Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00327: Dyck paths —inverse Kreweras complement⟶ Dyck paths
St001291: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep-1
Cc0005;cc-rep
[1]=>[1,0]=>[1,0]=>1
[1,2]=>[1,0,1,0]=>[1,1,0,0]=>1
[2,1]=>[1,1,0,0]=>[1,0,1,0]=>2
[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>1
[1,3,2]=>[1,0,1,1,0,0]=>[1,1,0,1,0,0]=>2
[2,1,3]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>2
[2,3,1]=>[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>3
[3,1,2]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>3
[3,2,1]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>3
[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>1
[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0]=>2
[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>2
[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>3
[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>3
[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>3
[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>2
[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0]=>3
[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>3
[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>4
[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>4
[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>4
[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>3
[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>4
[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>3
[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>4
[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>4
[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>4
[4,1,2,3]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>4
[4,1,3,2]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>4
[4,2,1,3]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>4
[4,2,3,1]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>4
[4,3,1,2]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>4
[4,3,2,1]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>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]=>1
[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>2
[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>2
[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>3
[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>3
[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>2
[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>3
[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>3
[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>4
[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>4
[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>4
[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>3
[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>4
[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>3
[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>4
[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>4
[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>4
[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>4
[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>4
[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>4
[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>4
[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>4
[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>4
[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>2
[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>3
[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>3
[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>4
[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>4
[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>4
[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>4
[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>4
[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>5
[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>5
[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>5
[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>4
[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>5
[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>4
[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>5
[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>5
[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>5
[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>5
[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>5
[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>5
[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>5
[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>5
[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>5
[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>3
[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>4
[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>4
[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>5
[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>5
[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>5
[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>3
[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>4
[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>4
[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>5
[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>5
[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>5
[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>5
[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>4
[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>5
[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>5
[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>5
[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>5
[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>5
[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>5
[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>5
[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>5
[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>5
[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>4
[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>5
[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>4
[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>5
[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>4
[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>5
[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>4
[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>5
[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>4
[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>5
[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>4
[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>5
[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>5
[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>5
[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>5
[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>5
[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>5
[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>5
[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,1,3,4,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,1,4,2,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,2,3,1,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>5
[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>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]=>1
[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>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]=>2
[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>4
[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,3,6,2,5,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[1,4,2,6,3,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,4,2,6,5,3]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,4,6,2,5,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,4,6,5,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,2,4,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>2
[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>4
[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>4
[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>5
[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>4
[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>5
[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>5
[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>5
[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>3
[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>4
[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>4
[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>5
[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>5
[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>5
[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>4
[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>5
[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>5
[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>6
[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>6
[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>6
[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>5
[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>5
[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>6
[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>6
[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[2,3,6,1,5,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[2,3,6,4,1,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[2,3,6,5,1,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>4
[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>5
[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>5
[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>6
[2,4,1,6,5,3]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>6
[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>4
[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>5
[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>5
[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>6
[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>6
[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>5
[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>6
[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>5
[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>6
[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>6
[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>6
[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[2,4,6,1,5,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,1,4,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,1,4,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,1,5,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,3,1,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,3,1,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,3,4,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,3,5,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,5,1,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>4
[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>4
[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>5
[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>5
[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>6
[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>6
[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,1,6,2,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,1,6,4,5,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>4
[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>4
[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>5
[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>5
[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>6
[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>6
[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,2,6,4,1,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>5
[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>5
[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>6
[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[3,4,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>5
[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>5
[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>6
[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>6
[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>6
[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>6
[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>6
[3,4,6,2,1,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>6
[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>6
[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>6
[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>6
[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>6
[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>6
[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>6
[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>6
[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>6
[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>6
[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,2,1,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,2,4,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,1,2,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,1,3,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[4,1,6,2,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,1,6,2,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[4,2,1,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[4,2,6,1,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,1,2,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,1,2,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,1,2,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,1,3,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,1,3,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,1,3,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,1,6,2,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,2,1,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,2,3,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,3,1,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,3,1,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,4,1,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,2,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,2,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,3,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,3,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,3,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,3,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,4,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,4,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,4,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,4,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,4,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,5,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,5,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,5,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,5,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,5,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,1,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,3,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,3,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,3,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,3,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,4,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,4,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,4,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,4,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,4,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,5,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,5,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,5,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,1,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,1,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,2,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,4,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,4,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,4,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,4,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,4,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,4,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,1,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,1,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,5,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,1,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,1,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,1,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,1,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,2,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,2,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
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 summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
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 Kreweras complement
Description
Return the inverse of the Kreweras complement of a Dyck path, regarded as a noncrossing set partition.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.
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!