Identifier
- St000013: Dyck paths ⟶ ℤ (values match St000442The maximal area to the right of an up step of a Dyck path.)
Values
=>
Cc0005;cc-rep
[]=>0
[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]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>3
[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]=>2
[1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0]=>4
[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]=>2
[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[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]=>4
[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0]=>3
[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]=>3
[1,0,1,1,1,0,0,1,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[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]=>2
[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]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[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]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[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]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[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]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[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]=>3
[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]=>4
[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]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[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]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[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]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>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]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[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]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[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]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2
[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]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[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]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3
[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]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[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]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>3
[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]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[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]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>3
[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]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>6
[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]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[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]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[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]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>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]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[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]=>3
[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]=>4
[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]=>4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4
[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]=>4
[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]=>4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[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]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[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]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>5
[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]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[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]=>4
[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]=>4
[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]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[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]=>4
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[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]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[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]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[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]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4
[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]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[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]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[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]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>6
[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]=>4
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>3
[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]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[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]=>3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[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]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[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]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>5
[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]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>7
[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]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>7
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[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]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4
[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]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[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]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[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]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[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]=>3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>5
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[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]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[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]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>4
[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]=>3
[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]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[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]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>8
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>8
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>8
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[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]=>9
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>9
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>11
[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
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>6
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>5
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>6
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>6
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>6
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>6
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>5
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>11
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[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]=>12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]=>11
[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>7
[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]=>13
[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
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>10
[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]=>14
[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]=>1
[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]=>15
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>13
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>15
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]=>24
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Description
The height of a Dyck path.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
Code
def statistic(x): return x.height()
Created
Sep 27, 2011 at 19:30 by Chris Berg
Updated
Feb 13, 2024 at 15:15 by Martin Rubey
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