Identifier
- St000011: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[]=>0
[1,0]=>1
[1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>2
[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]=>1
[1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>3
[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]=>4
[1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>2
[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]=>1
[1,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>2
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>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]=>4
[1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>5
[1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[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]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[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]=>3
[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]=>2
[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]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>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]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>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]=>1
[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]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>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]=>2
[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]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[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]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>3
[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]=>2
[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]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[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]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>2
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[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]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>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]=>3
[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]=>3
[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]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3
[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]=>3
[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]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>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]=>3
[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]=>3
[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]=>3
[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]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4
[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]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[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]=>4
[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]=>2
[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]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[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]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[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]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[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]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[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]=>4
[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]=>2
[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]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[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]=>2
[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]=>1
[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]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[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]=>1
[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]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>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]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[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]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[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]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[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]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>3
[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]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[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]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[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]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[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]=>2
[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]=>3
[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]=>2
[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]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[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]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[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]=>1
[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]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[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]=>2
[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]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>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]=>2
[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]=>2
[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]=>3
[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]=>2
[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]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>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]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>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]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>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]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[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]=>2
[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]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>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]=>2
[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]=>2
[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]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>3
[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]=>2
[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]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2
[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]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[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]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[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
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>3
[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
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>3
[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]=>3
[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]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>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]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>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]=>5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[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]=>5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[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]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[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]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[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]=>5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[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
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[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]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[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]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[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]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[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
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[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]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>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]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>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
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>2
[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
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>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]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>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]=>2
[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]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>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]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>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]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>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]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>2
[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]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>2
[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]=>2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>2
[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]=>2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>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
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>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]=>1
[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
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>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
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>1
[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
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[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]=>7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>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]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>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
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>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]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>10
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>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
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>12
[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]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>13
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>14
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>2
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Description
The number of touch points (or returns) of a Dyck path.
This is the number of points, excluding the origin, where the Dyck path has height 0.
This is the number of points, excluding the origin, where the Dyck path has height 0.
Code
def statistic(x): return x.number_of_touch_points()
Created
Sep 27, 2011 at 19:28 by Chris Berg
Updated
Dec 26, 2022 at 18:34 by Martin Rubey
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