Identifier
-
Mp00253:
Decorated permutations
—permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[2,1]=>[2,1]=>[1,2]=>[1,0,1,0]=>1
[+,3,2]=>[1,3,2]=>[2,3,1]=>[1,1,0,1,0,0]=>1
[-,3,2]=>[1,3,2]=>[2,3,1]=>[1,1,0,1,0,0]=>1
[2,3,1]=>[2,3,1]=>[1,3,2]=>[1,0,1,1,0,0]=>1
[3,1,2]=>[3,1,2]=>[2,1,3]=>[1,1,0,0,1,0]=>1
[3,+,1]=>[3,2,1]=>[1,2,3]=>[1,0,1,0,1,0]=>2
[3,-,1]=>[3,2,1]=>[1,2,3]=>[1,0,1,0,1,0]=>2
[+,+,4,3]=>[1,2,4,3]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>1
[-,+,4,3]=>[1,2,4,3]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>1
[+,-,4,3]=>[1,2,4,3]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>1
[-,-,4,3]=>[1,2,4,3]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>1
[+,3,4,2]=>[1,3,4,2]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>1
[-,3,4,2]=>[1,3,4,2]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>1
[+,4,2,3]=>[1,4,2,3]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>1
[-,4,2,3]=>[1,4,2,3]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>1
[+,4,+,2]=>[1,4,3,2]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>1
[-,4,+,2]=>[1,4,3,2]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>1
[+,4,-,2]=>[1,4,3,2]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>1
[-,4,-,2]=>[1,4,3,2]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>1
[2,1,4,3]=>[2,1,4,3]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>1
[2,3,4,1]=>[2,3,4,1]=>[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>1
[2,4,1,3]=>[2,4,1,3]=>[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>1
[2,4,+,1]=>[2,4,3,1]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>2
[2,4,-,1]=>[2,4,3,1]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>2
[3,1,4,2]=>[3,1,4,2]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>1
[3,+,4,1]=>[3,2,4,1]=>[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>1
[3,-,4,1]=>[3,2,4,1]=>[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>1
[3,4,1,2]=>[3,4,1,2]=>[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>1
[3,4,2,1]=>[3,4,2,1]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>2
[4,1,2,3]=>[4,1,2,3]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>1
[4,1,+,2]=>[4,1,3,2]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>2
[4,1,-,2]=>[4,1,3,2]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>2
[4,+,1,3]=>[4,2,1,3]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>1
[4,-,1,3]=>[4,2,1,3]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>1
[4,+,+,1]=>[4,2,3,1]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>2
[4,-,+,1]=>[4,2,3,1]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>2
[4,+,-,1]=>[4,2,3,1]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>2
[4,-,-,1]=>[4,2,3,1]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>2
[4,3,1,2]=>[4,3,1,2]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>2
[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>3
[+,+,+,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[-,+,+,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[+,-,+,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[+,+,-,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[-,-,+,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[-,+,-,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[+,-,-,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[-,-,-,5,4]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[+,+,4,5,3]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[-,+,4,5,3]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[+,-,4,5,3]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[-,-,4,5,3]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[+,+,5,3,4]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>1
[-,+,5,3,4]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>1
[+,-,5,3,4]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>1
[-,-,5,3,4]=>[1,2,5,3,4]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>1
[+,+,5,+,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[-,+,5,+,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[+,-,5,+,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[+,+,5,-,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[-,-,5,+,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[-,+,5,-,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[+,-,5,-,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[-,-,5,-,3]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>1
[+,3,2,5,4]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[-,3,2,5,4]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[+,3,4,5,2]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[-,3,4,5,2]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[+,3,5,2,4]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>1
[-,3,5,2,4]=>[1,3,5,2,4]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>1
[+,3,5,+,2]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>1
[-,3,5,+,2]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>1
[+,3,5,-,2]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>1
[-,3,5,-,2]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>1
[+,4,2,5,3]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[-,4,2,5,3]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[+,4,+,5,2]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[-,4,+,5,2]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[+,4,-,5,2]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[-,4,-,5,2]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[+,4,5,2,3]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>1
[-,4,5,2,3]=>[1,4,5,2,3]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>1
[+,4,5,3,2]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>1
[-,4,5,3,2]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>1
[+,5,2,3,4]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>1
[-,5,2,3,4]=>[1,5,2,3,4]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>1
[+,5,2,+,3]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>1
[-,5,2,+,3]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>1
[+,5,2,-,3]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>1
[-,5,2,-,3]=>[1,5,2,4,3]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>1
[+,5,+,2,4]=>[1,5,3,2,4]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>1
[-,5,+,2,4]=>[1,5,3,2,4]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>1
[+,5,-,2,4]=>[1,5,3,2,4]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>1
[-,5,-,2,4]=>[1,5,3,2,4]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>1
[+,5,+,+,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[-,5,+,+,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[+,5,-,+,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[+,5,+,-,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[-,5,-,+,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[-,5,+,-,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[+,5,-,-,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[-,5,-,-,2]=>[1,5,3,4,2]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>2
[+,5,4,2,3]=>[1,5,4,2,3]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>1
[-,5,4,2,3]=>[1,5,4,2,3]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>1
[+,5,4,3,2]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>1
[-,5,4,3,2]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,1,+,5,4]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>1
[2,1,-,5,4]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>1
[2,1,4,5,3]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>1
[2,1,5,3,4]=>[2,1,5,3,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>1
[2,1,5,+,3]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>1
[2,1,5,-,3]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>1
[2,3,1,5,4]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>1
[2,3,4,5,1]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>1
[2,3,5,1,4]=>[2,3,5,1,4]=>[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>1
[2,3,5,+,1]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>2
[2,3,5,-,1]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>2
[2,4,1,5,3]=>[2,4,1,5,3]=>[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>1
[2,4,+,5,1]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>1
[2,4,-,5,1]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>1
[2,4,5,1,3]=>[2,4,5,1,3]=>[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>1
[2,4,5,3,1]=>[2,4,5,3,1]=>[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]=>2
[2,5,1,3,4]=>[2,5,1,3,4]=>[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>1
[2,5,1,+,3]=>[2,5,1,4,3]=>[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>1
[2,5,1,-,3]=>[2,5,1,4,3]=>[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>1
[2,5,+,1,4]=>[2,5,3,1,4]=>[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>1
[2,5,-,1,4]=>[2,5,3,1,4]=>[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>1
[2,5,+,+,1]=>[2,5,3,4,1]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>2
[2,5,-,+,1]=>[2,5,3,4,1]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>2
[2,5,+,-,1]=>[2,5,3,4,1]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>2
[2,5,-,-,1]=>[2,5,3,4,1]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>2
[2,5,4,1,3]=>[2,5,4,1,3]=>[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]=>1
[2,5,4,3,1]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>1
[3,1,2,5,4]=>[3,1,2,5,4]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>1
[3,1,4,5,2]=>[3,1,4,5,2]=>[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]=>1
[3,1,5,2,4]=>[3,1,5,2,4]=>[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>1
[3,1,5,+,2]=>[3,1,5,4,2]=>[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>1
[3,1,5,-,2]=>[3,1,5,4,2]=>[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>1
[3,+,1,5,4]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>1
[3,-,1,5,4]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>1
[3,+,4,5,1]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]=>1
[3,-,4,5,1]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]=>1
[3,+,5,1,4]=>[3,2,5,1,4]=>[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>1
[3,-,5,1,4]=>[3,2,5,1,4]=>[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>1
[3,+,5,+,1]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>2
[3,-,5,+,1]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>2
[3,+,5,-,1]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>2
[3,-,5,-,1]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>2
[3,4,1,5,2]=>[3,4,1,5,2]=>[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]=>1
[3,4,2,5,1]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]=>1
[3,4,5,1,2]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>1
[3,4,5,2,1]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]=>2
[3,5,1,2,4]=>[3,5,1,2,4]=>[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>1
[3,5,1,+,2]=>[3,5,1,4,2]=>[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>2
[3,5,1,-,2]=>[3,5,1,4,2]=>[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>2
[3,5,2,1,4]=>[3,5,2,1,4]=>[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>1
[3,5,2,+,1]=>[3,5,2,4,1]=>[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>2
[3,5,2,-,1]=>[3,5,2,4,1]=>[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>2
[3,5,4,1,2]=>[3,5,4,1,2]=>[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>2
[3,5,4,2,1]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>3
[4,1,2,5,3]=>[4,1,2,5,3]=>[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]=>1
[4,1,+,5,2]=>[4,1,3,5,2]=>[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]=>1
[4,1,-,5,2]=>[4,1,3,5,2]=>[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]=>1
[4,1,5,2,3]=>[4,1,5,2,3]=>[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>1
[4,1,5,3,2]=>[4,1,5,3,2]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>1
[4,+,1,5,3]=>[4,2,1,5,3]=>[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>1
[4,-,1,5,3]=>[4,2,1,5,3]=>[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>1
[4,+,+,5,1]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[4,-,+,5,1]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[4,+,-,5,1]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[4,-,-,5,1]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[4,+,5,1,3]=>[4,2,5,1,3]=>[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]=>1
[4,-,5,1,3]=>[4,2,5,1,3]=>[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]=>1
[4,+,5,3,1]=>[4,2,5,3,1]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>2
[4,-,5,3,1]=>[4,2,5,3,1]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>2
[4,3,1,5,2]=>[4,3,1,5,2]=>[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]=>1
[4,3,2,5,1]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[4,3,5,1,2]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]=>1
[4,3,5,2,1]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]=>2
[4,5,1,2,3]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>1
[4,5,1,3,2]=>[4,5,1,3,2]=>[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,1,3]=>[4,5,2,1,3]=>[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>1
[4,5,2,3,1]=>[4,5,2,3,1]=>[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]=>2
[4,5,+,1,2]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>2
[4,5,-,1,2]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>2
[4,5,+,2,1]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>3
[4,5,-,2,1]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>3
[5,1,2,3,4]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,1,2,+,3]=>[5,1,2,4,3]=>[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>2
[5,1,2,-,3]=>[5,1,2,4,3]=>[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>2
[5,1,+,2,4]=>[5,1,3,2,4]=>[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,1,-,2,4]=>[5,1,3,2,4]=>[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,1,+,+,2]=>[5,1,3,4,2]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>2
[5,1,-,+,2]=>[5,1,3,4,2]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>2
[5,1,+,-,2]=>[5,1,3,4,2]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>2
[5,1,-,-,2]=>[5,1,3,4,2]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>2
[5,1,4,2,3]=>[5,1,4,2,3]=>[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>2
[5,1,4,3,2]=>[5,1,4,3,2]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>1
[5,+,1,3,4]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,-,1,3,4]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,+,1,+,3]=>[5,2,1,4,3]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>2
[5,-,1,+,3]=>[5,2,1,4,3]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>2
[5,+,1,-,3]=>[5,2,1,4,3]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>2
[5,-,1,-,3]=>[5,2,1,4,3]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>2
[5,+,+,1,4]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,-,+,1,4]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,+,-,1,4]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,-,-,1,4]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,+,+,+,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,-,+,+,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,+,-,+,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,+,+,-,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,-,-,+,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,-,+,-,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,+,-,-,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,-,-,-,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,+,4,1,3]=>[5,2,4,1,3]=>[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>2
[5,-,4,1,3]=>[5,2,4,1,3]=>[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>2
[5,+,4,3,1]=>[5,2,4,3,1]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>3
[5,-,4,3,1]=>[5,2,4,3,1]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>3
[5,3,1,2,4]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,3,1,+,2]=>[5,3,1,4,2]=>[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>2
[5,3,1,-,2]=>[5,3,1,4,2]=>[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>2
[5,3,2,1,4]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>1
[5,3,2,+,1]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,3,2,-,1]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>2
[5,3,4,1,2]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>2
[5,3,4,2,1]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>3
[5,4,1,2,3]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,2]=>[5,4,1,3,2]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>3
[5,4,2,1,3]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>2
[5,4,2,3,1]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>3
[5,4,+,1,2]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>3
[5,4,-,1,2]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>3
[5,4,+,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>4
[5,4,-,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>4
[+,+,+,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,+,+,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,-,+,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,+,-,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,+,+,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,-,+,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,+,-,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,+,+,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,-,-,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,-,+,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,+,-,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,-,-,+,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,-,+,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,+,-,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,-,-,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,-,-,-,6,5]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,+,+,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,+,+,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,-,+,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,+,-,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,-,+,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,+,-,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,-,-,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,-,-,5,6,4]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,+,+,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,+,+,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,-,+,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,+,-,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,-,+,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,+,-,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,-,-,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,-,-,6,4,5]=>[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,+,+,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,+,+,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,-,+,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,+,-,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,+,+,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,-,+,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,+,-,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,+,+,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,-,-,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,-,+,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,+,-,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,-,-,6,+,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,-,+,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,+,-,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,-,-,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,-,-,6,-,4]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,+,4,3,6,5]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,+,4,3,6,5]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,-,4,3,6,5]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,-,4,3,6,5]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,+,4,5,6,3]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,+,4,5,6,3]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,-,4,5,6,3]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,-,4,5,6,3]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,+,4,6,3,5]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,+,4,6,3,5]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,-,4,6,3,5]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,-,4,6,3,5]=>[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,+,4,6,+,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[-,+,4,6,+,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[+,-,4,6,+,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[+,+,4,6,-,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[-,-,4,6,+,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[-,+,4,6,-,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[+,-,4,6,-,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[-,-,4,6,-,3]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[+,+,5,3,6,4]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,+,5,3,6,4]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,-,5,3,6,4]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,-,5,3,6,4]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,+,5,+,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,+,5,+,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,-,5,+,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,+,5,-,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,-,5,+,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,+,5,-,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,-,5,-,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,-,5,-,6,3]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,+,5,6,3,4]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[-,+,5,6,3,4]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[+,-,5,6,3,4]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[-,-,5,6,3,4]=>[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[+,+,5,6,4,3]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[-,+,5,6,4,3]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[+,-,5,6,4,3]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[-,-,5,6,4,3]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[+,+,6,3,4,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,+,6,3,4,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,-,6,3,4,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,-,6,3,4,5]=>[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,+,6,3,+,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[-,+,6,3,+,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[+,-,6,3,+,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[+,+,6,3,-,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[-,-,6,3,+,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[-,+,6,3,-,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[+,-,6,3,-,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[-,-,6,3,-,4]=>[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[+,+,6,+,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,+,6,+,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,-,6,+,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,+,6,-,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,-,6,+,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,+,6,-,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,-,6,-,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,-,6,-,3,5]=>[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,+,6,+,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,+,6,+,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,-,6,+,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,+,6,-,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,+,6,+,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,-,6,+,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,+,6,-,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,+,6,+,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,-,6,-,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,-,6,+,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,+,6,-,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,-,6,-,+,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,-,6,+,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,+,6,-,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,-,6,-,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,-,6,-,-,3]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,+,6,5,3,4]=>[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[-,+,6,5,3,4]=>[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[+,-,6,5,3,4]=>[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[-,-,6,5,3,4]=>[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[+,+,6,5,4,3]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[-,+,6,5,4,3]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[+,-,6,5,4,3]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[-,-,6,5,4,3]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[+,3,2,+,6,5]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,3,2,+,6,5]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,3,2,-,6,5]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,3,2,-,6,5]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,3,2,5,6,4]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,3,2,5,6,4]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,3,2,6,4,5]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,3,2,6,4,5]=>[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,3,2,6,+,4]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,3,2,6,+,4]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,3,2,6,-,4]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[-,3,2,6,-,4]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[+,3,4,2,6,5]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,3,4,2,6,5]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,3,4,5,6,2]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,3,4,5,6,2]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,3,4,6,2,5]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,3,4,6,2,5]=>[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,3,4,6,+,2]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[-,3,4,6,+,2]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[+,3,4,6,-,2]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[-,3,4,6,-,2]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[+,3,5,2,6,4]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,3,5,2,6,4]=>[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,3,5,+,6,2]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,3,5,+,6,2]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,3,5,-,6,2]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,3,5,-,6,2]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,3,5,6,2,4]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[-,3,5,6,2,4]=>[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[+,3,5,6,4,2]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[-,3,5,6,4,2]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[+,3,6,2,4,5]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,3,6,2,4,5]=>[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,3,6,2,+,4]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[-,3,6,2,+,4]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[+,3,6,2,-,4]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[-,3,6,2,-,4]=>[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[+,3,6,+,2,5]=>[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,3,6,+,2,5]=>[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,3,6,-,2,5]=>[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,3,6,-,2,5]=>[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,3,6,+,+,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[-,3,6,+,+,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[+,3,6,-,+,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[+,3,6,+,-,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[-,3,6,-,+,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[-,3,6,+,-,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[+,3,6,-,-,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[-,3,6,-,-,2]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[+,3,6,5,2,4]=>[1,3,6,5,2,4]=>[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[-,3,6,5,2,4]=>[1,3,6,5,2,4]=>[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[+,3,6,5,4,2]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[-,3,6,5,4,2]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[+,4,2,3,6,5]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,4,2,3,6,5]=>[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,4,2,5,6,3]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,4,2,5,6,3]=>[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,4,2,6,3,5]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,4,2,6,3,5]=>[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,4,2,6,+,3]=>[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[-,4,2,6,+,3]=>[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[+,4,2,6,-,3]=>[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[-,4,2,6,-,3]=>[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[+,4,+,2,6,5]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,4,+,2,6,5]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,4,-,2,6,5]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[-,4,-,2,6,5]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[+,4,+,5,6,2]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,4,+,5,6,2]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,4,-,5,6,2]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,4,-,5,6,2]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,4,+,6,2,5]=>[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,4,+,6,2,5]=>[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,4,-,6,2,5]=>[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[-,4,-,6,2,5]=>[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[+,4,+,6,+,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[-,4,+,6,+,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[+,4,-,6,+,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[+,4,+,6,-,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[-,4,-,6,+,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[-,4,+,6,-,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[+,4,-,6,-,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[-,4,-,6,-,2]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[+,4,5,2,6,3]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,4,5,2,6,3]=>[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,4,5,3,6,2]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,4,5,3,6,2]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,4,5,6,2,3]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[-,4,5,6,2,3]=>[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[+,4,5,6,3,2]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[-,4,5,6,3,2]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[+,4,6,2,3,5]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,4,6,2,3,5]=>[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,4,6,2,+,3]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,4,6,2,+,3]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,4,6,2,-,3]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[-,4,6,2,-,3]=>[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[+,4,6,3,2,5]=>[1,4,6,3,2,5]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[-,4,6,3,2,5]=>[1,4,6,3,2,5]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[+,4,6,3,+,2]=>[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[-,4,6,3,+,2]=>[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[+,4,6,3,-,2]=>[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[-,4,6,3,-,2]=>[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[+,4,6,5,2,3]=>[1,4,6,5,2,3]=>[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[-,4,6,5,2,3]=>[1,4,6,5,2,3]=>[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[+,4,6,5,3,2]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[-,4,6,5,3,2]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[+,5,2,3,6,4]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,5,2,3,6,4]=>[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,5,2,+,6,3]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,5,2,+,6,3]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,5,2,-,6,3]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,5,2,-,6,3]=>[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,5,2,6,3,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[-,5,2,6,3,4]=>[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[+,5,2,6,4,3]=>[1,5,2,6,4,3]=>[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[-,5,2,6,4,3]=>[1,5,2,6,4,3]=>[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[+,5,+,2,6,4]=>[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,5,+,2,6,4]=>[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,5,-,2,6,4]=>[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[-,5,-,2,6,4]=>[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[+,5,+,+,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,5,+,+,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,5,-,+,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,5,+,-,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,5,-,+,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,5,+,-,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,5,-,-,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,5,-,-,6,2]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,5,+,6,2,4]=>[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[-,5,+,6,2,4]=>[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[+,5,-,6,2,4]=>[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[-,5,-,6,2,4]=>[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[+,5,+,6,4,2]=>[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[-,5,+,6,4,2]=>[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[+,5,-,6,4,2]=>[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[-,5,-,6,4,2]=>[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[+,5,4,2,6,3]=>[1,5,4,2,6,3]=>[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[-,5,4,2,6,3]=>[1,5,4,2,6,3]=>[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[+,5,4,3,6,2]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[-,5,4,3,6,2]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[+,5,4,6,2,3]=>[1,5,4,6,2,3]=>[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[-,5,4,6,2,3]=>[1,5,4,6,2,3]=>[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[+,5,4,6,3,2]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[-,5,4,6,3,2]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[+,5,6,2,3,4]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[-,5,6,2,3,4]=>[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[+,5,6,2,4,3]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[-,5,6,2,4,3]=>[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[+,5,6,3,2,4]=>[1,5,6,3,2,4]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[-,5,6,3,2,4]=>[1,5,6,3,2,4]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[+,5,6,3,4,2]=>[1,5,6,3,4,2]=>[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[-,5,6,3,4,2]=>[1,5,6,3,4,2]=>[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[+,5,6,+,2,3]=>[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[-,5,6,+,2,3]=>[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[+,5,6,-,2,3]=>[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[-,5,6,-,2,3]=>[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[+,5,6,+,3,2]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[-,5,6,+,3,2]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[+,5,6,-,3,2]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[-,5,6,-,3,2]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[+,6,2,3,4,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,2,3,4,5]=>[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,2,3,+,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[-,6,2,3,+,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[+,6,2,3,-,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[-,6,2,3,-,4]=>[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[+,6,2,+,3,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,2,+,3,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,2,-,3,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,2,-,3,5]=>[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,2,+,+,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[-,6,2,+,+,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[+,6,2,-,+,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[+,6,2,+,-,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[-,6,2,-,+,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[-,6,2,+,-,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[+,6,2,-,-,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[-,6,2,-,-,3]=>[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[+,6,2,5,3,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[-,6,2,5,3,4]=>[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[+,6,2,5,4,3]=>[1,6,2,5,4,3]=>[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[-,6,2,5,4,3]=>[1,6,2,5,4,3]=>[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[+,6,+,2,4,5]=>[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,+,2,4,5]=>[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,-,2,4,5]=>[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,-,2,4,5]=>[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,+,2,+,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[-,6,+,2,+,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[+,6,-,2,+,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[+,6,+,2,-,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[-,6,-,2,+,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[-,6,+,2,-,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[+,6,-,2,-,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[-,6,-,2,-,4]=>[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[+,6,+,+,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,+,+,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,-,+,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,+,-,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,-,+,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,+,-,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,-,-,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,-,-,2,5]=>[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,+,+,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,+,+,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,-,+,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,+,-,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,+,+,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,-,+,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,+,-,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,+,+,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,-,-,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,-,+,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,+,-,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,-,-,+,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,-,+,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,+,-,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,-,-,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,-,-,-,2]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,+,5,2,4]=>[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[-,6,+,5,2,4]=>[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[+,6,-,5,2,4]=>[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[-,6,-,5,2,4]=>[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[+,6,+,5,4,2]=>[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[-,6,+,5,4,2]=>[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[+,6,-,5,4,2]=>[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[-,6,-,5,4,2]=>[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[+,6,4,2,3,5]=>[1,6,4,2,3,5]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,4,2,3,5]=>[1,6,4,2,3,5]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,4,2,+,3]=>[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[-,6,4,2,+,3]=>[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[+,6,4,2,-,3]=>[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[-,6,4,2,-,3]=>[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[+,6,4,3,2,5]=>[1,6,4,3,2,5]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[-,6,4,3,2,5]=>[1,6,4,3,2,5]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[+,6,4,3,+,2]=>[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,4,3,+,2]=>[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,4,3,-,2]=>[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[-,6,4,3,-,2]=>[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[+,6,4,5,2,3]=>[1,6,4,5,2,3]=>[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[-,6,4,5,2,3]=>[1,6,4,5,2,3]=>[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[+,6,4,5,3,2]=>[1,6,4,5,3,2]=>[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[-,6,4,5,3,2]=>[1,6,4,5,3,2]=>[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[+,6,5,2,3,4]=>[1,6,5,2,3,4]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[-,6,5,2,3,4]=>[1,6,5,2,3,4]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[+,6,5,2,4,3]=>[1,6,5,2,4,3]=>[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[-,6,5,2,4,3]=>[1,6,5,2,4,3]=>[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[+,6,5,3,2,4]=>[1,6,5,3,2,4]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[-,6,5,3,2,4]=>[1,6,5,3,2,4]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[+,6,5,3,4,2]=>[1,6,5,3,4,2]=>[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>1
[-,6,5,3,4,2]=>[1,6,5,3,4,2]=>[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>1
[+,6,5,+,2,3]=>[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[-,6,5,+,2,3]=>[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[+,6,5,-,2,3]=>[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[-,6,5,-,2,3]=>[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[+,6,5,+,3,2]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[-,6,5,+,3,2]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[+,6,5,-,3,2]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[-,6,5,-,3,2]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[2,1,+,+,6,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,1,-,+,6,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,1,+,-,6,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,1,-,-,6,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,1,+,5,6,4]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,1,-,5,6,4]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,1,+,6,4,5]=>[2,1,3,6,4,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,1,-,6,4,5]=>[2,1,3,6,4,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,1,+,6,+,4]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[2,1,-,6,+,4]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[2,1,+,6,-,4]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[2,1,-,6,-,4]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,1,4,5,6,3]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,1,4,6,3,5]=>[2,1,4,6,3,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,1,4,6,+,3]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[2,1,4,6,-,3]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[2,1,5,3,6,4]=>[2,1,5,3,6,4]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,1,5,+,6,3]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,1,5,-,6,3]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,1,5,6,3,4]=>[2,1,5,6,3,4]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[2,1,5,6,4,3]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,1,6,3,+,4]=>[2,1,6,3,5,4]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[2,1,6,3,-,4]=>[2,1,6,3,5,4]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[2,1,6,+,3,5]=>[2,1,6,4,3,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,1,6,-,3,5]=>[2,1,6,4,3,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,1,6,+,+,3]=>[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[2,1,6,-,+,3]=>[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[2,1,6,+,-,3]=>[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[2,1,6,-,-,3]=>[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[2,1,6,5,3,4]=>[2,1,6,5,3,4]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[2,3,1,+,6,5]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,3,1,-,6,5]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,3,1,5,6,4]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,3,1,6,4,5]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,3,1,6,+,4]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[2,3,1,6,-,4]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[2,3,4,1,6,5]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,3,4,6,1,5]=>[2,3,4,6,1,5]=>[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,3,4,6,+,1]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[2,3,4,6,-,1]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[2,3,5,1,6,4]=>[2,3,5,1,6,4]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,3,5,+,6,1]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,3,5,-,6,1]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,3,5,6,1,4]=>[2,3,5,6,1,4]=>[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[2,3,5,6,4,1]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[2,3,6,1,4,5]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,3,6,1,+,4]=>[2,3,6,1,5,4]=>[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[2,3,6,1,-,4]=>[2,3,6,1,5,4]=>[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[2,3,6,+,1,5]=>[2,3,6,4,1,5]=>[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,3,6,-,1,5]=>[2,3,6,4,1,5]=>[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,3,6,+,+,1]=>[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[2,3,6,-,+,1]=>[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[2,3,6,+,-,1]=>[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[2,3,6,-,-,1]=>[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[2,3,6,5,1,4]=>[2,3,6,5,1,4]=>[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[2,3,6,5,4,1]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[2,4,1,3,6,5]=>[2,4,1,3,6,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,4,1,5,6,3]=>[2,4,1,5,6,3]=>[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,4,1,6,3,5]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,4,1,6,+,3]=>[2,4,1,6,5,3]=>[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[2,4,1,6,-,3]=>[2,4,1,6,5,3]=>[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[2,4,+,1,6,5]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,4,-,1,6,5]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[2,4,+,5,6,1]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,4,-,5,6,1]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,4,+,6,1,5]=>[2,4,3,6,1,5]=>[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,4,-,6,1,5]=>[2,4,3,6,1,5]=>[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,4,+,6,+,1]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[2,4,-,6,+,1]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[2,4,+,6,-,1]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[2,4,-,6,-,1]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[2,4,5,1,6,3]=>[2,4,5,1,6,3]=>[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,4,5,3,6,1]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,4,5,6,1,3]=>[2,4,5,6,1,3]=>[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[2,4,5,6,3,1]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,4,6,1,+,3]=>[2,4,6,1,5,3]=>[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[2,4,6,1,-,3]=>[2,4,6,1,5,3]=>[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[2,4,6,3,1,5]=>[2,4,6,3,1,5]=>[5,1,3,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[2,4,6,3,+,1]=>[2,4,6,3,5,1]=>[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[2,4,6,3,-,1]=>[2,4,6,3,5,1]=>[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[2,4,6,5,1,3]=>[2,4,6,5,1,3]=>[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[2,4,6,5,3,1]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[2,5,1,3,6,4]=>[2,5,1,3,6,4]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,5,1,+,6,3]=>[2,5,1,4,6,3]=>[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,5,1,-,6,3]=>[2,5,1,4,6,3]=>[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,5,1,6,3,4]=>[2,5,1,6,3,4]=>[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[2,5,1,6,4,3]=>[2,5,1,6,4,3]=>[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[2,5,+,1,6,4]=>[2,5,3,1,6,4]=>[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,5,-,1,6,4]=>[2,5,3,1,6,4]=>[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[2,5,+,+,6,1]=>[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,5,-,+,6,1]=>[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,5,+,-,6,1]=>[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,5,-,-,6,1]=>[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,5,+,6,1,4]=>[2,5,3,6,1,4]=>[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[2,5,-,6,1,4]=>[2,5,3,6,1,4]=>[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[2,5,+,6,4,1]=>[2,5,3,6,4,1]=>[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[2,5,-,6,4,1]=>[2,5,3,6,4,1]=>[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[2,5,4,1,6,3]=>[2,5,4,1,6,3]=>[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[2,5,4,3,6,1]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,5,4,6,1,3]=>[2,5,4,6,1,3]=>[3,1,6,4,5,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[2,5,4,6,3,1]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[2,5,6,1,3,4]=>[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[2,5,6,1,4,3]=>[2,5,6,1,4,3]=>[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[2,5,6,3,1,4]=>[2,5,6,3,1,4]=>[4,1,3,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[2,5,6,3,4,1]=>[2,5,6,3,4,1]=>[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[2,5,6,+,1,3]=>[2,5,6,4,1,3]=>[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[2,5,6,-,1,3]=>[2,5,6,4,1,3]=>[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[2,5,6,+,3,1]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[2,5,6,-,3,1]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[2,6,1,3,4,5]=>[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,1,3,+,4]=>[2,6,1,3,5,4]=>[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[2,6,1,3,-,4]=>[2,6,1,3,5,4]=>[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[2,6,1,+,3,5]=>[2,6,1,4,3,5]=>[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,1,-,3,5]=>[2,6,1,4,3,5]=>[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,1,+,+,3]=>[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[2,6,1,-,+,3]=>[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[2,6,1,+,-,3]=>[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[2,6,1,-,-,3]=>[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[2,6,1,5,3,4]=>[2,6,1,5,3,4]=>[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[2,6,1,5,4,3]=>[2,6,1,5,4,3]=>[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[2,6,+,1,4,5]=>[2,6,3,1,4,5]=>[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,-,1,4,5]=>[2,6,3,1,4,5]=>[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,+,1,+,4]=>[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[2,6,-,1,+,4]=>[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[2,6,+,1,-,4]=>[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[2,6,-,1,-,4]=>[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[2,6,+,+,1,5]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,-,+,1,5]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,+,-,1,5]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,-,-,1,5]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,+,+,+,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,-,+,+,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,+,-,+,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,+,+,-,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,-,-,+,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,-,+,-,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,+,-,-,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,-,-,-,1]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,+,5,1,4]=>[2,6,3,5,1,4]=>[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[2,6,-,5,1,4]=>[2,6,3,5,1,4]=>[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[2,6,+,5,4,1]=>[2,6,3,5,4,1]=>[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[2,6,-,5,4,1]=>[2,6,3,5,4,1]=>[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[2,6,4,1,3,5]=>[2,6,4,1,3,5]=>[5,3,1,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,4,1,+,3]=>[2,6,4,1,5,3]=>[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[2,6,4,1,-,3]=>[2,6,4,1,5,3]=>[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[2,6,4,3,1,5]=>[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[2,6,4,3,+,1]=>[2,6,4,3,5,1]=>[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,4,3,-,1]=>[2,6,4,3,5,1]=>[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[2,6,4,5,1,3]=>[2,6,4,5,1,3]=>[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[2,6,4,5,3,1]=>[2,6,4,5,3,1]=>[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[2,6,5,1,3,4]=>[2,6,5,1,3,4]=>[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[2,6,5,1,4,3]=>[2,6,5,1,4,3]=>[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[2,6,5,3,1,4]=>[2,6,5,3,1,4]=>[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[2,6,5,3,4,1]=>[2,6,5,3,4,1]=>[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[2,6,5,+,1,3]=>[2,6,5,4,1,3]=>[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[2,6,5,-,1,3]=>[2,6,5,4,1,3]=>[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[2,6,5,+,3,1]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,-,3,1]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[3,1,2,+,6,5]=>[3,1,2,4,6,5]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,1,2,-,6,5]=>[3,1,2,4,6,5]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,1,2,5,6,4]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,1,2,6,+,4]=>[3,1,2,6,5,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[3,1,2,6,-,4]=>[3,1,2,6,5,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[3,1,4,2,6,5]=>[3,1,4,2,6,5]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,1,4,5,6,2]=>[3,1,4,5,6,2]=>[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,1,4,6,2,5]=>[3,1,4,6,2,5]=>[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,1,4,6,+,2]=>[3,1,4,6,5,2]=>[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[3,1,4,6,-,2]=>[3,1,4,6,5,2]=>[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[3,1,5,2,6,4]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,1,5,+,6,2]=>[3,1,5,4,6,2]=>[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,1,5,-,6,2]=>[3,1,5,4,6,2]=>[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,1,5,6,2,4]=>[3,1,5,6,2,4]=>[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[3,1,5,6,4,2]=>[3,1,5,6,4,2]=>[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[3,1,6,2,4,5]=>[3,1,6,2,4,5]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,1,6,2,+,4]=>[3,1,6,2,5,4]=>[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[3,1,6,2,-,4]=>[3,1,6,2,5,4]=>[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[3,1,6,+,2,5]=>[3,1,6,4,2,5]=>[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,1,6,-,2,5]=>[3,1,6,4,2,5]=>[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,1,6,+,+,2]=>[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,1,6,-,+,2]=>[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,1,6,+,-,2]=>[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,1,6,-,-,2]=>[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,1,6,5,2,4]=>[3,1,6,5,2,4]=>[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[3,1,6,5,4,2]=>[3,1,6,5,4,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[3,+,1,+,6,5]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,-,1,+,6,5]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,+,1,-,6,5]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,-,1,-,6,5]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,+,1,5,6,4]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,-,1,5,6,4]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,+,1,6,4,5]=>[3,2,1,6,4,5]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,-,1,6,4,5]=>[3,2,1,6,4,5]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,+,1,6,+,4]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[3,-,1,6,+,4]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[3,+,1,6,-,4]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[3,-,1,6,-,4]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[3,+,4,1,6,5]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,-,4,1,6,5]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,+,4,5,6,1]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,-,4,5,6,1]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,+,4,6,1,5]=>[3,2,4,6,1,5]=>[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,-,4,6,1,5]=>[3,2,4,6,1,5]=>[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,+,4,6,+,1]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[3,-,4,6,+,1]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[3,+,4,6,-,1]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[3,-,4,6,-,1]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[3,+,5,1,6,4]=>[3,2,5,1,6,4]=>[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,-,5,1,6,4]=>[3,2,5,1,6,4]=>[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,+,5,+,6,1]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,-,5,+,6,1]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,+,5,-,6,1]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,-,5,-,6,1]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,+,5,6,1,4]=>[3,2,5,6,1,4]=>[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[3,-,5,6,1,4]=>[3,2,5,6,1,4]=>[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[3,+,5,6,4,1]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[3,-,5,6,4,1]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[3,+,6,1,4,5]=>[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,-,6,1,4,5]=>[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,+,6,1,+,4]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[3,-,6,1,+,4]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[3,+,6,1,-,4]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[3,-,6,1,-,4]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[3,+,6,+,1,5]=>[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,-,6,+,1,5]=>[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,+,6,-,1,5]=>[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,-,6,-,1,5]=>[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,+,6,+,+,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,-,6,+,+,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,+,6,-,+,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,+,6,+,-,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,-,6,-,+,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,-,6,+,-,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,+,6,-,-,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,-,6,-,-,1]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,+,6,5,1,4]=>[3,2,6,5,1,4]=>[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[3,-,6,5,1,4]=>[3,2,6,5,1,4]=>[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[3,+,6,5,4,1]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[3,-,6,5,4,1]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[3,4,1,2,6,5]=>[3,4,1,2,6,5]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,4,1,5,6,2]=>[3,4,1,5,6,2]=>[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,4,1,6,2,5]=>[3,4,1,6,2,5]=>[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,4,1,6,+,2]=>[3,4,1,6,5,2]=>[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[3,4,1,6,-,2]=>[3,4,1,6,5,2]=>[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[3,4,2,1,6,5]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,4,2,6,1,5]=>[3,4,2,6,1,5]=>[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[3,4,2,6,+,1]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[3,4,2,6,-,1]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[3,4,5,1,6,2]=>[3,4,5,1,6,2]=>[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,4,5,6,1,2]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[3,4,6,1,2,5]=>[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,4,6,1,+,2]=>[3,4,6,1,5,2]=>[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,4,6,1,-,2]=>[3,4,6,1,5,2]=>[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,4,6,2,1,5]=>[3,4,6,2,1,5]=>[5,1,2,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,4,6,2,+,1]=>[3,4,6,2,5,1]=>[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,4,6,2,-,1]=>[3,4,6,2,5,1]=>[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[3,4,6,5,1,2]=>[3,4,6,5,1,2]=>[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[3,4,6,5,2,1]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[3,5,1,2,6,4]=>[3,5,1,2,6,4]=>[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,5,1,+,6,2]=>[3,5,1,4,6,2]=>[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,5,1,-,6,2]=>[3,5,1,4,6,2]=>[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,5,1,6,2,4]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[3,5,1,6,4,2]=>[3,5,1,6,4,2]=>[2,4,6,1,5,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[3,5,2,1,6,4]=>[3,5,2,1,6,4]=>[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[3,5,2,+,6,1]=>[3,5,2,4,6,1]=>[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,5,2,-,6,1]=>[3,5,2,4,6,1]=>[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,5,2,6,1,4]=>[3,5,2,6,1,4]=>[4,1,6,2,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[3,5,2,6,4,1]=>[3,5,2,6,4,1]=>[1,4,6,2,5,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[3,5,4,1,6,2]=>[3,5,4,1,6,2]=>[2,6,1,4,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,5,4,2,6,1]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[3,5,4,6,1,2]=>[3,5,4,6,1,2]=>[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[3,5,4,6,2,1]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[3,5,6,1,2,4]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[3,5,6,1,4,2]=>[3,5,6,1,4,2]=>[2,4,1,6,5,3]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[3,5,6,2,1,4]=>[3,5,6,2,1,4]=>[4,1,2,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[3,5,6,2,4,1]=>[3,5,6,2,4,1]=>[1,4,2,6,5,3]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[3,5,6,+,1,2]=>[3,5,6,4,1,2]=>[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[3,5,6,-,1,2]=>[3,5,6,4,1,2]=>[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[3,5,6,+,2,1]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[3,5,6,-,2,1]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[3,6,1,2,4,5]=>[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,1,2,+,4]=>[3,6,1,2,5,4]=>[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[3,6,1,2,-,4]=>[3,6,1,2,5,4]=>[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[3,6,1,+,2,5]=>[3,6,1,4,2,5]=>[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,1,-,2,5]=>[3,6,1,4,2,5]=>[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,1,+,+,2]=>[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[3,6,1,-,+,2]=>[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[3,6,1,+,-,2]=>[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[3,6,1,-,-,2]=>[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[3,6,1,5,2,4]=>[3,6,1,5,2,4]=>[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[3,6,2,1,4,5]=>[3,6,2,1,4,5]=>[5,4,1,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,2,1,+,4]=>[3,6,2,1,5,4]=>[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[3,6,2,1,-,4]=>[3,6,2,1,5,4]=>[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[3,6,2,+,1,5]=>[3,6,2,4,1,5]=>[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,2,-,1,5]=>[3,6,2,4,1,5]=>[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,2,+,+,1]=>[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[3,6,2,-,+,1]=>[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[3,6,2,+,-,1]=>[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[3,6,2,-,-,1]=>[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[3,6,2,5,4,1]=>[3,6,2,5,4,1]=>[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[3,6,4,1,2,5]=>[3,6,4,1,2,5]=>[5,2,1,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,4,1,+,2]=>[3,6,4,1,5,2]=>[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[3,6,4,1,-,2]=>[3,6,4,1,5,2]=>[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[3,6,4,2,1,5]=>[3,6,4,2,1,5]=>[5,1,2,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[3,6,4,2,+,1]=>[3,6,4,2,5,1]=>[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[3,6,4,2,-,1]=>[3,6,4,2,5,1]=>[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[3,6,4,5,1,2]=>[3,6,4,5,1,2]=>[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[3,6,4,5,2,1]=>[3,6,4,5,2,1]=>[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[3,6,5,1,2,4]=>[3,6,5,1,2,4]=>[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[3,6,5,1,4,2]=>[3,6,5,1,4,2]=>[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>1
[3,6,5,2,1,4]=>[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[3,6,5,2,4,1]=>[3,6,5,2,4,1]=>[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[3,6,5,+,1,2]=>[3,6,5,4,1,2]=>[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>1
[3,6,5,-,1,2]=>[3,6,5,4,1,2]=>[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>1
[3,6,5,+,2,1]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[3,6,5,-,2,1]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,1,2,5,6,3]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,1,2,6,3,5]=>[4,1,2,6,3,5]=>[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,1,2,6,+,3]=>[4,1,2,6,5,3]=>[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[4,1,2,6,-,3]=>[4,1,2,6,5,3]=>[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[4,1,+,2,6,5]=>[4,1,3,2,6,5]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,1,-,2,6,5]=>[4,1,3,2,6,5]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,1,+,5,6,2]=>[4,1,3,5,6,2]=>[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,1,-,5,6,2]=>[4,1,3,5,6,2]=>[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,1,+,6,2,5]=>[4,1,3,6,2,5]=>[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,1,-,6,2,5]=>[4,1,3,6,2,5]=>[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,1,+,6,+,2]=>[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[4,1,-,6,+,2]=>[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[4,1,+,6,-,2]=>[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[4,1,-,6,-,2]=>[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[4,1,5,2,6,3]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,1,5,3,6,2]=>[4,1,5,3,6,2]=>[2,6,3,5,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,1,5,6,2,3]=>[4,1,5,6,2,3]=>[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[4,1,5,6,3,2]=>[4,1,5,6,3,2]=>[2,3,6,5,1,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[4,1,6,2,3,5]=>[4,1,6,2,3,5]=>[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,1,6,2,+,3]=>[4,1,6,2,5,3]=>[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[4,1,6,2,-,3]=>[4,1,6,2,5,3]=>[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[4,1,6,3,2,5]=>[4,1,6,3,2,5]=>[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,1,6,3,+,2]=>[4,1,6,3,5,2]=>[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[4,1,6,3,-,2]=>[4,1,6,3,5,2]=>[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[4,1,6,5,2,3]=>[4,1,6,5,2,3]=>[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[4,1,6,5,3,2]=>[4,1,6,5,3,2]=>[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[4,+,1,3,6,5]=>[4,2,1,3,6,5]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,-,1,3,6,5]=>[4,2,1,3,6,5]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,+,1,5,6,3]=>[4,2,1,5,6,3]=>[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,-,1,5,6,3]=>[4,2,1,5,6,3]=>[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,+,1,6,3,5]=>[4,2,1,6,3,5]=>[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,-,1,6,3,5]=>[4,2,1,6,3,5]=>[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,+,1,6,+,3]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[4,-,1,6,+,3]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[4,+,1,6,-,3]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[4,-,1,6,-,3]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[4,+,+,1,6,5]=>[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,-,+,1,6,5]=>[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,+,-,1,6,5]=>[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,-,-,1,6,5]=>[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,+,+,5,6,1]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,-,+,5,6,1]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,+,-,5,6,1]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,-,-,5,6,1]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,+,+,6,1,5]=>[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,-,+,6,1,5]=>[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,+,-,6,1,5]=>[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,-,-,6,1,5]=>[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,+,+,6,+,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,-,+,6,+,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,+,-,6,+,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,+,+,6,-,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,-,-,6,+,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,-,+,6,-,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,+,-,6,-,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,-,-,6,-,1]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,+,5,1,6,3]=>[4,2,5,1,6,3]=>[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,-,5,1,6,3]=>[4,2,5,1,6,3]=>[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,+,5,3,6,1]=>[4,2,5,3,6,1]=>[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,-,5,3,6,1]=>[4,2,5,3,6,1]=>[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,+,5,6,1,3]=>[4,2,5,6,1,3]=>[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[4,-,5,6,1,3]=>[4,2,5,6,1,3]=>[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[4,+,5,6,3,1]=>[4,2,5,6,3,1]=>[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[4,-,5,6,3,1]=>[4,2,5,6,3,1]=>[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[4,+,6,1,3,5]=>[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,-,6,1,3,5]=>[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,+,6,1,+,3]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[4,-,6,1,+,3]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[4,+,6,1,-,3]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[4,-,6,1,-,3]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[4,+,6,3,1,5]=>[4,2,6,3,1,5]=>[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,-,6,3,1,5]=>[4,2,6,3,1,5]=>[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,+,6,3,+,1]=>[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[4,-,6,3,+,1]=>[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[4,+,6,3,-,1]=>[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[4,-,6,3,-,1]=>[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[4,+,6,5,1,3]=>[4,2,6,5,1,3]=>[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[4,-,6,5,1,3]=>[4,2,6,5,1,3]=>[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[4,+,6,5,3,1]=>[4,2,6,5,3,1]=>[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[4,-,6,5,3,1]=>[4,2,6,5,3,1]=>[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[4,3,1,2,6,5]=>[4,3,1,2,6,5]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,3,1,5,6,2]=>[4,3,1,5,6,2]=>[2,6,5,1,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,3,1,6,2,5]=>[4,3,1,6,2,5]=>[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,3,1,6,+,2]=>[4,3,1,6,5,2]=>[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[4,3,1,6,-,2]=>[4,3,1,6,5,2]=>[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,3,2,6,1,5]=>[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[4,3,2,6,+,1]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,3,2,6,-,1]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[4,3,5,1,6,2]=>[4,3,5,1,6,2]=>[2,6,1,5,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,3,5,6,1,2]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[4,3,6,1,2,5]=>[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,3,6,1,+,2]=>[4,3,6,1,5,2]=>[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[4,3,6,1,-,2]=>[4,3,6,1,5,2]=>[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[4,3,6,2,1,5]=>[4,3,6,2,1,5]=>[5,1,2,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[4,3,6,2,+,1]=>[4,3,6,2,5,1]=>[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[4,3,6,2,-,1]=>[4,3,6,2,5,1]=>[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[4,3,6,5,1,2]=>[4,3,6,5,1,2]=>[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[4,3,6,5,2,1]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[4,5,1,2,6,3]=>[4,5,1,2,6,3]=>[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,5,1,3,6,2]=>[4,5,1,3,6,2]=>[2,6,3,1,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,5,1,6,2,3]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[4,5,1,6,3,2]=>[4,5,1,6,3,2]=>[2,3,6,1,5,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[4,5,2,1,6,3]=>[4,5,2,1,6,3]=>[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,5,2,3,6,1]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,5,2,6,1,3]=>[4,5,2,6,1,3]=>[3,1,6,2,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[4,5,2,6,3,1]=>[4,5,2,6,3,1]=>[1,3,6,2,5,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[4,5,+,1,6,2]=>[4,5,3,1,6,2]=>[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,5,-,1,6,2]=>[4,5,3,1,6,2]=>[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[4,5,+,2,6,1]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,5,-,2,6,1]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[4,5,+,6,1,2]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[4,5,-,6,1,2]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[4,5,+,6,2,1]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[4,5,-,6,2,1]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[4,5,6,1,3,2]=>[4,5,6,1,3,2]=>[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[4,5,6,2,1,3]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[4,5,6,2,3,1]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>2
[4,5,6,3,1,2]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[4,6,1,2,3,5]=>[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,1,2,+,3]=>[4,6,1,2,5,3]=>[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[4,6,1,2,-,3]=>[4,6,1,2,5,3]=>[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[4,6,1,3,2,5]=>[4,6,1,3,2,5]=>[5,2,3,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,1,3,+,2]=>[4,6,1,3,5,2]=>[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[4,6,1,3,-,2]=>[4,6,1,3,5,2]=>[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[4,6,1,5,2,3]=>[4,6,1,5,2,3]=>[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[4,6,1,5,3,2]=>[4,6,1,5,3,2]=>[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[4,6,2,1,3,5]=>[4,6,2,1,3,5]=>[5,3,1,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,2,1,+,3]=>[4,6,2,1,5,3]=>[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[4,6,2,1,-,3]=>[4,6,2,1,5,3]=>[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[4,6,2,3,1,5]=>[4,6,2,3,1,5]=>[5,1,3,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,2,3,+,1]=>[4,6,2,3,5,1]=>[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[4,6,2,3,-,1]=>[4,6,2,3,5,1]=>[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[4,6,2,5,1,3]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[4,6,2,5,3,1]=>[4,6,2,5,3,1]=>[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[4,6,+,1,2,5]=>[4,6,3,1,2,5]=>[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,-,1,2,5]=>[4,6,3,1,2,5]=>[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,+,1,+,2]=>[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[4,6,-,1,+,2]=>[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[4,6,+,1,-,2]=>[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[4,6,-,1,-,2]=>[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[4,6,+,2,1,5]=>[4,6,3,2,1,5]=>[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,-,2,1,5]=>[4,6,3,2,1,5]=>[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,6,+,2,+,1]=>[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[4,6,-,2,+,1]=>[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[4,6,+,2,-,1]=>[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[4,6,-,2,-,1]=>[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[4,6,+,5,1,2]=>[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[4,6,-,5,1,2]=>[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[4,6,+,5,2,1]=>[4,6,3,5,2,1]=>[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[4,6,-,5,2,1]=>[4,6,3,5,2,1]=>[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[4,6,5,1,2,3]=>[4,6,5,1,2,3]=>[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>3
[4,6,5,2,1,3]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[4,6,5,2,3,1]=>[4,6,5,2,3,1]=>[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>3
[4,6,5,3,1,2]=>[4,6,5,3,1,2]=>[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[4,6,5,3,2,1]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[5,1,2,3,6,4]=>[5,1,2,3,6,4]=>[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,1,2,+,6,3]=>[5,1,2,4,6,3]=>[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,1,2,-,6,3]=>[5,1,2,4,6,3]=>[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,1,2,6,3,4]=>[5,1,2,6,3,4]=>[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,1,2,6,4,3]=>[5,1,2,6,4,3]=>[3,4,6,2,1,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[5,1,+,2,6,4]=>[5,1,3,2,6,4]=>[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,1,-,2,6,4]=>[5,1,3,2,6,4]=>[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,1,+,+,6,2]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,1,-,+,6,2]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,1,+,-,6,2]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,1,-,-,6,2]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,1,+,6,2,4]=>[5,1,3,6,2,4]=>[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,1,-,6,2,4]=>[5,1,3,6,2,4]=>[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,1,+,6,4,2]=>[5,1,3,6,4,2]=>[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[5,1,-,6,4,2]=>[5,1,3,6,4,2]=>[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[5,1,4,2,6,3]=>[5,1,4,2,6,3]=>[3,6,2,4,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,1,4,3,6,2]=>[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,1,4,6,2,3]=>[5,1,4,6,2,3]=>[3,2,6,4,1,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[5,1,4,6,3,2]=>[5,1,4,6,3,2]=>[2,3,6,4,1,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[5,1,6,2,3,4]=>[5,1,6,2,3,4]=>[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,1,6,2,4,3]=>[5,1,6,2,4,3]=>[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[5,1,6,3,2,4]=>[5,1,6,3,2,4]=>[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,1,6,3,4,2]=>[5,1,6,3,4,2]=>[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[5,1,6,+,2,3]=>[5,1,6,4,2,3]=>[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[5,1,6,-,2,3]=>[5,1,6,4,2,3]=>[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[5,1,6,+,3,2]=>[5,1,6,4,3,2]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[5,1,6,-,3,2]=>[5,1,6,4,3,2]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[5,+,1,3,6,4]=>[5,2,1,3,6,4]=>[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,-,1,3,6,4]=>[5,2,1,3,6,4]=>[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,+,1,+,6,3]=>[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,-,1,+,6,3]=>[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,+,1,-,6,3]=>[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,-,1,-,6,3]=>[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,+,1,6,3,4]=>[5,2,1,6,3,4]=>[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,-,1,6,3,4]=>[5,2,1,6,3,4]=>[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,+,1,6,4,3]=>[5,2,1,6,4,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[5,-,1,6,4,3]=>[5,2,1,6,4,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[5,+,+,1,6,4]=>[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,-,+,1,6,4]=>[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,+,-,1,6,4]=>[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,-,-,1,6,4]=>[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,+,+,+,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,-,+,+,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,+,-,+,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,+,+,-,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,-,-,+,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,-,+,-,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,+,-,-,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,-,-,-,6,1]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,+,+,6,1,4]=>[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,-,+,6,1,4]=>[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,+,-,6,1,4]=>[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,-,-,6,1,4]=>[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,+,+,6,4,1]=>[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[5,-,+,6,4,1]=>[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[5,+,-,6,4,1]=>[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[5,-,-,6,4,1]=>[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[5,+,4,1,6,3]=>[5,2,4,1,6,3]=>[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,-,4,1,6,3]=>[5,2,4,1,6,3]=>[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,+,4,3,6,1]=>[5,2,4,3,6,1]=>[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,-,4,3,6,1]=>[5,2,4,3,6,1]=>[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,+,4,6,1,3]=>[5,2,4,6,1,3]=>[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[5,-,4,6,1,3]=>[5,2,4,6,1,3]=>[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[5,+,4,6,3,1]=>[5,2,4,6,3,1]=>[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[5,-,4,6,3,1]=>[5,2,4,6,3,1]=>[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[5,+,6,1,3,4]=>[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,-,6,1,3,4]=>[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,+,6,1,4,3]=>[5,2,6,1,4,3]=>[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[5,-,6,1,4,3]=>[5,2,6,1,4,3]=>[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[5,+,6,3,1,4]=>[5,2,6,3,1,4]=>[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,-,6,3,1,4]=>[5,2,6,3,1,4]=>[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,+,6,3,4,1]=>[5,2,6,3,4,1]=>[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[5,-,6,3,4,1]=>[5,2,6,3,4,1]=>[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[5,+,6,+,1,3]=>[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[5,-,6,+,1,3]=>[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[5,+,6,-,1,3]=>[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[5,-,6,-,1,3]=>[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[5,+,6,+,3,1]=>[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[5,-,6,+,3,1]=>[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[5,+,6,-,3,1]=>[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[5,-,6,-,3,1]=>[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[5,3,1,2,6,4]=>[5,3,1,2,6,4]=>[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,3,1,+,6,2]=>[5,3,1,4,6,2]=>[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,3,1,-,6,2]=>[5,3,1,4,6,2]=>[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,3,1,6,2,4]=>[5,3,1,6,2,4]=>[4,2,6,1,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,3,1,6,4,2]=>[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[5,3,2,1,6,4]=>[5,3,2,1,6,4]=>[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,3,2,+,6,1]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,3,2,-,6,1]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[5,3,2,6,4,1]=>[5,3,2,6,4,1]=>[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[5,3,4,1,6,2]=>[5,3,4,1,6,2]=>[2,6,1,4,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,3,4,2,6,1]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,3,4,6,1,2]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[5,3,4,6,2,1]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[5,3,6,1,2,4]=>[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,3,6,1,4,2]=>[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[5,3,6,2,1,4]=>[5,3,6,2,1,4]=>[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[5,3,6,2,4,1]=>[5,3,6,2,4,1]=>[1,4,2,6,3,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[5,3,6,+,1,2]=>[5,3,6,4,1,2]=>[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[5,3,6,-,1,2]=>[5,3,6,4,1,2]=>[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[5,3,6,+,2,1]=>[5,3,6,4,2,1]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[5,3,6,-,2,1]=>[5,3,6,4,2,1]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[5,4,1,2,6,3]=>[5,4,1,2,6,3]=>[3,6,2,1,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,4,1,3,6,2]=>[5,4,1,3,6,2]=>[2,6,3,1,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,4,1,6,2,3]=>[5,4,1,6,2,3]=>[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[5,4,1,6,3,2]=>[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[5,4,2,1,6,3]=>[5,4,2,1,6,3]=>[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[5,4,2,3,6,1]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,4,2,6,1,3]=>[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[5,4,2,6,3,1]=>[5,4,2,6,3,1]=>[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[5,4,+,1,6,2]=>[5,4,3,1,6,2]=>[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,4,-,1,6,2]=>[5,4,3,1,6,2]=>[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[5,4,+,2,6,1]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,4,-,2,6,1]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[5,4,+,6,1,2]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[5,4,-,6,1,2]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[5,4,+,6,2,1]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[5,4,-,6,2,1]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[5,4,6,1,2,3]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[5,4,6,1,3,2]=>[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[5,4,6,2,3,1]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>2
[5,4,6,3,1,2]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[5,6,1,2,3,4]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,1,2,4,3]=>[5,6,1,2,4,3]=>[3,4,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[5,6,1,3,2,4]=>[5,6,1,3,2,4]=>[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,1,3,4,2]=>[5,6,1,3,4,2]=>[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>2
[5,6,1,+,2,3]=>[5,6,1,4,2,3]=>[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[5,6,1,-,2,3]=>[5,6,1,4,2,3]=>[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[5,6,1,+,3,2]=>[5,6,1,4,3,2]=>[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[5,6,1,-,3,2]=>[5,6,1,4,3,2]=>[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[5,6,2,1,3,4]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,2,1,4,3]=>[5,6,2,1,4,3]=>[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[5,6,2,3,1,4]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,2,3,4,1]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[5,6,2,+,1,3]=>[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[5,6,2,-,1,3]=>[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[5,6,2,+,3,1]=>[5,6,2,4,3,1]=>[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[5,6,2,-,3,1]=>[5,6,2,4,3,1]=>[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[5,6,+,1,2,4]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,-,1,2,4]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,+,1,4,2]=>[5,6,3,1,4,2]=>[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>2
[5,6,-,1,4,2]=>[5,6,3,1,4,2]=>[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>2
[5,6,+,2,1,4]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,-,2,1,4]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,6,+,2,4,1]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[5,6,-,2,4,1]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[5,6,+,+,1,2]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[5,6,-,+,1,2]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[5,6,+,-,1,2]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[5,6,-,-,1,2]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[5,6,+,+,2,1]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>3
[5,6,-,+,2,1]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>3
[5,6,+,-,2,1]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>3
[5,6,-,-,2,1]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>3
[5,6,4,1,2,3]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[5,6,4,1,3,2]=>[5,6,4,1,3,2]=>[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[5,6,4,2,1,3]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[5,6,4,2,3,1]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>3
[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,2,3,+,4]=>[6,1,2,3,5,4]=>[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,2,3,-,4]=>[6,1,2,3,5,4]=>[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,2,+,3,5]=>[6,1,2,4,3,5]=>[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,2,-,3,5]=>[6,1,2,4,3,5]=>[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,2,+,+,3]=>[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,1,2,-,+,3]=>[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,1,2,+,-,3]=>[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,1,2,-,-,3]=>[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,1,2,5,3,4]=>[6,1,2,5,3,4]=>[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,1,2,5,4,3]=>[6,1,2,5,4,3]=>[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[6,1,+,2,4,5]=>[6,1,3,2,4,5]=>[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,-,2,4,5]=>[6,1,3,2,4,5]=>[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,+,2,+,4]=>[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,-,2,+,4]=>[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,+,2,-,4]=>[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,-,2,-,4]=>[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,+,+,2,5]=>[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,-,+,2,5]=>[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,+,-,2,5]=>[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,-,-,2,5]=>[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,+,+,+,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,-,+,+,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,+,-,+,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,+,+,-,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,-,-,+,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,-,+,-,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,+,-,-,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,-,-,-,2]=>[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,+,5,2,4]=>[6,1,3,5,2,4]=>[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,1,-,5,2,4]=>[6,1,3,5,2,4]=>[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,1,+,5,4,2]=>[6,1,3,5,4,2]=>[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>1
[6,1,-,5,4,2]=>[6,1,3,5,4,2]=>[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>1
[6,1,4,2,3,5]=>[6,1,4,2,3,5]=>[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,4,2,+,3]=>[6,1,4,2,5,3]=>[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,1,4,2,-,3]=>[6,1,4,2,5,3]=>[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,1,4,3,2,5]=>[6,1,4,3,2,5]=>[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,1,4,3,+,2]=>[6,1,4,3,5,2]=>[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,4,3,-,2]=>[6,1,4,3,5,2]=>[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,1,4,5,2,3]=>[6,1,4,5,2,3]=>[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[6,1,4,5,3,2]=>[6,1,4,5,3,2]=>[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[6,1,5,2,3,4]=>[6,1,5,2,3,4]=>[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,1,5,2,4,3]=>[6,1,5,2,4,3]=>[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[6,1,5,3,2,4]=>[6,1,5,3,2,4]=>[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,1,5,3,4,2]=>[6,1,5,3,4,2]=>[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[6,1,5,+,2,3]=>[6,1,5,4,2,3]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[6,1,5,-,2,3]=>[6,1,5,4,2,3]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[6,1,5,+,3,2]=>[6,1,5,4,3,2]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[6,1,5,-,3,2]=>[6,1,5,4,3,2]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[6,+,1,3,4,5]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,1,3,4,5]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,1,3,+,4]=>[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,-,1,3,+,4]=>[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,+,1,3,-,4]=>[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,-,1,3,-,4]=>[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,+,1,+,3,5]=>[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,1,+,3,5]=>[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,1,-,3,5]=>[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,1,-,3,5]=>[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,1,+,+,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,-,1,+,+,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,+,1,-,+,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,+,1,+,-,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,-,1,-,+,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,-,1,+,-,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,+,1,-,-,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,-,1,-,-,3]=>[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,+,1,5,3,4]=>[6,2,1,5,3,4]=>[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,-,1,5,3,4]=>[6,2,1,5,3,4]=>[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,+,1,5,4,3]=>[6,2,1,5,4,3]=>[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[6,-,1,5,4,3]=>[6,2,1,5,4,3]=>[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[6,+,+,1,4,5]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,+,1,4,5]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,-,1,4,5]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,-,1,4,5]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,+,1,+,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,-,+,1,+,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,+,-,1,+,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,+,+,1,-,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,-,-,1,+,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,-,+,1,-,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,+,-,1,-,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,-,-,1,-,4]=>[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,+,+,+,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,+,+,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,-,+,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,+,-,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,-,+,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,+,-,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,-,-,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,-,-,1,5]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,+,+,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,+,+,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,-,+,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,+,-,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,+,+,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,-,+,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,+,-,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,+,+,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,-,-,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,-,+,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,+,-,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,-,-,+,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,-,+,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,+,-,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,-,-,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,-,-,-,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,+,5,1,4]=>[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,-,+,5,1,4]=>[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,+,-,5,1,4]=>[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,-,-,5,1,4]=>[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,+,+,5,4,1]=>[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[6,-,+,5,4,1]=>[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[6,+,-,5,4,1]=>[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[6,-,-,5,4,1]=>[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[6,+,4,1,3,5]=>[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,4,1,3,5]=>[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,4,1,+,3]=>[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,-,4,1,+,3]=>[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,+,4,1,-,3]=>[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,-,4,1,-,3]=>[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,+,4,3,1,5]=>[6,2,4,3,1,5]=>[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,-,4,3,1,5]=>[6,2,4,3,1,5]=>[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,+,4,3,+,1]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,4,3,+,1]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,4,3,-,1]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,-,4,3,-,1]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,+,4,5,1,3]=>[6,2,4,5,1,3]=>[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[6,-,4,5,1,3]=>[6,2,4,5,1,3]=>[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[6,+,4,5,3,1]=>[6,2,4,5,3,1]=>[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[6,-,4,5,3,1]=>[6,2,4,5,3,1]=>[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[6,+,5,1,3,4]=>[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,-,5,1,3,4]=>[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,+,5,1,4,3]=>[6,2,5,1,4,3]=>[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[6,-,5,1,4,3]=>[6,2,5,1,4,3]=>[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[6,+,5,3,1,4]=>[6,2,5,3,1,4]=>[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,-,5,3,1,4]=>[6,2,5,3,1,4]=>[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,+,5,3,4,1]=>[6,2,5,3,4,1]=>[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[6,-,5,3,4,1]=>[6,2,5,3,4,1]=>[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[6,+,5,+,1,3]=>[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[6,-,5,+,1,3]=>[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[6,+,5,-,1,3]=>[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[6,-,5,-,1,3]=>[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[6,+,5,+,3,1]=>[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[6,-,5,+,3,1]=>[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[6,+,5,-,3,1]=>[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[6,-,5,-,3,1]=>[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,4,5]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,1,2,+,4]=>[6,3,1,2,5,4]=>[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,3,1,2,-,4]=>[6,3,1,2,5,4]=>[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,3,1,+,2,5]=>[6,3,1,4,2,5]=>[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,1,-,2,5]=>[6,3,1,4,2,5]=>[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,1,+,+,2]=>[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,3,1,-,+,2]=>[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,3,1,+,-,2]=>[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,3,1,-,-,2]=>[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,3,1,5,2,4]=>[6,3,1,5,2,4]=>[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,3,1,5,4,2]=>[6,3,1,5,4,2]=>[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>1
[6,3,2,1,4,5]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,2,1,+,4]=>[6,3,2,1,5,4]=>[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,3,2,1,-,4]=>[6,3,2,1,5,4]=>[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,3,2,+,1,5]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,2,-,1,5]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,2,+,+,1]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,3,2,-,+,1]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,3,2,+,-,1]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,3,2,-,-,1]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,3,2,5,1,4]=>[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[6,3,4,1,2,5]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,4,1,+,2]=>[6,3,4,1,5,2]=>[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,3,4,1,-,2]=>[6,3,4,1,5,2]=>[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,3,4,2,1,5]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,3,4,2,+,1]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,3,4,2,-,1]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,3,4,5,1,2]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>2
[6,3,4,5,2,1]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[6,3,5,1,2,4]=>[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,3,5,1,4,2]=>[6,3,5,1,4,2]=>[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[6,3,5,2,1,4]=>[6,3,5,2,1,4]=>[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[6,3,5,2,4,1]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[6,3,5,+,1,2]=>[6,3,5,4,1,2]=>[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[6,3,5,-,1,2]=>[6,3,5,4,1,2]=>[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[6,3,5,+,2,1]=>[6,3,5,4,2,1]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[6,3,5,-,2,1]=>[6,3,5,4,2,1]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[6,4,1,2,3,5]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,1,2,+,3]=>[6,4,1,2,5,3]=>[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,4,1,2,-,3]=>[6,4,1,2,5,3]=>[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,4,1,3,2,5]=>[6,4,1,3,2,5]=>[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,1,3,+,2]=>[6,4,1,3,5,2]=>[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,4,1,3,-,2]=>[6,4,1,3,5,2]=>[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,4,1,5,2,3]=>[6,4,1,5,2,3]=>[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[6,4,1,5,3,2]=>[6,4,1,5,3,2]=>[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[6,4,2,1,3,5]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,2,1,+,3]=>[6,4,2,1,5,3]=>[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,4,2,1,-,3]=>[6,4,2,1,5,3]=>[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[6,4,2,3,1,5]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,2,3,+,1]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,4,2,3,-,1]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,4,2,5,1,3]=>[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[6,4,2,5,3,1]=>[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[6,4,+,1,2,5]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,-,1,2,5]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,+,1,+,2]=>[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,4,-,1,+,2]=>[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,4,+,1,-,2]=>[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,4,-,1,-,2]=>[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[6,4,+,2,1,5]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,-,2,1,5]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[6,4,+,2,+,1]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,4,-,2,+,1]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,4,+,2,-,1]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,4,-,2,-,1]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[6,4,+,5,1,2]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>2
[6,4,-,5,1,2]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>2
[6,4,+,5,2,1]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[6,4,-,5,2,1]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[6,4,5,1,2,3]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>2
[6,4,5,1,3,2]=>[6,4,5,1,3,2]=>[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[6,4,5,2,1,3]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>2
[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>3
[6,4,5,3,1,2]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>3
[6,4,5,3,2,1]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>4
[6,5,1,2,3,4]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,1,2,4,3]=>[6,5,1,2,4,3]=>[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[6,5,1,3,2,4]=>[6,5,1,3,2,4]=>[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,1,3,4,2]=>[6,5,1,3,4,2]=>[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[6,5,1,+,2,3]=>[6,5,1,4,2,3]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[6,5,1,-,2,3]=>[6,5,1,4,2,3]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[6,5,1,+,3,2]=>[6,5,1,4,3,2]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[6,5,1,-,3,2]=>[6,5,1,4,3,2]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[6,5,2,1,3,4]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,2,1,4,3]=>[6,5,2,1,4,3]=>[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[6,5,2,3,1,4]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,2,3,4,1]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>3
[6,5,2,+,1,3]=>[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[6,5,2,-,1,3]=>[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[6,5,2,+,3,1]=>[6,5,2,4,3,1]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>4
[6,5,2,-,3,1]=>[6,5,2,4,3,1]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>4
[6,5,+,1,2,4]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,-,1,2,4]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,+,1,4,2]=>[6,5,3,1,4,2]=>[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[6,5,-,1,4,2]=>[6,5,3,1,4,2]=>[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[6,5,+,2,1,4]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,-,2,1,4]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[6,5,+,2,4,1]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>3
[6,5,-,2,4,1]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>3
[6,5,+,+,1,2]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[6,5,-,+,1,2]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[6,5,+,-,1,2]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[6,5,-,-,1,2]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[6,5,+,+,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>4
[6,5,-,+,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>4
[6,5,+,-,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>4
[6,5,-,-,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>4
[6,5,4,1,2,3]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[6,5,4,1,3,2]=>[6,5,4,1,3,2]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[6,5,4,2,1,3]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[6,5,4,2,3,1]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>4
[6,5,4,3,1,2]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>4
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>5
search for individual values
searching the database for the individual values of this statistic
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
permutation
Description
The underlying permutation of the decorated permutation.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!