Identifier
- St000655: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>1
[1,1,0,0]=>2
[1,0,1,0,1,0]=>1
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>1
[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]=>1
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[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]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[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]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[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]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[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]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[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]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>11
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>1
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Description
The length of the minimal rise of a Dyck path.
For the length of a maximal rise, see St000444The length of the maximal rise of a Dyck path..
For the length of a maximal rise, see St000444The length of the maximal rise of a Dyck path..
Code
def statistic(D): return min(D.rise_composition())
Created
Nov 30, 2016 at 16:01 by Christian Stump
Updated
Mar 18, 2018 at 20:10 by Martin Rubey
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