Identifier
-
Mp00256:
Decorated permutations
—upper permutation⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep-2
Cc0005;cc-rep
[+]=>[1]=>[1,0]=>[1,0]=>0
[-]=>[1]=>[1,0]=>[1,0]=>0
[+,+]=>[1,2]=>[1,0,1,0]=>[1,1,0,0]=>0
[-,+]=>[2,1]=>[1,1,0,0]=>[1,0,1,0]=>1
[+,-]=>[1,2]=>[1,0,1,0]=>[1,1,0,0]=>0
[-,-]=>[1,2]=>[1,0,1,0]=>[1,1,0,0]=>0
[2,1]=>[2,1]=>[1,1,0,0]=>[1,0,1,0]=>1
[+,+,+]=>[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>0
[-,+,+]=>[2,3,1]=>[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>1
[+,-,+]=>[1,3,2]=>[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>2
[+,+,-]=>[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>0
[-,+,-]=>[2,1,3]=>[1,1,0,0,1,0]=>[1,1,0,1,0,0]=>2
[+,-,-]=>[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>0
[-,-,-]=>[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>0
[+,3,2]=>[1,3,2]=>[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>2
[2,1,+]=>[2,3,1]=>[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>1
[2,1,-]=>[2,1,3]=>[1,1,0,0,1,0]=>[1,1,0,1,0,0]=>2
[3,1,2]=>[2,3,1]=>[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>1
[3,+,1]=>[2,3,1]=>[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>1
[+,+,+,+]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0
[-,+,+,+]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[+,-,+,+]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>1
[+,+,-,+]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>3
[+,+,+,-]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0
[-,+,-,+]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[-,+,+,-]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>2
[+,-,+,-]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>4
[+,+,-,-]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0
[-,+,-,-]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>3
[+,-,-,-]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0
[-,-,-,-]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0
[+,+,4,3]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>3
[-,+,4,3]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[+,3,2,+]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>1
[+,3,2,-]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>4
[+,4,2,3]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>1
[+,4,+,2]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>1
[2,1,+,+]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[2,1,-,+]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[2,1,+,-]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>2
[2,1,-,-]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>3
[2,1,4,3]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[3,1,2,+]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[3,1,2,-]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>2
[3,1,4,2]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[3,+,1,+]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[3,+,1,-]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>2
[3,+,4,1]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[4,1,2,3]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[4,1,+,2]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[4,1,-,2]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[4,+,1,3]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[4,+,+,1]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>2
[4,+,-,1]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>3
[+,+,+,+,+]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[-,+,+,+,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[+,-,+,+,+]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[+,+,-,+,+]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>1
[+,+,+,-,+]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>4
[+,+,+,+,-]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[-,-,+,+,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[-,+,+,-,+]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[-,+,+,+,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[+,-,+,-,+]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,-,+,+,-]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>2
[+,+,-,+,-]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>6
[+,+,+,-,-]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[-,+,+,-,-]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[+,-,+,-,-]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>6
[+,+,-,-,-]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[-,+,-,-,-]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>4
[+,-,-,-,-]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[-,-,-,-,-]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[+,+,+,5,4]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>4
[-,+,+,5,4]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[+,-,+,5,4]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,+,4,3,+]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>1
[+,+,4,3,-]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>6
[+,+,5,3,4]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>1
[+,+,5,+,3]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>1
[+,3,2,+,+]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,3,2,+,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,3,2,-,+]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,3,2,+,-]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>2
[+,3,2,-,-]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>6
[+,3,2,5,4]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,4,2,3,+]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,4,2,3,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,4,2,3,-]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>2
[+,4,2,5,3]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,4,+,2,+]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,4,+,2,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,4,+,2,-]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>2
[+,4,+,5,2]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,5,2,3,4]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,5,2,3,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,5,2,+,3]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,5,2,+,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,5,2,-,3]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[+,5,+,2,4]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,5,+,2,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,5,+,+,2]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[-,5,+,+,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,5,+,-,2]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>4
[2,1,+,+,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[2,1,+,-,+]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[2,1,+,+,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[2,1,+,-,-]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[2,1,-,-,-]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>4
[2,1,+,5,4]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[2,3,1,+,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[2,4,1,3,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[2,4,+,1,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[2,5,1,3,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[2,5,1,+,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[2,5,+,1,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[2,5,+,+,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,1,2,+,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[3,1,2,-,+]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[3,1,2,+,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[3,1,2,-,-]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[3,1,2,5,4]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[3,+,1,+,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[3,-,1,+,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,+,1,-,+]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[3,+,1,+,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[3,+,1,-,-]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[3,+,1,5,4]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[3,4,1,2,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,4,2,1,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,5,1,2,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,5,1,+,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,5,2,1,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[3,5,2,+,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,1,2,3,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[4,1,2,3,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[4,1,2,5,3]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[4,1,+,2,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[4,1,+,2,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[4,1,+,5,2]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[4,+,1,3,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[4,-,1,3,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,+,1,3,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[4,+,1,5,3]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[4,+,+,1,+]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[4,-,+,1,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,+,+,1,-]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4
[4,+,+,5,1]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[4,3,1,2,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,3,2,1,+]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,5,1,2,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,5,1,3,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,5,2,1,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,5,2,3,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,5,+,1,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[4,5,+,2,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,1,2,3,4]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,1,2,+,3]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,1,2,-,3]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[5,1,+,2,4]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,1,+,+,2]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,1,+,-,2]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[5,+,1,3,4]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,-,1,3,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,+,1,+,3]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,-,1,+,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,+,1,-,3]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[5,+,+,1,4]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,-,+,1,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,+,+,+,1]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[5,-,+,+,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,+,+,-,1]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[5,3,1,2,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,3,1,+,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,3,2,1,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,3,2,+,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,4,1,2,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,4,1,3,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,4,2,1,3]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,4,2,3,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,4,+,1,2]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[5,4,+,2,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[+,+,+,+,+,+]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[-,+,+,+,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[+,-,+,+,+,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[+,+,-,+,+,+]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[+,+,+,-,+,+]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[+,+,+,+,-,+]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[+,+,+,+,+,-]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[-,-,+,+,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[-,+,-,+,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[-,+,+,+,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[-,+,+,+,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[+,-,-,+,+,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,-,+,+,-,+]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[+,-,+,+,+,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[+,+,-,+,-,+]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,+,-,+,+,-]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[+,+,+,-,+,-]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>8
[+,+,+,+,-,-]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[-,-,+,+,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[-,+,+,+,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[+,-,+,-,+,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,-,+,+,-,-]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[+,+,-,+,-,-]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>9
[+,+,+,-,-,-]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[-,+,+,-,-,-]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[+,-,+,-,-,-]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>8
[+,+,-,-,-,-]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[-,+,-,-,-,-]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[+,-,-,-,-,-]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[-,-,-,-,-,-]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[+,+,+,+,6,5]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[-,+,+,+,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[+,-,+,+,6,5]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[+,+,-,+,6,5]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[-,-,+,+,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,+,+,5,4,+]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[+,+,+,5,4,-]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>8
[+,-,+,5,4,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,+,+,6,4,5]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[+,+,+,6,+,4]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[+,+,4,3,+,+]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,4,3,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,4,3,+,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,4,3,-,+]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,+,4,3,+,-]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[+,+,4,3,-,-]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>9
[+,+,4,3,6,5]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,+,5,3,4,+]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,5,3,4,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,5,3,4,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,5,3,4,-]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[+,+,5,3,6,4]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,+,5,+,3,+]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,5,+,3,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,5,+,3,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,5,+,3,-]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[+,+,5,+,6,3]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,+,6,3,4,5]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,6,3,4,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,6,3,4,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,6,3,+,4]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,6,3,+,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,6,3,+,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,6,3,-,4]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,+,6,+,3,5]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,6,+,3,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,6,+,3,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,6,+,+,3]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[-,+,6,+,+,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[+,-,6,+,+,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,+,6,+,-,3]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[+,3,2,+,+,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,3,2,+,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,3,2,+,-,+]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[+,3,2,+,+,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[-,3,2,+,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,3,2,-,+,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,3,2,+,-,-]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[+,3,2,-,-,-]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>8
[+,3,2,+,6,5]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,3,2,+,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,3,2,5,4,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,3,4,2,+,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,3,5,2,4,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,3,5,+,2,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,3,6,2,4,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,3,6,2,+,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,3,6,+,2,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,3,6,+,+,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,2,3,+,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,4,2,3,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,4,2,3,-,+]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[+,4,2,3,+,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[-,4,2,3,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,4,2,3,-,-]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[+,4,2,3,6,5]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,4,2,3,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,4,2,5,3,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,4,+,2,+,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,4,+,2,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,4,-,2,+,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,+,2,-,+]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[+,4,+,2,+,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[-,4,+,2,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,4,+,2,-,-]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[+,4,+,2,6,5]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,4,+,2,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,4,+,5,2,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,4,5,2,3,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,5,3,2,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,6,2,3,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,6,2,+,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,6,3,2,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,4,6,3,+,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,2,3,4,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,5,2,3,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,5,2,3,4,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[+,5,2,3,6,4]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,5,2,3,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,5,2,+,3,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,5,2,+,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,5,2,+,3,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[+,5,2,-,3,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,5,2,+,6,3]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,5,2,+,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,5,+,2,4,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,5,+,2,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,5,-,2,4,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,+,2,4,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[+,5,+,2,6,4]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,5,+,2,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,5,+,+,2,+]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,5,+,+,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,5,-,+,2,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,+,+,2,-]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[+,5,+,-,2,-]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>8
[+,5,+,+,6,2]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,5,+,+,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,5,4,2,3,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,4,3,2,+]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,6,2,3,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,6,2,4,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,6,3,2,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,6,3,4,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,6,+,2,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,5,6,+,3,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,2,3,4,5]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,2,3,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,2,3,+,4]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,2,3,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,2,3,-,4]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,6,2,3,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,6,2,+,3,5]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,2,+,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,2,+,+,3]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,2,+,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,2,+,-,3]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,6,2,+,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,6,+,2,4,5]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,+,2,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,-,2,4,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,+,2,+,4]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,+,2,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,-,2,+,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,+,2,-,4]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,6,+,2,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,6,+,+,2,5]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,+,+,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,-,+,2,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,+,+,+,2]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[-,6,+,+,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[+,6,-,+,+,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,+,+,-,2]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[-,6,+,+,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[+,6,4,2,3,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,4,2,+,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,4,3,2,5]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,4,3,+,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,5,2,3,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,5,2,4,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,5,3,2,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,5,3,4,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,5,+,2,3]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[+,6,5,+,3,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[2,1,+,+,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[2,1,-,+,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,+,+,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[2,1,+,+,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[2,1,+,+,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[2,1,+,-,-,-]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[2,1,-,-,-,-]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[2,1,+,+,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[2,1,4,3,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,5,3,4,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,5,+,3,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,6,3,4,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,6,3,+,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,6,+,3,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,1,6,+,+,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[2,3,1,+,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,3,1,+,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,3,1,+,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,4,1,3,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,4,1,3,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,4,1,3,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,4,+,1,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,4,+,1,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,4,+,1,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,5,1,3,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,5,1,3,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,5,1,+,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,5,1,+,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,5,+,1,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,5,+,1,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,5,+,+,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,5,+,+,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,6,1,3,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,1,3,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,1,3,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,6,1,+,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,1,+,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,1,+,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,6,+,1,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,+,1,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,+,1,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[2,6,+,+,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,+,+,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[2,6,+,+,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,1,2,+,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[3,1,2,+,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[3,1,2,+,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[3,1,2,+,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[3,1,2,-,-,-]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[3,1,2,+,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[3,1,4,2,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,1,5,2,4,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,1,5,+,2,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,1,6,2,4,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,1,6,2,+,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,1,6,+,2,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,1,6,+,+,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,1,+,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[3,-,1,+,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,+,1,+,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[3,+,1,+,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[3,-,1,+,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,+,1,+,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[3,+,1,-,-,-]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[3,+,1,+,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[3,-,1,+,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,+,4,1,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,5,1,4,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,5,+,1,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,6,1,4,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,6,1,+,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,6,+,1,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,+,6,+,+,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[3,4,1,2,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,4,1,2,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,4,1,2,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,4,2,1,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,4,2,1,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,4,2,1,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,5,1,2,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,5,1,2,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,5,1,+,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,5,1,+,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,5,2,1,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,5,2,1,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,5,2,+,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,5,2,+,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,6,1,2,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,1,2,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,1,2,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,6,1,+,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,1,+,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,1,+,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,6,2,1,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,2,1,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,2,1,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[3,6,2,+,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,2,+,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[3,6,2,+,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,1,2,3,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[4,1,2,3,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,1,2,3,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[4,1,2,3,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[4,1,2,3,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,1,+,2,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[4,1,-,2,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,1,+,2,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,1,+,2,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[4,1,+,2,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[4,1,+,2,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,1,5,2,3,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,1,5,3,2,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,1,6,2,3,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,1,6,2,+,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,1,6,3,2,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,1,6,3,+,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,1,3,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[4,-,1,3,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,+,1,3,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,+,1,3,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[4,-,1,3,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,+,1,3,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[4,+,1,3,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,-,1,3,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,+,+,1,+,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[4,-,+,1,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,+,-,1,+,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,+,1,-,+]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,+,+,1,+,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[4,-,+,1,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,+,+,1,-,-]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[4,+,+,1,6,5]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,-,+,1,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,+,5,1,3,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,5,3,1,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,6,1,3,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,6,1,+,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,6,3,1,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,+,6,3,+,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[4,3,1,2,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,3,1,2,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,3,1,2,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,3,2,1,+,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,3,2,1,-,+]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,3,2,1,6,5]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,5,1,2,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,5,1,2,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,5,1,3,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,5,1,3,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,5,2,1,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,5,2,1,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,5,2,3,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,5,2,3,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,5,+,1,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,5,+,1,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,5,+,2,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,5,+,2,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,6,1,2,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,1,2,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,1,2,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,6,1,3,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,1,3,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,1,3,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,6,2,1,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,2,1,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,2,1,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,6,2,3,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,2,3,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,2,3,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,6,+,1,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,+,1,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,+,1,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[4,6,+,2,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,+,2,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[4,6,+,2,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,1,2,3,4,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,1,2,3,4,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,1,2,3,6,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,1,2,+,3,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,1,2,+,3,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,1,2,+,6,3]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,1,+,2,4,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,1,-,2,4,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,+,2,4,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,1,+,2,6,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,1,+,+,2,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,1,-,+,2,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,+,+,2,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,1,+,+,6,2]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,1,4,2,3,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,4,3,2,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,6,2,3,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,6,2,4,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,6,3,2,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,6,3,4,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,6,+,2,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,1,6,+,3,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,1,3,4,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,-,1,3,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,+,1,3,4,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,+,1,3,6,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,-,1,3,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,+,1,+,3,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,-,1,+,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,+,1,+,3,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,+,1,+,6,3]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,-,1,+,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,+,+,1,4,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,-,+,1,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,+,-,1,4,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,+,1,4,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,+,+,1,6,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,-,+,1,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,+,+,+,1,+]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[5,-,+,+,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,+,-,+,1,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,+,+,1,-]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[5,+,+,+,6,1]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[5,-,+,+,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,+,4,1,3,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,4,3,1,+]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,6,1,3,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,6,1,4,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,6,3,1,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,6,3,4,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,6,+,1,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,+,6,+,3,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,3,1,2,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,3,1,2,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,3,1,+,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,3,1,+,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,3,2,1,4,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,3,2,1,6,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,3,2,+,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,3,2,+,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,1,2,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,4,1,2,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,1,3,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,4,1,3,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,2,1,3,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,4,2,1,6,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,2,3,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,4,2,3,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,+,1,2,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,4,+,1,6,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,+,2,1,+]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,4,+,2,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,1,2,4,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,1,3,2,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,1,3,4,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,1,+,2,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,1,+,3,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,2,1,3,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,2,1,4,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,2,3,1,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,2,3,4,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,2,+,1,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,2,+,3,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,+,1,2,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,+,1,4,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,+,2,1,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,+,2,4,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,+,+,1,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[5,6,+,+,2,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,2,3,+,4]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,2,3,-,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,1,2,+,3,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,2,+,+,3]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,2,+,-,3]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,1,+,2,4,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,-,2,4,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,+,2,+,4]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,-,2,+,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,+,2,-,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,1,+,+,2,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,-,+,2,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,+,+,+,2]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,1,-,+,+,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,+,+,-,2]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,1,4,2,3,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,4,2,+,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,4,3,2,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,4,3,+,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,5,2,3,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,5,2,4,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,5,3,2,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,5,3,4,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,5,+,2,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,1,5,+,3,2]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,1,3,4,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,1,3,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,1,3,+,4]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,1,3,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,1,3,-,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,-,1,3,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,+,1,+,3,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,1,+,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,1,+,+,3]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,1,+,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,1,+,-,3]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,-,1,+,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,+,+,1,4,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,+,1,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,-,1,4,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,+,1,+,4]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,+,1,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,-,1,+,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,+,1,-,4]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,-,+,1,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,+,+,+,1,5]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,+,+,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,-,+,1,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,+,+,+,1]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[6,-,+,+,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,+,-,+,+,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,+,+,-,1]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[6,-,+,+,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,+,4,1,3,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,4,1,+,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,4,3,1,5]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,4,3,+,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,5,1,3,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,5,1,4,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,5,3,1,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,5,3,4,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,5,+,1,3]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,+,5,+,3,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,3,1,2,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,1,2,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,1,2,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,3,1,+,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,1,+,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,1,+,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,3,2,1,4,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,2,1,+,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,2,1,-,4]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,3,2,+,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,2,+,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,3,2,+,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,4,1,2,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,1,2,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,1,2,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,4,1,3,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,1,3,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,1,3,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,4,2,1,3,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,2,1,+,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,2,1,-,3]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,4,2,3,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,2,3,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,2,3,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,4,+,1,2,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,+,1,+,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,+,1,-,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,4,+,2,1,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,+,2,+,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,4,+,2,-,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[6,5,1,2,3,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,1,2,4,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,1,3,2,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,1,3,4,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,1,+,2,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,1,+,3,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,2,1,3,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,2,1,4,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,2,3,1,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,2,3,4,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,2,+,1,3]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,2,+,3,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,+,1,2,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,+,1,4,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,+,2,1,4]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,+,2,4,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,+,+,1,2]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[6,5,+,+,2,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
upper permutation
Description
The upper 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 $v$.
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 $v$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!