Identifier
- St000376: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0,1,0]=>0
[1,1,0,0]=>0
[1,0,1,0,1,0]=>0
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>0
[1,1,0,1,0,0]=>0
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,0,0]=>0
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,0]=>0
[1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0]=>0
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0]=>7
[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>6
[1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>6
[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,1,1,0,0,0]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>5
[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,0]=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,0]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>9
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>8
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>9
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>7
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>9
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>8
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>7
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>7
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>9
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>8
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>7
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>9
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>9
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>6
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>9
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>6
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>6
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>6
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>9
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>12
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>9
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>13
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>9
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>12
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>11
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>10
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>10
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>10
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>9
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>9
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>9
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>11
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>11
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>10
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>10
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>10
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>11
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>10
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>11
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>10
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>13
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>11
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>10
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>10
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>9
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>12
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>8
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>11
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>9
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>14
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>13
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>12
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>12
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>7
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>12
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>11
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>11
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>10
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>10
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>12
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>11
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>11
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>10
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>10
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>10
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>9
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>9
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>8
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>11
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>10
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>10
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>9
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>9
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>13
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>9
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>9
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>14
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>13
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>12
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>13
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>12
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>12
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>11
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>11
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>11
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>13
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>11
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>10
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>10
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>9
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>9
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>13
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>9
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>12
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>11
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>12
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>12
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>11
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>11
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>10
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>10
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>11
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>9
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>9
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>9
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>10
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>12
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>11
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>11
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>11
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>10
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>11
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>9
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>10
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>10
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>11
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>11
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>10
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>9
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>8
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>9
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>9
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>12
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>12
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>10
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>10
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>14
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>12
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>11
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>10
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>10
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>13
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>10
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>10
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>12
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>11
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>12
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>12
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>11
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>9
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>8
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>13
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>7
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>11
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>10
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>9
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>9
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>8
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>8
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>7
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>6
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>10
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>9
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>8
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>12
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>9
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>13
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>9
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>7
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>11
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>12
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>10
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>10
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>9
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>9
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>9
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>12
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>11
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>11
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>10
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>10
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>10
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>14
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>7
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>12
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>10
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>11
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>9
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>10
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>13
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>10
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>8
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>9
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>9
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>8
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>11
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>10
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>9
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>9
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>10
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>9
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>13
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>12
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>10
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>9
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>12
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>11
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>7
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>7
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>10
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>10
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>11
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>11
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>10
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>10
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>9
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>9
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>10
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>10
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>9
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>8
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>12
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
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Description
The bounce deficit of a Dyck path.
For a Dyck path $D$ of semilength $n$, this is defined as
$$\binom{n}{2} - \operatorname{area}(D) - \operatorname{bounce}(D).$$
The zeta map Mp00032inverse zeta map sends this statistic to the dinv deficit St000369The dinv deficit of a Dyck path., both are thus equidistributed.
For a Dyck path $D$ of semilength $n$, this is defined as
$$\binom{n}{2} - \operatorname{area}(D) - \operatorname{bounce}(D).$$
The zeta map Mp00032inverse zeta map sends this statistic to the dinv deficit St000369The dinv deficit of a Dyck path., both are thus equidistributed.
References
[1] Lee, K., Li, L., Loehr, N. A. A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers arXiv:1602.01126
Code
def statistic(D):
return binomial(len(D)/2,2)-D.area()-D.bounce()
Created
Feb 05, 2016 at 21:03 by Christian Stump
Updated
Feb 05, 2016 at 21:03 by Christian Stump
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