Identifier
- St000439: Dyck paths ⟶ ℤ (values match St000025The number of initial rises of a Dyck path.)
Values
=>
Cc0005;cc-rep
[1,0]=>2
[1,0,1,0]=>2
[1,1,0,0]=>3
[1,0,1,0,1,0]=>2
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>3
[1,1,0,1,0,0]=>3
[1,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,0,1,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[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]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[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]=>2
[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]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[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]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>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]=>3
[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]=>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]=>4
[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]=>4
[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]=>4
[1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,0]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>5
[1,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[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]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[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]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[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]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[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]=>3
[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]=>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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[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]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[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]=>3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>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]=>3
[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]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4
[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]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>4
[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]=>4
[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]=>4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4
[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]=>4
[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]=>4
[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]=>4
[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]=>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]=>4
[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]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>4
[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]=>4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>4
[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]=>4
[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]=>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]=>4
[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]=>4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>4
[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]=>4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[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]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>4
[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]=>4
[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]=>4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4
[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]=>4
[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]=>4
[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]=>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]=>4
[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]=>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]=>4
[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]=>4
[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]=>4
[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]=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>5
[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]=>5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>5
[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]=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>5
[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]=>5
[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]=>5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>5
[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]=>5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>5
[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]=>5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[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]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[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]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[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]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[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]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[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]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[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]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>9
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>11
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>12
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>7
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Description
The position of the first down step of a Dyck path.
Code
def statistic(D): return D.index(0)+1
Created
Feb 28, 2016 at 08:51 by Christian Stump
Updated
Dec 12, 2018 at 23:54 by Martin Rubey
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