Identifier
-
Mp00255:
Decorated permutations
—lower permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤ (values match St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.)
Values
=>
Cc0005;cc-rep
[-,+]=>[2,1]=>[1,2]=>[1,0,1,0]=>2
[-,+,+]=>[2,3,1]=>[2,1,3]=>[1,1,0,0,1,0]=>2
[-,-,+]=>[3,1,2]=>[1,3,2]=>[1,0,1,1,0,0]=>2
[-,+,-]=>[2,1,3]=>[2,3,1]=>[1,1,0,1,0,0]=>2
[-,3,2]=>[2,1,3]=>[2,3,1]=>[1,1,0,1,0,0]=>2
[3,+,1]=>[2,1,3]=>[2,3,1]=>[1,1,0,1,0,0]=>2
[-,+,+,+]=>[2,3,4,1]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>2
[-,-,+,+]=>[3,4,1,2]=>[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>2
[-,+,-,+]=>[2,4,1,3]=>[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>2
[-,+,+,-]=>[2,3,1,4]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>2
[-,-,-,+]=>[4,1,2,3]=>[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>2
[-,-,+,-]=>[3,1,2,4]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>2
[-,+,-,-]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[-,+,4,3]=>[2,3,1,4]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>2
[-,-,4,3]=>[3,1,2,4]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>2
[-,3,2,+]=>[2,4,1,3]=>[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>2
[-,3,2,-]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[-,3,4,2]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[-,4,2,3]=>[2,3,1,4]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>2
[-,4,+,2]=>[3,2,1,4]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>3
[-,4,-,2]=>[2,1,4,3]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>2
[2,4,+,1]=>[3,1,2,4]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>2
[3,+,1,+]=>[2,1,4,3]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>2
[3,+,1,-]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[3,+,4,1]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[3,4,2,1]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[4,+,1,3]=>[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>2
[4,+,+,1]=>[2,3,1,4]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>2
[4,-,+,1]=>[3,1,4,2]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>2
[4,+,-,1]=>[2,1,4,3]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>2
[4,3,2,1]=>[2,1,4,3]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>2
[-,+,+,+,+]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>2
[-,-,+,+,+]=>[3,4,5,1,2]=>[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>2
[-,+,-,+,+]=>[2,4,5,1,3]=>[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,+,+,-,+]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,+,+,+,-]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,-,-,+,+]=>[4,5,1,2,3]=>[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>2
[-,-,+,-,+]=>[3,5,1,2,4]=>[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>2
[-,-,+,+,-]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>2
[-,+,-,-,+]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,+,-,+,-]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,+,+,-,-]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,-,-,-,+]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>2
[-,-,-,+,-]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>2
[-,-,+,-,-]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[-,+,-,-,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,+,+,5,4]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,-,+,5,4]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>2
[-,+,-,5,4]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,-,-,5,4]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>2
[-,+,4,3,+]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,-,4,3,+]=>[3,5,1,2,4]=>[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>2
[-,+,4,3,-]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,-,4,3,-]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[-,+,4,5,3]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,-,4,5,3]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[-,+,5,3,4]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,-,5,3,4]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>2
[-,+,5,+,3]=>[2,4,3,1,5]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,-,5,+,3]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>3
[-,+,5,-,3]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,-,5,-,3]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[-,3,2,+,+]=>[2,4,5,1,3]=>[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,3,2,-,+]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,3,2,+,-]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,3,2,-,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,3,2,5,4]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,3,4,2,+]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,3,4,2,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,3,4,5,2]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,3,5,2,4]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,3,5,+,2]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>3
[-,3,5,-,2]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,4,2,3,+]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,4,2,3,-]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,4,2,5,3]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,4,+,2,+]=>[3,2,5,1,4]=>[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>3
[-,4,-,2,+]=>[2,5,1,4,3]=>[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,4,+,2,-]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>3
[-,4,-,2,-]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,4,+,5,2]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>3
[-,4,-,5,2]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,4,5,2,3]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,4,5,3,2]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>3
[-,5,2,3,4]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,5,2,+,3]=>[2,4,3,1,5]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[-,5,2,-,3]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,5,+,2,4]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>3
[-,5,-,2,4]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,5,+,+,2]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>3
[-,5,-,+,2]=>[4,2,1,5,3]=>[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>3
[-,5,+,-,2]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>3
[-,5,-,-,2]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,5,4,2,3]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[-,5,4,3,2]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>3
[2,3,5,+,1]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>2
[2,4,+,1,+]=>[3,1,5,2,4]=>[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[2,4,+,1,-]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[2,4,+,5,1]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[2,4,5,3,1]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[2,5,+,1,4]=>[3,1,4,2,5]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[2,5,+,+,1]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>2
[2,5,-,+,1]=>[4,1,2,5,3]=>[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]=>2
[2,5,+,-,1]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[2,5,4,3,1]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[3,+,1,+,+]=>[2,1,4,5,3]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,1,-,+]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,1,+,-]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,1,-,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,1,5,4]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,4,1,+]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,4,1,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,4,5,1]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,5,1,4]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,+,5,+,1]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[3,-,5,+,1]=>[4,1,3,2,5]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>2
[3,+,5,-,1]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,4,2,1,+]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,4,2,1,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,4,2,5,1]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,4,5,2,1]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,5,2,1,4]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,5,2,+,1]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[3,5,2,-,1]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[3,5,4,2,1]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,1,3,+]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,1,3,-]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,1,5,3]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,+,1,+]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,-,+,1,+]=>[3,1,5,4,2]=>[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>2
[4,+,-,1,+]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,+,1,-]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,-,+,1,-]=>[3,1,4,2,5]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[4,+,-,1,-]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,+,5,1]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,-,+,5,1]=>[3,1,4,2,5]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[4,+,-,5,1]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,5,1,3]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,+,5,3,1]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,-,5,3,1]=>[3,1,4,2,5]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[4,3,2,1,+]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,3,2,1,-]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,3,2,5,1]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,3,5,2,1]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,5,2,1,3]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[4,5,2,3,1]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,5,+,1,2]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>2
[4,5,+,2,1]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>3
[4,5,-,2,1]=>[2,1,4,5,3]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,1,3,4]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,1,+,3]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,1,-,3]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,+,1,4]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[5,-,+,1,4]=>[3,1,4,5,2]=>[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]=>2
[5,+,-,1,4]=>[2,1,4,5,3]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,+,+,1]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>2
[5,-,+,+,1]=>[3,4,1,5,2]=>[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>2
[5,+,-,+,1]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>2
[5,+,+,-,1]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[5,-,-,+,1]=>[4,1,5,2,3]=>[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]=>2
[5,-,+,-,1]=>[3,1,5,2,4]=>[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[5,+,-,-,1]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,4,1,3]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,+,4,3,1]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[5,-,4,3,1]=>[3,1,5,2,4]=>[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[5,3,2,1,4]=>[2,1,4,5,3]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,3,2,+,1]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>2
[5,3,2,-,1]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,3,4,2,1]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,4,2,1,3]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>2
[5,4,2,3,1]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[5,4,+,1,2]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>2
[5,4,+,2,1]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>3
[5,4,-,2,1]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>2
[-,+,+,+,+,+]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>2
[-,-,+,+,+,+]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,+,-,+,+,+]=>[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,+,+,-,+,+]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,+,+,+,-,+]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,+,+,+,+,-]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,-,+,+,+]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>2
[-,-,+,-,+,+]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,-,+,+,-,+]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,-,+,+,+,-]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,-,-,+,+]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,-,+,-,+]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,-,+,+,-]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,+,-,-,+]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,+,-,+,-]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,+,+,-,-]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,-,-,+,+]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[-,-,-,+,-,+]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[-,-,-,+,+,-]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[-,-,+,-,-,+]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,-,+,-,+,-]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,-,+,+,-,-]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,-,-,-,+]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,+,-,-,+,-]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,+,-,+,-,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,+,+,-,-,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,-,-,-,+]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>2
[-,-,-,-,+,-]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[-,-,-,+,-,-]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[-,-,+,-,-,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,-,-,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,+,+,+,6,5]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,+,+,6,5]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,-,+,6,5]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,+,-,6,5]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,-,+,6,5]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[-,-,+,-,6,5]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,-,-,6,5]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,-,-,6,5]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[-,+,+,5,4,+]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,+,5,4,+]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,-,5,4,+]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,+,5,4,-]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,-,5,4,+]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[-,-,+,5,4,-]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,-,5,4,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,-,5,4,-]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[-,+,+,5,6,4]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,+,5,6,4]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,-,5,6,4]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,-,5,6,4]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[-,+,+,6,4,5]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,+,6,4,5]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,-,6,4,5]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,-,6,4,5]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[-,+,+,6,+,4]=>[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,+,6,+,4]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,-,6,+,4]=>[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,+,6,-,4]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,-,6,+,4]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>3
[-,-,+,6,-,4]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,-,6,-,4]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,-,6,-,4]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[-,+,4,3,+,+]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,4,3,+,+]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,4,3,-,+]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,4,3,+,-]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,4,3,-,+]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,-,4,3,+,-]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,4,3,-,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,4,3,-,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,4,3,6,5]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,4,3,6,5]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,4,5,3,+]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,4,5,3,+]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,4,5,3,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,4,5,3,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,4,5,6,3]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,4,5,6,3]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,4,6,3,5]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,4,6,3,5]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,4,6,+,3]=>[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,4,6,+,3]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[-,+,4,6,-,3]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,4,6,-,3]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,5,3,4,+]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,5,3,4,+]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,5,3,4,-]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,5,3,4,-]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,5,3,6,4]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,5,3,6,4]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,5,+,3,+]=>[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,5,+,3,+]=>[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[-,+,5,-,3,+]=>[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,5,+,3,-]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,5,-,3,+]=>[3,6,1,2,5,4]=>[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,-,5,+,3,-]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[-,+,5,-,3,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,5,-,3,-]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,5,+,6,3]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,5,+,6,3]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[-,+,5,-,6,3]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,5,-,6,3]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,5,6,3,4]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,5,6,3,4]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,5,6,4,3]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,5,6,4,3]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[-,+,6,3,4,5]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,6,3,4,5]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,6,3,+,4]=>[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,6,3,+,4]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[-,+,6,3,-,4]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,6,3,-,4]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,6,+,3,5]=>[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,6,+,3,5]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[-,+,6,-,3,5]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,6,-,3,5]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,6,+,+,3]=>[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,-,6,+,+,3]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[-,+,6,-,+,3]=>[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,+,6,+,-,3]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,6,-,+,3]=>[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[-,-,6,+,-,3]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[-,+,6,-,-,3]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,-,6,-,-,3]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[-,+,6,5,3,4]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,6,5,3,4]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[-,+,6,5,4,3]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,-,6,5,4,3]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[-,3,2,+,+,+]=>[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,3,2,-,+,+]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,+,-,+]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,+,+,-]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,-,-,+]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,2,-,+,-]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,2,+,-,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,2,-,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,2,+,6,5]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,-,6,5]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,2,5,4,+]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,5,4,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,2,5,6,4]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,2,6,4,5]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,6,+,4]=>[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,2,6,-,4]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,4,2,+,+]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,4,2,-,+]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,4,2,+,-]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,4,2,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,4,2,6,5]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,4,5,2,+]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,4,5,2,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,4,5,6,2]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,4,6,2,5]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,4,6,+,2]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[-,3,4,6,-,2]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,5,2,4,+]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,5,2,4,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,5,2,6,4]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,5,+,2,+]=>[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[-,3,5,-,2,+]=>[2,6,1,3,5,4]=>[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,5,+,2,-]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,3,5,-,2,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,5,+,6,2]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,3,5,-,6,2]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,5,6,2,4]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,5,6,4,2]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,3,6,2,4,5]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,6,2,+,4]=>[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,3,6,2,-,4]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,6,+,2,5]=>[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[-,3,6,-,2,5]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,6,+,+,2]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[-,3,6,-,+,2]=>[5,2,1,3,6,4]=>[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[-,3,6,+,-,2]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,3,6,-,-,2]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,3,6,5,2,4]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,3,6,5,4,2]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,4,2,3,+,+]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,4,2,3,-,+]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,2,3,+,-]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,2,3,-,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,2,3,6,5]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,2,5,3,+]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,2,5,3,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,2,5,6,3]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,2,6,3,5]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,2,6,+,3]=>[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,2,6,-,3]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,+,2,+,+]=>[3,2,5,6,1,4]=>[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[-,4,-,2,+,+]=>[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,+,2,-,+]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,+,2,+,-]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,-,2,-,+]=>[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,-,2,+,-]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,+,2,-,-]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,-,2,-,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,4,+,2,6,5]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,-,2,6,5]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,+,5,2,+]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,-,5,2,+]=>[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,+,5,2,-]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,-,5,2,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,4,+,5,6,2]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,-,5,6,2]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,4,+,6,2,5]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,-,6,2,5]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,+,6,+,2]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,4,-,6,+,2]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[-,4,+,6,-,2]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,-,6,-,2]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,4,5,2,3,+]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,5,2,3,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,5,2,6,3]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,5,3,2,+]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,5,3,2,-]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,5,3,6,2]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,5,6,2,3]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,5,6,3,2]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,6,2,3,5]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,6,2,+,3]=>[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,4,6,2,-,3]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,6,3,2,5]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,4,6,3,+,2]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,4,6,3,-,2]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,4,6,5,2,3]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,4,6,5,3,2]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,5,2,3,4,+]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,5,2,3,4,-]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,2,3,6,4]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,2,+,3,+]=>[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,5,2,-,3,+]=>[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,2,+,3,-]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,2,-,3,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,2,+,6,3]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,2,-,6,3]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,2,6,3,4]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,2,6,4,3]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,+,2,4,+]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[-,5,-,2,4,+]=>[2,4,6,1,5,3]=>[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,+,2,4,-]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,5,-,2,4,-]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,+,2,6,4]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,5,-,2,6,4]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,+,+,2,+]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>3
[-,5,-,+,2,+]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[-,5,+,-,2,+]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,5,+,+,2,-]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,5,-,-,2,+]=>[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,-,+,2,-]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,5,+,-,2,-]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,5,-,-,2,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,5,+,+,6,2]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,5,-,+,6,2]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,5,+,-,6,2]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,5,-,-,6,2]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,5,+,6,2,4]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,5,-,6,2,4]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,+,6,4,2]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,5,-,6,4,2]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,5,4,2,3,+]=>[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,4,2,3,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,4,2,6,3]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,4,3,2,+]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,5,4,3,2,-]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,5,4,3,6,2]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,5,4,6,2,3]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,4,6,3,2]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,5,6,2,3,4]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,6,2,4,3]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,5,6,3,2,4]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,5,6,3,4,2]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,5,6,+,2,3]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[-,5,6,-,2,3]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,5,6,+,3,2]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[-,5,6,-,3,2]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,6,2,3,4,5]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,6,2,3,+,4]=>[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,6,2,3,-,4]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,2,+,3,5]=>[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,6,2,-,3,5]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,2,+,+,3]=>[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[-,6,2,-,+,3]=>[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,2,+,-,3]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,2,-,-,3]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,2,5,3,4]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,2,5,4,3]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,+,2,4,5]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[-,6,-,2,4,5]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,+,2,+,4]=>[3,2,5,4,1,6]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[-,6,-,2,+,4]=>[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,+,2,-,4]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,6,-,2,-,4]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,+,+,2,5]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>3
[-,6,-,+,2,5]=>[4,2,5,1,6,3]=>[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[-,6,+,-,2,5]=>[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,6,-,-,2,5]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,+,+,+,2]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>3
[-,6,-,+,+,2]=>[4,5,2,1,6,3]=>[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[-,6,+,-,+,2]=>[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,6,+,+,-,2]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,6,-,-,+,2]=>[5,2,1,6,3,4]=>[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[-,6,-,+,-,2]=>[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,6,+,-,-,2]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,6,-,-,-,2]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[-,6,+,5,2,4]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,6,-,5,2,4]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,+,5,4,2]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,6,-,5,4,2]=>[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[-,6,4,2,3,5]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,4,2,+,3]=>[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,4,2,-,3]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,4,3,2,5]=>[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,6,4,3,+,2]=>[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,6,4,3,-,2]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,6,4,5,2,3]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,4,5,3,2]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[-,6,5,2,3,4]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,5,2,4,3]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[-,6,5,3,2,4]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[-,6,5,3,4,2]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[-,6,5,+,2,3]=>[4,2,3,1,6,5]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[-,6,5,-,2,3]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[-,6,5,+,3,2]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[-,6,5,-,3,2]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[2,3,4,6,+,1]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[2,3,5,+,1,+]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,3,5,+,1,-]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,3,5,+,6,1]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,3,5,6,4,1]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,3,6,+,1,5]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,3,6,+,+,1]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[2,3,6,-,+,1]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[2,3,6,+,-,1]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,3,6,5,4,1]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,4,+,1,+,+]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,1,-,+]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,1,+,-]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,1,-,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,1,6,5]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,5,1,+]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,5,1,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,5,6,1]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,6,1,5]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,+,6,+,1]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,4,-,6,+,1]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[2,4,+,6,-,1]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,5,3,1,+]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,5,3,1,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,5,3,6,1]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,5,6,3,1]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,6,3,1,5]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,6,3,+,1]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,4,6,3,-,1]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,4,6,5,3,1]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,1,4,+]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,1,4,-]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,1,6,4]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,+,1,+]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,5,-,+,1,+]=>[4,1,6,2,5,3]=>[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,5,+,-,1,+]=>[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,+,1,-]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,5,-,+,1,-]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,5,+,-,1,-]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,+,6,1]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,5,-,+,6,1]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,5,+,-,6,1]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,6,1,4]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,+,6,4,1]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,5,-,6,4,1]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,5,4,3,1,+]=>[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,4,3,1,-]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,4,3,6,1]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,4,6,3,1]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,6,3,1,4]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,5,6,3,4,1]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,5,6,+,1,3]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,5,6,+,3,1]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[2,5,6,-,3,1]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,1,4,5]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,1,+,4]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,1,-,4]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,+,1,5]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,6,-,+,1,5]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,6,+,-,1,5]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,+,+,1]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[2,6,-,+,+,1]=>[4,5,1,2,6,3]=>[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[2,6,+,-,+,1]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,6,+,+,-,1]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,6,-,-,+,1]=>[5,1,2,6,3,4]=>[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[2,6,-,+,-,1]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,6,+,-,-,1]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,5,1,4]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,+,5,4,1]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,6,-,5,4,1]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,6,4,3,1,5]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,4,3,+,1]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,6,4,3,-,1]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,4,5,3,1]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,5,3,1,4]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[2,6,5,3,4,1]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[2,6,5,+,1,3]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[2,6,5,+,3,1]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[2,6,5,-,3,1]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[3,+,1,+,+,+]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,-,+,+]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,+,-,+]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,+,+,-]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,-,-,+]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,-,+,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,+,-,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,-,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,+,6,5]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,-,6,5]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,5,4,+]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,5,4,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,5,6,4]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,6,4,5]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,6,+,4]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,1,6,-,4]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,1,+,+]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,1,-,+]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,1,+,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,1,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,1,6,5]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,5,1,+]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,5,1,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,5,6,1]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,6,1,5]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,4,6,+,1]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,4,6,+,1]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[3,+,4,6,-,1]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,1,4,+]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,1,4,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,1,6,4]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,+,1,+]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,5,+,1,+]=>[4,1,6,3,2,5]=>[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,+,5,-,1,+]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,+,1,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,5,+,1,-]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,+,5,-,1,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,+,6,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,5,+,6,1]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,+,5,-,6,1]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,6,1,4]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,5,6,4,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,5,6,4,1]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,+,6,1,4,5]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,6,1,+,4]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,6,1,-,4]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,6,+,1,5]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,6,+,1,5]=>[4,1,5,3,2,6]=>[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,+,6,-,1,5]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,6,+,+,1]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[3,-,6,+,+,1]=>[4,5,1,3,2,6]=>[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,+,6,-,+,1]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,+,6,+,-,1]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,6,-,+,1]=>[5,1,3,2,6,4]=>[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[3,-,6,+,-,1]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,+,6,-,-,1]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,6,5,1,4]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,+,6,5,4,1]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,-,6,5,4,1]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,4,2,1,+,+]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,1,-,+]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,1,+,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,1,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,1,6,5]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,5,1,+]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,5,1,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,5,6,1]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,6,1,5]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,2,6,+,1]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,4,2,6,-,1]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,5,2,1,+]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,5,2,1,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,5,2,6,1]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,5,6,2,1]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,6,2,1,5]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,6,2,+,1]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,4,6,2,-,1]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,4,6,5,2,1]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,1,4,+]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,1,4,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,1,6,4]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,+,1,+]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,5,2,-,1,+]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,+,1,-]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,5,2,-,1,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,+,6,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,5,2,-,6,1]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,6,1,4]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,2,6,4,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,5,4,2,1,+]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,4,2,1,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,4,2,6,1]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,4,6,2,1]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,6,2,1,4]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,5,6,2,4,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,5,6,+,1,2]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,5,6,+,2,1]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[3,5,6,-,2,1]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,1,4,5]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,1,+,4]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,1,-,4]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,+,1,5]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,6,2,-,1,5]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,+,+,1]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[3,6,2,-,+,1]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,6,2,+,-,1]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,6,2,-,-,1]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,5,1,4]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,2,5,4,1]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,6,4,2,1,5]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,4,2,+,1]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,6,4,2,-,1]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,4,5,2,1]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,5,2,1,4]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[3,6,5,2,4,1]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[3,6,5,+,1,2]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[3,6,5,+,2,1]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[3,6,5,-,2,1]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,3,+,+]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,3,-,+]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,3,+,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,3,-,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,3,6,5]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,5,3,+]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,5,3,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,5,6,3]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,6,3,5]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,6,+,3]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,1,6,-,3]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,1,+,+]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,1,+,+]=>[3,1,5,6,4,2]=>[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,1,+,+]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,1,-,+]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,+,+,1,+,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,1,-,+]=>[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,-,+,1,+,-]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,1,-,+]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,-,1,+,-]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,1,-,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,1,-,-]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,1,-,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,1,6,5]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,1,6,5]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,1,6,5]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,5,1,+]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,5,1,+]=>[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,5,1,+]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,5,1,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,5,1,-]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,5,1,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,5,6,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,5,6,1]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,5,6,1]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,6,1,5]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,+,6,1,5]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,6,1,5]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,+,6,+,1]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[4,-,+,6,+,1]=>[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,+,-,6,+,1]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,+,+,6,-,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,-,6,+,1]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[4,-,+,6,-,1]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,-,6,-,1]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,5,1,3,+]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,5,1,3,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,5,1,6,3]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,5,3,1,+]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,5,3,1,+]=>[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,5,3,1,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,5,3,1,-]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,5,3,6,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,5,3,6,1]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,5,6,1,3]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,5,6,3,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,5,6,3,1]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,6,1,3,5]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,6,1,+,3]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,6,1,-,3]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,6,3,1,5]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,6,3,1,5]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,6,3,+,1]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[4,-,6,3,+,1]=>[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,+,6,3,-,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,6,3,-,1]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,+,6,5,1,3]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,+,6,5,3,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,-,6,5,3,1]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,3,2,1,+,+]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,1,-,+]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,1,+,-]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,1,-,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,1,6,5]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,5,1,+]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,5,1,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,5,6,1]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,6,1,5]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,2,6,+,1]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,3,2,6,-,1]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,5,2,1,+]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,5,2,1,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,5,2,6,1]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,5,6,2,1]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,6,2,1,5]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,6,2,+,1]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,3,6,2,-,1]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,3,6,5,2,1]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,2,1,3,+]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,2,1,3,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,2,1,6,3]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,2,3,1,+]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,5,2,3,1,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,5,2,3,6,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,5,2,6,1,3]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,2,6,3,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,5,+,1,2,+]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,5,+,1,2,-]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,5,+,1,6,2]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,5,+,2,1,+]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,5,-,2,1,+]=>[2,1,6,4,5,3]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,+,2,1,-]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,5,-,2,1,-]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,+,2,6,1]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,5,-,2,6,1]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,+,6,1,2]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,5,+,6,2,1]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,5,-,6,2,1]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,6,2,1,3]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,5,6,2,3,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,5,6,3,1,2]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,6,2,1,3,5]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,2,1,+,3]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,2,1,-,3]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,2,3,1,5]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,6,2,3,+,1]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[4,6,2,3,-,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,6,2,5,1,3]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,2,5,3,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,6,+,1,2,5]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,6,+,1,+,2]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,6,+,1,-,2]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,6,+,2,1,5]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,6,-,2,1,5]=>[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,+,2,+,1]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,6,-,2,+,1]=>[2,5,1,4,6,3]=>[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,6,+,2,-,1]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,6,-,2,-,1]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,+,5,1,2]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,6,+,5,2,1]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,6,-,5,2,1]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,5,2,1,3]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[4,6,5,2,3,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[4,6,5,3,2,1]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,+,1,3,4,+]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,3,4,-]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,3,6,4]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,+,3,+]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,-,3,+]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,+,3,-]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,-,3,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,+,6,3]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,-,6,3]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,6,3,4]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,1,6,4,3]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,1,4,+]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,+,1,4,+]=>[3,1,4,6,5,2]=>[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,-,1,4,+]=>[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,1,4,-]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,+,1,4,-]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,-,1,4,-]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,1,6,4]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,+,1,6,4]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,-,1,6,4]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,+,1,+]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,-,+,+,1,+]=>[3,4,1,6,5,2]=>[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[5,+,-,+,1,+]=>[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,+,+,-,1,+]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,+,+,+,1,-]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,-,-,+,1,+]=>[4,1,6,5,2,3]=>[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,-,+,-,1,+]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,-,+,+,1,-]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[5,+,-,-,1,+]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,-,+,1,-]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,+,+,-,1,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,-,+,1,-]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,-,+,-,1,-]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,-,-,1,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,+,6,1]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,-,+,+,6,1]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[5,+,-,+,6,1]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,+,+,-,6,1]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,-,+,6,1]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,-,+,-,6,1]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,-,-,6,1]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,6,1,4]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,+,6,1,4]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,-,6,1,4]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,+,6,4,1]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,-,+,6,4,1]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[5,+,-,6,4,1]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,-,6,4,1]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,+,4,1,3,+]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,4,1,3,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,4,1,6,3]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,4,3,1,+]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,4,3,1,+]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,4,3,1,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,4,3,1,-]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,4,3,6,1]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,4,3,6,1]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,4,6,1,3]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,4,6,3,1]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,4,6,3,1]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,6,1,3,4]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,6,1,4,3]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,6,3,1,4]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,6,3,1,4]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,+,6,3,4,1]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,-,6,3,4,1]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[5,+,6,+,1,3]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,6,+,1,3]=>[4,1,3,5,2,6]=>[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,+,6,-,1,3]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,+,6,+,3,1]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,-,6,+,3,1]=>[4,3,1,5,2,6]=>[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[5,+,6,-,3,1]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,-,6,-,3,1]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,3,2,1,4,+]=>[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,1,4,-]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,1,6,4]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,+,1,+]=>[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,2,-,1,+]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,+,1,-]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,2,-,1,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,+,6,1]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,2,-,6,1]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,6,1,4]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,2,6,4,1]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,4,2,1,+]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,4,2,1,-]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,4,2,6,1]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,4,6,2,1]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,6,2,1,4]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,6,+,1,2]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,3,6,+,2,1]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[5,3,6,-,2,1]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,2,1,3,+]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,2,1,3,-]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,2,1,6,3]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,2,3,1,+]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,2,3,1,-]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,2,3,6,1]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,2,6,1,3]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,2,6,3,1]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,+,1,2,+]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,4,+,1,2,-]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,4,+,1,6,2]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,4,+,2,1,+]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,4,-,2,1,+]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,+,2,1,-]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,4,-,2,1,-]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,+,2,6,1]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,4,-,2,6,1]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,+,6,1,2]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,4,+,6,2,1]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,4,-,6,2,1]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,6,2,1,3]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,6,3,1,2]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,4,6,3,2,1]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,6,2,1,3,4]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,6,2,1,4,3]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,6,2,3,1,4]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,6,2,3,4,1]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,6,2,+,1,3]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,6,2,-,1,3]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,6,2,+,3,1]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[5,6,2,-,3,1]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,6,+,1,2,4]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,6,+,1,4,2]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,6,+,2,1,4]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,6,-,2,1,4]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,6,+,2,4,1]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,6,-,2,4,1]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,6,+,+,1,2]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[5,6,-,+,1,2]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[5,6,+,-,1,2]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,6,+,+,2,1]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[5,6,-,+,2,1]=>[4,2,1,5,6,3]=>[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[5,6,+,-,2,1]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[5,6,-,-,2,1]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[5,6,4,2,3,1]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,6,4,3,1,2]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[5,6,4,3,2,1]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,+,1,3,4,5]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,3,+,4]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,3,-,4]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,+,3,5]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,-,3,5]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,+,+,3]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,-,+,3]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,+,-,3]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,-,-,3]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,5,3,4]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,1,5,4,3]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,1,4,5]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,+,1,4,5]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,-,1,4,5]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,1,+,4]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,+,1,+,4]=>[3,1,5,4,6,2]=>[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,-,1,+,4]=>[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,1,-,4]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,+,1,-,4]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,-,1,-,4]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,+,1,5]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,-,+,+,1,5]=>[3,4,1,5,6,2]=>[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,+,-,+,1,5]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,+,+,-,1,5]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,-,+,1,5]=>[4,1,5,6,2,3]=>[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[6,-,+,-,1,5]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,-,-,1,5]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,+,+,1]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[6,-,+,+,+,1]=>[3,4,5,1,6,2]=>[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[6,+,-,+,+,1]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,+,+,-,+,1]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,+,+,+,-,1]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,-,-,+,+,1]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[6,-,+,-,+,1]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,-,+,+,-,1]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,+,-,-,+,1]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,+,-,+,-,1]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,+,+,-,-,1]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,-,-,+,1]=>[5,1,6,2,3,4]=>[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[6,-,-,+,-,1]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[6,-,+,-,-,1]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,-,-,-,1]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,5,1,4]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,+,5,1,4]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,-,5,1,4]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,+,5,4,1]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,-,+,5,4,1]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,+,-,5,4,1]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,-,5,4,1]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[6,+,4,1,3,5]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,4,1,+,3]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,4,1,-,3]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,4,3,1,5]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,4,3,1,5]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,4,3,+,1]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,-,4,3,+,1]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,+,4,3,-,1]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,4,3,-,1]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,4,5,1,3]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,4,5,3,1]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,4,5,3,1]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,5,1,3,4]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,5,1,4,3]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,5,3,1,4]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,5,3,1,4]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,+,5,3,4,1]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,-,5,3,4,1]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,+,5,+,1,3]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,5,+,1,3]=>[4,1,3,6,2,5]=>[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[6,+,5,-,1,3]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,+,5,+,3,1]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,-,5,+,3,1]=>[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[6,+,5,-,3,1]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,-,5,-,3,1]=>[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,3,2,1,4,5]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,2,1,+,4]=>[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,2,1,-,4]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,2,+,1,5]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,3,2,-,1,5]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,2,+,+,1]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,3,2,-,+,1]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,3,2,+,-,1]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,3,2,-,-,1]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,2,5,1,4]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,2,5,4,1]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,3,4,2,1,5]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,4,2,+,1]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,3,4,2,-,1]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,4,5,2,1]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,5,2,1,4]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,3,5,2,4,1]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,3,5,+,1,2]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[6,3,5,+,2,1]=>[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[6,3,5,-,2,1]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,2,1,3,5]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,2,1,+,3]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,2,1,-,3]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,2,3,1,5]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,4,2,3,+,1]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,4,2,3,-,1]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,4,2,5,1,3]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,2,5,3,1]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,4,+,1,2,5]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,4,+,1,+,2]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,4,+,1,-,2]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,4,+,2,1,5]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,4,-,2,1,5]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,+,2,+,1]=>[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[6,4,-,2,+,1]=>[2,5,1,6,4,3]=>[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,4,+,2,-,1]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,4,-,2,-,1]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,+,5,1,2]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,4,+,5,2,1]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,4,-,5,2,1]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,5,2,1,3]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,4,5,2,3,1]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,4,5,3,1,2]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,4,5,3,2,1]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,5,2,1,3,4]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,5,2,1,4,3]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,5,2,3,1,4]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,5,2,3,4,1]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,5,2,+,1,3]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,5,2,-,1,3]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,5,2,+,3,1]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[6,5,2,-,3,1]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,5,+,1,2,4]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,5,+,1,4,2]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,5,+,2,1,4]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,5,-,2,1,4]=>[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,5,+,2,4,1]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[6,5,-,2,4,1]=>[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,5,+,+,1,2]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[6,5,-,+,1,2]=>[4,1,2,6,5,3]=>[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[6,5,+,-,1,2]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,5,+,+,2,1]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,5,-,+,2,1]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[6,5,+,-,2,1]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[6,5,-,-,2,1]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,5,4,2,1,3]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[6,5,4,2,3,1]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[6,5,4,3,1,2]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[6,5,4,3,2,1]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
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Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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
lower permutation
Description
The lower bound in the Grassmann interval corresponding to the decorated permutation.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.
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