Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
St000005: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1]=>[1,0]=>0
[1,2]=>[1,0,1,0]=>1
[2,1]=>[1,1,0,0]=>0
[1,2,3]=>[1,0,1,0,1,0]=>3
[1,3,2]=>[1,0,1,1,0,0]=>1
[2,1,3]=>[1,1,0,0,1,0]=>2
[2,3,1]=>[1,1,0,1,0,0]=>1
[3,1,2]=>[1,1,1,0,0,0]=>0
[3,2,1]=>[1,1,1,0,0,0]=>0
[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>6
[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>3
[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>4
[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>3
[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>1
[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>1
[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>5
[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>2
[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>4
[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>2
[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>1
[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>1
[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>3
[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>2
[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>3
[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>2
[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>1
[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>1
[4,1,2,3]=>[1,1,1,1,0,0,0,0]=>0
[4,1,3,2]=>[1,1,1,1,0,0,0,0]=>0
[4,2,1,3]=>[1,1,1,1,0,0,0,0]=>0
[4,2,3,1]=>[1,1,1,1,0,0,0,0]=>0
[4,3,1,2]=>[1,1,1,1,0,0,0,0]=>0
[4,3,2,1]=>[1,1,1,1,0,0,0,0]=>0
[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>10
[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>6
[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>7
[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>6
[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]=>3
[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]=>3
[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>8
[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]=>4
[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>7
[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>4
[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>3
[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]=>3
[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>5
[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>4
[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>5
[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>4
[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>3
[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>3
[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>1
[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>9
[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>5
[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>6
[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>5
[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]=>2
[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>2
[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>8
[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>4
[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>6
[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>4
[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>2
[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>2
[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>5
[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>4
[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>5
[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>4
[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>2
[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>2
[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]=>1
[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]=>1
[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]=>1
[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]=>1
[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>1
[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>7
[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>3
[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>6
[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]=>3
[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]=>2
[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>2
[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>7
[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>3
[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>6
[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>3
[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>2
[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>2
[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>5
[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>3
[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>5
[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>3
[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>2
[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>2
[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>1
[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>1
[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]=>1
[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>1
[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>1
[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>4
[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>3
[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>4
[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>3
[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>4
[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>3
[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>4
[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>3
[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>4
[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>3
[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>4
[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>3
[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>2
[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>1
[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>1
[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>1
[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>1
[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>1
[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,1,3,4,2]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,1,4,2,3]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,2,3,1,4]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]=>0
[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>0
[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>15
[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>10
[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>11
[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>10
[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>12
[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>7
[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>11
[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>6
[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>6
[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>13
[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>9
[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>8
[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>12
[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>7
[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>9
[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>7
[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>8
[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>7
[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>8
[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>7
[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,3,6,2,5,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>10
[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>9
[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,4,2,6,3,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,4,2,6,5,3]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>10
[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>9
[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>8
[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>8
[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,4,6,2,5,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,4,6,5,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,2,4,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>14
[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>9
[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>10
[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>9
[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>5
[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>5
[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>11
[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>6
[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>10
[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>6
[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>5
[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>5
[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>7
[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>6
[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>7
[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>6
[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>5
[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>5
[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>13
[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>8
[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>9
[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>8
[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>11
[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>6
[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>9
[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>6
[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>7
[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>6
[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>7
[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>6
[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>4
[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>4
[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[2,3,6,1,5,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[2,3,6,4,1,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[2,3,6,5,1,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>10
[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>9
[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[2,4,1,6,5,3]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>10
[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>9
[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>7
[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>7
[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[2,4,6,1,5,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,1,4,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,1,4,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,1,5,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,3,1,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,3,1,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,3,4,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,3,5,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,5,1,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>12
[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>7
[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>8
[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>7
[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>11
[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>6
[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>8
[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>6
[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>7
[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>6
[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>7
[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>6
[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,1,6,2,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,1,6,4,5,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>12
[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>7
[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>8
[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>7
[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>11
[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>6
[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>8
[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>6
[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>7
[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>6
[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>7
[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>6
[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,2,6,4,1,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>10
[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>5
[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>8
[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>10
[3,4,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>5
[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>8
[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>7
[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>7
[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,4,6,2,1,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,2,1,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,2,4,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,1,2,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,1,3,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[4,1,6,2,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,1,6,2,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[4,2,1,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[4,2,6,1,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,1,2,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,1,2,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,1,2,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,1,3,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,1,3,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,1,3,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,1,6,2,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,2,1,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,2,3,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,3,1,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,3,1,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,4,1,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,2,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,2,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,3,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,3,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,3,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,3,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,4,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,4,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,4,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,4,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,4,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,5,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,5,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,5,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,5,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,5,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,1,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,3,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,3,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,3,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,3,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,4,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,4,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,4,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,4,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,4,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,5,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,5,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,5,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,1,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,1,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,2,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,4,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,4,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,4,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,4,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,4,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,4,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,1,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,1,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,5,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,1,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,1,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,1,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,1,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,2,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,2,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
The bounce statistic of a Dyck path.
The bounce path $D'$ of a Dyck path $D$ is the Dyck path obtained from $D$ by starting at the end point $(2n,0)$, traveling north-west until hitting $D$, then bouncing back south-west to the $x$-axis, and repeating this procedure until finally reaching the point $(0,0)$.
The points where $D'$ touches the $x$-axis are called bounce points, and a bounce path is uniquely determined by its bounce points.
This statistic is given by the sum of all $i$ for which the bounce path $D'$ of $D$ touches the $x$-axis at $(2i,0)$.
In particular, the bounce statistics of $D$ and $D'$ coincide.
The bounce path $D'$ of a Dyck path $D$ is the Dyck path obtained from $D$ by starting at the end point $(2n,0)$, traveling north-west until hitting $D$, then bouncing back south-west to the $x$-axis, and repeating this procedure until finally reaching the point $(0,0)$.
The points where $D'$ touches the $x$-axis are called bounce points, and a bounce path is uniquely determined by its bounce points.
This statistic is given by the sum of all $i$ for which the bounce path $D'$ of $D$ touches the $x$-axis at $(2i,0)$.
In particular, the bounce statistics of $D$ and $D'$ coincide.
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.
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