1]=>4158
[12,8,2,5,11,7,1,3,9,4,10,6]=>[5,4,2,1]=>5775
[7,1,3,10,5,12,11,9,4,8,2,6]=>[4,3,2,2,1]=>5775
[7,1,3,12,10,5,11,9,4,8,2,6]=>[4,3,2,2,1]=>5775
[7,1,3,9,4,10,5,12,11,8,2,6]=>[5,4,2,1]=>5775
[7,1,3,9,4,12,10,5,11,8,2,6]=>[5,4,2,1]=>5775
[7,1,3,12,9,4,10,5,11,8,2,6]=>[5,4,2,1]=>5775
[9,4,10,5,12,11,7,1,3,8,2,6]=>[4,3,3,1,1]=>4158
[9,4,12,10,5,11,7,1,3,8,2,6]=>[4,3,3,1,1]=>4158
[12,9,4,10,5,11,7,1,3,8,2,6]=>[4,3,3,1,1]=>4158
[11,7,1,3,9,4,10,5,12,8,2,6]=>[5,4,2,1]=>5775
[8,2,7,1,3,9,4,10,5,12,11,6]=>[5,5,2]=>1320
[8,2,7,1,3,9,4,12,10,5,11,6]=>[5,5,2]=>1320
[8,2,7,1,3,12,9,4,10,5,11,6]=>[5,5,2]=>1320
[12,8,2,7,1,3,9,4,10,5,11,6]=>[5,5,1,1]=>1485
[8,2,12,7,1,3,9,4,10,5,11,6]=>[5,5,2]=>1320
[10,7,1,4,8,2,5,12,11,9,3,6]=>[4,3,3,2]=>2970
[12,10,7,1,4,8,2,5,11,9,3,6]=>[4,3,3,1,1]=>4158
[12,11,8,2,5,10,7,1,4,9,3,6]=>[4,3,2,1,1,1]=>5632
[11,8,2,5,12,10,7,1,4,9,3,6]=>[4,3,2,2,1]=>5775
[10,7,1,4,11,8,2,5,12,9,3,6]=>[4,3,3,2]=>2970
[12,11,9,3,7,1,4,8,2,5,10,6]=>[4,4,1,1,1,1]=>1925
[11,9,3,7,1,4,8,2,5,12,10,6]=>[4,4,2,1,1]=>4455
[9,3,7,1,4,12,11,8,2,5,10,6]=>[4,4,2,2]=>2640
[9,3,7,1,4,11,8,2,5,12,10,6]=>[4,4,3,1]=>2970
[11,8,2,5,12,9,3,7,1,4,10,6]=>[4,3,2,2,1]=>5775
[12,11,7,1,4,9,3,8,2,5,10,6]=>[4,3,2,1,1,1]=>5632
[11,7,1,4,9,3,8,2,5,12,10,6]=>[4,3,3,1,1]=>4158
[12,9,3,8,2,5,11,7,1,4,10,6]=>[4,3,3,1,1]=>4158
[9,3,12,8,2,5,11,7,1,4,10,6]=>[4,3,3,2]=>2970
[10,5,12,11,9,3,7,1,4,8,2,6]=>[3,3,2,2,1,1]=>2673
[12,10,5,11,9,3,7,1,4,8,2,6]=>[3,3,2,2,1,1]=>2673
[9,3,7,1,4,10,5,12,11,8,2,6]=>[4,4,2,2]=>2640
[9,3,7,1,4,12,10,5,11,8,2,6]=>[4,4,2,2]=>2640
[12,9,3,7,1,4,10,5,11,8,2,6]=>[4,4,2,1,1]=>4455
[10,5,12,11,7,1,4,9,3,8,2,6]=>[3,3,2,2,1,1]=>2673
[12,10,5,11,7,1,4,9,3,8,2,6]=>[3,3,2,2,1,1]=>2673
[11,7,1,4,10,5,12,9,3,8,2,6]=>[4,3,2,2,1]=>5775
[9,3,11,7,1,4,10,5,12,8,2,6]=>[4,4,2,2]=>2640
[9,3,8,2,7,1,4,10,5,12,11,6]=>[4,4,3,1]=>2970
[9,3,8,2,7,1,4,12,10,5,11,6]=>[4,4,3,1]=>2970
[12,9,3,8,2,7,1,4,10,5,11,6]=>[4,4,2,1,1]=>4455
[9,3,12,8,2,7,1,4,10,5,11,6]=>[4,4,2,2]=>2640
[8,2,9,3,12,7,1,4,10,5,11,6]=>[5,4,3]=>2112
[12,11,9,3,7,1,5,10,4,8,2,6]=>[3,3,2,1,1,1,1]=>1925
[11,9,3,7,1,5,12,10,4,8,2,6]=>[3,3,2,2,1,1]=>2673
[10,4,9,3,7,1,5,12,11,8,2,6]=>[3,3,3,2,1]=>2112
[12,10,4,9,3,7,1,5,11,8,2,6]=>[3,3,3,1,1,1]=>1650
[10,4,12,9,3,7,1,5,11,8,2,6]=>[3,3,3,2,1]=>2112
[12,11,7,1,5,10,4,9,3,8,2,6]=>[3,2,2,2,1,1,1]=>1408
[11,7,1,5,12,10,4,9,3,8,2,6]=>[3,2,2,2,2,1]=>1155
[10,4,11,7,1,5,12,9,3,8,2,6]=>[3,3,3,2,1]=>2112
[9,3,10,4,11,7,1,5,12,8,2,6]=>[4,4,3,1]=>2970
[10,4,9,3,8,2,7,1,5,12,11,6]=>[3,3,3,2,1]=>2112
[12,10,4,9,3,8,2,7,1,5,11,6]=>[3,3,2,2,1,1]=>2673
[10,4,12,9,3,8,2,7,1,5,11,6]=>[3,3,2,2,2]=>1320
[9,3,10,4,12,8,2,7,1,5,11,6]=>[4,3,3,2]=>2970
[8,2,9,3,10,4,12,7,1,5,11,6]=>[5,4,3]=>2112
[12,11,5,10,4,9,3,8,2,7,1,6]=>[2,2,2,2,2,1,1]=>297
[11,5,12,10,4,9,3,8,2,7,1,6]=>[2,2,2,2,2,2]=>132
[10,4,11,5,12,9,3,8,2,7,1,6]=>[3,3,2,2,2]=>1320
[9,3,10,4,11,5,12,8,2,7,1,6]=>[4,4,2,2]=>2640
[8,2,9,3,10,4,11,5,12,7,1,6]=>[5,5,2]=>1320
[4,1,7,8,3,6,5,2]=>[3,3,1,1]=>56
[1,7,5,8,4,3,6,2]=>[3,2,1,1,1]=>64
[5,8,1,6,4,7,2,3]=>[3,3,1,1]=>56
[2,4,7,5,1,8,6,3]=>[4,2,2]=>56
[2,3,7,1,8,5,6,4]=>[4,3,1]=>70
[6,5,1,2,7,4,8,3]=>[4,2,1,1]=>90
[3,6,5,7,8,2,4,1]=>[4,2,1,1]=>90
[3,6,5,1,8,7,4,2]=>[3,2,2,1]=>70
[7,8,1,2,5,4,3,6]=>[4,2,1,1]=>90
[2,8,4,3,5,1,7,6]=>[4,2,1,1]=>90
[5,2,4,7,6,8,1,3]=>[4,2,2]=>56
[3,1,5,7,4,8,6,2]=>[4,3,1]=>70
[4,1,7,6,8,2,5,3]=>[3,3,1,1]=>56
[7,2,6,4,1,5,3,8]=>[4,2,1,1]=>90
[1,2,6,5,8,3,7,4]=>[4,2,2]=>56
[7,3,5,6,1,4,2,8]=>[4,2,1,1]=>90
[5,8,3,1,6,7,4,2]=>[3,2,2,1]=>70
[4,5,8,1,7,3,6,2]=>[3,3,1,1]=>56
[4,7,1,6,8,5,2,3]=>[3,3,1,1]=>56
[5,8,7,1,6,4,2,3]=>[3,2,1,1,1]=>64
[1,7,3,8,2,5,4,6]=>[4,2,2]=>56
[5,3,1,8,6,7,4,2]=>[3,2,2,1]=>70
[6,2,7,1,4,3,5,8]=>[4,2,2]=>56
[9,5,4,3,2,1,6,7,8]=>[4,1,1,1,1,1]=>56
[10,3,4,1,2,5,6,7,8,9]=>[7,2,1]=>160
[8,3,2,6,5,1,7,4]=>[3,2,2,1]=>70
[2,6,8,4,7,1,3,5]=>[3,3,2]=>42
[7,8,6,3,2,5,4,1]=>[2,2,2,1,1]=>28
[1,6,4,8,2,3,5,7]=>[5,2,1]=>64
[2,8,5,6,4,1,7,3]=>[4,2,1,1]=>90
[1,4,7,3,5,8,6,2]=>[4,3,1]=>70
[3,7,8,2,5,1,6,4]=>[3,3,2]=>42
[8,6,1,4,3,2,7,5]=>[3,2,1,1,1]=>64
[7,3,8,2,4,1,5,6]=>[4,2,1,1]=>90
[6,3,7,8,1,2,5,4]=>[3,3,2]=>42
[7,6,1,5,2,3,8,4]=>[4,2,1,1]=>90
[5,1,8,6,7,2,3,4]=>[4,3,1]=>70
[5,7,1,6,8,2,3,4]=>[4,3,1]=>70
[6,8,4,2,1,7,3,5]=>[3,2,2,1]=>70
[6,3,2,8,1,7,4,5]=>[3,2,2,1]=>70
[6,4,1,3,7,8,5,2]=>[4,2,1,1]=>90
[6,8,5,4,3,7,1,2]=>[2,2,2,1,1]=>28
[5,7,4,8,3,1,2,6]=>[3,3,1,1]=>56
[6,1,2,4,8,3,7,5]=>[4,2,2]=>56
[1,6,4,7,5,3,2,8]=>[4,2,1,1]=>90
[1,6,5,3,2,7,4,8]=>[4,2,1,1]=>90
[1,6,8,7,4,5,3,2]=>[3,2,1,1,1]=>64
[1,4,7,5,3,2,6,8]=>[5,1,1,1]=>35
[1,7,5,4,3,2,8,6]=>[3,2,1,1,1]=>64
[1,4,7,5,3,2,8,6]=>[4,2,1,1]=>90
[1,7,4,6,8,5,3,2]=>[4,1,1,1,1]=>35
[6,8,7,2,3,5,4,1]=>[3,2,1,1,1]=>64
[5,7,6,1,8,2,4,3]=>[3,3,1,1]=>56
[4,8,6,5,7,2,3,1]=>[3,2,1,1,1]=>64
[2,7,8,5,1,4,3,6]=>[3,3,1,1]=>56
[8,5,6,2,4,7,3,1]=>[3,2,1,1,1]=>64
[8,1,3,6,4,5,2,7]=>[5,1,1,1]=>35
[1,2,3,7,4,8,5,9,6]=>[6,3]=>48
[1,2,3,4,7,5,9,8,6]=>[6,2,1]=>105
[1,2,6,3,7,4,9,8,5]=>[5,3,1]=>162
[1,2,3,8,6,4,9,7,5]=>[5,2,2]=>120
[1,2,3,6,4,9,8,7,5]=>[5,2,1,1]=>189
[5,1,6,2,7,3,9,8,4]=>[4,4,1]=>84
[1,5,2,8,6,3,9,7,4]=>[4,3,2]=>168
[1,5,2,6,3,9,8,7,4]=>[4,3,1,1]=>216
[1,2,7,5,3,9,8,6,4]=>[4,2,2,1]=>216
[1,2,5,3,9,8,7,6,4]=>[4,2,1,1,1]=>189
[4,1,7,5,2,9,8,6,3]=>[3,3,2,1]=>168
[4,1,5,2,9,8,7,6,3]=>[3,3,1,1,1]=>120
[1,6,4,2,9,8,7,5,3]=>[3,2,2,1,1]=>162
[1,4,2,9,8,7,6,5,3]=>[3,2,1,1,1,1]=>105
[7,5,3,1,9,8,6,4,2]=>[2,2,2,2,1]=>42
[5,3,1,9,8,7,6,4,2]=>[2,2,2,1,1,1]=>48
[1,2,3,4,8,5,9,6,10,7]=>[7,3]=>75
[1,2,3,4,5,8,6,10,9,7]=>[7,2,1]=>160
[1,2,3,7,4,8,5,10,9,6]=>[6,3,1]=>315
[1,2,3,4,9,7,5,10,8,6]=>[6,2,2]=>225
[1,2,3,4,7,5,10,9,8,6]=>[6,2,1,1]=>350
[1,6,2,7,3,8,4,10,9,5]=>[5,4,1]=>288
[1,2,6,3,9,7,4,10,8,5]=>[5,3,2]=>450
[1,2,6,3,7,4,10,9,8,5]=>[5,3,1,1]=>567
[1,2,3,8,6,4,10,9,7,5]=>[5,2,2,1]=>525
[1,2,3,6,4,10,9,8,7,5]=>[5,2,1,1,1]=>448
[5,1,6,2,9,7,3,10,8,4]=>[4,4,2]=>252
[5,1,6,2,7,3,10,9,8,4]=>[4,4,1,1]=>300
[1,5,2,6,3,10,9,8,7,4]=>[4,3,1,1,1]=>525
[1,2,7,5,3,10,9,8,6,4]=>[4,2,2,1,1]=>567
[1,2,5,3,10,9,8,7,6,4]=>[4,2,1,1,1,1]=>350
[7,4,1,8,5,2,10,9,6,3]=>[3,3,3,1]=>210
[4,1,9,7,5,2,10,8,6,3]=>[3,3,2,2]=>252
[4,1,7,5,2,10,9,8,6,3]=>[3,3,2,1,1]=>450
[4,1,5,2,10,9,8,7,6,3]=>[3,3,1,1,1,1]=>225
[1,8,6,4,2,10,9,7,5,3]=>[3,2,2,2,1]=>288
[1,6,4,2,10,9,8,7,5,3]=>[3,2,2,1,1,1]=>315
[1,4,2,10,9,8,7,6,5,3]=>[3,2,1,1,1,1,1]=>160
[7,5,3,1,10,9,8,6,4,2]=>[2,2,2,2,1,1]=>90
[5,3,1,10,9,8,7,6,4,2]=>[2,2,2,1,1,1,1]=>75
[4,3,1,6,2,5,8,7]=>[4,3,1]=>70
[7,5,2,1,8,4,3,6]=>[3,2,2,1]=>70
[5,3,1,4,7,8,2,6]=>[4,3,1]=>70
[7,1,2,4,8,3,5,6]=>[5,2,1]=>64
[8,6,1,3,5,7,4,2]=>[4,1,1,1,1]=>35
[7,1,5,8,2,3,4,6]=>[5,2,1]=>64
[3,6,8,5,1,4,2,7]=>[3,3,1,1]=>56
[5,2,4,1,6,8,3,7]=>[4,3,1]=>70
[4,3,1,2,5,7,6,8]=>[5,2,1]=>64
[1,2,3,4,5,8,9,7,6]=>[7,1,1]=>28
[1,2,3,4,8,9,6,7,5]=>[6,2,1]=>105
[1,2,3,8,9,5,6,7,4]=>[6,2,1]=>105
[1,2,4,7,8,5,6,3]=>[5,2,1]=>64
[1,2,8,9,4,5,6,7,3]=>[6,2,1]=>105
[5,3,1,8,4,2,6,7]=>[4,2,2]=>56
[2,1,6,5,8,7,3,4]=>[3,3,2]=>42
[6,1,5,4,7,3,8,2]=>[4,1,1,1,1]=>35
[5,3,2,8,7,1,6,4]=>[2,2,2,2]=>14
[8,6,7,4,1,3,5,2]=>[3,2,1,1,1]=>64
[4,1,3,6,5,2,8,7]=>[4,3,1]=>70
[4,6,3,2,5,1,8,7]=>[3,3,1,1]=>56
[4,8,3,2,6,5,7,1]=>[3,2,2,1]=>70
[4,8,3,6,5,2,7,1]=>[3,2,1,1,1]=>64
[8,1,6,2,5,4,7,3]=>[4,1,1,1,1]=>35
[2,4,3,8,6,1,7,5]=>[4,2,2]=>56
[2,6,3,8,5,4,7,1]=>[4,2,1,1]=>90
[6,1,3,2,5,8,7,4]=>[4,2,2]=>56
[6,8,4,2,5,3,7,1]=>[3,2,2,1]=>70
[6,8,4,3,5,2,7,1]=>[3,2,1,1,1]=>64
[8,1,4,6,5,3,7,2]=>[4,1,1,1,1]=>35
[1,4,2,5,6,7,9,8,3]=>[6,2,1]=>105
[2,3,4,5,6,7,8,9,1,11,10]=>[9,2]=>44
[2,1,4,5,6,9,7,3,8]=>[6,2,1]=>105
[3,5,4,6,1,2,8,7]=>[4,3,1]=>70
[3,1,5,2,9,6,7,8,4]=>[5,3,1]=>162
[4,5,1,6,8,7,9,2,3]=>[5,3,1]=>162
[1,4,2,5,6,7,8,10,9,3]=>[7,2,1]=>160
[3,4,1,5,6,7,8,9,10,11,2]=>[9,2]=>44
[1,3,4,5,6,7,8,9,11,2,10]=>[9,2]=>44
[2,1,4,5,6,7,10,8,3,9]=>[7,2,1]=>160
[2,3,1,5,9,6,7,4,8]=>[6,2,1]=>105
[1,2,4,5,7,9,6,3,8]=>[6,2,1]=>105
[3,4,6,5,7,1,2,9,8]=>[5,3,1]=>162
[3,1,9,4,2,6,7,8,5]=>[5,3,1]=>162
[7,3,5,6,1,8,2,4]=>[4,3,1]=>70
[1,2,5,3,9,6,8,7,4]=>[5,2,1,1]=>189
[3,1,5,2,6,10,7,8,9,4]=>[6,3,1]=>315
[4,5,1,7,6,8,2,9,3]=>[5,3,1]=>162
[4,5,1,6,7,9,8,10,2,3]=>[6,3,1]=>315
[1,4,2,5,6,7,8,9,11,10,3]=>[8,2,1]=>231
[3,4,1,5,6,7,8,9,10,11,12,2]=>[10,2]=>54
[5,7,6,3,4,2,8,1]=>[3,2,1,1,1]=>64
[4,6,7,2,3,5,8,1]=>[4,3,1]=>70
[6,5,4,8,7,2,3,1]=>[2,2,2,1,1]=>28
[7,2,8,3,9,4,10,5,1,6]=>[5,4,1]=>288
[7,2,8,3,9,4,10,1,5,6]=>[5,4,1]=>288
[7,2,8,3,9,10,4,5,1,6]=>[5,4,1]=>288
[7,2,8,3,9,10,4,1,5,6]=>[5,4,1]=>288
[7,2,8,3,9,10,1,4,5,6]=>[5,4,1]=>288
[7,2,8,9,3,4,10,5,1,6]=>[5,4,1]=>288
[7,2,8,9,3,4,10,1,5,6]=>[5,4,1]=>288
[7,2,8,9,3,10,4,5,1,6]=>[5,4,1]=>288
[7,2,8,9,3,10,4,1,5,6]=>[5,4,1]=>288
[7,2,8,9,3,10,1,4,5,6]=>[5,4,1]=>288
[7,2,8,9,10,3,4,5,1,6]=>[5,4,1]=>288
[7,2,8,9,10,3,4,1,5,6]=>[5,4,1]=>288
[7,2,8,9,10,3,1,4,5,6]=>[5,4,1]=>288
[7,8,2,3,9,4,10,5,1,6]=>[5,4,1]=>288
[7,8,2,3,9,4,10,1,5,6]=>[5,4,1]=>288
[7,8,2,3,9,10,4,5,1,6]=>[5,4,1]=>288
[7,8,2,3,9,10,4,1,5,6]=>[5,4,1]=>288
[7,8,2,3,9,10,1,4,5,6]=>[5,4,1]=>288
[7,8,2,9,3,4,10,5,1,6]=>[5,4,1]=>288
[7,8,2,9,3,4,10,1,5,6]=>[5,4,1]=>288
[7,8,2,9,3,10,4,5,1,6]=>[5,4,1]=>288
[7,8,2,9,3,10,4,1,5,6]=>[5,4,1]=>288
[7,8,2,9,3,10,1,4,5,6]=>[5,4,1]=>288
[7,8,2,9,10,3,4,5,1,6]=>[5,4,1]=>288
[7,8,2,9,10,3,4,1,5,6]=>[5,4,1]=>288
[7,8,2,9,10,3,1,4,5,6]=>[5,4,1]=>288
[7,8,2,9,10,1,3,4,5,6]=>[5,4,1]=>288
[7,8,9,2,3,4,10,5,1,6]=>[5,4,1]=>288
[7,8,9,2,3,4,10,1,5,6]=>[5,4,1]=>288
[7,8,9,2,3,10,4,5,1,6]=>[5,4,1]=>288
[7,8,9,2,3,10,4,1,5,6]=>[5,4,1]=>288
[7,8,9,2,3,10,1,4,5,6]=>[5,4,1]=>288
[7,8,9,2,10,3,4,5,1,6]=>[5,4,1]=>288
[7,8,9,2,10,3,4,1,5,6]=>[5,4,1]=>288
[7,8,9,2,10,3,1,4,5,6]=>[5,4,1]=>288
[7,8,9,2,10,1,3,4,5,6]=>[5,4,1]=>288
[7,8,9,10,2,3,4,1,5,6]=>[5,4,1]=>288
[7,8,9,10,2,3,1,4,5,6]=>[5,4,1]=>288
[7,8,9,10,2,1,3,4,5,6]=>[5,4,1]=>288
[8,2,9,3,10,4,11,5,12,6,1,7]=>[6,5,1]=>1155
[8,2,9,3,10,4,11,5,12,1,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,4,11,12,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,3,10,4,11,12,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,4,11,12,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,3,10,11,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,4,11,5,12,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,3,4,11,5,12,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,4,11,12,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,3,4,11,12,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,4,11,12,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,3,11,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,3,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,12,3,4,5,6,1,7]=>[6,5,1]=>1155
[8,2,9,10,11,12,3,4,5,1,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,12,3,4,1,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,12,3,1,4,5,6,7]=>[6,5,1]=>1155
[8,2,9,10,11,12,1,3,4,5,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,4,11,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,2,3,10,4,11,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,4,11,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,3,10,4,11,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,4,11,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,3,10,11,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,4,11,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,3,4,11,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,4,11,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,3,4,11,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,4,11,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,3,11,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,3,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,12,3,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,2,10,11,12,3,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,12,3,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,12,3,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,2,10,11,12,1,3,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,4,11,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,3,4,11,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,4,11,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,3,4,11,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,4,11,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,3,11,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,3,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,12,3,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,2,11,12,3,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,12,3,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,12,3,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,2,11,12,1,3,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,4,5,12,6,1,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,4,5,12,1,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,4,12,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,4,12,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,4,12,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,12,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,12,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,12,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,3,12,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,12,3,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,11,2,12,3,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,12,3,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,12,3,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,2,12,1,3,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,12,2,3,4,5,6,1,7]=>[6,5,1]=>1155
[8,9,10,11,12,2,3,4,5,1,6,7]=>[6,5,1]=>1155
[8,9,10,11,12,2,3,4,1,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,12,2,3,1,4,5,6,7]=>[6,5,1]=>1155
[8,9,10,11,12,2,1,3,4,5,6,7]=>[6,5,1]=>1155
[4,8,7,6,5,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[5,9,8,7,6,4,3,2,1,10]=>[3,1,1,1,1,1,1,1]=>36
[5,8,7,4,6,3,2,1,9]=>[3,2,1,1,1,1]=>105
[8,4,7,6,5,3,2,1,9]=>[3,1,1,1,1,1,1]=>28
[5,7,4,3,6,2,1,8]=>[3,2,1,1,1]=>64
[6,9,8,5,7,4,1,3,2]=>[2,2,2,1,1,1]=>48
[9,8,7,5,1,6,4,3,2]=>[2,2,1,1,1,1,1]=>27
[10,9,8,6,1,7,5,4,3,2]=>[2,2,1,1,1,1,1,1]=>35
[1,2,8,3,4,5,6,9,7]=>[7,2]=>27
[1,9,5,2,3,8,4,6,7]=>[6,2,1]=>105
[1,2,9,3,4,5,6,7,10,8]=>[8,2]=>35
[1,8,2,9,4,3,5,6,7]=>[6,2,1]=>105
[1,3,2,4,9,8,5,6,7]=>[6,2,1]=>105
[2,1,3,4,5,9,8,6,7]=>[6,2,1]=>105
[1,2,3,4,5,9,6,7,10,8]=>[8,2]=>35
[9,1,7,2,3,4,5,8,6]=>[6,2,1]=>105
[1,10,6,2,3,4,9,5,7,8]=>[7,2,1]=>160
[1,2,10,3,4,5,6,7,8,11,9]=>[9,2]=>44
[1,8,5,2,3,4,6,9,7]=>[6,2,1]=>105
[9,8,1,2,3,5,6,4,7]=>[6,1,1,1]=>56
[1,5,2,9,3,10,4,6,7,8]=>[7,3]=>75
[1,4,2,3,9,5,6,8,7]=>[6,2,1]=>105
[1,8,5,6,2,3,7,4]=>[4,3,1]=>70
[4,9,8,1,2,5,3,6,7]=>[5,2,1,1]=>189
[1,2,4,3,10,9,5,6,7,8]=>[7,2,1]=>160
[1,3,2,4,5,9,6,8,7]=>[6,2,1]=>105
[1,8,3,9,4,2,5,6,7]=>[6,2,1]=>105
[1,3,2,4,5,10,9,6,7,8]=>[7,2,1]=>160
[1,2,3,4,5,10,6,7,8,11,9]=>[9,2]=>44
[2,3,1,4,9,8,5,6,7]=>[6,2,1]=>105
[2,1,3,4,5,9,6,10,7,8]=>[7,3]=>75
[8,5,6,1,3,2,7,4]=>[3,3,1,1]=>56
[5,3,7,8,2,6,1,4]=>[3,2,2,1]=>70
[4,5,8,3,6,1,7,2]=>[4,2,2]=>56
[4,5,8,7,2,3,1,6]=>[3,3,1,1]=>56
[5,7,1,3,6,2,4,8]=>[4,2,2]=>56
[4,7,1,3,2,5,8,6]=>[4,3,1]=>70
[5,8,7,3,4,2,6,1]=>[3,2,1,1,1]=>64
[8,5,2,3,7,4,6,1]=>[4,2,1,1]=>90
[4,7,6,3,5,2,8,1]=>[3,2,1,1,1]=>64
[5,3,1,6,4,8,7,2]=>[3,3,2]=>42
[8,5,1,2,7,6,4,3]=>[3,2,1,1,1]=>64
[10,7,8,1,2,3,4,5,6,9]=>[7,2,1]=>160
[6,7,10,1,2,3,4,5,8,9]=>[7,3]=>75
[3,7,8,5,6,2,4,1]=>[3,2,2,1]=>70
[1,10,2,3,4,7,5,6,8,9]=>[8,1,1]=>36
[7,4,3,6,2,5,8,1]=>[3,2,1,1,1]=>64
[4,3,8,7,1,6,2,5]=>[3,2,2,1]=>70
[1,5,3,8,4,7,2,6]=>[4,2,2]=>56
[8,2,3,1,6,5,7,4]=>[4,2,1,1]=>90
[8,4,2,7,1,3,6,5]=>[3,2,2,1]=>70
[8,4,2,3,1,6,7,5]=>[4,2,1,1]=>90
[4,7,2,3,6,5,8,1]=>[4,2,1,1]=>90
[3,8,2,6,4,7,1,5]=>[3,3,1,1]=>56
[1,7,5,8,6,2,4,3]=>[3,2,2,1]=>70
[6,5,1,7,4,8,3,2]=>[3,2,1,1,1]=>64
[7,6,3,5,1,4,8,2]=>[3,2,1,1,1]=>64
[6,5,4,1,7,2,3,8]=>[4,2,1,1]=>90
[8,3,6,1,7,4,5,2]=>[3,3,1,1]=>56
[7,1,2,6,4,8,3,5]=>[4,2,1,1]=>90
[3,5,1,8,6,2,4,7]=>[4,3,1]=>70
[1,8,7,5,4,6,2,3]=>[3,2,1,1,1]=>64
[8,1,6,7,4,5,3,2]=>[3,2,1,1,1]=>64
[8,1,6,4,7,5,3,2]=>[3,2,1,1,1]=>64
[6,4,8,1,5,3,7,2]=>[3,2,2,1]=>70
[1,6,4,3,5,8,2,7]=>[4,2,1,1]=>90
[5,1,4,3,7,8,6,2]=>[4,2,1,1]=>90
[5,7,1,8,6,3,2,4]=>[3,3,1,1]=>56
[5,7,6,3,4,2,1,8]=>[3,2,1,1,1]=>64
[4,3,6,1,2,7,8,5]=>[4,3,1]=>70
[3,1,4,5,6,7,9,2,10,8]=>[7,3]=>75
[5,8,3,6,7,2,4,1]=>[3,2,2,1]=>70
[8,1,6,2,5,7,4,3]=>[4,1,1,1,1]=>35
[2,7,1,5,3,6,8,4]=>[4,3,1]=>70
[6,8,7,3,4,2,5,1]=>[3,2,1,1,1]=>64
[1,8,6,2,4,7,5,3]=>[4,2,1,1]=>90
[5,7,3,6,4,2,1,8]=>[3,2,1,1,1]=>64
[5,7,3,6,4,1,8,2]=>[3,2,2,1]=>70
[3,7,5,6,4,1,8,2]=>[4,2,1,1]=>90
[7,1,8,2,3,4,5,9,6]=>[6,3]=>48
[6,8,1,2,3,4,5,9,7]=>[6,3]=>48
[9,6,7,4,5,2,3,1,8]=>[3,2,2,1,1]=>162
[9,8,6,5,4,3,7,2,1]=>[2,1,1,1,1,1,1,1]=>8
[2,8,5,7,3,4,6,1]=>[4,2,1,1]=>90
[2,3,6,4,5,1,7,8,9]=>[7,1,1]=>28
[2,3,4,8,5,6,7,1,9]=>[7,1,1]=>28
[3,5,4,7,2,6,1,8,9]=>[5,2,1,1]=>189
[2,6,4,1,5,3,7,8,9]=>[6,2,1]=>105
[4,5,2,6,3,1,7,8,9]=>[6,2,1]=>105
[3,6,4,5,9,2,7,8,1]=>[5,2,1,1]=>189
[2,5,4,7,8,6,3,1,9]=>[5,2,1,1]=>189
[4,6,2,5,8,3,7,1,9]=>[4,3,1,1]=>216
[3,5,7,6,1,4,2,8,9]=>[5,2,1,1]=>189
[5,6,2,3,7,4,1,8,9]=>[5,3,1]=>162
[5,7,2,3,6,9,4,8,1]=>[4,3,1,1]=>216
[2,8,4,1,6,3,7,5,9]=>[5,3,1]=>162
[4,6,7,8,3,1,5,2,9]=>[5,2,2]=>120
[6,7,2,3,4,8,5,1,9]=>[5,3,1]=>162
[3,5,9,7,1,8,2,6,4]=>[4,3,1,1]=>216
[5,7,8,3,9,4,1,6,2]=>[4,3,2]=>168
[7,8,2,3,4,5,9,6,1]=>[5,3,1]=>162
[2,4,3,1,5,6,7,8,9,10]=>[8,1,1]=>36
[2,3,6,4,5,1,7,8,9,10]=>[8,1,1]=>36
[3,4,5,2,1,6,7,8,9,10]=>[8,1,1]=>36
[2,3,4,8,5,6,7,1,9,10]=>[8,1,1]=>36
[3,5,4,7,2,6,1,8,9,10]=>[6,2,1,1]=>350
[2,6,4,1,5,3,7,8,9,10]=>[7,2,1]=>160
[4,5,2,6,3,1,7,8,9,10]=>[7,2,1]=>160
[3,6,4,5,9,2,7,8,1,10]=>[6,2,1,1]=>350
[2,5,4,7,8,6,3,1,9,10]=>[6,2,1,1]=>350
[4,6,2,5,8,3,7,1,9,10]=>[5,3,1,1]=>567
[3,5,7,6,1,4,2,8,9,10]=>[6,2,1,1]=>350
[5,6,2,3,7,4,1,8,9,10]=>[6,3,1]=>315
[2,5,4,8,6,10,7,3,9,1]=>[5,3,1,1]=>567
[4,7,2,5,6,10,3,8,9,1]=>[5,3,1,1]=>567
[2,3,9,5,6,1,7,8,4,10]=>[7,2,1]=>160
[5,7,2,3,6,9,4,8,1,10]=>[5,3,1,1]=>567
[2,8,4,1,6,3,7,5,9,10]=>[6,3,1]=>315
[4,6,7,8,3,1,5,2,9,10]=>[6,2,2]=>225
[6,7,2,3,4,8,5,1,9,10]=>[6,3,1]=>315
[3,6,4,10,8,7,1,5,9,2]=>[4,2,2,1,1]=>567
[2,7,4,9,6,3,10,8,5,1]=>[4,3,2,1]=>768
[4,6,8,7,3,9,10,5,2,1]=>[5,2,1,1,1]=>448
[6,8,2,3,4,7,10,5,9,1]=>[5,3,1,1]=>567
[3,5,9,7,1,8,2,6,4,10]=>[5,3,1,1]=>567
[5,7,8,3,9,4,1,6,2,10]=>[5,3,2]=>450
[7,8,2,3,4,5,9,6,1,10]=>[6,3,1]=>315
[4,6,8,10,9,1,5,2,7,3]=>[4,3,2,1]=>768
[6,8,9,3,4,10,5,1,7,2]=>[4,4,2]=>252
[8,9,2,3,4,5,6,10,7,1]=>[6,3,1]=>315
[2,1,3,8,5,4,6,7]=>[5,2,1]=>64
[5,3,6,8,2,4,1,7]=>[3,3,1,1]=>56
[1,7,8,6,3,2,4,5]=>[4,2,1,1]=>90
[7,1,2,5,3,8,4,6]=>[5,2,1]=>64
[3,7,4,2,5,1,8,6]=>[4,2,1,1]=>90
[1,8,3,4,5,7,2,6]=>[5,2,1]=>64
[7,5,8,2,4,3,6,1]=>[3,2,1,1,1]=>64
[6,5,8,2,3,4,1,7]=>[4,2,1,1]=>90
[8,1,5,3,4,6,2,7]=>[5,1,1,1]=>35
[5,8,7,2,4,3,6,1]=>[3,2,1,1,1]=>64
[1,7,2,4,8,5,6,3]=>[5,2,1]=>64
[5,8,2,3,7,4,6,1]=>[4,2,1,1]=>90
[7,8,2,3,5,4,6,1]=>[4,2,1,1]=>90
[8,4,1,3,2,6,5,7]=>[4,2,1,1]=>90
[8,7,2,3,5,4,6,1]=>[4,1,1,1,1]=>35
[1,7,6,8,4,5,3,2]=>[3,2,1,1,1]=>64
[2,7,3,1,8,5,6,4]=>[4,2,2]=>56
[3,8,5,2,1,6,7,4]=>[4,2,1,1]=>90
[10,1,2,9,6,3,4,5,7,8]=>[7,1,1,1]=>84
[4,1,2,10,3,5,9,6,7,8]=>[7,2,1]=>160
[4,8,7,1,2,5,3,6]=>[4,2,1,1]=>90
[8,7,2,6,1,4,3,5]=>[3,2,1,1,1]=>64
[6,1,7,3,8,2,4,5]=>[4,3,1]=>70
[7,1,8,6,4,2,3,5]=>[4,2,1,1]=>90
[4,1,3,5,8,2,6,7]=>[5,2,1]=>64
[1,8,5,7,4,6,3,2]=>[3,2,1,1,1]=>64
[1,4,7,6,8,3,5,2]=>[4,2,1,1]=>90
[1,7,2,8,6,5,3,4]=>[4,2,1,1]=>90
[5,7,1,6,4,2,3,8]=>[4,2,1,1]=>90
[4,8,2,7,5,1,6,3]=>[3,2,2,1]=>70
[2,8,4,6,7,1,5,3]=>[4,2,1,1]=>90
[3,8,5,1,4,2,6,7]=>[4,2,1,1]=>90
[1,7,6,2,5,3,8,4]=>[4,2,1,1]=>90
[1,7,5,2,4,3,8,6]=>[4,2,1,1]=>90
[2,8,5,1,4,3,6,7]=>[4,2,1,1]=>90
[9,7,6,5,4,3,2,8,1]=>[2,1,1,1,1,1,1,1]=>8
[3,1,4,6,2,5,8,7,9]=>[5,4]=>42
[1,3,2,5,7,4,6,9,8]=>[5,4]=>42
[1,9,8,5,6,7,4,3,2]=>[4,1,1,1,1,1]=>56
[1,10,9,8,5,6,7,4,3,2]=>[4,1,1,1,1,1,1]=>84
[1,9,8,5,4,6,7,3,2]=>[4,1,1,1,1,1]=>56
[1,10,9,5,6,7,8,4,3,2]=>[5,1,1,1,1,1]=>126
[1,9,5,4,6,7,8,3,2]=>[5,1,1,1,1]=>70
[1,10,4,5,6,7,8,9,3,2]=>[7,1,1,1]=>84
[3,1,2,5,7,6,8,4]=>[5,2,1]=>64
[5,1,7,3,2,6,8,4]=>[4,2,2]=>56
[4,7,2,3,5,1,6,8]=>[5,2,1]=>64
[4,8,2,3,7,5,1,6]=>[4,2,1,1]=>90
[8,7,2,4,3,5,6,1]=>[4,1,1,1,1]=>35
[8,6,2,4,3,5,1,7]=>[4,1,1,1,1]=>35
[8,1,2,4,7,3,5,6]=>[5,2,1]=>64
[7,6,2,8,4,5,1,3]=>[3,2,2,1]=>70
[6,8,1,5,7,3,2,4]=>[3,2,2,1]=>70
[4,1,7,5,6,8,2,3]=>[4,3,1]=>70
[3,7,6,2,1,4,5,8]=>[4,2,1,1]=>90
[1,6,8,7,2,5,4,3]=>[3,2,1,1,1]=>64
[1,4,8,7,6,3,5,2]=>[3,2,1,1,1]=>64
[1,2,3,4,7,5,6,9,8]=>[7,2]=>27
[4,6,7,5,2,3,1,8]=>[4,2,1,1]=>90
[6,2,5,3,1,8,7,4]=>[3,2,2,1]=>70
[6,2,5,3,8,7,1,4]=>[3,2,2,1]=>70
[6,4,5,3,8,7,1,2]=>[3,2,2,1]=>70
[1,6,4,5,8,7,3,2]=>[4,2,1,1]=>90
[8,4,7,5,2,3,1,6]=>[3,2,1,1,1]=>64
[8,2,7,4,5,3,1,6]=>[4,1,1,1,1]=>35
[8,2,4,7,5,3,1,6]=>[4,1,1,1,1]=>35
[8,2,6,7,5,3,1,4]=>[3,2,1,1,1]=>64
[8,4,6,7,5,3,1,2]=>[3,2,1,1,1]=>64
[6,4,5,8,7,3,1,2]=>[3,2,2,1]=>70
[6,2,8,7,5,3,1,4]=>[3,2,1,1,1]=>64
[4,6,5,3,8,7,1,2]=>[3,2,2,1]=>70
[6,7,2,4,5,3,1,8]=>[4,2,1,1]=>90
[6,8,7,4,5,3,1,2]=>[2,2,2,1,1]=>28
[2,8,4,7,5,3,1,6]=>[4,1,1,1,1]=>35
[5,8,7,4,6,3,1,2]=>[2,2,2,1,1]=>28
[6,5,8,4,7,2,1,3]=>[2,2,2,1,1]=>28
[4,8,6,2,5,7,1,3]=>[3,2,2,1]=>70
[8,1,6,2,5,7,3,4]=>[4,2,1,1]=>90
[6,8,1,2,4,7,3,5]=>[4,2,2]=>56
[8,1,5,3,2,7,4,6]=>[4,2,1,1]=>90
[8,3,7,6,2,5,4,1]=>[2,2,1,1,1,1]=>20
[1,2,7,4,5,6,8,9,3]=>[7,1,1]=>28
[5,3,1,2,6,7,8,9,10,4]=>[7,2,1]=>160
[7,3,4,5,1,2,8,9,10,6]=>[6,3,1]=>315
[8,3,4,5,6,1,2,9,10,7]=>[6,3,1]=>315
[1,2,3,4,7,8,5,6,9]=>[7,2]=>27
[1,2,3,4,6,5,8,7,9]=>[7,2]=>27
[1,2,3,4,8,9,5,6,7]=>[7,2]=>27
[4,6,1,3,5,8,2,7]=>[4,3,1]=>70
[4,5,1,3,8,7,2,6]=>[3,3,2]=>42
[6,2,7,1,8,3,4,5]=>[4,3,1]=>70
[6,4,5,8,1,7,2,3]=>[3,3,2]=>42
[6,2,8,5,1,4,7,3]=>[3,2,2,1]=>70
[2,4,7,6,1,8,3,5]=>[4,3,1]=>70
[2,1,7,8,9,3,4,5,6]=>[5,4]=>42
[2,6,7,8,9,10,1,3,4,5]=>[6,4]=>90
[9,7,5,3,8,6,4,2,1]=>[2,2,2,1,1,1]=>48
[10,8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[7,4,5,8,6,3,2,1]=>[3,2,1,1,1]=>64
[8,6,9,7,4,3,2,1,5]=>[2,2,2,1,1,1]=>48
[8,6,3,2,1,4,9,7,5]=>[3,2,2,1,1]=>162
[8,6,4,9,7,5,2,1,3]=>[2,2,2,2,1]=>42
[10,8,6,4,9,7,5,3,2,1]=>[2,2,2,1,1,1,1]=>75
[9,7,5,3,8,6,4,1,2]=>[2,2,2,2,1]=>42
[10,8,6,4,2,1,9,7,5,3]=>[2,2,2,2,1,1]=>90
[11,9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[9,6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1,1]=>28
[10,8,9,6,5,4,3,2,1,7]=>[2,2,1,1,1,1,1,1]=>35
[10,8,11,9,7,6,5,4,3,2,1]=>[2,2,1,1,1,1,1,1,1]=>44
[8,5,6,9,7,4,3,2,1]=>[3,2,1,1,1,1]=>105
[9,7,10,8,5,4,3,2,1,6]=>[2,2,2,1,1,1,1]=>75
[10,8,6,5,4,3,2,1,11,9,7]=>[2,2,2,1,1,1,1,1]=>110
[8,6,3,2,1,9,7,4,5]=>[3,2,2,1,1]=>162
[9,7,8,4,3,2,1,5,6]=>[3,2,1,1,1,1]=>105
[9,7,4,3,2,1,5,10,8,6]=>[3,2,2,1,1,1]=>315
[10,8,6,11,9,7,5,4,3,2,1]=>[2,2,2,1,1,1,1,1]=>110
[8,6,3,4,9,7,5,2,1]=>[3,2,2,1,1]=>162
[8,6,9,7,3,2,1,4,5]=>[3,2,2,1,1]=>162
[9,7,5,10,8,6,3,2,1,4]=>[2,2,2,2,1,1]=>90
[11,9,7,5,10,8,6,4,3,2,1]=>[2,2,2,1,1,1,1,1]=>110
[9,7,5,2,3,8,6,4,1]=>[3,2,2,1,1]=>162
[8,6,2,1,3,4,9,7,5]=>[4,2,2,1]=>216
[10,8,6,4,9,7,5,2,1,3]=>[2,2,2,2,1,1]=>90
[11,9,7,5,3,2,1,10,8,6,4]=>[2,2,2,2,1,1,1]=>165
[8,6,4,9,7,5,1,2,3]=>[3,2,2,2]=>84
[10,8,6,4,1,2,9,7,5,3]=>[3,2,2,2,1]=>288
[11,9,7,5,3,10,8,6,4,2,1]=>[2,2,2,2,1,1,1]=>165
[10,8,6,4,2,11,9,7,5,3,1]=>[2,2,2,2,2,1]=>132
[2,5,1,6,3,7,4,8,9]=>[6,3]=>48
[2,6,1,7,3,8,4,9,5]=>[5,4]=>42
[3,4,6,1,7,2,8,5,9]=>[6,3]=>48
[3,2,6,1,7,4,8,5,9]=>[5,3,1]=>162
[4,2,5,6,1,7,3,8,9]=>[6,2,1]=>105
[3,4,2,6,1,7,5,8,9]=>[6,2,1]=>105
[4,2,5,7,1,8,3,9,6]=>[5,3,1]=>162
[3,4,2,7,1,8,5,9,6]=>[5,3,1]=>162
[5,3,6,4,7,1,8,2,9]=>[5,2,2]=>120
[3,5,2,6,7,1,8,4,9]=>[6,2,1]=>105
[4,3,5,2,7,1,8,6,9]=>[5,2,1,1]=>189
[4,6,2,7,5,8,1,9,3]=>[5,2,2]=>120
[4,3,6,2,7,8,1,9,5]=>[5,2,1,1]=>189
[4,5,3,6,2,8,1,9,7]=>[5,2,1,1]=>189
[2,5,1,6,3,7,4,8,9,10]=>[7,3]=>75
[3,4,5,1,6,2,7,8,9,10]=>[8,2]=>35
[2,6,1,7,3,8,4,9,5,10]=>[6,4]=>90
[3,4,6,1,7,2,8,5,9,10]=>[7,3]=>75
[3,2,6,1,7,4,8,5,9,10]=>[6,3,1]=>315
[4,2,5,6,1,7,3,8,9,10]=>[7,2,1]=>160
[3,4,2,6,1,7,5,8,9,10]=>[7,2,1]=>160
[3,2,7,1,8,4,9,5,10,6]=>[5,4,1]=>288
[4,5,6,7,1,8,2,9,3,10]=>[7,3]=>75
[3,4,2,7,1,8,5,9,6,10]=>[6,3,1]=>315
[5,3,6,4,7,1,8,2,9,10]=>[6,2,2]=>225
[3,5,2,6,7,1,8,4,9,10]=>[7,2,1]=>160
[4,3,5,2,7,1,8,6,9,10]=>[6,2,1,1]=>350
[5,2,6,7,8,1,9,3,10,4]=>[6,3,1]=>315
[5,3,6,4,8,1,9,2,10,7]=>[5,3,2]=>450
[3,5,2,6,8,1,9,4,10,7]=>[6,3,1]=>315
[4,3,5,2,8,1,9,6,10,7]=>[5,3,1,1]=>567
[4,6,2,7,5,8,1,9,3,10]=>[6,2,2]=>225
[4,3,6,2,7,8,1,9,5,10]=>[6,2,1,1]=>350
[4,5,3,6,2,8,1,9,7,10]=>[6,2,1,1]=>350
[5,3,7,2,8,6,9,1,10,4]=>[5,2,2,1]=>525
[4,5,3,7,2,8,9,1,10,6]=>[6,2,1,1]=>350
[5,4,6,3,7,2,9,1,10,8]=>[5,2,1,1,1]=>448
[6,1,7,8,9,2,3,4,5]=>[5,4]=>42
[5,6,7,8,9,11,1,2,3,4,10]=>[6,5]=>132
[4,5,6,7,1,9,2,3,8]=>[5,4]=>42
[3,5,6,7,9,1,2,4,8]=>[5,4]=>42
[5,1,6,7,8,2,9,3,4]=>[5,4]=>42
[4,1,6,7,8,9,2,3,5]=>[5,4]=>42
[5,1,6,7,8,9,10,2,3,4]=>[6,4]=>90
[6,1,7,8,9,10,11,2,3,4,5]=>[6,5]=>132
[7,4,1,3,6,8,2,5]=>[4,2,1,1]=>90
[6,8,1,2,7,3,4,5]=>[5,2,1]=>64
[1,6,2,8,7,3,4,5]=>[5,2,1]=>64
[1,6,8,5,7,4,3,2]=>[3,2,1,1,1]=>64
[3,8,1,2,4,7,6,5]=>[4,2,1,1]=>90
[1,4,5,7,3,6,8,2]=>[5,2,1]=>64
[2,3,8,1,4,6,5,7]=>[5,2,1]=>64
[3,6,2,4,7,5,8,1]=>[4,3,1]=>70
[3,1,8,4,6,2,5,7]=>[4,3,1]=>70
[4,2,7,3,5,8,1,6]=>[4,3,1]=>70
[3,1,8,4,5,6,2,7]=>[5,2,1]=>64
[4,2,7,8,6,3,1,5]=>[3,3,1,1]=>56
[7,1,4,2,8,6,3,5]=>[4,2,2]=>56
[2,3,7,4,8,1,6,5]=>[4,2,2]=>56
[1,6,3,5,8,7,4,2]=>[4,2,1,1]=>90
[8,4,6,3,5,1,7,2]=>[3,2,2,1]=>70
[7,3,2,6,8,4,5,1]=>[3,3,1,1]=>56
[2,4,5,7,1,6,8,3]=>[5,2,1]=>64
[8,4,2,6,7,3,5,1]=>[3,3,1,1]=>56
[4,1,5,7,8,6,2,3]=>[4,3,1]=>70
[6,1,4,8,2,3,7,5]=>[4,2,2]=>56
[7,6,2,3,5,8,4,1]=>[4,1,1,1,1]=>35
[2,8,5,7,6,3,4,1]=>[3,2,1,1,1]=>64
[2,5,7,8,6,4,1,3]=>[4,2,1,1]=>90
[7,4,1,6,2,5,8,3]=>[4,2,1,1]=>90
[2,3,1,5,6,8,9,4,7]=>[6,3]=>48
[5,6,2,4,8,7,3,1]=>[3,3,1,1]=>56
[8,5,6,2,3,7,4,1]=>[3,3,1,1]=>56
[7,8,1,4,5,6,2,3]=>[4,2,2]=>56
[5,6,7,8,9,1,3,4,2]=>[5,3,1]=>162
[6,7,8,9,1,3,4,5,2]=>[4,4,1]=>84
[6,7,8,9,1,4,5,2,3]=>[4,3,2]=>168
[6,7,8,9,1,4,5,3,2]=>[4,3,1,1]=>216
[6,7,8,9,1,5,4,3,2]=>[4,2,1,1,1]=>189
[7,8,9,1,4,5,6,2,3]=>[4,3,2]=>168
[7,8,9,1,4,5,6,3,2]=>[4,3,1,1]=>216
[7,8,9,1,5,6,3,4,2]=>[3,3,2,1]=>168
[7,8,9,1,5,6,4,3,2]=>[3,3,1,1,1]=>120
[7,8,9,1,6,5,4,3,2]=>[3,2,1,1,1,1]=>105
[8,9,1,5,6,7,3,4,2]=>[4,2,2,1]=>216
[8,9,1,5,6,7,4,3,2]=>[4,2,1,1,1]=>189
[8,9,1,6,7,4,5,2,3]=>[3,2,2,2]=>84
[8,9,1,6,7,4,5,3,2]=>[3,2,2,1,1]=>162
[8,9,1,6,7,5,4,3,2]=>[3,2,1,1,1,1]=>105
[9,1,7,8,5,6,3,4,2]=>[3,2,2,1,1]=>162
[9,1,7,8,5,6,4,3,2]=>[3,2,1,1,1,1]=>105
[5,6,7,8,9,10,1,3,4,2]=>[6,3,1]=>315
[5,6,7,8,9,10,1,4,3,2]=>[6,2,1,1]=>350
[7,8,9,10,1,4,5,6,2,3]=>[4,4,2]=>252
[7,8,9,10,1,4,5,6,3,2]=>[4,4,1,1]=>300
[7,8,9,10,1,5,6,4,3,2]=>[4,3,1,1,1]=>525
[7,8,9,10,1,6,5,4,3,2]=>[4,2,1,1,1,1]=>350
[8,9,10,1,4,5,6,7,2,3]=>[5,3,2]=>450
[8,9,10,1,4,5,6,7,3,2]=>[5,3,1,1]=>567
[8,9,10,1,5,6,7,2,3,4]=>[4,3,3]=>210
[8,9,10,1,5,6,7,4,3,2]=>[4,3,1,1,1]=>525
[8,9,10,1,6,7,4,5,2,3]=>[3,3,2,2]=>252
[8,9,10,1,6,7,4,5,3,2]=>[3,3,2,1,1]=>450
[8,9,10,1,6,7,5,4,3,2]=>[3,3,1,1,1,1]=>225
[8,9,10,1,7,6,5,4,3,2]=>[3,2,1,1,1,1,1]=>160
[9,10,1,6,7,8,3,4,5,2]=>[4,3,2,1]=>768
[9,10,1,6,7,8,4,5,2,3]=>[4,2,2,2]=>300
[9,10,1,6,7,8,4,5,3,2]=>[4,2,2,1,1]=>567
[9,10,1,6,7,8,5,4,3,2]=>[4,2,1,1,1,1]=>350
[9,10,1,7,8,5,6,3,4,2]=>[3,2,2,2,1]=>288
[9,10,1,7,8,5,6,4,3,2]=>[3,2,2,1,1,1]=>315
[9,10,1,7,8,6,5,4,3,2]=>[3,2,1,1,1,1,1]=>160
[10,1,8,9,6,7,4,5,3,2]=>[3,2,2,1,1,1]=>315
[10,1,8,9,6,7,5,4,3,2]=>[3,2,1,1,1,1,1]=>160
[10,1,8,9,7,6,5,4,3,2]=>[3,1,1,1,1,1,1,1]=>36
[2,6,1,4,7,5,8,3]=>[4,3,1]=>70
[3,1,5,7,2,6,8,4]=>[4,3,1]=>70
[3,1,7,5,2,6,8,4]=>[4,3,1]=>70
[3,2,7,5,1,6,8,4]=>[4,2,2]=>56
[5,2,7,3,1,6,8,4]=>[4,2,2]=>56
[6,7,2,1,3,4,8,5]=>[4,3,1]=>70
[4,6,3,1,2,7,8,5]=>[4,3,1]=>70
[2,3,4,5,7,9,6,8,1]=>[6,2,1]=>105
[2,3,4,6,9,5,7,8,1]=>[6,2,1]=>105
[2,3,5,6,8,4,7,1]=>[5,2,1]=>64
[2,3,5,9,4,6,7,8,1]=>[6,2,1]=>105
[2,4,5,8,3,6,7,1]=>[5,2,1]=>64
[2,4,9,3,5,6,7,8,1]=>[6,2,1]=>105
[5,9,8,7,6,4,3,1,2]=>[2,2,1,1,1,1,1]=>27
[5,4,8,7,6,3,2,1,9]=>[3,2,1,1,1,1]=>105
[4,5,8,7,6,3,1,2]=>[3,2,1,1,1]=>64
[6,5,9,8,7,4,3,1,2]=>[2,2,2,1,1,1]=>48
[8,7,4,6,5,3,1,2]=>[2,2,1,1,1,1]=>20
[9,5,8,7,6,4,3,1,2]=>[2,2,1,1,1,1,1]=>27
[6,10,9,8,7,5,4,3,1,2]=>[2,2,1,1,1,1,1,1]=>35
[8,1,4,3,6,2,5,7]=>[4,2,1,1]=>90
[1,6,3,7,8,4,2,5]=>[4,3,1]=>70
[7,4,2,8,5,6,3,1]=>[3,2,2,1]=>70
[5,2,1,3,8,4,6,7]=>[5,2,1]=>64
[1,4,3,5,8,2,6,7]=>[5,2,1]=>64
[2,1,3,8,6,4,5,7]=>[5,2,1]=>64
[1,3,6,4,5,8,2,7]=>[5,2,1]=>64
[6,1,4,3,5,8,2,7]=>[4,2,1,1]=>90
[6,5,1,3,8,2,4,7]=>[4,2,1,1]=>90
[1,4,3,8,6,2,5,7]=>[4,2,2]=>56
[4,1,3,8,6,2,5,7]=>[4,2,2]=>56
[7,1,5,4,6,3,8,2]=>[4,1,1,1,1]=>35
[6,4,7,8,3,5,1,2]=>[3,2,2,1]=>70
[3,5,6,7,1,8,4,2]=>[5,2,1]=>64
[1,7,5,4,3,8,2,6]=>[3,2,1,1,1]=>64
[4,5,8,1,7,3,2,6]=>[3,3,1,1]=>56
[4,6,7,1,3,8,2,5]=>[4,3,1]=>70
[2,3,4,5,6,1,8,9,7]=>[7,2]=>27
[2,3,4,5,1,7,8,9,6]=>[7,2]=>27
[2,6,3,1,4,7,8,5]=>[5,2,1]=>64
[2,9,3,4,5,6,1,7,8]=>[7,1,1]=>28
[2,3,4,5,6,7,1,9,10,8]=>[8,2]=>35
[2,7,3,4,1,8,5,6]=>[5,2,1]=>64
[2,8,3,4,5,1,6,9,7]=>[6,2,1]=>105
[2,7,3,4,1,5,8,9,6]=>[6,2,1]=>105
[2,3,4,5,1,7,8,9,10,6]=>[8,2]=>35
[2,6,3,1,4,7,8,9,5]=>[6,2,1]=>105
[2,3,1,5,6,7,8,9,10,4]=>[8,2]=>35
[4,2,5,3,7,6,9,8,1]=>[4,4,1]=>84
[4,2,6,3,7,5,9,8,1]=>[4,4,1]=>84
[4,2,6,3,8,5,9,7,1]=>[4,4,1]=>84
[4,2,6,3,8,5,1,7,9]=>[5,3,1]=>162
[4,2,6,3,5,8,1,7]=>[4,3,1]=>70
[4,2,6,3,8,5,7,1,9]=>[5,3,1]=>162
[4,2,6,3,5,8,7,1,9]=>[5,3,1]=>162
[4,2,3,6,5,8,7,1,9]=>[5,3,1]=>162
[4,2,5,3,7,6,9,8,1,10]=>[5,4,1]=>288
[5,2,6,3,7,4,9,8,1]=>[4,4,1]=>84
[4,2,6,3,7,5,9,8,1,10]=>[5,4,1]=>288
[4,2,7,3,8,5,9,6,1]=>[4,4,1]=>84
[4,2,6,3,8,5,9,7,1,10]=>[5,4,1]=>288
[4,2,6,3,9,5,1,7,8]=>[5,3,1]=>162
[4,2,6,3,8,5,10,7,1,9]=>[5,4,1]=>288
[4,2,6,3,8,5,7,9,1]=>[5,3,1]=>162
[4,2,6,3,8,5,10,7,9,1]=>[5,4,1]=>288
[4,2,6,3,5,8,1,7,9]=>[5,3,1]=>162
[4,2,6,3,8,5,7,10,9,1]=>[5,4,1]=>288
[4,2,3,6,8,5,7,1,9]=>[5,3,1]=>162
[4,2,6,3,5,8,7,10,9,1]=>[5,4,1]=>288
[2,4,6,3,5,8,7,1,9]=>[5,3,1]=>162
[4,2,3,6,5,8,7,10,9,1]=>[5,4,1]=>288
[7,4,2,6,8,5,3,1]=>[3,2,1,1,1]=>64
[8,5,2,4,6,3,1,7]=>[4,1,1,1,1]=>35
[7,4,1,2,8,5,6,3]=>[4,2,2]=>56
[6,4,1,8,5,2,3,7]=>[4,2,2]=>56
[8,4,1,6,3,5,2,7]=>[4,2,1,1]=>90
[7,3,4,1,6,8,5,2]=>[4,2,1,1]=>90
[8,6,2,3,5,7,4,1]=>[4,1,1,1,1]=>35
[8,6,2,5,7,3,4,1]=>[3,2,1,1,1]=>64
[6,3,4,8,5,1,2,7]=>[4,2,2]=>56
[8,5,1,2,7,4,6,3]=>[4,2,1,1]=>90
[7,2,6,8,3,4,5,1]=>[4,2,1,1]=>90
[1,6,7,5,4,8,2,3]=>[4,2,1,1]=>90
[1,8,5,4,2,6,3,7]=>[4,2,1,1]=>90
[3,4,5,6,9,2,1,8,7]=>[5,2,2]=>120
[3,4,5,8,2,9,1,7,6]=>[5,2,2]=>120
[3,4,7,2,8,9,1,5,6]=>[5,3,1]=>162
[3,6,2,7,8,9,1,5,4]=>[5,2,2]=>120
[5,2,6,7,8,9,1,4,3]=>[5,2,2]=>120
[3,4,5,6,7,8,9,11,1,10,2]=>[8,2,1]=>231
[3,4,5,6,9,1,7,8,2]=>[6,2,1]=>105
[3,4,5,6,7,10,2,1,9,8]=>[6,2,2]=>225
[3,4,5,6,7,8,10,11,1,9,2]=>[8,2,1]=>231
[3,4,5,8,9,6,1,7,2]=>[5,2,2]=>120
[3,4,5,6,9,2,10,1,8,7]=>[6,2,2]=>225
[3,4,7,8,5,9,1,2,6]=>[5,3,1]=>162
[3,4,5,9,2,6,1,8,7]=>[5,2,2]=>120
[3,4,5,8,2,9,10,1,6,7]=>[6,3,1]=>315
[3,4,5,6,8,9,10,11,1,7,2]=>[8,2,1]=>231
[3,6,7,4,8,9,1,5,2]=>[5,2,2]=>120
[3,4,8,2,5,9,1,7,6]=>[4,3,2]=>168
[3,4,7,2,8,9,10,1,6,5]=>[6,2,2]=>225
[3,4,5,7,8,9,10,11,1,6,2]=>[8,2,1]=>231
[5,6,3,7,8,9,1,4,2]=>[5,2,2]=>120
[3,7,2,4,8,9,1,5,6]=>[4,4,1]=>84
[3,6,2,7,8,9,10,1,5,4]=>[6,2,2]=>225
[6,2,3,7,8,9,1,5,4]=>[5,2,2]=>120
[5,2,6,7,8,9,10,1,3,4]=>[6,3,1]=>315
[3,5,6,7,8,9,10,11,1,4,2]=>[8,2,1]=>231
[4,5,6,7,8,9,10,11,1,3,2]=>[8,2,1]=>231
[8,9,7,6,5,4,1,3,2]=>[2,2,1,1,1,1,1]=>27
[8,7,9,6,5,4,1,3,2]=>[2,2,1,1,1,1,1]=>27
[9,7,8,6,5,4,1,3,2]=>[2,2,1,1,1,1,1]=>27
[9,10,8,7,6,5,4,1,3,2]=>[2,2,1,1,1,1,1,1]=>35
[10,8,7,6,5,4,3,2,9,1]=>[2,1,1,1,1,1,1,1,1]=>9
[1,3,2,4,5,6,9,7,8]=>[7,2]=>27
[2,3,1,4,5,6,9,7,8]=>[7,2]=>27
[5,8,6,1,2,4,3,7]=>[4,2,1,1]=>90
[4,1,5,7,3,6,8,2]=>[4,3,1]=>70
[1,4,5,7,6,8,2,3]=>[5,2,1]=>64
[5,7,2,1,6,8,4,3]=>[3,2,2,1]=>70
[2,6,3,1,7,8,5,4]=>[4,2,2]=>56
[6,2,5,7,4,1,8,3]=>[4,2,1,1]=>90
[3,6,1,8,7,4,5,2]=>[3,3,1,1]=>56
[4,3,9,5,6,7,8,2,1]=>[5,2,1,1]=>189
[10,2,3,4,5,6,7,8,9,11,1]=>[9,1,1]=>45
[2,9,4,5,6,7,8,1,10,3]=>[7,2,1]=>160
[3,2,8,5,6,7,1,9,4]=>[5,2,2]=>120
[7,8,4,5,6,1,3,9,2]=>[4,2,2,1]=>216
[3,4,1,9,6,7,8,2,5]=>[5,3,1]=>162
[4,8,9,5,6,7,2,1,3]=>[4,2,2,1]=>216
[4,3,10,5,6,7,8,9,2,1]=>[6,2,1,1]=>350
[11,2,3,4,5,6,7,8,9,10,12,1]=>[10,1,1]=>55
[2,10,4,5,6,7,8,9,1,11,3]=>[8,2,1]=>231
[3,2,9,5,6,7,8,1,10,4]=>[6,2,2]=>225
[8,9,4,5,6,7,1,3,10,2]=>[5,2,2,1]=>525
[4,2,3,8,6,7,1,9,5]=>[5,2,2]=>120
[6,8,4,5,1,3,7,9,2]=>[4,2,2,1]=>216
[4,7,1,3,5,6,8,2]=>[5,2,1]=>64
[4,3,5,7,8,2,6,1]=>[4,2,1,1]=>90
[3,5,1,4,9,7,8,2,6]=>[4,3,2]=>168
[8,3,4,9,6,7,2,5,1]=>[4,2,2,1]=>216
[3,4,1,10,6,7,8,9,2,5]=>[6,3,1]=>315
[4,7,9,5,6,2,1,8,3]=>[4,2,2,1]=>216
[4,9,10,5,6,7,8,2,1,3]=>[5,2,2,1]=>525
[4,3,11,5,6,7,8,9,10,2,1]=>[7,2,1,1]=>594
[5,3,2,7,6,4,1,8]=>[3,2,2,1]=>70
[5,3,7,4,6,2,1,8]=>[4,2,1,1]=>90
[5,7,3,2,1,8,6,4]=>[3,2,2,1]=>70
[5,7,6,3,2,1,8,4]=>[3,2,1,1,1]=>64
[3,2,7,5,4,1,8,6]=>[3,3,1,1]=>56
[1,7,3,5,4,2,6,8]=>[5,1,1,1]=>35
[5,3,7,4,1,8,6,2]=>[3,3,2]=>42
[7,3,5,4,1,6,8,2]=>[4,2,1,1]=>90
[7,5,1,6,8,3,2,4]=>[3,3,1,1]=>56
[5,3,1,7,6,8,2,4]=>[3,3,2]=>42
[7,1,5,3,2,4,8,6]=>[4,2,1,1]=>90
[8,1,2,5,3,4,6,7,9]=>[7,1,1]=>28
[7,1,5,2,4,3,6,8]=>[5,1,1,1]=>35
[1,9,2,3,6,4,5,7,8]=>[7,1,1]=>28
[9,1,2,3,6,4,5,7,8,10]=>[8,1,1]=>36
[8,1,2,6,4,3,5,7,9]=>[6,1,1,1]=>56
[8,1,2,6,3,5,4,7,9]=>[6,1,1,1]=>56
[1,9,2,3,7,5,4,6,8]=>[6,1,1,1]=>56
[1,9,2,3,7,4,6,5,8]=>[6,1,1,1]=>56
[5,6,7,8,9,3,2,1,4]=>[5,2,1,1]=>189
[6,7,8,9,3,4,1,2,5]=>[4,3,2]=>168
[6,7,8,9,3,4,2,1,5]=>[4,3,1,1]=>216
[7,8,9,3,4,5,1,2,6]=>[4,3,2]=>168
[7,8,9,3,4,5,2,1,6]=>[4,3,1,1]=>216
[7,8,9,4,5,2,3,1,6]=>[3,3,2,1]=>168
[7,8,9,4,5,3,2,1,6]=>[3,3,1,1,1]=>120
[8,9,4,5,6,2,3,1,7]=>[4,2,2,1]=>216
[8,9,4,5,6,3,2,1,7]=>[4,2,1,1,1]=>189
[8,9,5,6,3,4,1,2,7]=>[3,2,2,2]=>84
[8,9,5,6,3,4,2,1,7]=>[3,2,2,1,1]=>162
[8,9,5,6,4,3,2,1,7]=>[3,2,1,1,1,1]=>105
[9,6,7,4,5,3,2,1,8]=>[3,2,1,1,1,1]=>105
[5,6,7,8,9,10,3,2,1,4]=>[6,2,1,1]=>350
[7,8,9,10,3,4,5,1,2,6]=>[4,4,2]=>252
[7,8,9,10,3,4,5,2,1,6]=>[4,4,1,1]=>300
[7,8,9,10,4,5,2,3,1,6]=>[4,3,2,1]=>768
[7,8,9,10,4,5,3,2,1,6]=>[4,3,1,1,1]=>525
[7,8,9,10,5,4,3,2,1,6]=>[4,2,1,1,1,1]=>350
[8,9,10,3,4,5,6,1,2,7]=>[5,3,2]=>450
[8,9,10,3,4,5,6,2,1,7]=>[5,3,1,1]=>567
[8,9,10,4,5,6,1,2,3,7]=>[4,3,3]=>210
[8,9,10,4,5,6,3,2,1,7]=>[4,3,1,1,1]=>525
[8,9,10,5,6,3,4,1,2,7]=>[3,3,2,2]=>252
[8,9,10,5,6,3,4,2,1,7]=>[3,3,2,1,1]=>450
[8,9,10,5,6,4,3,2,1,7]=>[3,3,1,1,1,1]=>225
[8,9,10,6,5,4,3,2,1,7]=>[3,2,1,1,1,1,1]=>160
[9,10,5,6,7,2,3,4,1,8]=>[4,3,2,1]=>768
[9,10,5,6,7,3,4,1,2,8]=>[4,2,2,2]=>300
[9,10,5,6,7,3,4,2,1,8]=>[4,2,2,1,1]=>567
[9,10,5,6,7,4,3,2,1,8]=>[4,2,1,1,1,1]=>350
[9,10,6,7,4,5,3,2,1,8]=>[3,2,2,1,1,1]=>315
[9,10,6,7,5,4,3,2,1,8]=>[3,2,1,1,1,1,1]=>160
[9,10,7,6,5,4,3,2,1,8]=>[2,2,1,1,1,1,1,1]=>35
[10,7,8,5,6,3,4,2,1,9]=>[3,2,2,1,1,1]=>315
[10,7,8,5,6,4,3,2,1,9]=>[3,2,1,1,1,1,1]=>160
[10,7,8,6,5,4,3,2,1,9]=>[3,1,1,1,1,1,1,1]=>36
[1,8,3,6,2,4,7,5]=>[4,3,1]=>70
[1,8,7,5,6,4,2,3]=>[3,2,1,1,1]=>64
[6,8,2,1,5,4,3,7]=>[3,2,2,1]=>70
[10,9,1,2,3,7,8,4,5,6]=>[6,2,1,1]=>350
[10,9,1,2,8,7,3,4,5,6]=>[6,1,1,1,1]=>126
[9,8,1,10,7,2,3,4,5,6]=>[6,2,1,1]=>350
[8,6,1,2,3,4,5,9,10,7]=>[7,2,1]=>160
[5,7,1,2,3,4,8,9,10,6]=>[7,3]=>75
[8,11,1,2,3,4,5,9,10,6,7]=>[7,3,1]=>550
[10,4,1,2,3,7,8,9,5,6]=>[6,3,1]=>315
[10,11,1,2,3,4,8,9,5,6,7]=>[7,2,2]=>385
[10,3,1,2,9,7,8,4,5,6]=>[5,3,1,1]=>567
[10,11,1,2,3,9,8,4,5,6,7]=>[7,2,1,1]=>594
[2,9,1,10,8,7,3,4,5,6]=>[5,3,1,1]=>567
[10,9,1,2,11,8,3,4,5,6,7]=>[7,2,1,1]=>594
[9,8,1,10,11,2,3,4,5,6,7]=>[7,3,1]=>550
[11,8,9,10,1,2,3,4,5,6,7]=>[7,3,1]=>550
[6,3,2,1,5,8,4,7]=>[3,3,1,1]=>56
[4,3,5,6,2,8,1,7]=>[4,2,1,1]=>90
[6,3,5,2,7,8,4,1]=>[4,2,1,1]=>90
[4,5,3,1,6,8,2,7]=>[4,3,1]=>70
[3,4,6,7,5,1,8,2]=>[5,2,1]=>64
[7,4,1,2,5,6,8,3]=>[5,2,1]=>64
[4,8,2,6,7,1,5,3]=>[3,2,2,1]=>70
[6,5,8,3,7,1,4,2]=>[2,2,2,2]=>14
[9,1,2,8,4,3,5,6,7]=>[6,1,1,1]=>56
[8,1,9,3,2,4,6,5,7]=>[5,2,2]=>120
[9,8,2,1,3,5,6,4,7]=>[5,2,1,1]=>189
[8,1,9,2,4,5,6,3,7]=>[6,2,1]=>105
[2,3,4,10,6,7,8,9,1,5]=>[7,2,1]=>160
[2,3,10,5,6,7,8,9,1,4]=>[7,2,1]=>160
[2,3,4,5,6,10,1,9,7,8]=>[7,2,1]=>160
[2,3,4,5,6,7,11,9,10,1,8]=>[8,2,1]=>231
[2,3,4,5,10,1,8,9,6,7]=>[6,3,1]=>315
[2,3,4,5,6,11,8,9,10,1,7]=>[8,2,1]=>231
[2,3,4,5,11,7,8,9,10,1,6]=>[8,2,1]=>231
[2,3,10,1,6,7,8,9,4,5]=>[6,3,1]=>315
[2,3,4,11,6,7,8,9,10,1,5]=>[8,2,1]=>231
[2,3,11,5,6,7,8,9,10,1,4]=>[8,2,1]=>231
[1,5,2,4,7,6,8,3]=>[5,2,1]=>64
[1,4,3,6,5,8,7,9,2]=>[5,3,1]=>162
[1,4,2,6,5,8,7,9,3]=>[5,3,1]=>162
[1,5,2,6,4,8,7,9,3]=>[5,3,1]=>162
[1,5,2,7,4,8,6,9,3]=>[5,3,1]=>162
[1,5,2,7,4,9,6,8,3]=>[5,3,1]=>162
[1,5,2,7,4,6,9,8,3]=>[5,3,1]=>162
[1,5,2,4,7,6,9,8,3]=>[5,3,1]=>162
[1,2,5,4,7,6,9,8,3]=>[5,3,1]=>162
[1,4,2,6,5,8,7,10,9,3]=>[5,4,1]=>288
[1,5,2,6,3,8,7,9,4]=>[5,3,1]=>162
[1,5,2,6,4,8,7,10,9,3]=>[5,4,1]=>288
[1,6,2,7,4,8,5,9,3]=>[5,3,1]=>162
[1,5,2,7,4,8,6,10,9,3]=>[5,4,1]=>288
[1,5,2,8,4,9,6,7,3]=>[5,3,1]=>162
[1,5,2,7,4,9,6,10,8,3]=>[5,4,1]=>288
[1,5,2,7,4,6,8,9,3]=>[6,2,1]=>105
[1,5,2,7,4,9,6,8,10,3]=>[6,3,1]=>315
[1,5,2,4,7,9,6,8,3]=>[5,3,1]=>162
[1,5,2,7,4,6,9,8,10,3]=>[6,3,1]=>315
[1,2,5,7,4,6,9,8,3]=>[5,3,1]=>162
[1,5,2,4,7,6,9,8,10,3]=>[6,3,1]=>315
[1,2,5,4,7,6,9,8,10,3]=>[6,3,1]=>315
[2,5,4,7,1,8,3,6]=>[4,3,1]=>70
[8,1,2,4,6,3,5,7]=>[5,2,1]=>64
[3,4,5,6,8,9,7,1,2]=>[6,2,1]=>105
[3,4,5,7,8,9,6,1,2]=>[6,2,1]=>105
[3,5,6,7,8,9,4,1,2]=>[6,2,1]=>105
[4,5,6,7,8,9,3,1,2]=>[6,2,1]=>105
[3,4,5,6,7,9,10,8,1,2]=>[7,2,1]=>160
[3,4,5,8,1,9,7,6,2]=>[5,2,1,1]=>189
[3,4,5,6,8,9,10,7,1,2]=>[7,2,1]=>160
[3,4,7,1,8,9,6,5,2]=>[5,2,1,1]=>189
[3,6,1,7,8,9,4,5,2]=>[5,3,1]=>162
[3,4,6,7,8,9,10,5,1,2]=>[7,2,1]=>160
[5,1,6,7,8,9,4,3,2]=>[5,2,1,1]=>189
[3,5,6,7,8,9,10,4,1,2]=>[7,2,1]=>160
[1,5,6,7,8,9,3,2,4]=>[6,2,1]=>105
[3,4,5,6,7,10,1,8,9,2]=>[7,2,1]=>160
[3,4,5,6,7,8,10,11,9,1,2]=>[8,2,1]=>231
[3,4,5,8,9,6,7,1,2]=>[5,2,2]=>120
[3,4,5,6,9,1,10,8,7,2]=>[6,2,1,1]=>350
[3,4,5,6,7,9,10,11,8,1,2]=>[8,2,1]=>231
[3,4,7,8,5,9,6,1,2]=>[5,2,2]=>120
[3,4,5,9,1,6,7,8,2]=>[6,2,1]=>105
[3,4,5,8,1,9,10,7,6,2]=>[6,2,1,1]=>350
[3,4,8,1,5,9,7,6,2]=>[4,3,1,1]=>216
[3,4,7,1,8,9,10,5,6,2]=>[6,3,1]=>315
[3,4,5,7,8,9,10,11,6,1,2]=>[8,2,1]=>231
[5,6,3,7,8,9,4,1,2]=>[5,2,2]=>120
[3,7,8,4,5,6,1,2]=>[4,2,2]=>56
[3,7,1,4,8,9,6,5,2]=>[4,3,1,1]=>216
[3,6,1,7,8,9,10,5,4,2]=>[6,2,1,1]=>350
[3,4,6,7,8,9,10,11,5,1,2]=>[8,2,1]=>231
[5,2,6,7,8,9,3,1,4]=>[5,3,1]=>162
[6,1,3,7,8,9,4,5,2]=>[5,3,1]=>162
[5,1,6,7,8,9,10,4,3,2]=>[6,2,1,1]=>350
[1,2,6,7,8,9,4,3,5]=>[6,2,1]=>105
[4,5,6,7,8,9,10,11,3,1,2]=>[8,2,1]=>231
[4,5,6,7,8,9,10,11,2,1,3]=>[8,2,1]=>231
[1,3,8,6,7,4,5,2]=>[4,2,1,1]=>90
[2,6,5,3,7,1,8,4]=>[4,2,1,1]=>90
[5,7,1,3,6,4,8,2]=>[4,2,1,1]=>90
[8,2,5,4,1,7,3,6]=>[3,3,1,1]=>56
[8,1,7,6,4,2,3,5]=>[4,1,1,1,1]=>35
[6,4,8,7,3,2,5,1]=>[2,2,2,1,1]=>28
[5,6,2,8,7,4,3,1]=>[3,2,1,1,1]=>64
[3,7,5,6,4,2,8,1]=>[4,1,1,1,1]=>35
[5,2,3,8,6,1,4,7]=>[4,2,2]=>56
[1,4,3,8,5,6,2,7]=>[5,2,1]=>64
[7,8,2,6,4,3,5,1]=>[3,2,1,1,1]=>64
[4,5,8,7,2,3,6,1]=>[3,3,1,1]=>56
[7,8,6,1,4,2,5,3]=>[3,2,2,1]=>70
[6,10,5,1,2,3,4,7,8,9]=>[7,2,1]=>160
[10,5,4,1,2,3,6,7,8,9]=>[7,1,1,1]=>84
[8,3,6,5,2,7,1,4]=>[3,2,1,1,1]=>64
[5,1,3,6,4,2,7,8]=>[5,2,1]=>64
[6,1,2,4,7,5,3,8]=>[5,2,1]=>64
[8,3,1,4,6,7,2,5]=>[4,3,1]=>70
[7,8,5,1,2,6,3,4]=>[4,2,2]=>56
[6,4,5,1,8,7,3,2]=>[3,2,2,1]=>70
[8,6,2,1,7,3,5,4]=>[3,2,2,1]=>70
[9,3,4,5,6,8,7,2,1]=>[5,1,1,1,1]=>70
[9,4,3,5,6,7,8,2,1]=>[5,1,1,1,1]=>70
[10,9,3,4,5,6,8,7,2,1]=>[5,1,1,1,1,1]=>126
[9,8,3,4,5,7,6,2,1]=>[4,1,1,1,1,1]=>56
[9,8,4,3,5,6,7,2,1]=>[4,1,1,1,1,1]=>56
[10,9,4,3,5,6,7,8,2,1]=>[5,1,1,1,1,1]=>126
[11,10,3,4,5,6,7,9,8,2,1]=>[6,1,1,1,1,1]=>252
[10,3,4,5,6,7,9,8,2,1]=>[6,1,1,1,1]=>126
[9,3,4,5,6,2,8,7,1]=>[5,2,1,1]=>189
[9,2,4,5,6,8,7,3,1]=>[5,1,1,1,1]=>70
[9,4,3,5,6,7,2,8,1]=>[5,1,1,1,1]=>70
[9,3,2,5,6,7,8,4,1]=>[5,2,1,1]=>189
[10,4,3,5,6,7,8,9,2,1]=>[6,1,1,1,1]=>126
[11,10,4,3,5,6,7,8,9,2,1]=>[6,1,1,1,1,1]=>252
[7,8,6,1,4,3,5,2]=>[3,2,1,1,1]=>64
[4,6,3,5,7,2,8,1,9]=>[5,2,1,1]=>189
[5,6,3,4,7,2,8,1,9]=>[5,2,1,1]=>189
[4,3,6,2,5,7,1,8]=>[4,2,1,1]=>90
[1,5,7,4,6,8,3,9,2]=>[5,2,1,1]=>189
[1,6,5,7,3,4,8,2]=>[4,2,1,1]=>90
[1,6,7,4,5,8,3,9,2]=>[5,2,1,1]=>189
[1,7,5,6,8,4,9,3,10,2]=>[6,1,1,1,1]=>126
[1,2,3,4,8,5,9,6,7]=>[7,2]=>27
[1,2,3,4,5,8,6,9,7,10]=>[8,2]=>35
[1,2,3,7,4,5,8,6,9]=>[7,2]=>27
[1,2,3,4,8,6,5,7,9]=>[7,1,1]=>28
[1,2,3,4,9,7,5,6,8]=>[7,1,1]=>28
[1,2,3,4,5,9,6,10,7,8]=>[8,2]=>35
[8,2,6,5,1,7,4,3]=>[3,2,1,1,1]=>64
[7,6,4,1,2,5,8,3]=>[4,2,1,1]=>90
[2,6,5,4,8,7,1,3]=>[3,2,2,1]=>70
[5,6,7,1,3,2,4,8]=>[4,3,1]=>70
[7,1,8,4,3,2,6,5]=>[3,2,2,1]=>70
[2,1,4,9,3,5,6,7,8]=>[6,3]=>48
[3,7,1,2,4,5,6,9,8]=>[6,3]=>48
[3,1,2,6,9,4,5,7,8]=>[6,3]=>48
[4,6,1,2,3,5,9,7,8]=>[6,3]=>48
[1,8,5,2,7,6,4,3]=>[3,2,1,1,1]=>64
[1,7,6,8,2,5,4,3]=>[3,2,1,1,1]=>64
[1,7,8,6,2,5,4,3]=>[3,2,1,1,1]=>64
[4,6,5,7,1,8,2,3]=>[4,3,1]=>70
[7,5,3,6,8,4,2,1]=>[3,2,1,1,1]=>64
[7,2,5,6,4,8,3,1]=>[4,1,1,1,1]=>35
[7,4,6,2,8,5,3,1]=>[3,2,1,1,1]=>64
[9,7,6,5,4,3,8,2,1]=>[2,1,1,1,1,1,1,1]=>8
[9,8,6,5,4,7,3,2,1]=>[2,1,1,1,1,1,1,1]=>8
[5,4,3,2,1,9,7,8,6]=>[3,2,2,1,1]=>162
[10,8,7,6,5,4,3,9,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[10,9,7,6,5,4,8,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>9
[1,6,3,4,2,5,8,7]=>[5,2,1]=>64
[1,5,7,6,2,3,8,4]=>[4,3,1]=>70
[1,4,3,7,6,2,5,8]=>[4,2,2]=>56
[3,7,4,6,8,1,5,2]=>[4,2,1,1]=>90
[4,8,3,1,7,6,2,5]=>[3,2,2,1]=>70
[5,6,1,4,3,8,7,2]=>[3,3,1,1]=>56
[5,8,6,4,3,1,7,2]=>[3,2,1,1,1]=>64
[4,1,3,7,8,6,5,2]=>[4,2,1,1]=>90
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Description
The number of standard Young tableaux of the partition.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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