Identifier
- St000676: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[]=>0
[1,0]=>1
[1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,0]=>5
[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]=>5
[1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,0]=>4
[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]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[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]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>4
[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]=>4
[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,0]=>5
[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]=>5
[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]=>4
[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]=>4
[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]=>5
[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]=>4
[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]=>4
[1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[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]=>3
[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]=>3
[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[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]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[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]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,0]=>4
[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]=>4
[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>3
[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]=>3
[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[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]=>5
[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]=>4
[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]=>4
[1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[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]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>5
[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]=>4
[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]=>5
[1,1,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,0]=>2
[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]=>4
[1,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>5
[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]=>5
[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]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5
[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]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[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]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6
[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]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>5
[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]=>5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[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]=>5
[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]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[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]=>5
[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]=>5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4
[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]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4
[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]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[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]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[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]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>4
[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]=>3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3
[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]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>4
[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]=>4
[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]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>6
[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]=>5
[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]=>5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[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]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[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]=>2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>4
[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]=>4
[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]=>3
[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]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>6
[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]=>5
[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]=>5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>5
[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]=>5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>5
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>5
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4
[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]=>5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>5
[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]=>5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[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]=>4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[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]=>5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[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]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3
[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]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4
[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]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>5
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4
[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]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>3
[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]=>3
[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]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[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]=>3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[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]=>2
[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]=>4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>3
[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]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>6
[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]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>6
[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]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5
[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]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5
[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]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6
[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]=>6
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>6
[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]=>5
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5
[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]=>5
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6
[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]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>5
[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]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5
[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]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>4
[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]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>5
[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]=>5
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>5
[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]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>6
[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]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5
[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]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5
[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]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>6
[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]=>6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>5
[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]=>5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>5
[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]=>5
[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]=>5
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>6
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>5
[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]=>5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>4
[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]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>5
[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]=>5
[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]=>5
[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]=>4
[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]=>4
[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]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[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]=>6
[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]=>6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4
[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]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>5
[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]=>5
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[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]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5
[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]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[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]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>5
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Description
The number of odd rises of a Dyck path.
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
References
[1] Elizalde, S., Deutsch, E. A simple and unusual bijection for Dyck paths and its consequences MathSciNet:2028229
[2] The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000329
[3] Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n. OEIS:A007318
[4] Houston, R. Counting particular Dyck paths MathOverflow:285079
[2] The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000329
[3] Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n. OEIS:A007318
[4] Houston, R. Counting particular Dyck paths MathOverflow:285079
Code
def statistic(D):
return D[::2].count(1)
Created
Dec 27, 2016 at 00:06 by Martin Rubey
Updated
Nov 03, 2017 at 20:52 by Martin Rubey
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