Identifier
-
Mp00255:
Decorated permutations
—lower permutation⟶
Permutations
St000001: Permutations ⟶ ℤ
Values
=>
[+]=>[1]=>1
[-]=>[1]=>1
[+,+]=>[1,2]=>1
[-,+]=>[2,1]=>1
[+,-]=>[1,2]=>1
[-,-]=>[1,2]=>1
[2,1]=>[1,2]=>1
[+,+,+]=>[1,2,3]=>1
[-,+,+]=>[2,3,1]=>1
[+,-,+]=>[1,3,2]=>1
[+,+,-]=>[1,2,3]=>1
[-,-,+]=>[3,1,2]=>1
[-,+,-]=>[2,1,3]=>1
[+,-,-]=>[1,2,3]=>1
[-,-,-]=>[1,2,3]=>1
[+,3,2]=>[1,2,3]=>1
[-,3,2]=>[2,1,3]=>1
[2,1,+]=>[1,3,2]=>1
[2,1,-]=>[1,2,3]=>1
[2,3,1]=>[1,2,3]=>1
[3,1,2]=>[1,2,3]=>1
[3,+,1]=>[2,1,3]=>1
[3,-,1]=>[1,3,2]=>1
[+,+,+,+]=>[1,2,3,4]=>1
[-,+,+,+]=>[2,3,4,1]=>1
[+,-,+,+]=>[1,3,4,2]=>1
[+,+,-,+]=>[1,2,4,3]=>1
[+,+,+,-]=>[1,2,3,4]=>1
[-,-,+,+]=>[3,4,1,2]=>2
[-,+,-,+]=>[2,4,1,3]=>2
[-,+,+,-]=>[2,3,1,4]=>1
[+,-,-,+]=>[1,4,2,3]=>1
[+,-,+,-]=>[1,3,2,4]=>1
[+,+,-,-]=>[1,2,3,4]=>1
[-,-,-,+]=>[4,1,2,3]=>1
[-,-,+,-]=>[3,1,2,4]=>1
[-,+,-,-]=>[2,1,3,4]=>1
[+,-,-,-]=>[1,2,3,4]=>1
[-,-,-,-]=>[1,2,3,4]=>1
[+,+,4,3]=>[1,2,3,4]=>1
[-,+,4,3]=>[2,3,1,4]=>1
[+,-,4,3]=>[1,3,2,4]=>1
[-,-,4,3]=>[3,1,2,4]=>1
[+,3,2,+]=>[1,2,4,3]=>1
[-,3,2,+]=>[2,4,1,3]=>2
[+,3,2,-]=>[1,2,3,4]=>1
[-,3,2,-]=>[2,1,3,4]=>1
[+,3,4,2]=>[1,2,3,4]=>1
[-,3,4,2]=>[2,1,3,4]=>1
[+,4,2,3]=>[1,2,3,4]=>1
[-,4,2,3]=>[2,3,1,4]=>1
[+,4,+,2]=>[1,3,2,4]=>1
[-,4,+,2]=>[3,2,1,4]=>2
[+,4,-,2]=>[1,2,4,3]=>1
[-,4,-,2]=>[2,1,4,3]=>2
[2,1,+,+]=>[1,3,4,2]=>1
[2,1,-,+]=>[1,4,2,3]=>1
[2,1,+,-]=>[1,3,2,4]=>1
[2,1,-,-]=>[1,2,3,4]=>1
[2,1,4,3]=>[1,3,2,4]=>1
[2,3,1,+]=>[1,4,2,3]=>1
[2,3,1,-]=>[1,2,3,4]=>1
[2,3,4,1]=>[1,2,3,4]=>1
[2,4,1,3]=>[1,3,2,4]=>1
[2,4,+,1]=>[3,1,2,4]=>1
[2,4,-,1]=>[1,2,4,3]=>1
[3,1,2,+]=>[1,2,4,3]=>1
[3,1,2,-]=>[1,2,3,4]=>1
[3,1,4,2]=>[1,2,3,4]=>1
[3,+,1,+]=>[2,1,4,3]=>2
[3,-,1,+]=>[1,4,3,2]=>2
[3,+,1,-]=>[2,1,3,4]=>1
[3,-,1,-]=>[1,3,2,4]=>1
[3,+,4,1]=>[2,1,3,4]=>1
[3,-,4,1]=>[1,3,2,4]=>1
[3,4,1,2]=>[1,2,3,4]=>1
[3,4,2,1]=>[2,1,3,4]=>1
[4,1,2,3]=>[1,2,3,4]=>1
[4,1,+,2]=>[1,3,2,4]=>1
[4,1,-,2]=>[1,2,4,3]=>1
[4,+,1,3]=>[2,1,3,4]=>1
[4,-,1,3]=>[1,3,4,2]=>1
[4,+,+,1]=>[2,3,1,4]=>1
[4,-,+,1]=>[3,1,4,2]=>2
[4,+,-,1]=>[2,1,4,3]=>2
[4,-,-,1]=>[1,4,2,3]=>1
[4,3,1,2]=>[1,2,4,3]=>1
[4,3,2,1]=>[2,1,4,3]=>2
[+,+,+,+,+]=>[1,2,3,4,5]=>1
[-,+,+,+,+]=>[2,3,4,5,1]=>1
[+,-,+,+,+]=>[1,3,4,5,2]=>1
[+,+,-,+,+]=>[1,2,4,5,3]=>1
[+,+,+,-,+]=>[1,2,3,5,4]=>1
[+,+,+,+,-]=>[1,2,3,4,5]=>1
[-,-,+,+,+]=>[3,4,5,1,2]=>5
[-,+,-,+,+]=>[2,4,5,1,3]=>5
[-,+,+,-,+]=>[2,3,5,1,4]=>3
[-,+,+,+,-]=>[2,3,4,1,5]=>1
[+,-,-,+,+]=>[1,4,5,2,3]=>2
[+,-,+,-,+]=>[1,3,5,2,4]=>2
[+,-,+,+,-]=>[1,3,4,2,5]=>1
[+,+,-,-,+]=>[1,2,5,3,4]=>1
[+,+,-,+,-]=>[1,2,4,3,5]=>1
[+,+,+,-,-]=>[1,2,3,4,5]=>1
[-,-,-,+,+]=>[4,5,1,2,3]=>5
[-,-,+,-,+]=>[3,5,1,2,4]=>5
[-,-,+,+,-]=>[3,4,1,2,5]=>2
[-,+,-,-,+]=>[2,5,1,3,4]=>3
[-,+,-,+,-]=>[2,4,1,3,5]=>2
[-,+,+,-,-]=>[2,3,1,4,5]=>1
[+,-,-,-,+]=>[1,5,2,3,4]=>1
[+,-,-,+,-]=>[1,4,2,3,5]=>1
[+,-,+,-,-]=>[1,3,2,4,5]=>1
[+,+,-,-,-]=>[1,2,3,4,5]=>1
[-,-,-,-,+]=>[5,1,2,3,4]=>1
[-,-,-,+,-]=>[4,1,2,3,5]=>1
[-,-,+,-,-]=>[3,1,2,4,5]=>1
[-,+,-,-,-]=>[2,1,3,4,5]=>1
[+,-,-,-,-]=>[1,2,3,4,5]=>1
[-,-,-,-,-]=>[1,2,3,4,5]=>1
[+,+,+,5,4]=>[1,2,3,4,5]=>1
[-,+,+,5,4]=>[2,3,4,1,5]=>1
[+,-,+,5,4]=>[1,3,4,2,5]=>1
[+,+,-,5,4]=>[1,2,4,3,5]=>1
[-,-,+,5,4]=>[3,4,1,2,5]=>2
[-,+,-,5,4]=>[2,4,1,3,5]=>2
[+,-,-,5,4]=>[1,4,2,3,5]=>1
[-,-,-,5,4]=>[4,1,2,3,5]=>1
[+,+,4,3,+]=>[1,2,3,5,4]=>1
[-,+,4,3,+]=>[2,3,5,1,4]=>3
[+,-,4,3,+]=>[1,3,5,2,4]=>2
[+,+,4,3,-]=>[1,2,3,4,5]=>1
[-,-,4,3,+]=>[3,5,1,2,4]=>5
[-,+,4,3,-]=>[2,3,1,4,5]=>1
[+,-,4,3,-]=>[1,3,2,4,5]=>1
[-,-,4,3,-]=>[3,1,2,4,5]=>1
[+,+,4,5,3]=>[1,2,3,4,5]=>1
[-,+,4,5,3]=>[2,3,1,4,5]=>1
[+,-,4,5,3]=>[1,3,2,4,5]=>1
[-,-,4,5,3]=>[3,1,2,4,5]=>1
[+,+,5,3,4]=>[1,2,3,4,5]=>1
[-,+,5,3,4]=>[2,3,4,1,5]=>1
[+,-,5,3,4]=>[1,3,4,2,5]=>1
[-,-,5,3,4]=>[3,4,1,2,5]=>2
[+,+,5,+,3]=>[1,2,4,3,5]=>1
[-,+,5,+,3]=>[2,4,3,1,5]=>3
[+,-,5,+,3]=>[1,4,3,2,5]=>2
[+,+,5,-,3]=>[1,2,3,5,4]=>1
[-,-,5,+,3]=>[4,3,1,2,5]=>5
[-,+,5,-,3]=>[2,3,1,5,4]=>3
[+,-,5,-,3]=>[1,3,2,5,4]=>2
[-,-,5,-,3]=>[3,1,2,5,4]=>3
[+,3,2,+,+]=>[1,2,4,5,3]=>1
[-,3,2,+,+]=>[2,4,5,1,3]=>5
[+,3,2,-,+]=>[1,2,5,3,4]=>1
[+,3,2,+,-]=>[1,2,4,3,5]=>1
[-,3,2,-,+]=>[2,5,1,3,4]=>3
[-,3,2,+,-]=>[2,4,1,3,5]=>2
[+,3,2,-,-]=>[1,2,3,4,5]=>1
[-,3,2,-,-]=>[2,1,3,4,5]=>1
[+,3,2,5,4]=>[1,2,4,3,5]=>1
[-,3,2,5,4]=>[2,4,1,3,5]=>2
[+,3,4,2,+]=>[1,2,5,3,4]=>1
[-,3,4,2,+]=>[2,5,1,3,4]=>3
[+,3,4,2,-]=>[1,2,3,4,5]=>1
[-,3,4,2,-]=>[2,1,3,4,5]=>1
[+,3,4,5,2]=>[1,2,3,4,5]=>1
[-,3,4,5,2]=>[2,1,3,4,5]=>1
[+,3,5,2,4]=>[1,2,4,3,5]=>1
[-,3,5,2,4]=>[2,4,1,3,5]=>2
[+,3,5,+,2]=>[1,4,2,3,5]=>1
[-,3,5,+,2]=>[4,2,1,3,5]=>3
[+,3,5,-,2]=>[1,2,3,5,4]=>1
[-,3,5,-,2]=>[2,1,3,5,4]=>2
[+,4,2,3,+]=>[1,2,3,5,4]=>1
[-,4,2,3,+]=>[2,3,5,1,4]=>3
[+,4,2,3,-]=>[1,2,3,4,5]=>1
[-,4,2,3,-]=>[2,3,1,4,5]=>1
[+,4,2,5,3]=>[1,2,3,4,5]=>1
[-,4,2,5,3]=>[2,3,1,4,5]=>1
[+,4,+,2,+]=>[1,3,2,5,4]=>2
[-,4,+,2,+]=>[3,2,5,1,4]=>11
[+,4,-,2,+]=>[1,2,5,4,3]=>2
[+,4,+,2,-]=>[1,3,2,4,5]=>1
[-,4,-,2,+]=>[2,5,1,4,3]=>11
[-,4,+,2,-]=>[3,2,1,4,5]=>2
[+,4,-,2,-]=>[1,2,4,3,5]=>1
[-,4,-,2,-]=>[2,1,4,3,5]=>2
[+,4,+,5,2]=>[1,3,2,4,5]=>1
[-,4,+,5,2]=>[3,2,1,4,5]=>2
[+,4,-,5,2]=>[1,2,4,3,5]=>1
[-,4,-,5,2]=>[2,1,4,3,5]=>2
[+,4,5,2,3]=>[1,2,3,4,5]=>1
[-,4,5,2,3]=>[2,3,1,4,5]=>1
[+,4,5,3,2]=>[1,3,2,4,5]=>1
[-,4,5,3,2]=>[3,2,1,4,5]=>2
[+,5,2,3,4]=>[1,2,3,4,5]=>1
[-,5,2,3,4]=>[2,3,4,1,5]=>1
[+,5,2,+,3]=>[1,2,4,3,5]=>1
[-,5,2,+,3]=>[2,4,3,1,5]=>3
[+,5,2,-,3]=>[1,2,3,5,4]=>1
[-,5,2,-,3]=>[2,3,1,5,4]=>3
[+,5,+,2,4]=>[1,3,2,4,5]=>1
[-,5,+,2,4]=>[3,2,4,1,5]=>3
[+,5,-,2,4]=>[1,2,4,5,3]=>1
[-,5,-,2,4]=>[2,4,1,5,3]=>5
[+,5,+,+,2]=>[1,3,4,2,5]=>1
[-,5,+,+,2]=>[3,4,2,1,5]=>5
[+,5,-,+,2]=>[1,4,2,5,3]=>2
[+,5,+,-,2]=>[1,3,2,5,4]=>2
[-,5,-,+,2]=>[4,2,1,5,3]=>11
[-,5,+,-,2]=>[3,2,1,5,4]=>8
[+,5,-,-,2]=>[1,2,5,3,4]=>1
[-,5,-,-,2]=>[2,1,5,3,4]=>3
[+,5,4,2,3]=>[1,2,3,5,4]=>1
[-,5,4,2,3]=>[2,3,1,5,4]=>3
[+,5,4,3,2]=>[1,3,2,5,4]=>2
[-,5,4,3,2]=>[3,2,1,5,4]=>8
[2,1,+,+,+]=>[1,3,4,5,2]=>1
[2,1,-,+,+]=>[1,4,5,2,3]=>2
[2,1,+,-,+]=>[1,3,5,2,4]=>2
[2,1,+,+,-]=>[1,3,4,2,5]=>1
[2,1,-,-,+]=>[1,5,2,3,4]=>1
[2,1,-,+,-]=>[1,4,2,3,5]=>1
[2,1,+,-,-]=>[1,3,2,4,5]=>1
[2,1,-,-,-]=>[1,2,3,4,5]=>1
[2,1,+,5,4]=>[1,3,4,2,5]=>1
[2,1,-,5,4]=>[1,4,2,3,5]=>1
[2,1,4,3,+]=>[1,3,5,2,4]=>2
[2,1,4,3,-]=>[1,3,2,4,5]=>1
[2,1,4,5,3]=>[1,3,2,4,5]=>1
[2,1,5,3,4]=>[1,3,4,2,5]=>1
[2,1,5,+,3]=>[1,4,3,2,5]=>2
[2,1,5,-,3]=>[1,3,2,5,4]=>2
[2,3,1,+,+]=>[1,4,5,2,3]=>2
[2,3,1,-,+]=>[1,5,2,3,4]=>1
[2,3,1,+,-]=>[1,4,2,3,5]=>1
[2,3,1,-,-]=>[1,2,3,4,5]=>1
[2,3,1,5,4]=>[1,4,2,3,5]=>1
[2,3,4,1,+]=>[1,5,2,3,4]=>1
[2,3,4,1,-]=>[1,2,3,4,5]=>1
[2,3,4,5,1]=>[1,2,3,4,5]=>1
[2,3,5,1,4]=>[1,4,2,3,5]=>1
[2,3,5,+,1]=>[4,1,2,3,5]=>1
[2,3,5,-,1]=>[1,2,3,5,4]=>1
[2,4,1,3,+]=>[1,3,5,2,4]=>2
[2,4,1,3,-]=>[1,3,2,4,5]=>1
[2,4,1,5,3]=>[1,3,2,4,5]=>1
[2,4,+,1,+]=>[3,1,5,2,4]=>5
[2,4,-,1,+]=>[1,5,2,4,3]=>3
[2,4,+,1,-]=>[3,1,2,4,5]=>1
[2,4,-,1,-]=>[1,2,4,3,5]=>1
[2,4,+,5,1]=>[3,1,2,4,5]=>1
[2,4,-,5,1]=>[1,2,4,3,5]=>1
[2,4,5,1,3]=>[1,3,2,4,5]=>1
[2,4,5,3,1]=>[3,1,2,4,5]=>1
[2,5,1,3,4]=>[1,3,4,2,5]=>1
[2,5,1,+,3]=>[1,4,3,2,5]=>2
[2,5,1,-,3]=>[1,3,2,5,4]=>2
[2,5,+,1,4]=>[3,1,4,2,5]=>2
[2,5,-,1,4]=>[1,4,2,5,3]=>2
[2,5,+,+,1]=>[3,4,1,2,5]=>2
[2,5,-,+,1]=>[4,1,2,5,3]=>3
[2,5,+,-,1]=>[3,1,2,5,4]=>3
[2,5,-,-,1]=>[1,2,5,3,4]=>1
[2,5,4,1,3]=>[1,3,2,5,4]=>2
[2,5,4,3,1]=>[3,1,2,5,4]=>3
[3,1,2,+,+]=>[1,2,4,5,3]=>1
[3,1,2,-,+]=>[1,2,5,3,4]=>1
[3,1,2,+,-]=>[1,2,4,3,5]=>1
[3,1,2,-,-]=>[1,2,3,4,5]=>1
[3,1,2,5,4]=>[1,2,4,3,5]=>1
[3,1,4,2,+]=>[1,2,5,3,4]=>1
[3,1,4,2,-]=>[1,2,3,4,5]=>1
[3,1,4,5,2]=>[1,2,3,4,5]=>1
[3,1,5,2,4]=>[1,2,4,3,5]=>1
[3,1,5,+,2]=>[1,4,2,3,5]=>1
[3,1,5,-,2]=>[1,2,3,5,4]=>1
[3,+,1,+,+]=>[2,1,4,5,3]=>3
[3,-,1,+,+]=>[1,4,5,3,2]=>5
[3,+,1,-,+]=>[2,1,5,3,4]=>3
[3,+,1,+,-]=>[2,1,4,3,5]=>2
[3,-,1,-,+]=>[1,5,3,2,4]=>3
[3,-,1,+,-]=>[1,4,3,2,5]=>2
[3,+,1,-,-]=>[2,1,3,4,5]=>1
[3,-,1,-,-]=>[1,3,2,4,5]=>1
[3,+,1,5,4]=>[2,1,4,3,5]=>2
[3,-,1,5,4]=>[1,4,3,2,5]=>2
[3,+,4,1,+]=>[2,1,5,3,4]=>3
[3,-,4,1,+]=>[1,5,3,2,4]=>3
[3,+,4,1,-]=>[2,1,3,4,5]=>1
[3,-,4,1,-]=>[1,3,2,4,5]=>1
[3,+,4,5,1]=>[2,1,3,4,5]=>1
[3,-,4,5,1]=>[1,3,2,4,5]=>1
[3,+,5,1,4]=>[2,1,4,3,5]=>2
[3,-,5,1,4]=>[1,4,3,2,5]=>2
[3,+,5,+,1]=>[2,4,1,3,5]=>2
[3,-,5,+,1]=>[4,1,3,2,5]=>3
[3,+,5,-,1]=>[2,1,3,5,4]=>2
[3,-,5,-,1]=>[1,3,2,5,4]=>2
[3,4,1,2,+]=>[1,2,5,3,4]=>1
[3,4,1,2,-]=>[1,2,3,4,5]=>1
[3,4,1,5,2]=>[1,2,3,4,5]=>1
[3,4,2,1,+]=>[2,1,5,3,4]=>3
[3,4,2,1,-]=>[2,1,3,4,5]=>1
[3,4,2,5,1]=>[2,1,3,4,5]=>1
[3,4,5,1,2]=>[1,2,3,4,5]=>1
[3,4,5,2,1]=>[2,1,3,4,5]=>1
[3,5,1,2,4]=>[1,2,4,3,5]=>1
[3,5,1,+,2]=>[1,4,2,3,5]=>1
[3,5,1,-,2]=>[1,2,3,5,4]=>1
[3,5,2,1,4]=>[2,1,4,3,5]=>2
[3,5,2,+,1]=>[2,4,1,3,5]=>2
[3,5,2,-,1]=>[2,1,3,5,4]=>2
[3,5,4,1,2]=>[1,2,3,5,4]=>1
[3,5,4,2,1]=>[2,1,3,5,4]=>2
[4,1,2,3,+]=>[1,2,3,5,4]=>1
[4,1,2,3,-]=>[1,2,3,4,5]=>1
[4,1,2,5,3]=>[1,2,3,4,5]=>1
[4,1,+,2,+]=>[1,3,2,5,4]=>2
[4,1,-,2,+]=>[1,2,5,4,3]=>2
[4,1,+,2,-]=>[1,3,2,4,5]=>1
[4,1,-,2,-]=>[1,2,4,3,5]=>1
[4,1,+,5,2]=>[1,3,2,4,5]=>1
[4,1,-,5,2]=>[1,2,4,3,5]=>1
[4,1,5,2,3]=>[1,2,3,4,5]=>1
[4,1,5,3,2]=>[1,3,2,4,5]=>1
[4,+,1,3,+]=>[2,1,3,5,4]=>2
[4,-,1,3,+]=>[1,3,5,4,2]=>3
[4,+,1,3,-]=>[2,1,3,4,5]=>1
[4,-,1,3,-]=>[1,3,4,2,5]=>1
[4,+,1,5,3]=>[2,1,3,4,5]=>1
[4,-,1,5,3]=>[1,3,4,2,5]=>1
[4,+,+,1,+]=>[2,3,1,5,4]=>3
[4,-,+,1,+]=>[3,1,5,4,2]=>11
[4,+,-,1,+]=>[2,1,5,4,3]=>8
[4,+,+,1,-]=>[2,3,1,4,5]=>1
[4,-,-,1,+]=>[1,5,4,2,3]=>5
[4,-,+,1,-]=>[3,1,4,2,5]=>2
[4,+,-,1,-]=>[2,1,4,3,5]=>2
[4,-,-,1,-]=>[1,4,2,3,5]=>1
[4,+,+,5,1]=>[2,3,1,4,5]=>1
[4,-,+,5,1]=>[3,1,4,2,5]=>2
[4,+,-,5,1]=>[2,1,4,3,5]=>2
[4,-,-,5,1]=>[1,4,2,3,5]=>1
[4,+,5,1,3]=>[2,1,3,4,5]=>1
[4,-,5,1,3]=>[1,3,4,2,5]=>1
[4,+,5,3,1]=>[2,3,1,4,5]=>1
[4,-,5,3,1]=>[3,1,4,2,5]=>2
[4,3,1,2,+]=>[1,2,5,4,3]=>2
[4,3,1,2,-]=>[1,2,4,3,5]=>1
[4,3,1,5,2]=>[1,2,4,3,5]=>1
[4,3,2,1,+]=>[2,1,5,4,3]=>8
[4,3,2,1,-]=>[2,1,4,3,5]=>2
[4,3,2,5,1]=>[2,1,4,3,5]=>2
[4,3,5,1,2]=>[1,2,4,3,5]=>1
[4,3,5,2,1]=>[2,1,4,3,5]=>2
[4,5,1,2,3]=>[1,2,3,4,5]=>1
[4,5,1,3,2]=>[1,3,2,4,5]=>1
[4,5,2,1,3]=>[2,1,3,4,5]=>1
[4,5,2,3,1]=>[2,3,1,4,5]=>1
[4,5,+,1,2]=>[3,1,2,4,5]=>1
[4,5,-,1,2]=>[1,2,4,5,3]=>1
[4,5,+,2,1]=>[3,2,1,4,5]=>2
[4,5,-,2,1]=>[2,1,4,5,3]=>3
[5,1,2,3,4]=>[1,2,3,4,5]=>1
[5,1,2,+,3]=>[1,2,4,3,5]=>1
[5,1,2,-,3]=>[1,2,3,5,4]=>1
[5,1,+,2,4]=>[1,3,2,4,5]=>1
[5,1,-,2,4]=>[1,2,4,5,3]=>1
[5,1,+,+,2]=>[1,3,4,2,5]=>1
[5,1,-,+,2]=>[1,4,2,5,3]=>2
[5,1,+,-,2]=>[1,3,2,5,4]=>2
[5,1,-,-,2]=>[1,2,5,3,4]=>1
[5,1,4,2,3]=>[1,2,3,5,4]=>1
[5,1,4,3,2]=>[1,3,2,5,4]=>2
[5,+,1,3,4]=>[2,1,3,4,5]=>1
[5,-,1,3,4]=>[1,3,4,5,2]=>1
[5,+,1,+,3]=>[2,1,4,3,5]=>2
[5,-,1,+,3]=>[1,4,3,5,2]=>3
[5,+,1,-,3]=>[2,1,3,5,4]=>2
[5,-,1,-,3]=>[1,3,5,2,4]=>2
[5,+,+,1,4]=>[2,3,1,4,5]=>1
[5,-,+,1,4]=>[3,1,4,5,2]=>3
[5,+,-,1,4]=>[2,1,4,5,3]=>3
[5,-,-,1,4]=>[1,4,5,2,3]=>2
[5,+,+,+,1]=>[2,3,4,1,5]=>1
[5,-,+,+,1]=>[3,4,1,5,2]=>5
[5,+,-,+,1]=>[2,4,1,5,3]=>5
[5,+,+,-,1]=>[2,3,1,5,4]=>3
[5,-,-,+,1]=>[4,1,5,2,3]=>5
[5,-,+,-,1]=>[3,1,5,2,4]=>5
[5,+,-,-,1]=>[2,1,5,3,4]=>3
[5,-,-,-,1]=>[1,5,2,3,4]=>1
[5,+,4,1,3]=>[2,1,3,5,4]=>2
[5,-,4,1,3]=>[1,3,5,2,4]=>2
[5,+,4,3,1]=>[2,3,1,5,4]=>3
[5,-,4,3,1]=>[3,1,5,2,4]=>5
[5,3,1,2,4]=>[1,2,4,5,3]=>1
[5,3,1,+,2]=>[1,4,2,5,3]=>2
[5,3,1,-,2]=>[1,2,5,3,4]=>1
[5,3,2,1,4]=>[2,1,4,5,3]=>3
[5,3,2,+,1]=>[2,4,1,5,3]=>5
[5,3,2,-,1]=>[2,1,5,3,4]=>3
[5,3,4,1,2]=>[1,2,5,3,4]=>1
[5,3,4,2,1]=>[2,1,5,3,4]=>3
[5,4,1,2,3]=>[1,2,3,5,4]=>1
[5,4,1,3,2]=>[1,3,2,5,4]=>2
[5,4,2,1,3]=>[2,1,3,5,4]=>2
[5,4,2,3,1]=>[2,3,1,5,4]=>3
[5,4,+,1,2]=>[3,1,2,5,4]=>3
[5,4,-,1,2]=>[1,2,5,4,3]=>2
[5,4,+,2,1]=>[3,2,1,5,4]=>8
[5,4,-,2,1]=>[2,1,5,4,3]=>8
[+,+,+,+,+,+]=>[1,2,3,4,5,6]=>1
[-,+,+,+,+,+]=>[2,3,4,5,6,1]=>1
[+,-,+,+,+,+]=>[1,3,4,5,6,2]=>1
[+,+,-,+,+,+]=>[1,2,4,5,6,3]=>1
[+,+,+,-,+,+]=>[1,2,3,5,6,4]=>1
[+,+,+,+,-,+]=>[1,2,3,4,6,5]=>1
[+,+,+,+,+,-]=>[1,2,3,4,5,6]=>1
[-,-,+,+,+,+]=>[3,4,5,6,1,2]=>14
[-,+,-,+,+,+]=>[2,4,5,6,1,3]=>14
[-,+,+,-,+,+]=>[2,3,5,6,1,4]=>9
[-,+,+,+,-,+]=>[2,3,4,6,1,5]=>4
[-,+,+,+,+,-]=>[2,3,4,5,1,6]=>1
[+,-,-,+,+,+]=>[1,4,5,6,2,3]=>5
[+,-,+,-,+,+]=>[1,3,5,6,2,4]=>5
[+,-,+,+,-,+]=>[1,3,4,6,2,5]=>3
[+,-,+,+,+,-]=>[1,3,4,5,2,6]=>1
[+,+,-,-,+,+]=>[1,2,5,6,3,4]=>2
[+,+,-,+,-,+]=>[1,2,4,6,3,5]=>2
[+,+,-,+,+,-]=>[1,2,4,5,3,6]=>1
[+,+,+,-,-,+]=>[1,2,3,6,4,5]=>1
[+,+,+,-,+,-]=>[1,2,3,5,4,6]=>1
[+,+,+,+,-,-]=>[1,2,3,4,5,6]=>1
[-,-,-,+,+,+]=>[4,5,6,1,2,3]=>42
[-,-,+,-,+,+]=>[3,5,6,1,2,4]=>42
[-,-,+,+,-,+]=>[3,4,6,1,2,5]=>21
[-,-,+,+,+,-]=>[3,4,5,1,2,6]=>5
[-,+,-,-,+,+]=>[2,5,6,1,3,4]=>21
[-,+,-,+,-,+]=>[2,4,6,1,3,5]=>16
[-,+,-,+,+,-]=>[2,4,5,1,3,6]=>5
[-,+,+,-,-,+]=>[2,3,6,1,4,5]=>6
[-,+,+,-,+,-]=>[2,3,5,1,4,6]=>3
[-,+,+,+,-,-]=>[2,3,4,1,5,6]=>1
[+,-,-,-,+,+]=>[1,5,6,2,3,4]=>5
[+,-,-,+,-,+]=>[1,4,6,2,3,5]=>5
[+,-,-,+,+,-]=>[1,4,5,2,3,6]=>2
[+,-,+,-,-,+]=>[1,3,6,2,4,5]=>3
[+,-,+,-,+,-]=>[1,3,5,2,4,6]=>2
[+,-,+,+,-,-]=>[1,3,4,2,5,6]=>1
[+,+,-,-,-,+]=>[1,2,6,3,4,5]=>1
[+,+,-,-,+,-]=>[1,2,5,3,4,6]=>1
[+,+,-,+,-,-]=>[1,2,4,3,5,6]=>1
[+,+,+,-,-,-]=>[1,2,3,4,5,6]=>1
[-,-,-,-,+,+]=>[5,6,1,2,3,4]=>14
[-,-,-,+,-,+]=>[4,6,1,2,3,5]=>14
[-,-,-,+,+,-]=>[4,5,1,2,3,6]=>5
[-,-,+,-,-,+]=>[3,6,1,2,4,5]=>9
[-,-,+,-,+,-]=>[3,5,1,2,4,6]=>5
[-,-,+,+,-,-]=>[3,4,1,2,5,6]=>2
[-,+,-,-,-,+]=>[2,6,1,3,4,5]=>4
[-,+,-,-,+,-]=>[2,5,1,3,4,6]=>3
[-,+,-,+,-,-]=>[2,4,1,3,5,6]=>2
[-,+,+,-,-,-]=>[2,3,1,4,5,6]=>1
[+,-,-,-,-,+]=>[1,6,2,3,4,5]=>1
[+,-,-,-,+,-]=>[1,5,2,3,4,6]=>1
[+,-,-,+,-,-]=>[1,4,2,3,5,6]=>1
[+,-,+,-,-,-]=>[1,3,2,4,5,6]=>1
[+,+,-,-,-,-]=>[1,2,3,4,5,6]=>1
[-,-,-,-,-,+]=>[6,1,2,3,4,5]=>1
[-,-,-,-,+,-]=>[5,1,2,3,4,6]=>1
[-,-,-,+,-,-]=>[4,1,2,3,5,6]=>1
[-,-,+,-,-,-]=>[3,1,2,4,5,6]=>1
[-,+,-,-,-,-]=>[2,1,3,4,5,6]=>1
[+,-,-,-,-,-]=>[1,2,3,4,5,6]=>1
[-,-,-,-,-,-]=>[1,2,3,4,5,6]=>1
[+,+,+,+,6,5]=>[1,2,3,4,5,6]=>1
[-,+,+,+,6,5]=>[2,3,4,5,1,6]=>1
[+,-,+,+,6,5]=>[1,3,4,5,2,6]=>1
[+,+,-,+,6,5]=>[1,2,4,5,3,6]=>1
[+,+,+,-,6,5]=>[1,2,3,5,4,6]=>1
[-,-,+,+,6,5]=>[3,4,5,1,2,6]=>5
[-,+,-,+,6,5]=>[2,4,5,1,3,6]=>5
[-,+,+,-,6,5]=>[2,3,5,1,4,6]=>3
[+,-,-,+,6,5]=>[1,4,5,2,3,6]=>2
[+,-,+,-,6,5]=>[1,3,5,2,4,6]=>2
[+,+,-,-,6,5]=>[1,2,5,3,4,6]=>1
[-,-,-,+,6,5]=>[4,5,1,2,3,6]=>5
[-,-,+,-,6,5]=>[3,5,1,2,4,6]=>5
[-,+,-,-,6,5]=>[2,5,1,3,4,6]=>3
[+,-,-,-,6,5]=>[1,5,2,3,4,6]=>1
[-,-,-,-,6,5]=>[5,1,2,3,4,6]=>1
[+,+,+,5,4,+]=>[1,2,3,4,6,5]=>1
[-,+,+,5,4,+]=>[2,3,4,6,1,5]=>4
[+,-,+,5,4,+]=>[1,3,4,6,2,5]=>3
[+,+,-,5,4,+]=>[1,2,4,6,3,5]=>2
[+,+,+,5,4,-]=>[1,2,3,4,5,6]=>1
[-,-,+,5,4,+]=>[3,4,6,1,2,5]=>21
[-,+,-,5,4,+]=>[2,4,6,1,3,5]=>16
[-,+,+,5,4,-]=>[2,3,4,1,5,6]=>1
[+,-,-,5,4,+]=>[1,4,6,2,3,5]=>5
[+,-,+,5,4,-]=>[1,3,4,2,5,6]=>1
[+,+,-,5,4,-]=>[1,2,4,3,5,6]=>1
[-,-,-,5,4,+]=>[4,6,1,2,3,5]=>14
[-,-,+,5,4,-]=>[3,4,1,2,5,6]=>2
[-,+,-,5,4,-]=>[2,4,1,3,5,6]=>2
[+,-,-,5,4,-]=>[1,4,2,3,5,6]=>1
[-,-,-,5,4,-]=>[4,1,2,3,5,6]=>1
[+,+,+,5,6,4]=>[1,2,3,4,5,6]=>1
[-,+,+,5,6,4]=>[2,3,4,1,5,6]=>1
[+,-,+,5,6,4]=>[1,3,4,2,5,6]=>1
[+,+,-,5,6,4]=>[1,2,4,3,5,6]=>1
[-,-,+,5,6,4]=>[3,4,1,2,5,6]=>2
[-,+,-,5,6,4]=>[2,4,1,3,5,6]=>2
[+,-,-,5,6,4]=>[1,4,2,3,5,6]=>1
[-,-,-,5,6,4]=>[4,1,2,3,5,6]=>1
[+,+,+,6,4,5]=>[1,2,3,4,5,6]=>1
[-,+,+,6,4,5]=>[2,3,4,5,1,6]=>1
[+,-,+,6,4,5]=>[1,3,4,5,2,6]=>1
[+,+,-,6,4,5]=>[1,2,4,5,3,6]=>1
[-,-,+,6,4,5]=>[3,4,5,1,2,6]=>5
[-,+,-,6,4,5]=>[2,4,5,1,3,6]=>5
[+,-,-,6,4,5]=>[1,4,5,2,3,6]=>2
[-,-,-,6,4,5]=>[4,5,1,2,3,6]=>5
[+,+,+,6,+,4]=>[1,2,3,5,4,6]=>1
[-,+,+,6,+,4]=>[2,3,5,4,1,6]=>4
[+,-,+,6,+,4]=>[1,3,5,4,2,6]=>3
[+,+,-,6,+,4]=>[1,2,5,4,3,6]=>2
[+,+,+,6,-,4]=>[1,2,3,4,6,5]=>1
[-,-,+,6,+,4]=>[3,5,4,1,2,6]=>21
[-,+,-,6,+,4]=>[2,5,4,1,3,6]=>16
[-,+,+,6,-,4]=>[2,3,4,1,6,5]=>4
[+,-,-,6,+,4]=>[1,5,4,2,3,6]=>5
[+,-,+,6,-,4]=>[1,3,4,2,6,5]=>3
[+,+,-,6,-,4]=>[1,2,4,3,6,5]=>2
[-,-,-,6,+,4]=>[5,4,1,2,3,6]=>14
[-,-,+,6,-,4]=>[3,4,1,2,6,5]=>10
[-,+,-,6,-,4]=>[2,4,1,3,6,5]=>8
[+,-,-,6,-,4]=>[1,4,2,3,6,5]=>3
[-,-,-,6,-,4]=>[4,1,2,3,6,5]=>4
[+,+,4,3,+,+]=>[1,2,3,5,6,4]=>1
[-,+,4,3,+,+]=>[2,3,5,6,1,4]=>9
[+,-,4,3,+,+]=>[1,3,5,6,2,4]=>5
[+,+,4,3,-,+]=>[1,2,3,6,4,5]=>1
[+,+,4,3,+,-]=>[1,2,3,5,4,6]=>1
[-,-,4,3,+,+]=>[3,5,6,1,2,4]=>42
[-,+,4,3,-,+]=>[2,3,6,1,4,5]=>6
[-,+,4,3,+,-]=>[2,3,5,1,4,6]=>3
[+,-,4,3,-,+]=>[1,3,6,2,4,5]=>3
[+,-,4,3,+,-]=>[1,3,5,2,4,6]=>2
[+,+,4,3,-,-]=>[1,2,3,4,5,6]=>1
[-,-,4,3,-,+]=>[3,6,1,2,4,5]=>9
[-,-,4,3,+,-]=>[3,5,1,2,4,6]=>5
[-,+,4,3,-,-]=>[2,3,1,4,5,6]=>1
[+,-,4,3,-,-]=>[1,3,2,4,5,6]=>1
[-,-,4,3,-,-]=>[3,1,2,4,5,6]=>1
[+,+,4,3,6,5]=>[1,2,3,5,4,6]=>1
[-,+,4,3,6,5]=>[2,3,5,1,4,6]=>3
[+,-,4,3,6,5]=>[1,3,5,2,4,6]=>2
[-,-,4,3,6,5]=>[3,5,1,2,4,6]=>5
[+,+,4,5,3,+]=>[1,2,3,6,4,5]=>1
[-,+,4,5,3,+]=>[2,3,6,1,4,5]=>6
[+,-,4,5,3,+]=>[1,3,6,2,4,5]=>3
[+,+,4,5,3,-]=>[1,2,3,4,5,6]=>1
[-,-,4,5,3,+]=>[3,6,1,2,4,5]=>9
[-,+,4,5,3,-]=>[2,3,1,4,5,6]=>1
[+,-,4,5,3,-]=>[1,3,2,4,5,6]=>1
[-,-,4,5,3,-]=>[3,1,2,4,5,6]=>1
[+,+,4,5,6,3]=>[1,2,3,4,5,6]=>1
[-,+,4,5,6,3]=>[2,3,1,4,5,6]=>1
[+,-,4,5,6,3]=>[1,3,2,4,5,6]=>1
[-,-,4,5,6,3]=>[3,1,2,4,5,6]=>1
[+,+,4,6,3,5]=>[1,2,3,5,4,6]=>1
[-,+,4,6,3,5]=>[2,3,5,1,4,6]=>3
[+,-,4,6,3,5]=>[1,3,5,2,4,6]=>2
[-,-,4,6,3,5]=>[3,5,1,2,4,6]=>5
[+,+,4,6,+,3]=>[1,2,5,3,4,6]=>1
[-,+,4,6,+,3]=>[2,5,3,1,4,6]=>6
[+,-,4,6,+,3]=>[1,5,3,2,4,6]=>3
[+,+,4,6,-,3]=>[1,2,3,4,6,5]=>1
[-,-,4,6,+,3]=>[5,3,1,2,4,6]=>9
[-,+,4,6,-,3]=>[2,3,1,4,6,5]=>3
[+,-,4,6,-,3]=>[1,3,2,4,6,5]=>2
[-,-,4,6,-,3]=>[3,1,2,4,6,5]=>3
[+,+,5,3,4,+]=>[1,2,3,4,6,5]=>1
[-,+,5,3,4,+]=>[2,3,4,6,1,5]=>4
[+,-,5,3,4,+]=>[1,3,4,6,2,5]=>3
[+,+,5,3,4,-]=>[1,2,3,4,5,6]=>1
[-,-,5,3,4,+]=>[3,4,6,1,2,5]=>21
[-,+,5,3,4,-]=>[2,3,4,1,5,6]=>1
[+,-,5,3,4,-]=>[1,3,4,2,5,6]=>1
[-,-,5,3,4,-]=>[3,4,1,2,5,6]=>2
[+,+,5,3,6,4]=>[1,2,3,4,5,6]=>1
[-,+,5,3,6,4]=>[2,3,4,1,5,6]=>1
[+,-,5,3,6,4]=>[1,3,4,2,5,6]=>1
[-,-,5,3,6,4]=>[3,4,1,2,5,6]=>2
[+,+,5,+,3,+]=>[1,2,4,3,6,5]=>2
[-,+,5,+,3,+]=>[2,4,3,6,1,5]=>19
[+,-,5,+,3,+]=>[1,4,3,6,2,5]=>11
[+,+,5,-,3,+]=>[1,2,3,6,5,4]=>2
[+,+,5,+,3,-]=>[1,2,4,3,5,6]=>1
[-,-,5,+,3,+]=>[4,3,6,1,2,5]=>98
[-,+,5,-,3,+]=>[2,3,6,1,5,4]=>26
[-,+,5,+,3,-]=>[2,4,3,1,5,6]=>3
[+,-,5,-,3,+]=>[1,3,6,2,5,4]=>11
[+,-,5,+,3,-]=>[1,4,3,2,5,6]=>2
[+,+,5,-,3,-]=>[1,2,3,5,4,6]=>1
[-,-,5,-,3,+]=>[3,6,1,2,5,4]=>49
[-,-,5,+,3,-]=>[4,3,1,2,5,6]=>5
[-,+,5,-,3,-]=>[2,3,1,5,4,6]=>3
[+,-,5,-,3,-]=>[1,3,2,5,4,6]=>2
[-,-,5,-,3,-]=>[3,1,2,5,4,6]=>3
[+,+,5,+,6,3]=>[1,2,4,3,5,6]=>1
[-,+,5,+,6,3]=>[2,4,3,1,5,6]=>3
[+,-,5,+,6,3]=>[1,4,3,2,5,6]=>2
[+,+,5,-,6,3]=>[1,2,3,5,4,6]=>1
[-,-,5,+,6,3]=>[4,3,1,2,5,6]=>5
[-,+,5,-,6,3]=>[2,3,1,5,4,6]=>3
[+,-,5,-,6,3]=>[1,3,2,5,4,6]=>2
[-,-,5,-,6,3]=>[3,1,2,5,4,6]=>3
[+,+,5,6,3,4]=>[1,2,3,4,5,6]=>1
[-,+,5,6,3,4]=>[2,3,4,1,5,6]=>1
[+,-,5,6,3,4]=>[1,3,4,2,5,6]=>1
[-,-,5,6,3,4]=>[3,4,1,2,5,6]=>2
[+,+,5,6,4,3]=>[1,2,4,3,5,6]=>1
[-,+,5,6,4,3]=>[2,4,3,1,5,6]=>3
[+,-,5,6,4,3]=>[1,4,3,2,5,6]=>2
[-,-,5,6,4,3]=>[4,3,1,2,5,6]=>5
[+,+,6,3,4,5]=>[1,2,3,4,5,6]=>1
[-,+,6,3,4,5]=>[2,3,4,5,1,6]=>1
[+,-,6,3,4,5]=>[1,3,4,5,2,6]=>1
[-,-,6,3,4,5]=>[3,4,5,1,2,6]=>5
[+,+,6,3,+,4]=>[1,2,3,5,4,6]=>1
[-,+,6,3,+,4]=>[2,3,5,4,1,6]=>4
[+,-,6,3,+,4]=>[1,3,5,4,2,6]=>3
[+,+,6,3,-,4]=>[1,2,3,4,6,5]=>1
[-,-,6,3,+,4]=>[3,5,4,1,2,6]=>21
[-,+,6,3,-,4]=>[2,3,4,1,6,5]=>4
[+,-,6,3,-,4]=>[1,3,4,2,6,5]=>3
[-,-,6,3,-,4]=>[3,4,1,2,6,5]=>10
[+,+,6,+,3,5]=>[1,2,4,3,5,6]=>1
[-,+,6,+,3,5]=>[2,4,3,5,1,6]=>4
[+,-,6,+,3,5]=>[1,4,3,5,2,6]=>3
[+,+,6,-,3,5]=>[1,2,3,5,6,4]=>1
[-,-,6,+,3,5]=>[4,3,5,1,2,6]=>21
[-,+,6,-,3,5]=>[2,3,5,1,6,4]=>9
[+,-,6,-,3,5]=>[1,3,5,2,6,4]=>5
[-,-,6,-,3,5]=>[3,5,1,2,6,4]=>21
[+,+,6,+,+,3]=>[1,2,4,5,3,6]=>1
[-,+,6,+,+,3]=>[2,4,5,3,1,6]=>9
[+,-,6,+,+,3]=>[1,4,5,3,2,6]=>5
[+,+,6,-,+,3]=>[1,2,5,3,6,4]=>2
[+,+,6,+,-,3]=>[1,2,4,3,6,5]=>2
[-,-,6,+,+,3]=>[4,5,3,1,2,6]=>42
[-,+,6,-,+,3]=>[2,5,3,1,6,4]=>26
[-,+,6,+,-,3]=>[2,4,3,1,6,5]=>15
[+,-,6,-,+,3]=>[1,5,3,2,6,4]=>11
[+,-,6,+,-,3]=>[1,4,3,2,6,5]=>8
[+,+,6,-,-,3]=>[1,2,3,6,4,5]=>1
[-,-,6,-,+,3]=>[5,3,1,2,6,4]=>49
[-,-,6,+,-,3]=>[4,3,1,2,6,5]=>30
[-,+,6,-,-,3]=>[2,3,1,6,4,5]=>6
[+,-,6,-,-,3]=>[1,3,2,6,4,5]=>3
[-,-,6,-,-,3]=>[3,1,2,6,4,5]=>6
[+,+,6,5,3,4]=>[1,2,3,4,6,5]=>1
[-,+,6,5,3,4]=>[2,3,4,1,6,5]=>4
[+,-,6,5,3,4]=>[1,3,4,2,6,5]=>3
[-,-,6,5,3,4]=>[3,4,1,2,6,5]=>10
[+,+,6,5,4,3]=>[1,2,4,3,6,5]=>2
[-,+,6,5,4,3]=>[2,4,3,1,6,5]=>15
[+,-,6,5,4,3]=>[1,4,3,2,6,5]=>8
[-,-,6,5,4,3]=>[4,3,1,2,6,5]=>30
[+,3,2,+,+,+]=>[1,2,4,5,6,3]=>1
[-,3,2,+,+,+]=>[2,4,5,6,1,3]=>14
[+,3,2,-,+,+]=>[1,2,5,6,3,4]=>2
[+,3,2,+,-,+]=>[1,2,4,6,3,5]=>2
[+,3,2,+,+,-]=>[1,2,4,5,3,6]=>1
[-,3,2,-,+,+]=>[2,5,6,1,3,4]=>21
[-,3,2,+,-,+]=>[2,4,6,1,3,5]=>16
[-,3,2,+,+,-]=>[2,4,5,1,3,6]=>5
[+,3,2,-,-,+]=>[1,2,6,3,4,5]=>1
[+,3,2,-,+,-]=>[1,2,5,3,4,6]=>1
[+,3,2,+,-,-]=>[1,2,4,3,5,6]=>1
[-,3,2,-,-,+]=>[2,6,1,3,4,5]=>4
[-,3,2,-,+,-]=>[2,5,1,3,4,6]=>3
[-,3,2,+,-,-]=>[2,4,1,3,5,6]=>2
[+,3,2,-,-,-]=>[1,2,3,4,5,6]=>1
[-,3,2,-,-,-]=>[2,1,3,4,5,6]=>1
[+,3,2,+,6,5]=>[1,2,4,5,3,6]=>1
[-,3,2,+,6,5]=>[2,4,5,1,3,6]=>5
[+,3,2,-,6,5]=>[1,2,5,3,4,6]=>1
[-,3,2,-,6,5]=>[2,5,1,3,4,6]=>3
[+,3,2,5,4,+]=>[1,2,4,6,3,5]=>2
[-,3,2,5,4,+]=>[2,4,6,1,3,5]=>16
[+,3,2,5,4,-]=>[1,2,4,3,5,6]=>1
[-,3,2,5,4,-]=>[2,4,1,3,5,6]=>2
[+,3,2,5,6,4]=>[1,2,4,3,5,6]=>1
[-,3,2,5,6,4]=>[2,4,1,3,5,6]=>2
[+,3,2,6,4,5]=>[1,2,4,5,3,6]=>1
[-,3,2,6,4,5]=>[2,4,5,1,3,6]=>5
[+,3,2,6,+,4]=>[1,2,5,4,3,6]=>2
[-,3,2,6,+,4]=>[2,5,4,1,3,6]=>16
[+,3,2,6,-,4]=>[1,2,4,3,6,5]=>2
[-,3,2,6,-,4]=>[2,4,1,3,6,5]=>8
[+,3,4,2,+,+]=>[1,2,5,6,3,4]=>2
[-,3,4,2,+,+]=>[2,5,6,1,3,4]=>21
[+,3,4,2,-,+]=>[1,2,6,3,4,5]=>1
[+,3,4,2,+,-]=>[1,2,5,3,4,6]=>1
[-,3,4,2,-,+]=>[2,6,1,3,4,5]=>4
[-,3,4,2,+,-]=>[2,5,1,3,4,6]=>3
[+,3,4,2,-,-]=>[1,2,3,4,5,6]=>1
[-,3,4,2,-,-]=>[2,1,3,4,5,6]=>1
[+,3,4,2,6,5]=>[1,2,5,3,4,6]=>1
[-,3,4,2,6,5]=>[2,5,1,3,4,6]=>3
[+,3,4,5,2,+]=>[1,2,6,3,4,5]=>1
[-,3,4,5,2,+]=>[2,6,1,3,4,5]=>4
[+,3,4,5,2,-]=>[1,2,3,4,5,6]=>1
[-,3,4,5,2,-]=>[2,1,3,4,5,6]=>1
[+,3,4,5,6,2]=>[1,2,3,4,5,6]=>1
[-,3,4,5,6,2]=>[2,1,3,4,5,6]=>1
[+,3,4,6,2,5]=>[1,2,5,3,4,6]=>1
[-,3,4,6,2,5]=>[2,5,1,3,4,6]=>3
[+,3,4,6,+,2]=>[1,5,2,3,4,6]=>1
[-,3,4,6,+,2]=>[5,2,1,3,4,6]=>4
[+,3,4,6,-,2]=>[1,2,3,4,6,5]=>1
[-,3,4,6,-,2]=>[2,1,3,4,6,5]=>2
[+,3,5,2,4,+]=>[1,2,4,6,3,5]=>2
[-,3,5,2,4,+]=>[2,4,6,1,3,5]=>16
[+,3,5,2,4,-]=>[1,2,4,3,5,6]=>1
[-,3,5,2,4,-]=>[2,4,1,3,5,6]=>2
[+,3,5,2,6,4]=>[1,2,4,3,5,6]=>1
[-,3,5,2,6,4]=>[2,4,1,3,5,6]=>2
[+,3,5,+,2,+]=>[1,4,2,6,3,5]=>5
[-,3,5,+,2,+]=>[4,2,6,1,3,5]=>56
[+,3,5,-,2,+]=>[1,2,6,3,5,4]=>3
[+,3,5,+,2,-]=>[1,4,2,3,5,6]=>1
[-,3,5,-,2,+]=>[2,6,1,3,5,4]=>19
[-,3,5,+,2,-]=>[4,2,1,3,5,6]=>3
[+,3,5,-,2,-]=>[1,2,3,5,4,6]=>1
[-,3,5,-,2,-]=>[2,1,3,5,4,6]=>2
[+,3,5,+,6,2]=>[1,4,2,3,5,6]=>1
[-,3,5,+,6,2]=>[4,2,1,3,5,6]=>3
[+,3,5,-,6,2]=>[1,2,3,5,4,6]=>1
[-,3,5,-,6,2]=>[2,1,3,5,4,6]=>2
[+,3,5,6,2,4]=>[1,2,4,3,5,6]=>1
[-,3,5,6,2,4]=>[2,4,1,3,5,6]=>2
[+,3,5,6,4,2]=>[1,4,2,3,5,6]=>1
[-,3,5,6,4,2]=>[4,2,1,3,5,6]=>3
[+,3,6,2,4,5]=>[1,2,4,5,3,6]=>1
[-,3,6,2,4,5]=>[2,4,5,1,3,6]=>5
[+,3,6,2,+,4]=>[1,2,5,4,3,6]=>2
[-,3,6,2,+,4]=>[2,5,4,1,3,6]=>16
[+,3,6,2,-,4]=>[1,2,4,3,6,5]=>2
[-,3,6,2,-,4]=>[2,4,1,3,6,5]=>8
[+,3,6,+,2,5]=>[1,4,2,5,3,6]=>2
[-,3,6,+,2,5]=>[4,2,5,1,3,6]=>16
[+,3,6,-,2,5]=>[1,2,5,3,6,4]=>2
[-,3,6,-,2,5]=>[2,5,1,3,6,4]=>11
[+,3,6,+,+,2]=>[1,4,5,2,3,6]=>2
[-,3,6,+,+,2]=>[4,5,2,1,3,6]=>21
[+,3,6,-,+,2]=>[1,5,2,3,6,4]=>3
[+,3,6,+,-,2]=>[1,4,2,3,6,5]=>3
[-,3,6,-,+,2]=>[5,2,1,3,6,4]=>19
[-,3,6,+,-,2]=>[4,2,1,3,6,5]=>15
[+,3,6,-,-,2]=>[1,2,3,6,4,5]=>1
[-,3,6,-,-,2]=>[2,1,3,6,4,5]=>3
[+,3,6,5,2,4]=>[1,2,4,3,6,5]=>2
[-,3,6,5,2,4]=>[2,4,1,3,6,5]=>8
[+,3,6,5,4,2]=>[1,4,2,3,6,5]=>3
[-,3,6,5,4,2]=>[4,2,1,3,6,5]=>15
[+,4,2,3,+,+]=>[1,2,3,5,6,4]=>1
[-,4,2,3,+,+]=>[2,3,5,6,1,4]=>9
[+,4,2,3,-,+]=>[1,2,3,6,4,5]=>1
[+,4,2,3,+,-]=>[1,2,3,5,4,6]=>1
[-,4,2,3,-,+]=>[2,3,6,1,4,5]=>6
[-,4,2,3,+,-]=>[2,3,5,1,4,6]=>3
[+,4,2,3,-,-]=>[1,2,3,4,5,6]=>1
[-,4,2,3,-,-]=>[2,3,1,4,5,6]=>1
[+,4,2,3,6,5]=>[1,2,3,5,4,6]=>1
[-,4,2,3,6,5]=>[2,3,5,1,4,6]=>3
[+,4,2,5,3,+]=>[1,2,3,6,4,5]=>1
[-,4,2,5,3,+]=>[2,3,6,1,4,5]=>6
[+,4,2,5,3,-]=>[1,2,3,4,5,6]=>1
[-,4,2,5,3,-]=>[2,3,1,4,5,6]=>1
[+,4,2,5,6,3]=>[1,2,3,4,5,6]=>1
[-,4,2,5,6,3]=>[2,3,1,4,5,6]=>1
[+,4,2,6,3,5]=>[1,2,3,5,4,6]=>1
[-,4,2,6,3,5]=>[2,3,5,1,4,6]=>3
[+,4,2,6,+,3]=>[1,2,5,3,4,6]=>1
[-,4,2,6,+,3]=>[2,5,3,1,4,6]=>6
[+,4,2,6,-,3]=>[1,2,3,4,6,5]=>1
[-,4,2,6,-,3]=>[2,3,1,4,6,5]=>3
[+,4,+,2,+,+]=>[1,3,2,5,6,4]=>3
[-,4,+,2,+,+]=>[3,2,5,6,1,4]=>49
[+,4,-,2,+,+]=>[1,2,5,6,4,3]=>5
[+,4,+,2,-,+]=>[1,3,2,6,4,5]=>3
[+,4,+,2,+,-]=>[1,3,2,5,4,6]=>2
[-,4,-,2,+,+]=>[2,5,6,1,4,3]=>98
[-,4,+,2,-,+]=>[3,2,6,1,4,5]=>26
[-,4,+,2,+,-]=>[3,2,5,1,4,6]=>11
[+,4,-,2,-,+]=>[1,2,6,4,3,5]=>3
[+,4,-,2,+,-]=>[1,2,5,4,3,6]=>2
[+,4,+,2,-,-]=>[1,3,2,4,5,6]=>1
[-,4,-,2,-,+]=>[2,6,1,4,3,5]=>19
[-,4,-,2,+,-]=>[2,5,1,4,3,6]=>11
[-,4,+,2,-,-]=>[3,2,1,4,5,6]=>2
[+,4,-,2,-,-]=>[1,2,4,3,5,6]=>1
[-,4,-,2,-,-]=>[2,1,4,3,5,6]=>2
[+,4,+,2,6,5]=>[1,3,2,5,4,6]=>2
[-,4,+,2,6,5]=>[3,2,5,1,4,6]=>11
[+,4,-,2,6,5]=>[1,2,5,4,3,6]=>2
[-,4,-,2,6,5]=>[2,5,1,4,3,6]=>11
[+,4,+,5,2,+]=>[1,3,2,6,4,5]=>3
[-,4,+,5,2,+]=>[3,2,6,1,4,5]=>26
[+,4,-,5,2,+]=>[1,2,6,4,3,5]=>3
[+,4,+,5,2,-]=>[1,3,2,4,5,6]=>1
[-,4,-,5,2,+]=>[2,6,1,4,3,5]=>19
[-,4,+,5,2,-]=>[3,2,1,4,5,6]=>2
[+,4,-,5,2,-]=>[1,2,4,3,5,6]=>1
[-,4,-,5,2,-]=>[2,1,4,3,5,6]=>2
[+,4,+,5,6,2]=>[1,3,2,4,5,6]=>1
[-,4,+,5,6,2]=>[3,2,1,4,5,6]=>2
[+,4,-,5,6,2]=>[1,2,4,3,5,6]=>1
[-,4,-,5,6,2]=>[2,1,4,3,5,6]=>2
[+,4,+,6,2,5]=>[1,3,2,5,4,6]=>2
[-,4,+,6,2,5]=>[3,2,5,1,4,6]=>11
[+,4,-,6,2,5]=>[1,2,5,4,3,6]=>2
[-,4,-,6,2,5]=>[2,5,1,4,3,6]=>11
[+,4,+,6,+,2]=>[1,3,5,2,4,6]=>2
[-,4,+,6,+,2]=>[3,5,2,1,4,6]=>16
[+,4,-,6,+,2]=>[1,5,2,4,3,6]=>3
[+,4,+,6,-,2]=>[1,3,2,4,6,5]=>2
[-,4,-,6,+,2]=>[5,2,1,4,3,6]=>19
[-,4,+,6,-,2]=>[3,2,1,4,6,5]=>8
[+,4,-,6,-,2]=>[1,2,4,3,6,5]=>2
[-,4,-,6,-,2]=>[2,1,4,3,6,5]=>6
[+,4,5,2,3,+]=>[1,2,3,6,4,5]=>1
[-,4,5,2,3,+]=>[2,3,6,1,4,5]=>6
[+,4,5,2,3,-]=>[1,2,3,4,5,6]=>1
[-,4,5,2,3,-]=>[2,3,1,4,5,6]=>1
[+,4,5,2,6,3]=>[1,2,3,4,5,6]=>1
[-,4,5,2,6,3]=>[2,3,1,4,5,6]=>1
[+,4,5,3,2,+]=>[1,3,2,6,4,5]=>3
[-,4,5,3,2,+]=>[3,2,6,1,4,5]=>26
[+,4,5,3,2,-]=>[1,3,2,4,5,6]=>1
[-,4,5,3,2,-]=>[3,2,1,4,5,6]=>2
[+,4,5,3,6,2]=>[1,3,2,4,5,6]=>1
[-,4,5,3,6,2]=>[3,2,1,4,5,6]=>2
[+,4,5,6,2,3]=>[1,2,3,4,5,6]=>1
[-,4,5,6,2,3]=>[2,3,1,4,5,6]=>1
[+,4,5,6,3,2]=>[1,3,2,4,5,6]=>1
[-,4,5,6,3,2]=>[3,2,1,4,5,6]=>2
[+,4,6,2,3,5]=>[1,2,3,5,4,6]=>1
[-,4,6,2,3,5]=>[2,3,5,1,4,6]=>3
[+,4,6,2,+,3]=>[1,2,5,3,4,6]=>1
[-,4,6,2,+,3]=>[2,5,3,1,4,6]=>6
[+,4,6,2,-,3]=>[1,2,3,4,6,5]=>1
[-,4,6,2,-,3]=>[2,3,1,4,6,5]=>3
[+,4,6,3,2,5]=>[1,3,2,5,4,6]=>2
[-,4,6,3,2,5]=>[3,2,5,1,4,6]=>11
[+,4,6,3,+,2]=>[1,3,5,2,4,6]=>2
[-,4,6,3,+,2]=>[3,5,2,1,4,6]=>16
[+,4,6,3,-,2]=>[1,3,2,4,6,5]=>2
[-,4,6,3,-,2]=>[3,2,1,4,6,5]=>8
[+,4,6,5,2,3]=>[1,2,3,4,6,5]=>1
[-,4,6,5,2,3]=>[2,3,1,4,6,5]=>3
[+,4,6,5,3,2]=>[1,3,2,4,6,5]=>2
[-,4,6,5,3,2]=>[3,2,1,4,6,5]=>8
[+,5,2,3,4,+]=>[1,2,3,4,6,5]=>1
[-,5,2,3,4,+]=>[2,3,4,6,1,5]=>4
[+,5,2,3,4,-]=>[1,2,3,4,5,6]=>1
[-,5,2,3,4,-]=>[2,3,4,1,5,6]=>1
[+,5,2,3,6,4]=>[1,2,3,4,5,6]=>1
[-,5,2,3,6,4]=>[2,3,4,1,5,6]=>1
[+,5,2,+,3,+]=>[1,2,4,3,6,5]=>2
[-,5,2,+,3,+]=>[2,4,3,6,1,5]=>19
[+,5,2,-,3,+]=>[1,2,3,6,5,4]=>2
[+,5,2,+,3,-]=>[1,2,4,3,5,6]=>1
[-,5,2,-,3,+]=>[2,3,6,1,5,4]=>26
[-,5,2,+,3,-]=>[2,4,3,1,5,6]=>3
[+,5,2,-,3,-]=>[1,2,3,5,4,6]=>1
[-,5,2,-,3,-]=>[2,3,1,5,4,6]=>3
[+,5,2,+,6,3]=>[1,2,4,3,5,6]=>1
[-,5,2,+,6,3]=>[2,4,3,1,5,6]=>3
[+,5,2,-,6,3]=>[1,2,3,5,4,6]=>1
[-,5,2,-,6,3]=>[2,3,1,5,4,6]=>3
[+,5,2,6,3,4]=>[1,2,3,4,5,6]=>1
[-,5,2,6,3,4]=>[2,3,4,1,5,6]=>1
[+,5,2,6,4,3]=>[1,2,4,3,5,6]=>1
[-,5,2,6,4,3]=>[2,4,3,1,5,6]=>3
[+,5,+,2,4,+]=>[1,3,2,4,6,5]=>2
[-,5,+,2,4,+]=>[3,2,4,6,1,5]=>19
[+,5,-,2,4,+]=>[1,2,4,6,5,3]=>3
[+,5,+,2,4,-]=>[1,3,2,4,5,6]=>1
[-,5,-,2,4,+]=>[2,4,6,1,5,3]=>56
[-,5,+,2,4,-]=>[3,2,4,1,5,6]=>3
[+,5,-,2,4,-]=>[1,2,4,5,3,6]=>1
[-,5,-,2,4,-]=>[2,4,1,5,3,6]=>5
[+,5,+,2,6,4]=>[1,3,2,4,5,6]=>1
[-,5,+,2,6,4]=>[3,2,4,1,5,6]=>3
[+,5,-,2,6,4]=>[1,2,4,5,3,6]=>1
[-,5,-,2,6,4]=>[2,4,1,5,3,6]=>5
[+,5,+,+,2,+]=>[1,3,4,2,6,5]=>3
[-,5,+,+,2,+]=>[3,4,2,6,1,5]=>49
[+,5,-,+,2,+]=>[1,4,2,6,5,3]=>11
[+,5,+,-,2,+]=>[1,3,2,6,5,4]=>8
[+,5,+,+,2,-]=>[1,3,4,2,5,6]=>1
[-,5,-,+,2,+]=>[4,2,6,1,5,3]=>244
[-,5,+,-,2,+]=>[3,2,6,1,5,4]=>132
[-,5,+,+,2,-]=>[3,4,2,1,5,6]=>5
[+,5,-,-,2,+]=>[1,2,6,5,3,4]=>5
[+,5,-,+,2,-]=>[1,4,2,5,3,6]=>2
[+,5,+,-,2,-]=>[1,3,2,5,4,6]=>2
[-,5,-,-,2,+]=>[2,6,1,5,3,4]=>49
[-,5,-,+,2,-]=>[4,2,1,5,3,6]=>11
[-,5,+,-,2,-]=>[3,2,1,5,4,6]=>8
[+,5,-,-,2,-]=>[1,2,5,3,4,6]=>1
[-,5,-,-,2,-]=>[2,1,5,3,4,6]=>3
[+,5,+,+,6,2]=>[1,3,4,2,5,6]=>1
[-,5,+,+,6,2]=>[3,4,2,1,5,6]=>5
[+,5,-,+,6,2]=>[1,4,2,5,3,6]=>2
[+,5,+,-,6,2]=>[1,3,2,5,4,6]=>2
[-,5,-,+,6,2]=>[4,2,1,5,3,6]=>11
[-,5,+,-,6,2]=>[3,2,1,5,4,6]=>8
[+,5,-,-,6,2]=>[1,2,5,3,4,6]=>1
[-,5,-,-,6,2]=>[2,1,5,3,4,6]=>3
[+,5,+,6,2,4]=>[1,3,2,4,5,6]=>1
[-,5,+,6,2,4]=>[3,2,4,1,5,6]=>3
[+,5,-,6,2,4]=>[1,2,4,5,3,6]=>1
[-,5,-,6,2,4]=>[2,4,1,5,3,6]=>5
[+,5,+,6,4,2]=>[1,3,4,2,5,6]=>1
[-,5,+,6,4,2]=>[3,4,2,1,5,6]=>5
[+,5,-,6,4,2]=>[1,4,2,5,3,6]=>2
[-,5,-,6,4,2]=>[4,2,1,5,3,6]=>11
[+,5,4,2,3,+]=>[1,2,3,6,5,4]=>2
[-,5,4,2,3,+]=>[2,3,6,1,5,4]=>26
[+,5,4,2,3,-]=>[1,2,3,5,4,6]=>1
[-,5,4,2,3,-]=>[2,3,1,5,4,6]=>3
[+,5,4,2,6,3]=>[1,2,3,5,4,6]=>1
[-,5,4,2,6,3]=>[2,3,1,5,4,6]=>3
[+,5,4,3,2,+]=>[1,3,2,6,5,4]=>8
[-,5,4,3,2,+]=>[3,2,6,1,5,4]=>132
[+,5,4,3,2,-]=>[1,3,2,5,4,6]=>2
[-,5,4,3,2,-]=>[3,2,1,5,4,6]=>8
[+,5,4,3,6,2]=>[1,3,2,5,4,6]=>2
[-,5,4,3,6,2]=>[3,2,1,5,4,6]=>8
[+,5,4,6,2,3]=>[1,2,3,5,4,6]=>1
[-,5,4,6,2,3]=>[2,3,1,5,4,6]=>3
[+,5,4,6,3,2]=>[1,3,2,5,4,6]=>2
[-,5,4,6,3,2]=>[3,2,1,5,4,6]=>8
[+,5,6,2,3,4]=>[1,2,3,4,5,6]=>1
[-,5,6,2,3,4]=>[2,3,4,1,5,6]=>1
[+,5,6,2,4,3]=>[1,2,4,3,5,6]=>1
[-,5,6,2,4,3]=>[2,4,3,1,5,6]=>3
[+,5,6,3,2,4]=>[1,3,2,4,5,6]=>1
[-,5,6,3,2,4]=>[3,2,4,1,5,6]=>3
[+,5,6,3,4,2]=>[1,3,4,2,5,6]=>1
[-,5,6,3,4,2]=>[3,4,2,1,5,6]=>5
[+,5,6,+,2,3]=>[1,4,2,3,5,6]=>1
[-,5,6,+,2,3]=>[4,2,3,1,5,6]=>6
[+,5,6,-,2,3]=>[1,2,3,5,6,4]=>1
[-,5,6,-,2,3]=>[2,3,1,5,6,4]=>6
[+,5,6,+,3,2]=>[1,4,3,2,5,6]=>2
[-,5,6,+,3,2]=>[4,3,2,1,5,6]=>16
[+,5,6,-,3,2]=>[1,3,2,5,6,4]=>3
[-,5,6,-,3,2]=>[3,2,1,5,6,4]=>20
[+,6,2,3,4,5]=>[1,2,3,4,5,6]=>1
[-,6,2,3,4,5]=>[2,3,4,5,1,6]=>1
[+,6,2,3,+,4]=>[1,2,3,5,4,6]=>1
[-,6,2,3,+,4]=>[2,3,5,4,1,6]=>4
[+,6,2,3,-,4]=>[1,2,3,4,6,5]=>1
[-,6,2,3,-,4]=>[2,3,4,1,6,5]=>4
[+,6,2,+,3,5]=>[1,2,4,3,5,6]=>1
[-,6,2,+,3,5]=>[2,4,3,5,1,6]=>4
[+,6,2,-,3,5]=>[1,2,3,5,6,4]=>1
[-,6,2,-,3,5]=>[2,3,5,1,6,4]=>9
[+,6,2,+,+,3]=>[1,2,4,5,3,6]=>1
[-,6,2,+,+,3]=>[2,4,5,3,1,6]=>9
[+,6,2,-,+,3]=>[1,2,5,3,6,4]=>2
[+,6,2,+,-,3]=>[1,2,4,3,6,5]=>2
[-,6,2,-,+,3]=>[2,5,3,1,6,4]=>26
[-,6,2,+,-,3]=>[2,4,3,1,6,5]=>15
[+,6,2,-,-,3]=>[1,2,3,6,4,5]=>1
[-,6,2,-,-,3]=>[2,3,1,6,4,5]=>6
[+,6,2,5,3,4]=>[1,2,3,4,6,5]=>1
[-,6,2,5,3,4]=>[2,3,4,1,6,5]=>4
[+,6,2,5,4,3]=>[1,2,4,3,6,5]=>2
[-,6,2,5,4,3]=>[2,4,3,1,6,5]=>15
[+,6,+,2,4,5]=>[1,3,2,4,5,6]=>1
[-,6,+,2,4,5]=>[3,2,4,5,1,6]=>4
[+,6,-,2,4,5]=>[1,2,4,5,6,3]=>1
[-,6,-,2,4,5]=>[2,4,5,1,6,3]=>14
[+,6,+,2,+,4]=>[1,3,2,5,4,6]=>2
[-,6,+,2,+,4]=>[3,2,5,4,1,6]=>19
[+,6,-,2,+,4]=>[1,2,5,4,6,3]=>3
[+,6,+,2,-,4]=>[1,3,2,4,6,5]=>2
[-,6,-,2,+,4]=>[2,5,4,1,6,3]=>56
[-,6,+,2,-,4]=>[3,2,4,1,6,5]=>15
[+,6,-,2,-,4]=>[1,2,4,6,3,5]=>2
[-,6,-,2,-,4]=>[2,4,1,6,3,5]=>16
[+,6,+,+,2,5]=>[1,3,4,2,5,6]=>1
[-,6,+,+,2,5]=>[3,4,2,5,1,6]=>9
[+,6,-,+,2,5]=>[1,4,2,5,6,3]=>3
[+,6,+,-,2,5]=>[1,3,2,5,6,4]=>3
[-,6,-,+,2,5]=>[4,2,5,1,6,3]=>56
[-,6,+,-,2,5]=>[3,2,5,1,6,4]=>40
[+,6,-,-,2,5]=>[1,2,5,6,3,4]=>2
[-,6,-,-,2,5]=>[2,5,1,6,3,4]=>21
[+,6,+,+,+,2]=>[1,3,4,5,2,6]=>1
[-,6,+,+,+,2]=>[3,4,5,2,1,6]=>14
[+,6,-,+,+,2]=>[1,4,5,2,6,3]=>5
[+,6,+,-,+,2]=>[1,3,5,2,6,4]=>5
[+,6,+,+,-,2]=>[1,3,4,2,6,5]=>3
[-,6,-,+,+,2]=>[4,5,2,1,6,3]=>98
[-,6,+,-,+,2]=>[3,5,2,1,6,4]=>77
[-,6,+,+,-,2]=>[3,4,2,1,6,5]=>30
[+,6,-,-,+,2]=>[1,5,2,6,3,4]=>5
[+,6,-,+,-,2]=>[1,4,2,6,3,5]=>5
[+,6,+,-,-,2]=>[1,3,2,6,4,5]=>3
[-,6,-,-,+,2]=>[5,2,1,6,3,4]=>49
[-,6,-,+,-,2]=>[4,2,1,6,3,5]=>40
[-,6,+,-,-,2]=>[3,2,1,6,4,5]=>20
[+,6,-,-,-,2]=>[1,2,6,3,4,5]=>1
[-,6,-,-,-,2]=>[2,1,6,3,4,5]=>4
[+,6,+,5,2,4]=>[1,3,2,4,6,5]=>2
[-,6,+,5,2,4]=>[3,2,4,1,6,5]=>15
[+,6,-,5,2,4]=>[1,2,4,6,3,5]=>2
[-,6,-,5,2,4]=>[2,4,1,6,3,5]=>16
[+,6,+,5,4,2]=>[1,3,4,2,6,5]=>3
[-,6,+,5,4,2]=>[3,4,2,1,6,5]=>30
[+,6,-,5,4,2]=>[1,4,2,6,3,5]=>5
[-,6,-,5,4,2]=>[4,2,1,6,3,5]=>40
[+,6,4,2,3,5]=>[1,2,3,5,6,4]=>1
[-,6,4,2,3,5]=>[2,3,5,1,6,4]=>9
[+,6,4,2,+,3]=>[1,2,5,3,6,4]=>2
[-,6,4,2,+,3]=>[2,5,3,1,6,4]=>26
[+,6,4,2,-,3]=>[1,2,3,6,4,5]=>1
[-,6,4,2,-,3]=>[2,3,1,6,4,5]=>6
[+,6,4,3,2,5]=>[1,3,2,5,6,4]=>3
[-,6,4,3,2,5]=>[3,2,5,1,6,4]=>40
[+,6,4,3,+,2]=>[1,3,5,2,6,4]=>5
[-,6,4,3,+,2]=>[3,5,2,1,6,4]=>77
[+,6,4,3,-,2]=>[1,3,2,6,4,5]=>3
[-,6,4,3,-,2]=>[3,2,1,6,4,5]=>20
[+,6,4,5,2,3]=>[1,2,3,6,4,5]=>1
[-,6,4,5,2,3]=>[2,3,1,6,4,5]=>6
[+,6,4,5,3,2]=>[1,3,2,6,4,5]=>3
[-,6,4,5,3,2]=>[3,2,1,6,4,5]=>20
[+,6,5,2,3,4]=>[1,2,3,4,6,5]=>1
[-,6,5,2,3,4]=>[2,3,4,1,6,5]=>4
[+,6,5,2,4,3]=>[1,2,4,3,6,5]=>2
[-,6,5,2,4,3]=>[2,4,3,1,6,5]=>15
[+,6,5,3,2,4]=>[1,3,2,4,6,5]=>2
[-,6,5,3,2,4]=>[3,2,4,1,6,5]=>15
[+,6,5,3,4,2]=>[1,3,4,2,6,5]=>3
[-,6,5,3,4,2]=>[3,4,2,1,6,5]=>30
[+,6,5,+,2,3]=>[1,4,2,3,6,5]=>3
[-,6,5,+,2,3]=>[4,2,3,1,6,5]=>36
[+,6,5,-,2,3]=>[1,2,3,6,5,4]=>2
[-,6,5,-,2,3]=>[2,3,1,6,5,4]=>20
[+,6,5,+,3,2]=>[1,4,3,2,6,5]=>8
[-,6,5,+,3,2]=>[4,3,2,1,6,5]=>112
[+,6,5,-,3,2]=>[1,3,2,6,5,4]=>8
[-,6,5,-,3,2]=>[3,2,1,6,5,4]=>80
[2,1,+,+,+,+]=>[1,3,4,5,6,2]=>1
[2,1,-,+,+,+]=>[1,4,5,6,2,3]=>5
[2,1,+,-,+,+]=>[1,3,5,6,2,4]=>5
[2,1,+,+,-,+]=>[1,3,4,6,2,5]=>3
[2,1,+,+,+,-]=>[1,3,4,5,2,6]=>1
[2,1,-,-,+,+]=>[1,5,6,2,3,4]=>5
[2,1,-,+,-,+]=>[1,4,6,2,3,5]=>5
[2,1,-,+,+,-]=>[1,4,5,2,3,6]=>2
[2,1,+,-,-,+]=>[1,3,6,2,4,5]=>3
[2,1,+,-,+,-]=>[1,3,5,2,4,6]=>2
[2,1,+,+,-,-]=>[1,3,4,2,5,6]=>1
[2,1,-,-,-,+]=>[1,6,2,3,4,5]=>1
[2,1,-,-,+,-]=>[1,5,2,3,4,6]=>1
[2,1,-,+,-,-]=>[1,4,2,3,5,6]=>1
[2,1,+,-,-,-]=>[1,3,2,4,5,6]=>1
[2,1,-,-,-,-]=>[1,2,3,4,5,6]=>1
[2,1,+,+,6,5]=>[1,3,4,5,2,6]=>1
[2,1,-,+,6,5]=>[1,4,5,2,3,6]=>2
[2,1,+,-,6,5]=>[1,3,5,2,4,6]=>2
[2,1,-,-,6,5]=>[1,5,2,3,4,6]=>1
[2,1,+,5,4,+]=>[1,3,4,6,2,5]=>3
[2,1,-,5,4,+]=>[1,4,6,2,3,5]=>5
[2,1,+,5,4,-]=>[1,3,4,2,5,6]=>1
[2,1,-,5,4,-]=>[1,4,2,3,5,6]=>1
[2,1,+,5,6,4]=>[1,3,4,2,5,6]=>1
[2,1,-,5,6,4]=>[1,4,2,3,5,6]=>1
[2,1,+,6,4,5]=>[1,3,4,5,2,6]=>1
[2,1,-,6,4,5]=>[1,4,5,2,3,6]=>2
[2,1,+,6,+,4]=>[1,3,5,4,2,6]=>3
[2,1,-,6,+,4]=>[1,5,4,2,3,6]=>5
[2,1,+,6,-,4]=>[1,3,4,2,6,5]=>3
[2,1,-,6,-,4]=>[1,4,2,3,6,5]=>3
[2,1,4,3,+,+]=>[1,3,5,6,2,4]=>5
[2,1,4,3,-,+]=>[1,3,6,2,4,5]=>3
[2,1,4,3,+,-]=>[1,3,5,2,4,6]=>2
[2,1,4,3,-,-]=>[1,3,2,4,5,6]=>1
[2,1,4,3,6,5]=>[1,3,5,2,4,6]=>2
[2,1,4,5,3,+]=>[1,3,6,2,4,5]=>3
[2,1,4,5,3,-]=>[1,3,2,4,5,6]=>1
[2,1,4,5,6,3]=>[1,3,2,4,5,6]=>1
[2,1,4,6,3,5]=>[1,3,5,2,4,6]=>2
[2,1,4,6,+,3]=>[1,5,3,2,4,6]=>3
[2,1,4,6,-,3]=>[1,3,2,4,6,5]=>2
[2,1,5,3,4,+]=>[1,3,4,6,2,5]=>3
[2,1,5,3,4,-]=>[1,3,4,2,5,6]=>1
[2,1,5,3,6,4]=>[1,3,4,2,5,6]=>1
[2,1,5,+,3,+]=>[1,4,3,6,2,5]=>11
[2,1,5,-,3,+]=>[1,3,6,2,5,4]=>11
[2,1,5,+,3,-]=>[1,4,3,2,5,6]=>2
[2,1,5,-,3,-]=>[1,3,2,5,4,6]=>2
[2,1,5,+,6,3]=>[1,4,3,2,5,6]=>2
[2,1,5,-,6,3]=>[1,3,2,5,4,6]=>2
[2,1,5,6,3,4]=>[1,3,4,2,5,6]=>1
[2,1,5,6,4,3]=>[1,4,3,2,5,6]=>2
[2,1,6,3,4,5]=>[1,3,4,5,2,6]=>1
[2,1,6,3,+,4]=>[1,3,5,4,2,6]=>3
[2,1,6,3,-,4]=>[1,3,4,2,6,5]=>3
[2,1,6,+,3,5]=>[1,4,3,5,2,6]=>3
[2,1,6,-,3,5]=>[1,3,5,2,6,4]=>5
[2,1,6,+,+,3]=>[1,4,5,3,2,6]=>5
[2,1,6,-,+,3]=>[1,5,3,2,6,4]=>11
[2,1,6,+,-,3]=>[1,4,3,2,6,5]=>8
[2,1,6,-,-,3]=>[1,3,2,6,4,5]=>3
[2,1,6,5,3,4]=>[1,3,4,2,6,5]=>3
[2,1,6,5,4,3]=>[1,4,3,2,6,5]=>8
[2,3,1,+,+,+]=>[1,4,5,6,2,3]=>5
[2,3,1,-,+,+]=>[1,5,6,2,3,4]=>5
[2,3,1,+,-,+]=>[1,4,6,2,3,5]=>5
[2,3,1,+,+,-]=>[1,4,5,2,3,6]=>2
[2,3,1,-,-,+]=>[1,6,2,3,4,5]=>1
[2,3,1,-,+,-]=>[1,5,2,3,4,6]=>1
[2,3,1,+,-,-]=>[1,4,2,3,5,6]=>1
[2,3,1,-,-,-]=>[1,2,3,4,5,6]=>1
[2,3,1,+,6,5]=>[1,4,5,2,3,6]=>2
[2,3,1,-,6,5]=>[1,5,2,3,4,6]=>1
[2,3,1,5,4,+]=>[1,4,6,2,3,5]=>5
[2,3,1,5,4,-]=>[1,4,2,3,5,6]=>1
[2,3,1,5,6,4]=>[1,4,2,3,5,6]=>1
[2,3,1,6,4,5]=>[1,4,5,2,3,6]=>2
[2,3,1,6,+,4]=>[1,5,4,2,3,6]=>5
[2,3,1,6,-,4]=>[1,4,2,3,6,5]=>3
[2,3,4,1,+,+]=>[1,5,6,2,3,4]=>5
[2,3,4,1,-,+]=>[1,6,2,3,4,5]=>1
[2,3,4,1,+,-]=>[1,5,2,3,4,6]=>1
[2,3,4,1,-,-]=>[1,2,3,4,5,6]=>1
[2,3,4,1,6,5]=>[1,5,2,3,4,6]=>1
[2,3,4,5,1,+]=>[1,6,2,3,4,5]=>1
[2,3,4,5,1,-]=>[1,2,3,4,5,6]=>1
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>1
[2,3,4,6,1,5]=>[1,5,2,3,4,6]=>1
[2,3,4,6,+,1]=>[5,1,2,3,4,6]=>1
[2,3,4,6,-,1]=>[1,2,3,4,6,5]=>1
[2,3,5,1,4,+]=>[1,4,6,2,3,5]=>5
[2,3,5,1,4,-]=>[1,4,2,3,5,6]=>1
[2,3,5,1,6,4]=>[1,4,2,3,5,6]=>1
[2,3,5,+,1,+]=>[4,1,6,2,3,5]=>14
[2,3,5,-,1,+]=>[1,6,2,3,5,4]=>4
[2,3,5,+,1,-]=>[4,1,2,3,5,6]=>1
[2,3,5,-,1,-]=>[1,2,3,5,4,6]=>1
[2,3,5,+,6,1]=>[4,1,2,3,5,6]=>1
[2,3,5,-,6,1]=>[1,2,3,5,4,6]=>1
[2,3,5,6,1,4]=>[1,4,2,3,5,6]=>1
[2,3,5,6,4,1]=>[4,1,2,3,5,6]=>1
[2,3,6,1,4,5]=>[1,4,5,2,3,6]=>2
[2,3,6,1,+,4]=>[1,5,4,2,3,6]=>5
[2,3,6,1,-,4]=>[1,4,2,3,6,5]=>3
[2,3,6,+,1,5]=>[4,1,5,2,3,6]=>5
[2,3,6,-,1,5]=>[1,5,2,3,6,4]=>3
[2,3,6,+,+,1]=>[4,5,1,2,3,6]=>5
[2,3,6,-,+,1]=>[5,1,2,3,6,4]=>4
[2,3,6,+,-,1]=>[4,1,2,3,6,5]=>4
[2,3,6,-,-,1]=>[1,2,3,6,4,5]=>1
[2,3,6,5,1,4]=>[1,4,2,3,6,5]=>3
[2,3,6,5,4,1]=>[4,1,2,3,6,5]=>4
[2,4,1,3,+,+]=>[1,3,5,6,2,4]=>5
[2,4,1,3,-,+]=>[1,3,6,2,4,5]=>3
[2,4,1,3,+,-]=>[1,3,5,2,4,6]=>2
[2,4,1,3,-,-]=>[1,3,2,4,5,6]=>1
[2,4,1,3,6,5]=>[1,3,5,2,4,6]=>2
[2,4,1,5,3,+]=>[1,3,6,2,4,5]=>3
[2,4,1,5,3,-]=>[1,3,2,4,5,6]=>1
[2,4,1,5,6,3]=>[1,3,2,4,5,6]=>1
[2,4,1,6,3,5]=>[1,3,5,2,4,6]=>2
[2,4,1,6,+,3]=>[1,5,3,2,4,6]=>3
[2,4,1,6,-,3]=>[1,3,2,4,6,5]=>2
[2,4,+,1,+,+]=>[3,1,5,6,2,4]=>21
[2,4,-,1,+,+]=>[1,5,6,2,4,3]=>21
[2,4,+,1,-,+]=>[3,1,6,2,4,5]=>9
[2,4,+,1,+,-]=>[3,1,5,2,4,6]=>5
[2,4,-,1,-,+]=>[1,6,2,4,3,5]=>4
[2,4,-,1,+,-]=>[1,5,2,4,3,6]=>3
[2,4,+,1,-,-]=>[3,1,2,4,5,6]=>1
[2,4,-,1,-,-]=>[1,2,4,3,5,6]=>1
[2,4,+,1,6,5]=>[3,1,5,2,4,6]=>5
[2,4,-,1,6,5]=>[1,5,2,4,3,6]=>3
[2,4,+,5,1,+]=>[3,1,6,2,4,5]=>9
[2,4,-,5,1,+]=>[1,6,2,4,3,5]=>4
[2,4,+,5,1,-]=>[3,1,2,4,5,6]=>1
[2,4,-,5,1,-]=>[1,2,4,3,5,6]=>1
[2,4,+,5,6,1]=>[3,1,2,4,5,6]=>1
[2,4,-,5,6,1]=>[1,2,4,3,5,6]=>1
[2,4,+,6,1,5]=>[3,1,5,2,4,6]=>5
[2,4,-,6,1,5]=>[1,5,2,4,3,6]=>3
[2,4,+,6,+,1]=>[3,5,1,2,4,6]=>5
[2,4,-,6,+,1]=>[5,1,2,4,3,6]=>4
[2,4,+,6,-,1]=>[3,1,2,4,6,5]=>3
[2,4,-,6,-,1]=>[1,2,4,3,6,5]=>2
[2,4,5,1,3,+]=>[1,3,6,2,4,5]=>3
[2,4,5,1,3,-]=>[1,3,2,4,5,6]=>1
[2,4,5,1,6,3]=>[1,3,2,4,5,6]=>1
[2,4,5,3,1,+]=>[3,1,6,2,4,5]=>9
[2,4,5,3,1,-]=>[3,1,2,4,5,6]=>1
[2,4,5,3,6,1]=>[3,1,2,4,5,6]=>1
[2,4,5,6,1,3]=>[1,3,2,4,5,6]=>1
[2,4,5,6,3,1]=>[3,1,2,4,5,6]=>1
[2,4,6,1,3,5]=>[1,3,5,2,4,6]=>2
[2,4,6,1,+,3]=>[1,5,3,2,4,6]=>3
[2,4,6,1,-,3]=>[1,3,2,4,6,5]=>2
[2,4,6,3,1,5]=>[3,1,5,2,4,6]=>5
[2,4,6,3,+,1]=>[3,5,1,2,4,6]=>5
[2,4,6,3,-,1]=>[3,1,2,4,6,5]=>3
[2,4,6,5,1,3]=>[1,3,2,4,6,5]=>2
[2,4,6,5,3,1]=>[3,1,2,4,6,5]=>3
[2,5,1,3,4,+]=>[1,3,4,6,2,5]=>3
[2,5,1,3,4,-]=>[1,3,4,2,5,6]=>1
[2,5,1,3,6,4]=>[1,3,4,2,5,6]=>1
[2,5,1,+,3,+]=>[1,4,3,6,2,5]=>11
[2,5,1,-,3,+]=>[1,3,6,2,5,4]=>11
[2,5,1,+,3,-]=>[1,4,3,2,5,6]=>2
[2,5,1,-,3,-]=>[1,3,2,5,4,6]=>2
[2,5,1,+,6,3]=>[1,4,3,2,5,6]=>2
[2,5,1,-,6,3]=>[1,3,2,5,4,6]=>2
[2,5,1,6,3,4]=>[1,3,4,2,5,6]=>1
[2,5,1,6,4,3]=>[1,4,3,2,5,6]=>2
[2,5,+,1,4,+]=>[3,1,4,6,2,5]=>11
[2,5,-,1,4,+]=>[1,4,6,2,5,3]=>16
[2,5,+,1,4,-]=>[3,1,4,2,5,6]=>2
[2,5,-,1,4,-]=>[1,4,2,5,3,6]=>2
[2,5,+,1,6,4]=>[3,1,4,2,5,6]=>2
[2,5,-,1,6,4]=>[1,4,2,5,3,6]=>2
[2,5,+,+,1,+]=>[3,4,1,6,2,5]=>21
[2,5,-,+,1,+]=>[4,1,6,2,5,3]=>56
[2,5,+,-,1,+]=>[3,1,6,2,5,4]=>40
[2,5,+,+,1,-]=>[3,4,1,2,5,6]=>2
[2,5,-,-,1,+]=>[1,6,2,5,3,4]=>9
[2,5,-,+,1,-]=>[4,1,2,5,3,6]=>3
[2,5,+,-,1,-]=>[3,1,2,5,4,6]=>3
[2,5,-,-,1,-]=>[1,2,5,3,4,6]=>1
[2,5,+,+,6,1]=>[3,4,1,2,5,6]=>2
[2,5,-,+,6,1]=>[4,1,2,5,3,6]=>3
[2,5,+,-,6,1]=>[3,1,2,5,4,6]=>3
[2,5,-,-,6,1]=>[1,2,5,3,4,6]=>1
[2,5,+,6,1,4]=>[3,1,4,2,5,6]=>2
[2,5,-,6,1,4]=>[1,4,2,5,3,6]=>2
[2,5,+,6,4,1]=>[3,4,1,2,5,6]=>2
[2,5,-,6,4,1]=>[4,1,2,5,3,6]=>3
[2,5,4,1,3,+]=>[1,3,6,2,5,4]=>11
[2,5,4,1,3,-]=>[1,3,2,5,4,6]=>2
[2,5,4,1,6,3]=>[1,3,2,5,4,6]=>2
[2,5,4,3,1,+]=>[3,1,6,2,5,4]=>40
[2,5,4,3,1,-]=>[3,1,2,5,4,6]=>3
[2,5,4,3,6,1]=>[3,1,2,5,4,6]=>3
[2,5,4,6,1,3]=>[1,3,2,5,4,6]=>2
[2,5,4,6,3,1]=>[3,1,2,5,4,6]=>3
[2,5,6,1,3,4]=>[1,3,4,2,5,6]=>1
[2,5,6,1,4,3]=>[1,4,3,2,5,6]=>2
[2,5,6,3,1,4]=>[3,1,4,2,5,6]=>2
[2,5,6,3,4,1]=>[3,4,1,2,5,6]=>2
[2,5,6,+,1,3]=>[4,1,3,2,5,6]=>3
[2,5,6,-,1,3]=>[1,3,2,5,6,4]=>3
[2,5,6,+,3,1]=>[4,3,1,2,5,6]=>5
[2,5,6,-,3,1]=>[3,1,2,5,6,4]=>6
[2,6,1,3,4,5]=>[1,3,4,5,2,6]=>1
[2,6,1,3,+,4]=>[1,3,5,4,2,6]=>3
[2,6,1,3,-,4]=>[1,3,4,2,6,5]=>3
[2,6,1,+,3,5]=>[1,4,3,5,2,6]=>3
[2,6,1,-,3,5]=>[1,3,5,2,6,4]=>5
[2,6,1,+,+,3]=>[1,4,5,3,2,6]=>5
[2,6,1,-,+,3]=>[1,5,3,2,6,4]=>11
[2,6,1,+,-,3]=>[1,4,3,2,6,5]=>8
[2,6,1,-,-,3]=>[1,3,2,6,4,5]=>3
[2,6,1,5,3,4]=>[1,3,4,2,6,5]=>3
[2,6,1,5,4,3]=>[1,4,3,2,6,5]=>8
[2,6,+,1,4,5]=>[3,1,4,5,2,6]=>3
[2,6,-,1,4,5]=>[1,4,5,2,6,3]=>5
[2,6,+,1,+,4]=>[3,1,5,4,2,6]=>11
[2,6,-,1,+,4]=>[1,5,4,2,6,3]=>16
[2,6,+,1,-,4]=>[3,1,4,2,6,5]=>8
[2,6,-,1,-,4]=>[1,4,2,6,3,5]=>5
[2,6,+,+,1,5]=>[3,4,1,5,2,6]=>5
[2,6,-,+,1,5]=>[4,1,5,2,6,3]=>16
[2,6,+,-,1,5]=>[3,1,5,2,6,4]=>16
[2,6,-,-,1,5]=>[1,5,2,6,3,4]=>5
[2,6,+,+,+,1]=>[3,4,5,1,2,6]=>5
[2,6,-,+,+,1]=>[4,5,1,2,6,3]=>21
[2,6,+,-,+,1]=>[3,5,1,2,6,4]=>21
[2,6,+,+,-,1]=>[3,4,1,2,6,5]=>10
[2,6,-,-,+,1]=>[5,1,2,6,3,4]=>9
[2,6,-,+,-,1]=>[4,1,2,6,3,5]=>9
[2,6,+,-,-,1]=>[3,1,2,6,4,5]=>6
[2,6,-,-,-,1]=>[1,2,6,3,4,5]=>1
[2,6,+,5,1,4]=>[3,1,4,2,6,5]=>8
[2,6,-,5,1,4]=>[1,4,2,6,3,5]=>5
[2,6,+,5,4,1]=>[3,4,1,2,6,5]=>10
[2,6,-,5,4,1]=>[4,1,2,6,3,5]=>9
[2,6,4,1,3,5]=>[1,3,5,2,6,4]=>5
[2,6,4,1,+,3]=>[1,5,3,2,6,4]=>11
[2,6,4,1,-,3]=>[1,3,2,6,4,5]=>3
[2,6,4,3,1,5]=>[3,1,5,2,6,4]=>16
[2,6,4,3,+,1]=>[3,5,1,2,6,4]=>21
[2,6,4,3,-,1]=>[3,1,2,6,4,5]=>6
[2,6,4,5,1,3]=>[1,3,2,6,4,5]=>3
[2,6,4,5,3,1]=>[3,1,2,6,4,5]=>6
[2,6,5,1,3,4]=>[1,3,4,2,6,5]=>3
[2,6,5,1,4,3]=>[1,4,3,2,6,5]=>8
[2,6,5,3,1,4]=>[3,1,4,2,6,5]=>8
[2,6,5,3,4,1]=>[3,4,1,2,6,5]=>10
[2,6,5,+,1,3]=>[4,1,3,2,6,5]=>15
[2,6,5,-,1,3]=>[1,3,2,6,5,4]=>8
[2,6,5,+,3,1]=>[4,3,1,2,6,5]=>30
[2,6,5,-,3,1]=>[3,1,2,6,5,4]=>20
[3,1,2,+,+,+]=>[1,2,4,5,6,3]=>1
[3,1,2,-,+,+]=>[1,2,5,6,3,4]=>2
[3,1,2,+,-,+]=>[1,2,4,6,3,5]=>2
[3,1,2,+,+,-]=>[1,2,4,5,3,6]=>1
[3,1,2,-,-,+]=>[1,2,6,3,4,5]=>1
[3,1,2,-,+,-]=>[1,2,5,3,4,6]=>1
[3,1,2,+,-,-]=>[1,2,4,3,5,6]=>1
[3,1,2,-,-,-]=>[1,2,3,4,5,6]=>1
[3,1,2,+,6,5]=>[1,2,4,5,3,6]=>1
[3,1,2,-,6,5]=>[1,2,5,3,4,6]=>1
[3,1,2,5,4,+]=>[1,2,4,6,3,5]=>2
[3,1,2,5,4,-]=>[1,2,4,3,5,6]=>1
[3,1,2,5,6,4]=>[1,2,4,3,5,6]=>1
[3,1,2,6,4,5]=>[1,2,4,5,3,6]=>1
[3,1,2,6,+,4]=>[1,2,5,4,3,6]=>2
[3,1,2,6,-,4]=>[1,2,4,3,6,5]=>2
[3,1,4,2,+,+]=>[1,2,5,6,3,4]=>2
[3,1,4,2,-,+]=>[1,2,6,3,4,5]=>1
[3,1,4,2,+,-]=>[1,2,5,3,4,6]=>1
[3,1,4,2,-,-]=>[1,2,3,4,5,6]=>1
[3,1,4,2,6,5]=>[1,2,5,3,4,6]=>1
[3,1,4,5,2,+]=>[1,2,6,3,4,5]=>1
[3,1,4,5,2,-]=>[1,2,3,4,5,6]=>1
[3,1,4,5,6,2]=>[1,2,3,4,5,6]=>1
[3,1,4,6,2,5]=>[1,2,5,3,4,6]=>1
[3,1,4,6,+,2]=>[1,5,2,3,4,6]=>1
[3,1,4,6,-,2]=>[1,2,3,4,6,5]=>1
[3,1,5,2,4,+]=>[1,2,4,6,3,5]=>2
[3,1,5,2,4,-]=>[1,2,4,3,5,6]=>1
[3,1,5,2,6,4]=>[1,2,4,3,5,6]=>1
[3,1,5,+,2,+]=>[1,4,2,6,3,5]=>5
[3,1,5,-,2,+]=>[1,2,6,3,5,4]=>3
[3,1,5,+,2,-]=>[1,4,2,3,5,6]=>1
[3,1,5,-,2,-]=>[1,2,3,5,4,6]=>1
[3,1,5,+,6,2]=>[1,4,2,3,5,6]=>1
[3,1,5,-,6,2]=>[1,2,3,5,4,6]=>1
[3,1,5,6,2,4]=>[1,2,4,3,5,6]=>1
[3,1,5,6,4,2]=>[1,4,2,3,5,6]=>1
[3,1,6,2,4,5]=>[1,2,4,5,3,6]=>1
[3,1,6,2,+,4]=>[1,2,5,4,3,6]=>2
[3,1,6,2,-,4]=>[1,2,4,3,6,5]=>2
[3,1,6,+,2,5]=>[1,4,2,5,3,6]=>2
[3,1,6,-,2,5]=>[1,2,5,3,6,4]=>2
[3,1,6,+,+,2]=>[1,4,5,2,3,6]=>2
[3,1,6,-,+,2]=>[1,5,2,3,6,4]=>3
[3,1,6,+,-,2]=>[1,4,2,3,6,5]=>3
[3,1,6,-,-,2]=>[1,2,3,6,4,5]=>1
[3,1,6,5,2,4]=>[1,2,4,3,6,5]=>2
[3,1,6,5,4,2]=>[1,4,2,3,6,5]=>3
[3,+,1,+,+,+]=>[2,1,4,5,6,3]=>4
[3,-,1,+,+,+]=>[1,4,5,6,3,2]=>14
[3,+,1,-,+,+]=>[2,1,5,6,3,4]=>10
[3,+,1,+,-,+]=>[2,1,4,6,3,5]=>8
[3,+,1,+,+,-]=>[2,1,4,5,3,6]=>3
[3,-,1,-,+,+]=>[1,5,6,3,2,4]=>21
[3,-,1,+,-,+]=>[1,4,6,3,2,5]=>16
[3,-,1,+,+,-]=>[1,4,5,3,2,6]=>5
[3,+,1,-,-,+]=>[2,1,6,3,4,5]=>4
[3,+,1,-,+,-]=>[2,1,5,3,4,6]=>3
[3,+,1,+,-,-]=>[2,1,4,3,5,6]=>2
[3,-,1,-,-,+]=>[1,6,3,2,4,5]=>4
[3,-,1,-,+,-]=>[1,5,3,2,4,6]=>3
[3,-,1,+,-,-]=>[1,4,3,2,5,6]=>2
[3,+,1,-,-,-]=>[2,1,3,4,5,6]=>1
[3,-,1,-,-,-]=>[1,3,2,4,5,6]=>1
[3,+,1,+,6,5]=>[2,1,4,5,3,6]=>3
[3,-,1,+,6,5]=>[1,4,5,3,2,6]=>5
[3,+,1,-,6,5]=>[2,1,5,3,4,6]=>3
[3,-,1,-,6,5]=>[1,5,3,2,4,6]=>3
[3,+,1,5,4,+]=>[2,1,4,6,3,5]=>8
[3,-,1,5,4,+]=>[1,4,6,3,2,5]=>16
[3,+,1,5,4,-]=>[2,1,4,3,5,6]=>2
[3,-,1,5,4,-]=>[1,4,3,2,5,6]=>2
[3,+,1,5,6,4]=>[2,1,4,3,5,6]=>2
[3,-,1,5,6,4]=>[1,4,3,2,5,6]=>2
[3,+,1,6,4,5]=>[2,1,4,5,3,6]=>3
[3,-,1,6,4,5]=>[1,4,5,3,2,6]=>5
[3,+,1,6,+,4]=>[2,1,5,4,3,6]=>8
[3,-,1,6,+,4]=>[1,5,4,3,2,6]=>16
[3,+,1,6,-,4]=>[2,1,4,3,6,5]=>6
[3,-,1,6,-,4]=>[1,4,3,2,6,5]=>8
[3,+,4,1,+,+]=>[2,1,5,6,3,4]=>10
[3,-,4,1,+,+]=>[1,5,6,3,2,4]=>21
[3,+,4,1,-,+]=>[2,1,6,3,4,5]=>4
[3,+,4,1,+,-]=>[2,1,5,3,4,6]=>3
[3,-,4,1,-,+]=>[1,6,3,2,4,5]=>4
[3,-,4,1,+,-]=>[1,5,3,2,4,6]=>3
[3,+,4,1,-,-]=>[2,1,3,4,5,6]=>1
[3,-,4,1,-,-]=>[1,3,2,4,5,6]=>1
[3,+,4,1,6,5]=>[2,1,5,3,4,6]=>3
[3,-,4,1,6,5]=>[1,5,3,2,4,6]=>3
[3,+,4,5,1,+]=>[2,1,6,3,4,5]=>4
[3,-,4,5,1,+]=>[1,6,3,2,4,5]=>4
[3,+,4,5,1,-]=>[2,1,3,4,5,6]=>1
[3,-,4,5,1,-]=>[1,3,2,4,5,6]=>1
[3,+,4,5,6,1]=>[2,1,3,4,5,6]=>1
[3,-,4,5,6,1]=>[1,3,2,4,5,6]=>1
[3,+,4,6,1,5]=>[2,1,5,3,4,6]=>3
[3,-,4,6,1,5]=>[1,5,3,2,4,6]=>3
[3,+,4,6,+,1]=>[2,5,1,3,4,6]=>3
[3,-,4,6,+,1]=>[5,1,3,2,4,6]=>4
[3,+,4,6,-,1]=>[2,1,3,4,6,5]=>2
[3,-,4,6,-,1]=>[1,3,2,4,6,5]=>2
[3,+,5,1,4,+]=>[2,1,4,6,3,5]=>8
[3,-,5,1,4,+]=>[1,4,6,3,2,5]=>16
[3,+,5,1,4,-]=>[2,1,4,3,5,6]=>2
[3,-,5,1,4,-]=>[1,4,3,2,5,6]=>2
[3,+,5,1,6,4]=>[2,1,4,3,5,6]=>2
[3,-,5,1,6,4]=>[1,4,3,2,5,6]=>2
[3,+,5,+,1,+]=>[2,4,1,6,3,5]=>16
[3,-,5,+,1,+]=>[4,1,6,3,2,5]=>56
[3,+,5,-,1,+]=>[2,1,6,3,5,4]=>15
[3,+,5,+,1,-]=>[2,4,1,3,5,6]=>2
[3,-,5,-,1,+]=>[1,6,3,2,5,4]=>19
[3,-,5,+,1,-]=>[4,1,3,2,5,6]=>3
[3,+,5,-,1,-]=>[2,1,3,5,4,6]=>2
[3,-,5,-,1,-]=>[1,3,2,5,4,6]=>2
[3,+,5,+,6,1]=>[2,4,1,3,5,6]=>2
[3,-,5,+,6,1]=>[4,1,3,2,5,6]=>3
[3,+,5,-,6,1]=>[2,1,3,5,4,6]=>2
[3,-,5,-,6,1]=>[1,3,2,5,4,6]=>2
[3,+,5,6,1,4]=>[2,1,4,3,5,6]=>2
[3,-,5,6,1,4]=>[1,4,3,2,5,6]=>2
[3,+,5,6,4,1]=>[2,4,1,3,5,6]=>2
[3,-,5,6,4,1]=>[4,1,3,2,5,6]=>3
[3,+,6,1,4,5]=>[2,1,4,5,3,6]=>3
[3,-,6,1,4,5]=>[1,4,5,3,2,6]=>5
[3,+,6,1,+,4]=>[2,1,5,4,3,6]=>8
[3,-,6,1,+,4]=>[1,5,4,3,2,6]=>16
[3,+,6,1,-,4]=>[2,1,4,3,6,5]=>6
[3,-,6,1,-,4]=>[1,4,3,2,6,5]=>8
[3,+,6,+,1,5]=>[2,4,1,5,3,6]=>5
[3,-,6,+,1,5]=>[4,1,5,3,2,6]=>16
[3,+,6,-,1,5]=>[2,1,5,3,6,4]=>8
[3,-,6,-,1,5]=>[1,5,3,2,6,4]=>11
[3,+,6,+,+,1]=>[2,4,5,1,3,6]=>5
[3,-,6,+,+,1]=>[4,5,1,3,2,6]=>21
[3,+,6,-,+,1]=>[2,5,1,3,6,4]=>11
[3,+,6,+,-,1]=>[2,4,1,3,6,5]=>8
[3,-,6,-,+,1]=>[5,1,3,2,6,4]=>19
[3,-,6,+,-,1]=>[4,1,3,2,6,5]=>15
[3,+,6,-,-,1]=>[2,1,3,6,4,5]=>3
[3,-,6,-,-,1]=>[1,3,2,6,4,5]=>3
[3,+,6,5,1,4]=>[2,1,4,3,6,5]=>6
[3,-,6,5,1,4]=>[1,4,3,2,6,5]=>8
[3,+,6,5,4,1]=>[2,4,1,3,6,5]=>8
[3,-,6,5,4,1]=>[4,1,3,2,6,5]=>15
[3,4,1,2,+,+]=>[1,2,5,6,3,4]=>2
[3,4,1,2,-,+]=>[1,2,6,3,4,5]=>1
[3,4,1,2,+,-]=>[1,2,5,3,4,6]=>1
[3,4,1,2,-,-]=>[1,2,3,4,5,6]=>1
[3,4,1,2,6,5]=>[1,2,5,3,4,6]=>1
[3,4,1,5,2,+]=>[1,2,6,3,4,5]=>1
[3,4,1,5,2,-]=>[1,2,3,4,5,6]=>1
[3,4,1,5,6,2]=>[1,2,3,4,5,6]=>1
[3,4,1,6,2,5]=>[1,2,5,3,4,6]=>1
[3,4,1,6,+,2]=>[1,5,2,3,4,6]=>1
[3,4,1,6,-,2]=>[1,2,3,4,6,5]=>1
[3,4,2,1,+,+]=>[2,1,5,6,3,4]=>10
[3,4,2,1,-,+]=>[2,1,6,3,4,5]=>4
[3,4,2,1,+,-]=>[2,1,5,3,4,6]=>3
[3,4,2,1,-,-]=>[2,1,3,4,5,6]=>1
[3,4,2,1,6,5]=>[2,1,5,3,4,6]=>3
[3,4,2,5,1,+]=>[2,1,6,3,4,5]=>4
[3,4,2,5,1,-]=>[2,1,3,4,5,6]=>1
[3,4,2,5,6,1]=>[2,1,3,4,5,6]=>1
[3,4,2,6,1,5]=>[2,1,5,3,4,6]=>3
[3,4,2,6,+,1]=>[2,5,1,3,4,6]=>3
[3,4,2,6,-,1]=>[2,1,3,4,6,5]=>2
[3,4,5,1,2,+]=>[1,2,6,3,4,5]=>1
[3,4,5,1,2,-]=>[1,2,3,4,5,6]=>1
[3,4,5,1,6,2]=>[1,2,3,4,5,6]=>1
[3,4,5,2,1,+]=>[2,1,6,3,4,5]=>4
[3,4,5,2,1,-]=>[2,1,3,4,5,6]=>1
[3,4,5,2,6,1]=>[2,1,3,4,5,6]=>1
[3,4,5,6,1,2]=>[1,2,3,4,5,6]=>1
[3,4,5,6,2,1]=>[2,1,3,4,5,6]=>1
[3,4,6,1,2,5]=>[1,2,5,3,4,6]=>1
[3,4,6,1,+,2]=>[1,5,2,3,4,6]=>1
[3,4,6,1,-,2]=>[1,2,3,4,6,5]=>1
[3,4,6,2,1,5]=>[2,1,5,3,4,6]=>3
[3,4,6,2,+,1]=>[2,5,1,3,4,6]=>3
[3,4,6,2,-,1]=>[2,1,3,4,6,5]=>2
[3,4,6,5,1,2]=>[1,2,3,4,6,5]=>1
[3,4,6,5,2,1]=>[2,1,3,4,6,5]=>2
[3,5,1,2,4,+]=>[1,2,4,6,3,5]=>2
[3,5,1,2,4,-]=>[1,2,4,3,5,6]=>1
[3,5,1,2,6,4]=>[1,2,4,3,5,6]=>1
[3,5,1,+,2,+]=>[1,4,2,6,3,5]=>5
[3,5,1,-,2,+]=>[1,2,6,3,5,4]=>3
[3,5,1,+,2,-]=>[1,4,2,3,5,6]=>1
[3,5,1,-,2,-]=>[1,2,3,5,4,6]=>1
[3,5,1,+,6,2]=>[1,4,2,3,5,6]=>1
[3,5,1,-,6,2]=>[1,2,3,5,4,6]=>1
[3,5,1,6,2,4]=>[1,2,4,3,5,6]=>1
[3,5,1,6,4,2]=>[1,4,2,3,5,6]=>1
[3,5,2,1,4,+]=>[2,1,4,6,3,5]=>8
[3,5,2,1,4,-]=>[2,1,4,3,5,6]=>2
[3,5,2,1,6,4]=>[2,1,4,3,5,6]=>2
[3,5,2,+,1,+]=>[2,4,1,6,3,5]=>16
[3,5,2,-,1,+]=>[2,1,6,3,5,4]=>15
[3,5,2,+,1,-]=>[2,4,1,3,5,6]=>2
[3,5,2,-,1,-]=>[2,1,3,5,4,6]=>2
[3,5,2,+,6,1]=>[2,4,1,3,5,6]=>2
[3,5,2,-,6,1]=>[2,1,3,5,4,6]=>2
[3,5,2,6,1,4]=>[2,1,4,3,5,6]=>2
[3,5,2,6,4,1]=>[2,4,1,3,5,6]=>2
[3,5,4,1,2,+]=>[1,2,6,3,5,4]=>3
[3,5,4,1,2,-]=>[1,2,3,5,4,6]=>1
[3,5,4,1,6,2]=>[1,2,3,5,4,6]=>1
[3,5,4,2,1,+]=>[2,1,6,3,5,4]=>15
[3,5,4,2,1,-]=>[2,1,3,5,4,6]=>2
[3,5,4,2,6,1]=>[2,1,3,5,4,6]=>2
[3,5,4,6,1,2]=>[1,2,3,5,4,6]=>1
[3,5,4,6,2,1]=>[2,1,3,5,4,6]=>2
[3,5,6,1,2,4]=>[1,2,4,3,5,6]=>1
[3,5,6,1,4,2]=>[1,4,2,3,5,6]=>1
[3,5,6,2,1,4]=>[2,1,4,3,5,6]=>2
[3,5,6,2,4,1]=>[2,4,1,3,5,6]=>2
[3,5,6,+,1,2]=>[4,1,2,3,5,6]=>1
[3,5,6,-,1,2]=>[1,2,3,5,6,4]=>1
[3,5,6,+,2,1]=>[4,2,1,3,5,6]=>3
[3,5,6,-,2,1]=>[2,1,3,5,6,4]=>3
[3,6,1,2,4,5]=>[1,2,4,5,3,6]=>1
[3,6,1,2,+,4]=>[1,2,5,4,3,6]=>2
[3,6,1,2,-,4]=>[1,2,4,3,6,5]=>2
[3,6,1,+,2,5]=>[1,4,2,5,3,6]=>2
[3,6,1,-,2,5]=>[1,2,5,3,6,4]=>2
[3,6,1,+,+,2]=>[1,4,5,2,3,6]=>2
[3,6,1,-,+,2]=>[1,5,2,3,6,4]=>3
[3,6,1,+,-,2]=>[1,4,2,3,6,5]=>3
[3,6,1,-,-,2]=>[1,2,3,6,4,5]=>1
[3,6,1,5,2,4]=>[1,2,4,3,6,5]=>2
[3,6,1,5,4,2]=>[1,4,2,3,6,5]=>3
[3,6,2,1,4,5]=>[2,1,4,5,3,6]=>3
[3,6,2,1,+,4]=>[2,1,5,4,3,6]=>8
[3,6,2,1,-,4]=>[2,1,4,3,6,5]=>6
[3,6,2,+,1,5]=>[2,4,1,5,3,6]=>5
[3,6,2,-,1,5]=>[2,1,5,3,6,4]=>8
[3,6,2,+,+,1]=>[2,4,5,1,3,6]=>5
[3,6,2,-,+,1]=>[2,5,1,3,6,4]=>11
[3,6,2,+,-,1]=>[2,4,1,3,6,5]=>8
[3,6,2,-,-,1]=>[2,1,3,6,4,5]=>3
[3,6,2,5,1,4]=>[2,1,4,3,6,5]=>6
[3,6,2,5,4,1]=>[2,4,1,3,6,5]=>8
[3,6,4,1,2,5]=>[1,2,5,3,6,4]=>2
[3,6,4,1,+,2]=>[1,5,2,3,6,4]=>3
[3,6,4,1,-,2]=>[1,2,3,6,4,5]=>1
[3,6,4,2,1,5]=>[2,1,5,3,6,4]=>8
[3,6,4,2,+,1]=>[2,5,1,3,6,4]=>11
[3,6,4,2,-,1]=>[2,1,3,6,4,5]=>3
[3,6,4,5,1,2]=>[1,2,3,6,4,5]=>1
[3,6,4,5,2,1]=>[2,1,3,6,4,5]=>3
[3,6,5,1,2,4]=>[1,2,4,3,6,5]=>2
[3,6,5,1,4,2]=>[1,4,2,3,6,5]=>3
[3,6,5,2,1,4]=>[2,1,4,3,6,5]=>6
[3,6,5,2,4,1]=>[2,4,1,3,6,5]=>8
[3,6,5,+,1,2]=>[4,1,2,3,6,5]=>4
[3,6,5,-,1,2]=>[1,2,3,6,5,4]=>2
[3,6,5,+,2,1]=>[4,2,1,3,6,5]=>15
[3,6,5,-,2,1]=>[2,1,3,6,5,4]=>8
[4,1,2,3,+,+]=>[1,2,3,5,6,4]=>1
[4,1,2,3,-,+]=>[1,2,3,6,4,5]=>1
[4,1,2,3,+,-]=>[1,2,3,5,4,6]=>1
[4,1,2,3,-,-]=>[1,2,3,4,5,6]=>1
[4,1,2,3,6,5]=>[1,2,3,5,4,6]=>1
[4,1,2,5,3,+]=>[1,2,3,6,4,5]=>1
[4,1,2,5,3,-]=>[1,2,3,4,5,6]=>1
[4,1,2,5,6,3]=>[1,2,3,4,5,6]=>1
[4,1,2,6,3,5]=>[1,2,3,5,4,6]=>1
[4,1,2,6,+,3]=>[1,2,5,3,4,6]=>1
[4,1,2,6,-,3]=>[1,2,3,4,6,5]=>1
[4,1,+,2,+,+]=>[1,3,2,5,6,4]=>3
[4,1,-,2,+,+]=>[1,2,5,6,4,3]=>5
[4,1,+,2,-,+]=>[1,3,2,6,4,5]=>3
[4,1,+,2,+,-]=>[1,3,2,5,4,6]=>2
[4,1,-,2,-,+]=>[1,2,6,4,3,5]=>3
[4,1,-,2,+,-]=>[1,2,5,4,3,6]=>2
[4,1,+,2,-,-]=>[1,3,2,4,5,6]=>1
[4,1,-,2,-,-]=>[1,2,4,3,5,6]=>1
[4,1,+,2,6,5]=>[1,3,2,5,4,6]=>2
[4,1,-,2,6,5]=>[1,2,5,4,3,6]=>2
[4,1,+,5,2,+]=>[1,3,2,6,4,5]=>3
[4,1,-,5,2,+]=>[1,2,6,4,3,5]=>3
[4,1,+,5,2,-]=>[1,3,2,4,5,6]=>1
[4,1,-,5,2,-]=>[1,2,4,3,5,6]=>1
[4,1,+,5,6,2]=>[1,3,2,4,5,6]=>1
[4,1,-,5,6,2]=>[1,2,4,3,5,6]=>1
[4,1,+,6,2,5]=>[1,3,2,5,4,6]=>2
[4,1,-,6,2,5]=>[1,2,5,4,3,6]=>2
[4,1,+,6,+,2]=>[1,3,5,2,4,6]=>2
[4,1,-,6,+,2]=>[1,5,2,4,3,6]=>3
[4,1,+,6,-,2]=>[1,3,2,4,6,5]=>2
[4,1,-,6,-,2]=>[1,2,4,3,6,5]=>2
[4,1,5,2,3,+]=>[1,2,3,6,4,5]=>1
[4,1,5,2,3,-]=>[1,2,3,4,5,6]=>1
[4,1,5,2,6,3]=>[1,2,3,4,5,6]=>1
[4,1,5,3,2,+]=>[1,3,2,6,4,5]=>3
[4,1,5,3,2,-]=>[1,3,2,4,5,6]=>1
[4,1,5,3,6,2]=>[1,3,2,4,5,6]=>1
[4,1,5,6,2,3]=>[1,2,3,4,5,6]=>1
[4,1,5,6,3,2]=>[1,3,2,4,5,6]=>1
[4,1,6,2,3,5]=>[1,2,3,5,4,6]=>1
[4,1,6,2,+,3]=>[1,2,5,3,4,6]=>1
[4,1,6,2,-,3]=>[1,2,3,4,6,5]=>1
[4,1,6,3,2,5]=>[1,3,2,5,4,6]=>2
[4,1,6,3,+,2]=>[1,3,5,2,4,6]=>2
[4,1,6,3,-,2]=>[1,3,2,4,6,5]=>2
[4,1,6,5,2,3]=>[1,2,3,4,6,5]=>1
[4,1,6,5,3,2]=>[1,3,2,4,6,5]=>2
[4,+,1,3,+,+]=>[2,1,3,5,6,4]=>3
[4,-,1,3,+,+]=>[1,3,5,6,4,2]=>9
[4,+,1,3,-,+]=>[2,1,3,6,4,5]=>3
[4,+,1,3,+,-]=>[2,1,3,5,4,6]=>2
[4,-,1,3,-,+]=>[1,3,6,4,2,5]=>6
[4,-,1,3,+,-]=>[1,3,5,4,2,6]=>3
[4,+,1,3,-,-]=>[2,1,3,4,5,6]=>1
[4,-,1,3,-,-]=>[1,3,4,2,5,6]=>1
[4,+,1,3,6,5]=>[2,1,3,5,4,6]=>2
[4,-,1,3,6,5]=>[1,3,5,4,2,6]=>3
[4,+,1,5,3,+]=>[2,1,3,6,4,5]=>3
[4,-,1,5,3,+]=>[1,3,6,4,2,5]=>6
[4,+,1,5,3,-]=>[2,1,3,4,5,6]=>1
[4,-,1,5,3,-]=>[1,3,4,2,5,6]=>1
[4,+,1,5,6,3]=>[2,1,3,4,5,6]=>1
[4,-,1,5,6,3]=>[1,3,4,2,5,6]=>1
[4,+,1,6,3,5]=>[2,1,3,5,4,6]=>2
[4,-,1,6,3,5]=>[1,3,5,4,2,6]=>3
[4,+,1,6,+,3]=>[2,1,5,3,4,6]=>3
[4,-,1,6,+,3]=>[1,5,3,4,2,6]=>6
[4,+,1,6,-,3]=>[2,1,3,4,6,5]=>2
[4,-,1,6,-,3]=>[1,3,4,2,6,5]=>3
[4,+,+,1,+,+]=>[2,3,1,5,6,4]=>6
[4,-,+,1,+,+]=>[3,1,5,6,4,2]=>49
[4,+,-,1,+,+]=>[2,1,5,6,4,3]=>30
[4,+,+,1,-,+]=>[2,3,1,6,4,5]=>6
[4,+,+,1,+,-]=>[2,3,1,5,4,6]=>3
[4,-,-,1,+,+]=>[1,5,6,4,2,3]=>42
[4,-,+,1,-,+]=>[3,1,6,4,2,5]=>26
[4,-,+,1,+,-]=>[3,1,5,4,2,6]=>11
[4,+,-,1,-,+]=>[2,1,6,4,3,5]=>15
[4,+,-,1,+,-]=>[2,1,5,4,3,6]=>8
[4,+,+,1,-,-]=>[2,3,1,4,5,6]=>1
[4,-,-,1,-,+]=>[1,6,4,2,3,5]=>9
[4,-,-,1,+,-]=>[1,5,4,2,3,6]=>5
[4,-,+,1,-,-]=>[3,1,4,2,5,6]=>2
[4,+,-,1,-,-]=>[2,1,4,3,5,6]=>2
[4,-,-,1,-,-]=>[1,4,2,3,5,6]=>1
[4,+,+,1,6,5]=>[2,3,1,5,4,6]=>3
[4,-,+,1,6,5]=>[3,1,5,4,2,6]=>11
[4,+,-,1,6,5]=>[2,1,5,4,3,6]=>8
[4,-,-,1,6,5]=>[1,5,4,2,3,6]=>5
[4,+,+,5,1,+]=>[2,3,1,6,4,5]=>6
[4,-,+,5,1,+]=>[3,1,6,4,2,5]=>26
[4,+,-,5,1,+]=>[2,1,6,4,3,5]=>15
[4,+,+,5,1,-]=>[2,3,1,4,5,6]=>1
[4,-,-,5,1,+]=>[1,6,4,2,3,5]=>9
[4,-,+,5,1,-]=>[3,1,4,2,5,6]=>2
[4,+,-,5,1,-]=>[2,1,4,3,5,6]=>2
[4,-,-,5,1,-]=>[1,4,2,3,5,6]=>1
[4,+,+,5,6,1]=>[2,3,1,4,5,6]=>1
[4,-,+,5,6,1]=>[3,1,4,2,5,6]=>2
[4,+,-,5,6,1]=>[2,1,4,3,5,6]=>2
[4,-,-,5,6,1]=>[1,4,2,3,5,6]=>1
[4,+,+,6,1,5]=>[2,3,1,5,4,6]=>3
[4,-,+,6,1,5]=>[3,1,5,4,2,6]=>11
[4,+,-,6,1,5]=>[2,1,5,4,3,6]=>8
[4,-,-,6,1,5]=>[1,5,4,2,3,6]=>5
[4,+,+,6,+,1]=>[2,3,5,1,4,6]=>3
[4,-,+,6,+,1]=>[3,5,1,4,2,6]=>16
[4,+,-,6,+,1]=>[2,5,1,4,3,6]=>11
[4,+,+,6,-,1]=>[2,3,1,4,6,5]=>3
[4,-,-,6,+,1]=>[5,1,4,2,3,6]=>9
[4,-,+,6,-,1]=>[3,1,4,2,6,5]=>8
[4,+,-,6,-,1]=>[2,1,4,3,6,5]=>6
[4,-,-,6,-,1]=>[1,4,2,3,6,5]=>3
[4,+,5,1,3,+]=>[2,1,3,6,4,5]=>3
[4,-,5,1,3,+]=>[1,3,6,4,2,5]=>6
[4,+,5,1,3,-]=>[2,1,3,4,5,6]=>1
[4,-,5,1,3,-]=>[1,3,4,2,5,6]=>1
[4,+,5,1,6,3]=>[2,1,3,4,5,6]=>1
[4,-,5,1,6,3]=>[1,3,4,2,5,6]=>1
[4,+,5,3,1,+]=>[2,3,1,6,4,5]=>6
[4,-,5,3,1,+]=>[3,1,6,4,2,5]=>26
[4,+,5,3,1,-]=>[2,3,1,4,5,6]=>1
[4,-,5,3,1,-]=>[3,1,4,2,5,6]=>2
[4,+,5,3,6,1]=>[2,3,1,4,5,6]=>1
[4,-,5,3,6,1]=>[3,1,4,2,5,6]=>2
[4,+,5,6,1,3]=>[2,1,3,4,5,6]=>1
[4,-,5,6,1,3]=>[1,3,4,2,5,6]=>1
[4,+,5,6,3,1]=>[2,3,1,4,5,6]=>1
[4,-,5,6,3,1]=>[3,1,4,2,5,6]=>2
[4,+,6,1,3,5]=>[2,1,3,5,4,6]=>2
[4,-,6,1,3,5]=>[1,3,5,4,2,6]=>3
[4,+,6,1,+,3]=>[2,1,5,3,4,6]=>3
[4,-,6,1,+,3]=>[1,5,3,4,2,6]=>6
[4,+,6,1,-,3]=>[2,1,3,4,6,5]=>2
[4,-,6,1,-,3]=>[1,3,4,2,6,5]=>3
[4,+,6,3,1,5]=>[2,3,1,5,4,6]=>3
[4,-,6,3,1,5]=>[3,1,5,4,2,6]=>11
[4,+,6,3,+,1]=>[2,3,5,1,4,6]=>3
[4,-,6,3,+,1]=>[3,5,1,4,2,6]=>16
[4,+,6,3,-,1]=>[2,3,1,4,6,5]=>3
[4,-,6,3,-,1]=>[3,1,4,2,6,5]=>8
[4,+,6,5,1,3]=>[2,1,3,4,6,5]=>2
[4,-,6,5,1,3]=>[1,3,4,2,6,5]=>3
[4,+,6,5,3,1]=>[2,3,1,4,6,5]=>3
[4,-,6,5,3,1]=>[3,1,4,2,6,5]=>8
[4,3,1,2,+,+]=>[1,2,5,6,4,3]=>5
[4,3,1,2,-,+]=>[1,2,6,4,3,5]=>3
[4,3,1,2,+,-]=>[1,2,5,4,3,6]=>2
[4,3,1,2,-,-]=>[1,2,4,3,5,6]=>1
[4,3,1,2,6,5]=>[1,2,5,4,3,6]=>2
[4,3,1,5,2,+]=>[1,2,6,4,3,5]=>3
[4,3,1,5,2,-]=>[1,2,4,3,5,6]=>1
[4,3,1,5,6,2]=>[1,2,4,3,5,6]=>1
[4,3,1,6,2,5]=>[1,2,5,4,3,6]=>2
[4,3,1,6,+,2]=>[1,5,2,4,3,6]=>3
[4,3,1,6,-,2]=>[1,2,4,3,6,5]=>2
[4,3,2,1,+,+]=>[2,1,5,6,4,3]=>30
[4,3,2,1,-,+]=>[2,1,6,4,3,5]=>15
[4,3,2,1,+,-]=>[2,1,5,4,3,6]=>8
[4,3,2,1,-,-]=>[2,1,4,3,5,6]=>2
[4,3,2,1,6,5]=>[2,1,5,4,3,6]=>8
[4,3,2,5,1,+]=>[2,1,6,4,3,5]=>15
[4,3,2,5,1,-]=>[2,1,4,3,5,6]=>2
[4,3,2,5,6,1]=>[2,1,4,3,5,6]=>2
[4,3,2,6,1,5]=>[2,1,5,4,3,6]=>8
[4,3,2,6,+,1]=>[2,5,1,4,3,6]=>11
[4,3,2,6,-,1]=>[2,1,4,3,6,5]=>6
[4,3,5,1,2,+]=>[1,2,6,4,3,5]=>3
[4,3,5,1,2,-]=>[1,2,4,3,5,6]=>1
[4,3,5,1,6,2]=>[1,2,4,3,5,6]=>1
[4,3,5,2,1,+]=>[2,1,6,4,3,5]=>15
[4,3,5,2,1,-]=>[2,1,4,3,5,6]=>2
[4,3,5,2,6,1]=>[2,1,4,3,5,6]=>2
[4,3,5,6,1,2]=>[1,2,4,3,5,6]=>1
[4,3,5,6,2,1]=>[2,1,4,3,5,6]=>2
[4,3,6,1,2,5]=>[1,2,5,4,3,6]=>2
[4,3,6,1,+,2]=>[1,5,2,4,3,6]=>3
[4,3,6,1,-,2]=>[1,2,4,3,6,5]=>2
[4,3,6,2,1,5]=>[2,1,5,4,3,6]=>8
[4,3,6,2,+,1]=>[2,5,1,4,3,6]=>11
[4,3,6,2,-,1]=>[2,1,4,3,6,5]=>6
[4,3,6,5,1,2]=>[1,2,4,3,6,5]=>2
[4,3,6,5,2,1]=>[2,1,4,3,6,5]=>6
[4,5,1,2,3,+]=>[1,2,3,6,4,5]=>1
[4,5,1,2,3,-]=>[1,2,3,4,5,6]=>1
[4,5,1,2,6,3]=>[1,2,3,4,5,6]=>1
[4,5,1,3,2,+]=>[1,3,2,6,4,5]=>3
[4,5,1,3,2,-]=>[1,3,2,4,5,6]=>1
[4,5,1,3,6,2]=>[1,3,2,4,5,6]=>1
[4,5,1,6,2,3]=>[1,2,3,4,5,6]=>1
[4,5,1,6,3,2]=>[1,3,2,4,5,6]=>1
[4,5,2,1,3,+]=>[2,1,3,6,4,5]=>3
[4,5,2,1,3,-]=>[2,1,3,4,5,6]=>1
[4,5,2,1,6,3]=>[2,1,3,4,5,6]=>1
[4,5,2,3,1,+]=>[2,3,1,6,4,5]=>6
[4,5,2,3,1,-]=>[2,3,1,4,5,6]=>1
[4,5,2,3,6,1]=>[2,3,1,4,5,6]=>1
[4,5,2,6,1,3]=>[2,1,3,4,5,6]=>1
[4,5,2,6,3,1]=>[2,3,1,4,5,6]=>1
[4,5,+,1,2,+]=>[3,1,2,6,4,5]=>6
[4,5,-,1,2,+]=>[1,2,6,4,5,3]=>6
[4,5,+,1,2,-]=>[3,1,2,4,5,6]=>1
[4,5,-,1,2,-]=>[1,2,4,5,3,6]=>1
[4,5,+,1,6,2]=>[3,1,2,4,5,6]=>1
[4,5,-,1,6,2]=>[1,2,4,5,3,6]=>1
[4,5,+,2,1,+]=>[3,2,1,6,4,5]=>20
[4,5,-,2,1,+]=>[2,1,6,4,5,3]=>36
[4,5,+,2,1,-]=>[3,2,1,4,5,6]=>2
[4,5,-,2,1,-]=>[2,1,4,5,3,6]=>3
[4,5,+,2,6,1]=>[3,2,1,4,5,6]=>2
[4,5,-,2,6,1]=>[2,1,4,5,3,6]=>3
[4,5,+,6,1,2]=>[3,1,2,4,5,6]=>1
[4,5,-,6,1,2]=>[1,2,4,5,3,6]=>1
[4,5,+,6,2,1]=>[3,2,1,4,5,6]=>2
[4,5,-,6,2,1]=>[2,1,4,5,3,6]=>3
[4,5,6,1,2,3]=>[1,2,3,4,5,6]=>1
[4,5,6,1,3,2]=>[1,3,2,4,5,6]=>1
[4,5,6,2,1,3]=>[2,1,3,4,5,6]=>1
[4,5,6,2,3,1]=>[2,3,1,4,5,6]=>1
[4,5,6,3,1,2]=>[3,1,2,4,5,6]=>1
[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>2
[4,6,1,2,3,5]=>[1,2,3,5,4,6]=>1
[4,6,1,2,+,3]=>[1,2,5,3,4,6]=>1
[4,6,1,2,-,3]=>[1,2,3,4,6,5]=>1
[4,6,1,3,2,5]=>[1,3,2,5,4,6]=>2
[4,6,1,3,+,2]=>[1,3,5,2,4,6]=>2
[4,6,1,3,-,2]=>[1,3,2,4,6,5]=>2
[4,6,1,5,2,3]=>[1,2,3,4,6,5]=>1
[4,6,1,5,3,2]=>[1,3,2,4,6,5]=>2
[4,6,2,1,3,5]=>[2,1,3,5,4,6]=>2
[4,6,2,1,+,3]=>[2,1,5,3,4,6]=>3
[4,6,2,1,-,3]=>[2,1,3,4,6,5]=>2
[4,6,2,3,1,5]=>[2,3,1,5,4,6]=>3
[4,6,2,3,+,1]=>[2,3,5,1,4,6]=>3
[4,6,2,3,-,1]=>[2,3,1,4,6,5]=>3
[4,6,2,5,1,3]=>[2,1,3,4,6,5]=>2
[4,6,2,5,3,1]=>[2,3,1,4,6,5]=>3
[4,6,+,1,2,5]=>[3,1,2,5,4,6]=>3
[4,6,-,1,2,5]=>[1,2,5,4,6,3]=>3
[4,6,+,1,+,2]=>[3,1,5,2,4,6]=>5
[4,6,-,1,+,2]=>[1,5,2,4,6,3]=>6
[4,6,+,1,-,2]=>[3,1,2,4,6,5]=>3
[4,6,-,1,-,2]=>[1,2,4,6,3,5]=>2
[4,6,+,2,1,5]=>[3,2,1,5,4,6]=>8
[4,6,-,2,1,5]=>[2,1,5,4,6,3]=>15
[4,6,+,2,+,1]=>[3,2,5,1,4,6]=>11
[4,6,-,2,+,1]=>[2,5,1,4,6,3]=>26
[4,6,+,2,-,1]=>[3,2,1,4,6,5]=>8
[4,6,-,2,-,1]=>[2,1,4,6,3,5]=>8
[4,6,+,5,1,2]=>[3,1,2,4,6,5]=>3
[4,6,-,5,1,2]=>[1,2,4,6,3,5]=>2
[4,6,+,5,2,1]=>[3,2,1,4,6,5]=>8
[4,6,-,5,2,1]=>[2,1,4,6,3,5]=>8
[4,6,5,1,2,3]=>[1,2,3,4,6,5]=>1
[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>2
[4,6,5,2,1,3]=>[2,1,3,4,6,5]=>2
[4,6,5,2,3,1]=>[2,3,1,4,6,5]=>3
[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>3
[4,6,5,3,2,1]=>[3,2,1,4,6,5]=>8
[5,1,2,3,4,+]=>[1,2,3,4,6,5]=>1
[5,1,2,3,4,-]=>[1,2,3,4,5,6]=>1
[5,1,2,3,6,4]=>[1,2,3,4,5,6]=>1
[5,1,2,+,3,+]=>[1,2,4,3,6,5]=>2
[5,1,2,-,3,+]=>[1,2,3,6,5,4]=>2
[5,1,2,+,3,-]=>[1,2,4,3,5,6]=>1
[5,1,2,-,3,-]=>[1,2,3,5,4,6]=>1
[5,1,2,+,6,3]=>[1,2,4,3,5,6]=>1
[5,1,2,-,6,3]=>[1,2,3,5,4,6]=>1
[5,1,2,6,3,4]=>[1,2,3,4,5,6]=>1
[5,1,2,6,4,3]=>[1,2,4,3,5,6]=>1
[5,1,+,2,4,+]=>[1,3,2,4,6,5]=>2
[5,1,-,2,4,+]=>[1,2,4,6,5,3]=>3
[5,1,+,2,4,-]=>[1,3,2,4,5,6]=>1
[5,1,-,2,4,-]=>[1,2,4,5,3,6]=>1
[5,1,+,2,6,4]=>[1,3,2,4,5,6]=>1
[5,1,-,2,6,4]=>[1,2,4,5,3,6]=>1
[5,1,+,+,2,+]=>[1,3,4,2,6,5]=>3
[5,1,-,+,2,+]=>[1,4,2,6,5,3]=>11
[5,1,+,-,2,+]=>[1,3,2,6,5,4]=>8
[5,1,+,+,2,-]=>[1,3,4,2,5,6]=>1
[5,1,-,-,2,+]=>[1,2,6,5,3,4]=>5
[5,1,-,+,2,-]=>[1,4,2,5,3,6]=>2
[5,1,+,-,2,-]=>[1,3,2,5,4,6]=>2
[5,1,-,-,2,-]=>[1,2,5,3,4,6]=>1
[5,1,+,+,6,2]=>[1,3,4,2,5,6]=>1
[5,1,-,+,6,2]=>[1,4,2,5,3,6]=>2
[5,1,+,-,6,2]=>[1,3,2,5,4,6]=>2
[5,1,-,-,6,2]=>[1,2,5,3,4,6]=>1
[5,1,+,6,2,4]=>[1,3,2,4,5,6]=>1
[5,1,-,6,2,4]=>[1,2,4,5,3,6]=>1
[5,1,+,6,4,2]=>[1,3,4,2,5,6]=>1
[5,1,-,6,4,2]=>[1,4,2,5,3,6]=>2
[5,1,4,2,3,+]=>[1,2,3,6,5,4]=>2
[5,1,4,2,3,-]=>[1,2,3,5,4,6]=>1
[5,1,4,2,6,3]=>[1,2,3,5,4,6]=>1
[5,1,4,3,2,+]=>[1,3,2,6,5,4]=>8
[5,1,4,3,2,-]=>[1,3,2,5,4,6]=>2
[5,1,4,3,6,2]=>[1,3,2,5,4,6]=>2
[5,1,4,6,2,3]=>[1,2,3,5,4,6]=>1
[5,1,4,6,3,2]=>[1,3,2,5,4,6]=>2
[5,1,6,2,3,4]=>[1,2,3,4,5,6]=>1
[5,1,6,2,4,3]=>[1,2,4,3,5,6]=>1
[5,1,6,3,2,4]=>[1,3,2,4,5,6]=>1
[5,1,6,3,4,2]=>[1,3,4,2,5,6]=>1
[5,1,6,+,2,3]=>[1,4,2,3,5,6]=>1
[5,1,6,-,2,3]=>[1,2,3,5,6,4]=>1
[5,1,6,+,3,2]=>[1,4,3,2,5,6]=>2
[5,1,6,-,3,2]=>[1,3,2,5,6,4]=>3
[5,+,1,3,4,+]=>[2,1,3,4,6,5]=>2
[5,-,1,3,4,+]=>[1,3,4,6,5,2]=>4
[5,+,1,3,4,-]=>[2,1,3,4,5,6]=>1
[5,-,1,3,4,-]=>[1,3,4,5,2,6]=>1
[5,+,1,3,6,4]=>[2,1,3,4,5,6]=>1
[5,-,1,3,6,4]=>[1,3,4,5,2,6]=>1
[5,+,1,+,3,+]=>[2,1,4,3,6,5]=>6
[5,-,1,+,3,+]=>[1,4,3,6,5,2]=>19
[5,+,1,-,3,+]=>[2,1,3,6,5,4]=>8
[5,+,1,+,3,-]=>[2,1,4,3,5,6]=>2
[5,-,1,-,3,+]=>[1,3,6,5,2,4]=>16
[5,-,1,+,3,-]=>[1,4,3,5,2,6]=>3
[5,+,1,-,3,-]=>[2,1,3,5,4,6]=>2
[5,-,1,-,3,-]=>[1,3,5,2,4,6]=>2
[5,+,1,+,6,3]=>[2,1,4,3,5,6]=>2
[5,-,1,+,6,3]=>[1,4,3,5,2,6]=>3
[5,+,1,-,6,3]=>[2,1,3,5,4,6]=>2
[5,-,1,-,6,3]=>[1,3,5,2,4,6]=>2
[5,+,1,6,3,4]=>[2,1,3,4,5,6]=>1
[5,-,1,6,3,4]=>[1,3,4,5,2,6]=>1
[5,+,1,6,4,3]=>[2,1,4,3,5,6]=>2
[5,-,1,6,4,3]=>[1,4,3,5,2,6]=>3
[5,+,+,1,4,+]=>[2,3,1,4,6,5]=>3
[5,-,+,1,4,+]=>[3,1,4,6,5,2]=>19
[5,+,-,1,4,+]=>[2,1,4,6,5,3]=>15
[5,+,+,1,4,-]=>[2,3,1,4,5,6]=>1
[5,-,-,1,4,+]=>[1,4,6,5,2,3]=>21
[5,-,+,1,4,-]=>[3,1,4,5,2,6]=>3
[5,+,-,1,4,-]=>[2,1,4,5,3,6]=>3
[5,-,-,1,4,-]=>[1,4,5,2,3,6]=>2
[5,+,+,1,6,4]=>[2,3,1,4,5,6]=>1
[5,-,+,1,6,4]=>[3,1,4,5,2,6]=>3
[5,+,-,1,6,4]=>[2,1,4,5,3,6]=>3
[5,-,-,1,6,4]=>[1,4,5,2,3,6]=>2
[5,+,+,+,1,+]=>[2,3,4,1,6,5]=>4
[5,-,+,+,1,+]=>[3,4,1,6,5,2]=>49
[5,+,-,+,1,+]=>[2,4,1,6,5,3]=>40
[5,+,+,-,1,+]=>[2,3,1,6,5,4]=>20
[5,+,+,+,1,-]=>[2,3,4,1,5,6]=>1
[5,-,-,+,1,+]=>[4,1,6,5,2,3]=>98
[5,-,+,-,1,+]=>[3,1,6,5,2,4]=>77
[5,-,+,+,1,-]=>[3,4,1,5,2,6]=>5
[5,+,-,-,1,+]=>[2,1,6,5,3,4]=>30
[5,+,-,+,1,-]=>[2,4,1,5,3,6]=>5
[5,+,+,-,1,-]=>[2,3,1,5,4,6]=>3
[5,-,-,-,1,+]=>[1,6,5,2,3,4]=>14
[5,-,-,+,1,-]=>[4,1,5,2,3,6]=>5
[5,-,+,-,1,-]=>[3,1,5,2,4,6]=>5
[5,+,-,-,1,-]=>[2,1,5,3,4,6]=>3
[5,-,-,-,1,-]=>[1,5,2,3,4,6]=>1
[5,+,+,+,6,1]=>[2,3,4,1,5,6]=>1
[5,-,+,+,6,1]=>[3,4,1,5,2,6]=>5
[5,+,-,+,6,1]=>[2,4,1,5,3,6]=>5
[5,+,+,-,6,1]=>[2,3,1,5,4,6]=>3
[5,-,-,+,6,1]=>[4,1,5,2,3,6]=>5
[5,-,+,-,6,1]=>[3,1,5,2,4,6]=>5
[5,+,-,-,6,1]=>[2,1,5,3,4,6]=>3
[5,-,-,-,6,1]=>[1,5,2,3,4,6]=>1
[5,+,+,6,1,4]=>[2,3,1,4,5,6]=>1
[5,-,+,6,1,4]=>[3,1,4,5,2,6]=>3
[5,+,-,6,1,4]=>[2,1,4,5,3,6]=>3
[5,-,-,6,1,4]=>[1,4,5,2,3,6]=>2
[5,+,+,6,4,1]=>[2,3,4,1,5,6]=>1
[5,-,+,6,4,1]=>[3,4,1,5,2,6]=>5
[5,+,-,6,4,1]=>[2,4,1,5,3,6]=>5
[5,-,-,6,4,1]=>[4,1,5,2,3,6]=>5
[5,+,4,1,3,+]=>[2,1,3,6,5,4]=>8
[5,-,4,1,3,+]=>[1,3,6,5,2,4]=>16
[5,+,4,1,3,-]=>[2,1,3,5,4,6]=>2
[5,-,4,1,3,-]=>[1,3,5,2,4,6]=>2
[5,+,4,1,6,3]=>[2,1,3,5,4,6]=>2
[5,-,4,1,6,3]=>[1,3,5,2,4,6]=>2
[5,+,4,3,1,+]=>[2,3,1,6,5,4]=>20
[5,-,4,3,1,+]=>[3,1,6,5,2,4]=>77
[5,+,4,3,1,-]=>[2,3,1,5,4,6]=>3
[5,-,4,3,1,-]=>[3,1,5,2,4,6]=>5
[5,+,4,3,6,1]=>[2,3,1,5,4,6]=>3
[5,-,4,3,6,1]=>[3,1,5,2,4,6]=>5
[5,+,4,6,1,3]=>[2,1,3,5,4,6]=>2
[5,-,4,6,1,3]=>[1,3,5,2,4,6]=>2
[5,+,4,6,3,1]=>[2,3,1,5,4,6]=>3
[5,-,4,6,3,1]=>[3,1,5,2,4,6]=>5
[5,+,6,1,3,4]=>[2,1,3,4,5,6]=>1
[5,-,6,1,3,4]=>[1,3,4,5,2,6]=>1
[5,+,6,1,4,3]=>[2,1,4,3,5,6]=>2
[5,-,6,1,4,3]=>[1,4,3,5,2,6]=>3
[5,+,6,3,1,4]=>[2,3,1,4,5,6]=>1
[5,-,6,3,1,4]=>[3,1,4,5,2,6]=>3
[5,+,6,3,4,1]=>[2,3,4,1,5,6]=>1
[5,-,6,3,4,1]=>[3,4,1,5,2,6]=>5
[5,+,6,+,1,3]=>[2,4,1,3,5,6]=>2
[5,-,6,+,1,3]=>[4,1,3,5,2,6]=>6
[5,+,6,-,1,3]=>[2,1,3,5,6,4]=>3
[5,-,6,-,1,3]=>[1,3,5,2,6,4]=>5
[5,+,6,+,3,1]=>[2,4,3,1,5,6]=>3
[5,-,6,+,3,1]=>[4,3,1,5,2,6]=>16
[5,+,6,-,3,1]=>[2,3,1,5,6,4]=>6
[5,-,6,-,3,1]=>[3,1,5,2,6,4]=>16
[5,3,1,2,4,+]=>[1,2,4,6,5,3]=>3
[5,3,1,2,4,-]=>[1,2,4,5,3,6]=>1
[5,3,1,2,6,4]=>[1,2,4,5,3,6]=>1
[5,3,1,+,2,+]=>[1,4,2,6,5,3]=>11
[5,3,1,-,2,+]=>[1,2,6,5,3,4]=>5
[5,3,1,+,2,-]=>[1,4,2,5,3,6]=>2
[5,3,1,-,2,-]=>[1,2,5,3,4,6]=>1
[5,3,1,+,6,2]=>[1,4,2,5,3,6]=>2
[5,3,1,-,6,2]=>[1,2,5,3,4,6]=>1
[5,3,1,6,2,4]=>[1,2,4,5,3,6]=>1
[5,3,1,6,4,2]=>[1,4,2,5,3,6]=>2
[5,3,2,1,4,+]=>[2,1,4,6,5,3]=>15
[5,3,2,1,4,-]=>[2,1,4,5,3,6]=>3
[5,3,2,1,6,4]=>[2,1,4,5,3,6]=>3
[5,3,2,+,1,+]=>[2,4,1,6,5,3]=>40
[5,3,2,-,1,+]=>[2,1,6,5,3,4]=>30
[5,3,2,+,1,-]=>[2,4,1,5,3,6]=>5
[5,3,2,-,1,-]=>[2,1,5,3,4,6]=>3
[5,3,2,+,6,1]=>[2,4,1,5,3,6]=>5
[5,3,2,-,6,1]=>[2,1,5,3,4,6]=>3
[5,3,2,6,1,4]=>[2,1,4,5,3,6]=>3
[5,3,2,6,4,1]=>[2,4,1,5,3,6]=>5
[5,3,4,1,2,+]=>[1,2,6,5,3,4]=>5
[5,3,4,1,2,-]=>[1,2,5,3,4,6]=>1
[5,3,4,1,6,2]=>[1,2,5,3,4,6]=>1
[5,3,4,2,1,+]=>[2,1,6,5,3,4]=>30
[5,3,4,2,1,-]=>[2,1,5,3,4,6]=>3
[5,3,4,2,6,1]=>[2,1,5,3,4,6]=>3
[5,3,4,6,1,2]=>[1,2,5,3,4,6]=>1
[5,3,4,6,2,1]=>[2,1,5,3,4,6]=>3
[5,3,6,1,2,4]=>[1,2,4,5,3,6]=>1
[5,3,6,1,4,2]=>[1,4,2,5,3,6]=>2
[5,3,6,2,1,4]=>[2,1,4,5,3,6]=>3
[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>5
[5,3,6,+,1,2]=>[4,1,2,5,3,6]=>3
[5,3,6,-,1,2]=>[1,2,5,3,6,4]=>2
[5,3,6,+,2,1]=>[4,2,1,5,3,6]=>11
[5,3,6,-,2,1]=>[2,1,5,3,6,4]=>8
[5,4,1,2,3,+]=>[1,2,3,6,5,4]=>2
[5,4,1,2,3,-]=>[1,2,3,5,4,6]=>1
[5,4,1,2,6,3]=>[1,2,3,5,4,6]=>1
[5,4,1,3,2,+]=>[1,3,2,6,5,4]=>8
[5,4,1,3,2,-]=>[1,3,2,5,4,6]=>2
[5,4,1,3,6,2]=>[1,3,2,5,4,6]=>2
[5,4,1,6,2,3]=>[1,2,3,5,4,6]=>1
[5,4,1,6,3,2]=>[1,3,2,5,4,6]=>2
[5,4,2,1,3,+]=>[2,1,3,6,5,4]=>8
[5,4,2,1,3,-]=>[2,1,3,5,4,6]=>2
[5,4,2,1,6,3]=>[2,1,3,5,4,6]=>2
[5,4,2,3,1,+]=>[2,3,1,6,5,4]=>20
[5,4,2,3,1,-]=>[2,3,1,5,4,6]=>3
[5,4,2,3,6,1]=>[2,3,1,5,4,6]=>3
[5,4,2,6,1,3]=>[2,1,3,5,4,6]=>2
[5,4,2,6,3,1]=>[2,3,1,5,4,6]=>3
[5,4,+,1,2,+]=>[3,1,2,6,5,4]=>20
[5,4,-,1,2,+]=>[1,2,6,5,4,3]=>16
[5,4,+,1,2,-]=>[3,1,2,5,4,6]=>3
[5,4,-,1,2,-]=>[1,2,5,4,3,6]=>2
[5,4,+,1,6,2]=>[3,1,2,5,4,6]=>3
[5,4,-,1,6,2]=>[1,2,5,4,3,6]=>2
[5,4,+,2,1,+]=>[3,2,1,6,5,4]=>80
[5,4,-,2,1,+]=>[2,1,6,5,4,3]=>112
[5,4,+,2,1,-]=>[3,2,1,5,4,6]=>8
[5,4,-,2,1,-]=>[2,1,5,4,3,6]=>8
[5,4,+,2,6,1]=>[3,2,1,5,4,6]=>8
[5,4,-,2,6,1]=>[2,1,5,4,3,6]=>8
[5,4,+,6,1,2]=>[3,1,2,5,4,6]=>3
[5,4,-,6,1,2]=>[1,2,5,4,3,6]=>2
[5,4,+,6,2,1]=>[3,2,1,5,4,6]=>8
[5,4,-,6,2,1]=>[2,1,5,4,3,6]=>8
[5,4,6,1,2,3]=>[1,2,3,5,4,6]=>1
[5,4,6,1,3,2]=>[1,3,2,5,4,6]=>2
[5,4,6,2,1,3]=>[2,1,3,5,4,6]=>2
[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>3
[5,4,6,3,1,2]=>[3,1,2,5,4,6]=>3
[5,4,6,3,2,1]=>[3,2,1,5,4,6]=>8
[5,6,1,2,3,4]=>[1,2,3,4,5,6]=>1
[5,6,1,2,4,3]=>[1,2,4,3,5,6]=>1
[5,6,1,3,2,4]=>[1,3,2,4,5,6]=>1
[5,6,1,3,4,2]=>[1,3,4,2,5,6]=>1
[5,6,1,+,2,3]=>[1,4,2,3,5,6]=>1
[5,6,1,-,2,3]=>[1,2,3,5,6,4]=>1
[5,6,1,+,3,2]=>[1,4,3,2,5,6]=>2
[5,6,1,-,3,2]=>[1,3,2,5,6,4]=>3
[5,6,2,1,3,4]=>[2,1,3,4,5,6]=>1
[5,6,2,1,4,3]=>[2,1,4,3,5,6]=>2
[5,6,2,3,1,4]=>[2,3,1,4,5,6]=>1
[5,6,2,3,4,1]=>[2,3,4,1,5,6]=>1
[5,6,2,+,1,3]=>[2,4,1,3,5,6]=>2
[5,6,2,-,1,3]=>[2,1,3,5,6,4]=>3
[5,6,2,+,3,1]=>[2,4,3,1,5,6]=>3
[5,6,2,-,3,1]=>[2,3,1,5,6,4]=>6
[5,6,+,1,2,4]=>[3,1,2,4,5,6]=>1
[5,6,-,1,2,4]=>[1,2,4,5,6,3]=>1
[5,6,+,1,4,2]=>[3,1,4,2,5,6]=>2
[5,6,-,1,4,2]=>[1,4,2,5,6,3]=>3
[5,6,+,2,1,4]=>[3,2,1,4,5,6]=>2
[5,6,-,2,1,4]=>[2,1,4,5,6,3]=>4
[5,6,+,2,4,1]=>[3,2,4,1,5,6]=>3
[5,6,-,2,4,1]=>[2,4,1,5,6,3]=>9
[5,6,+,+,1,2]=>[3,4,1,2,5,6]=>2
[5,6,-,+,1,2]=>[4,1,2,5,6,3]=>6
[5,6,+,-,1,2]=>[3,1,2,5,6,4]=>6
[5,6,-,-,1,2]=>[1,2,5,6,3,4]=>2
[5,6,+,+,2,1]=>[3,4,2,1,5,6]=>5
[5,6,-,+,2,1]=>[4,2,1,5,6,3]=>26
[5,6,+,-,2,1]=>[3,2,1,5,6,4]=>20
[5,6,-,-,2,1]=>[2,1,5,6,3,4]=>10
[5,6,4,1,2,3]=>[1,2,3,5,6,4]=>1
[5,6,4,1,3,2]=>[1,3,2,5,6,4]=>3
[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>3
[5,6,4,2,3,1]=>[2,3,1,5,6,4]=>6
[5,6,4,3,1,2]=>[3,1,2,5,6,4]=>6
[5,6,4,3,2,1]=>[3,2,1,5,6,4]=>20
[6,1,2,3,4,5]=>[1,2,3,4,5,6]=>1
[6,1,2,3,+,4]=>[1,2,3,5,4,6]=>1
[6,1,2,3,-,4]=>[1,2,3,4,6,5]=>1
[6,1,2,+,3,5]=>[1,2,4,3,5,6]=>1
[6,1,2,-,3,5]=>[1,2,3,5,6,4]=>1
[6,1,2,+,+,3]=>[1,2,4,5,3,6]=>1
[6,1,2,-,+,3]=>[1,2,5,3,6,4]=>2
[6,1,2,+,-,3]=>[1,2,4,3,6,5]=>2
[6,1,2,-,-,3]=>[1,2,3,6,4,5]=>1
[6,1,2,5,3,4]=>[1,2,3,4,6,5]=>1
[6,1,2,5,4,3]=>[1,2,4,3,6,5]=>2
[6,1,+,2,4,5]=>[1,3,2,4,5,6]=>1
[6,1,-,2,4,5]=>[1,2,4,5,6,3]=>1
[6,1,+,2,+,4]=>[1,3,2,5,4,6]=>2
[6,1,-,2,+,4]=>[1,2,5,4,6,3]=>3
[6,1,+,2,-,4]=>[1,3,2,4,6,5]=>2
[6,1,-,2,-,4]=>[1,2,4,6,3,5]=>2
[6,1,+,+,2,5]=>[1,3,4,2,5,6]=>1
[6,1,-,+,2,5]=>[1,4,2,5,6,3]=>3
[6,1,+,-,2,5]=>[1,3,2,5,6,4]=>3
[6,1,-,-,2,5]=>[1,2,5,6,3,4]=>2
[6,1,+,+,+,2]=>[1,3,4,5,2,6]=>1
[6,1,-,+,+,2]=>[1,4,5,2,6,3]=>5
[6,1,+,-,+,2]=>[1,3,5,2,6,4]=>5
[6,1,+,+,-,2]=>[1,3,4,2,6,5]=>3
[6,1,-,-,+,2]=>[1,5,2,6,3,4]=>5
[6,1,-,+,-,2]=>[1,4,2,6,3,5]=>5
[6,1,+,-,-,2]=>[1,3,2,6,4,5]=>3
[6,1,-,-,-,2]=>[1,2,6,3,4,5]=>1
[6,1,+,5,2,4]=>[1,3,2,4,6,5]=>2
[6,1,-,5,2,4]=>[1,2,4,6,3,5]=>2
[6,1,+,5,4,2]=>[1,3,4,2,6,5]=>3
[6,1,-,5,4,2]=>[1,4,2,6,3,5]=>5
[6,1,4,2,3,5]=>[1,2,3,5,6,4]=>1
[6,1,4,2,+,3]=>[1,2,5,3,6,4]=>2
[6,1,4,2,-,3]=>[1,2,3,6,4,5]=>1
[6,1,4,3,2,5]=>[1,3,2,5,6,4]=>3
[6,1,4,3,+,2]=>[1,3,5,2,6,4]=>5
[6,1,4,3,-,2]=>[1,3,2,6,4,5]=>3
[6,1,4,5,2,3]=>[1,2,3,6,4,5]=>1
[6,1,4,5,3,2]=>[1,3,2,6,4,5]=>3
[6,1,5,2,3,4]=>[1,2,3,4,6,5]=>1
[6,1,5,2,4,3]=>[1,2,4,3,6,5]=>2
[6,1,5,3,2,4]=>[1,3,2,4,6,5]=>2
[6,1,5,3,4,2]=>[1,3,4,2,6,5]=>3
[6,1,5,+,2,3]=>[1,4,2,3,6,5]=>3
[6,1,5,-,2,3]=>[1,2,3,6,5,4]=>2
[6,1,5,+,3,2]=>[1,4,3,2,6,5]=>8
[6,1,5,-,3,2]=>[1,3,2,6,5,4]=>8
[6,+,1,3,4,5]=>[2,1,3,4,5,6]=>1
[6,-,1,3,4,5]=>[1,3,4,5,6,2]=>1
[6,+,1,3,+,4]=>[2,1,3,5,4,6]=>2
[6,-,1,3,+,4]=>[1,3,5,4,6,2]=>4
[6,+,1,3,-,4]=>[2,1,3,4,6,5]=>2
[6,-,1,3,-,4]=>[1,3,4,6,2,5]=>3
[6,+,1,+,3,5]=>[2,1,4,3,5,6]=>2
[6,-,1,+,3,5]=>[1,4,3,5,6,2]=>4
[6,+,1,-,3,5]=>[2,1,3,5,6,4]=>3
[6,-,1,-,3,5]=>[1,3,5,6,2,4]=>5
[6,+,1,+,+,3]=>[2,1,4,5,3,6]=>3
[6,-,1,+,+,3]=>[1,4,5,3,6,2]=>9
[6,+,1,-,+,3]=>[2,1,5,3,6,4]=>8
[6,+,1,+,-,3]=>[2,1,4,3,6,5]=>6
[6,-,1,-,+,3]=>[1,5,3,6,2,4]=>16
[6,-,1,+,-,3]=>[1,4,3,6,2,5]=>11
[6,+,1,-,-,3]=>[2,1,3,6,4,5]=>3
[6,-,1,-,-,3]=>[1,3,6,2,4,5]=>3
[6,+,1,5,3,4]=>[2,1,3,4,6,5]=>2
[6,-,1,5,3,4]=>[1,3,4,6,2,5]=>3
[6,+,1,5,4,3]=>[2,1,4,3,6,5]=>6
[6,-,1,5,4,3]=>[1,4,3,6,2,5]=>11
[6,+,+,1,4,5]=>[2,3,1,4,5,6]=>1
[6,-,+,1,4,5]=>[3,1,4,5,6,2]=>4
[6,+,-,1,4,5]=>[2,1,4,5,6,3]=>4
[6,-,-,1,4,5]=>[1,4,5,6,2,3]=>5
[6,+,+,1,+,4]=>[2,3,1,5,4,6]=>3
[6,-,+,1,+,4]=>[3,1,5,4,6,2]=>19
[6,+,-,1,+,4]=>[2,1,5,4,6,3]=>15
[6,+,+,1,-,4]=>[2,3,1,4,6,5]=>3
[6,-,-,1,+,4]=>[1,5,4,6,2,3]=>21
[6,-,+,1,-,4]=>[3,1,4,6,2,5]=>11
[6,+,-,1,-,4]=>[2,1,4,6,3,5]=>8
[6,-,-,1,-,4]=>[1,4,6,2,3,5]=>5
[6,+,+,+,1,5]=>[2,3,4,1,5,6]=>1
[6,-,+,+,1,5]=>[3,4,1,5,6,2]=>9
[6,+,-,+,1,5]=>[2,4,1,5,6,3]=>9
[6,+,+,-,1,5]=>[2,3,1,5,6,4]=>6
[6,-,-,+,1,5]=>[4,1,5,6,2,3]=>21
[6,-,+,-,1,5]=>[3,1,5,6,2,4]=>21
[6,+,-,-,1,5]=>[2,1,5,6,3,4]=>10
[6,-,-,-,1,5]=>[1,5,6,2,3,4]=>5
[6,+,+,+,+,1]=>[2,3,4,5,1,6]=>1
[6,-,+,+,+,1]=>[3,4,5,1,6,2]=>14
[6,+,-,+,+,1]=>[2,4,5,1,6,3]=>14
[6,+,+,-,+,1]=>[2,3,5,1,6,4]=>9
[6,+,+,+,-,1]=>[2,3,4,1,6,5]=>4
[6,-,-,+,+,1]=>[4,5,1,6,2,3]=>42
[6,-,+,-,+,1]=>[3,5,1,6,2,4]=>42
[6,-,+,+,-,1]=>[3,4,1,6,2,5]=>21
[6,+,-,-,+,1]=>[2,5,1,6,3,4]=>21
[6,+,-,+,-,1]=>[2,4,1,6,3,5]=>16
[6,+,+,-,-,1]=>[2,3,1,6,4,5]=>6
[6,-,-,-,+,1]=>[5,1,6,2,3,4]=>14
[6,-,-,+,-,1]=>[4,1,6,2,3,5]=>14
[6,-,+,-,-,1]=>[3,1,6,2,4,5]=>9
[6,+,-,-,-,1]=>[2,1,6,3,4,5]=>4
[6,-,-,-,-,1]=>[1,6,2,3,4,5]=>1
[6,+,+,5,1,4]=>[2,3,1,4,6,5]=>3
[6,-,+,5,1,4]=>[3,1,4,6,2,5]=>11
[6,+,-,5,1,4]=>[2,1,4,6,3,5]=>8
[6,-,-,5,1,4]=>[1,4,6,2,3,5]=>5
[6,+,+,5,4,1]=>[2,3,4,1,6,5]=>4
[6,-,+,5,4,1]=>[3,4,1,6,2,5]=>21
[6,+,-,5,4,1]=>[2,4,1,6,3,5]=>16
[6,-,-,5,4,1]=>[4,1,6,2,3,5]=>14
[6,+,4,1,3,5]=>[2,1,3,5,6,4]=>3
[6,-,4,1,3,5]=>[1,3,5,6,2,4]=>5
[6,+,4,1,+,3]=>[2,1,5,3,6,4]=>8
[6,-,4,1,+,3]=>[1,5,3,6,2,4]=>16
[6,+,4,1,-,3]=>[2,1,3,6,4,5]=>3
[6,-,4,1,-,3]=>[1,3,6,2,4,5]=>3
[6,+,4,3,1,5]=>[2,3,1,5,6,4]=>6
[6,-,4,3,1,5]=>[3,1,5,6,2,4]=>21
[6,+,4,3,+,1]=>[2,3,5,1,6,4]=>9
[6,-,4,3,+,1]=>[3,5,1,6,2,4]=>42
[6,+,4,3,-,1]=>[2,3,1,6,4,5]=>6
[6,-,4,3,-,1]=>[3,1,6,2,4,5]=>9
[6,+,4,5,1,3]=>[2,1,3,6,4,5]=>3
[6,-,4,5,1,3]=>[1,3,6,2,4,5]=>3
[6,+,4,5,3,1]=>[2,3,1,6,4,5]=>6
[6,-,4,5,3,1]=>[3,1,6,2,4,5]=>9
[6,+,5,1,3,4]=>[2,1,3,4,6,5]=>2
[6,-,5,1,3,4]=>[1,3,4,6,2,5]=>3
[6,+,5,1,4,3]=>[2,1,4,3,6,5]=>6
[6,-,5,1,4,3]=>[1,4,3,6,2,5]=>11
[6,+,5,3,1,4]=>[2,3,1,4,6,5]=>3
[6,-,5,3,1,4]=>[3,1,4,6,2,5]=>11
[6,+,5,3,4,1]=>[2,3,4,1,6,5]=>4
[6,-,5,3,4,1]=>[3,4,1,6,2,5]=>21
[6,+,5,+,1,3]=>[2,4,1,3,6,5]=>8
[6,-,5,+,1,3]=>[4,1,3,6,2,5]=>26
[6,+,5,-,1,3]=>[2,1,3,6,5,4]=>8
[6,-,5,-,1,3]=>[1,3,6,2,5,4]=>11
[6,+,5,+,3,1]=>[2,4,3,1,6,5]=>15
[6,-,5,+,3,1]=>[4,3,1,6,2,5]=>77
[6,+,5,-,3,1]=>[2,3,1,6,5,4]=>20
[6,-,5,-,3,1]=>[3,1,6,2,5,4]=>40
[6,3,1,2,4,5]=>[1,2,4,5,6,3]=>1
[6,3,1,2,+,4]=>[1,2,5,4,6,3]=>3
[6,3,1,2,-,4]=>[1,2,4,6,3,5]=>2
[6,3,1,+,2,5]=>[1,4,2,5,6,3]=>3
[6,3,1,-,2,5]=>[1,2,5,6,3,4]=>2
[6,3,1,+,+,2]=>[1,4,5,2,6,3]=>5
[6,3,1,-,+,2]=>[1,5,2,6,3,4]=>5
[6,3,1,+,-,2]=>[1,4,2,6,3,5]=>5
[6,3,1,-,-,2]=>[1,2,6,3,4,5]=>1
[6,3,1,5,2,4]=>[1,2,4,6,3,5]=>2
[6,3,1,5,4,2]=>[1,4,2,6,3,5]=>5
[6,3,2,1,4,5]=>[2,1,4,5,6,3]=>4
[6,3,2,1,+,4]=>[2,1,5,4,6,3]=>15
[6,3,2,1,-,4]=>[2,1,4,6,3,5]=>8
[6,3,2,+,1,5]=>[2,4,1,5,6,3]=>9
[6,3,2,-,1,5]=>[2,1,5,6,3,4]=>10
[6,3,2,+,+,1]=>[2,4,5,1,6,3]=>14
[6,3,2,-,+,1]=>[2,5,1,6,3,4]=>21
[6,3,2,+,-,1]=>[2,4,1,6,3,5]=>16
[6,3,2,-,-,1]=>[2,1,6,3,4,5]=>4
[6,3,2,5,1,4]=>[2,1,4,6,3,5]=>8
[6,3,2,5,4,1]=>[2,4,1,6,3,5]=>16
[6,3,4,1,2,5]=>[1,2,5,6,3,4]=>2
[6,3,4,1,+,2]=>[1,5,2,6,3,4]=>5
[6,3,4,1,-,2]=>[1,2,6,3,4,5]=>1
[6,3,4,2,1,5]=>[2,1,5,6,3,4]=>10
[6,3,4,2,+,1]=>[2,5,1,6,3,4]=>21
[6,3,4,2,-,1]=>[2,1,6,3,4,5]=>4
[6,3,4,5,1,2]=>[1,2,6,3,4,5]=>1
[6,3,4,5,2,1]=>[2,1,6,3,4,5]=>4
[6,3,5,1,2,4]=>[1,2,4,6,3,5]=>2
[6,3,5,1,4,2]=>[1,4,2,6,3,5]=>5
[6,3,5,2,1,4]=>[2,1,4,6,3,5]=>8
[6,3,5,2,4,1]=>[2,4,1,6,3,5]=>16
[6,3,5,+,1,2]=>[4,1,2,6,3,5]=>9
[6,3,5,-,1,2]=>[1,2,6,3,5,4]=>3
[6,3,5,+,2,1]=>[4,2,1,6,3,5]=>40
[6,3,5,-,2,1]=>[2,1,6,3,5,4]=>15
[6,4,1,2,3,5]=>[1,2,3,5,6,4]=>1
[6,4,1,2,+,3]=>[1,2,5,3,6,4]=>2
[6,4,1,2,-,3]=>[1,2,3,6,4,5]=>1
[6,4,1,3,2,5]=>[1,3,2,5,6,4]=>3
[6,4,1,3,+,2]=>[1,3,5,2,6,4]=>5
[6,4,1,3,-,2]=>[1,3,2,6,4,5]=>3
[6,4,1,5,2,3]=>[1,2,3,6,4,5]=>1
[6,4,1,5,3,2]=>[1,3,2,6,4,5]=>3
[6,4,2,1,3,5]=>[2,1,3,5,6,4]=>3
[6,4,2,1,+,3]=>[2,1,5,3,6,4]=>8
[6,4,2,1,-,3]=>[2,1,3,6,4,5]=>3
[6,4,2,3,1,5]=>[2,3,1,5,6,4]=>6
[6,4,2,3,+,1]=>[2,3,5,1,6,4]=>9
[6,4,2,3,-,1]=>[2,3,1,6,4,5]=>6
[6,4,2,5,1,3]=>[2,1,3,6,4,5]=>3
[6,4,2,5,3,1]=>[2,3,1,6,4,5]=>6
[6,4,+,1,2,5]=>[3,1,2,5,6,4]=>6
[6,4,-,1,2,5]=>[1,2,5,6,4,3]=>5
[6,4,+,1,+,2]=>[3,1,5,2,6,4]=>16
[6,4,-,1,+,2]=>[1,5,2,6,4,3]=>16
[6,4,+,1,-,2]=>[3,1,2,6,4,5]=>6
[6,4,-,1,-,2]=>[1,2,6,4,3,5]=>3
[6,4,+,2,1,5]=>[3,2,1,5,6,4]=>20
[6,4,-,2,1,5]=>[2,1,5,6,4,3]=>30
[6,4,+,2,+,1]=>[3,2,5,1,6,4]=>40
[6,4,-,2,+,1]=>[2,5,1,6,4,3]=>77
[6,4,+,2,-,1]=>[3,2,1,6,4,5]=>20
[6,4,-,2,-,1]=>[2,1,6,4,3,5]=>15
[6,4,+,5,1,2]=>[3,1,2,6,4,5]=>6
[6,4,-,5,1,2]=>[1,2,6,4,3,5]=>3
[6,4,+,5,2,1]=>[3,2,1,6,4,5]=>20
[6,4,-,5,2,1]=>[2,1,6,4,3,5]=>15
[6,4,5,1,2,3]=>[1,2,3,6,4,5]=>1
[6,4,5,1,3,2]=>[1,3,2,6,4,5]=>3
[6,4,5,2,1,3]=>[2,1,3,6,4,5]=>3
[6,4,5,2,3,1]=>[2,3,1,6,4,5]=>6
[6,4,5,3,1,2]=>[3,1,2,6,4,5]=>6
[6,4,5,3,2,1]=>[3,2,1,6,4,5]=>20
[6,5,1,2,3,4]=>[1,2,3,4,6,5]=>1
[6,5,1,2,4,3]=>[1,2,4,3,6,5]=>2
[6,5,1,3,2,4]=>[1,3,2,4,6,5]=>2
[6,5,1,3,4,2]=>[1,3,4,2,6,5]=>3
[6,5,1,+,2,3]=>[1,4,2,3,6,5]=>3
[6,5,1,-,2,3]=>[1,2,3,6,5,4]=>2
[6,5,1,+,3,2]=>[1,4,3,2,6,5]=>8
[6,5,1,-,3,2]=>[1,3,2,6,5,4]=>8
[6,5,2,1,3,4]=>[2,1,3,4,6,5]=>2
[6,5,2,1,4,3]=>[2,1,4,3,6,5]=>6
[6,5,2,3,1,4]=>[2,3,1,4,6,5]=>3
[6,5,2,3,4,1]=>[2,3,4,1,6,5]=>4
[6,5,2,+,1,3]=>[2,4,1,3,6,5]=>8
[6,5,2,-,1,3]=>[2,1,3,6,5,4]=>8
[6,5,2,+,3,1]=>[2,4,3,1,6,5]=>15
[6,5,2,-,3,1]=>[2,3,1,6,5,4]=>20
[6,5,+,1,2,4]=>[3,1,2,4,6,5]=>3
[6,5,-,1,2,4]=>[1,2,4,6,5,3]=>3
[6,5,+,1,4,2]=>[3,1,4,2,6,5]=>8
[6,5,-,1,4,2]=>[1,4,2,6,5,3]=>11
[6,5,+,2,1,4]=>[3,2,1,4,6,5]=>8
[6,5,-,2,1,4]=>[2,1,4,6,5,3]=>15
[6,5,+,2,4,1]=>[3,2,4,1,6,5]=>15
[6,5,-,2,4,1]=>[2,4,1,6,5,3]=>40
[6,5,+,+,1,2]=>[3,4,1,2,6,5]=>10
[6,5,-,+,1,2]=>[4,1,2,6,5,3]=>26
[6,5,+,-,1,2]=>[3,1,2,6,5,4]=>20
[6,5,-,-,1,2]=>[1,2,6,5,3,4]=>5
[6,5,+,+,2,1]=>[3,4,2,1,6,5]=>30
[6,5,-,+,2,1]=>[4,2,1,6,5,3]=>132
[6,5,+,-,2,1]=>[3,2,1,6,5,4]=>80
[6,5,-,-,2,1]=>[2,1,6,5,3,4]=>30
[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>2
[6,5,4,1,3,2]=>[1,3,2,6,5,4]=>8
[6,5,4,2,1,3]=>[2,1,3,6,5,4]=>8
[6,5,4,2,3,1]=>[2,3,1,6,5,4]=>20
[6,5,4,3,1,2]=>[3,1,2,6,5,4]=>20
[6,5,4,3,2,1]=>[3,2,1,6,5,4]=>80
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Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
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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