Identifier
- St000920: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[]=>0
[1,0]=>1
[1,0,1,0]=>1
[1,1,0,0]=>1
[1,0,1,0,1,0]=>1
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>2
[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]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[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]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[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]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[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]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>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]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[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]=>2
[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]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[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]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[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]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[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]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[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]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[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]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[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]=>2
[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]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>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]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[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]=>2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>2
[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]=>2
[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]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>2
[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]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>2
[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]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>2
[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]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>3
[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]=>3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>3
[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]=>3
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>3
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[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]=>2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[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]=>2
[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]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[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]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[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]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[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]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>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]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[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]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>3
[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]=>3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[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]=>3
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[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]=>2
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[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]=>2
[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]=>2
[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]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[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]=>2
[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]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[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]=>3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>3
[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]=>3
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>3
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Description
The logarithmic height of a Dyck path.
This is the floor of the binary logarithm of the usual height increased by one:
$$ \lfloor\log_2(1+height(D))\rfloor $$
This is the floor of the binary logarithm of the usual height increased by one:
$$ \lfloor\log_2(1+height(D))\rfloor $$
References
[1] Françon, J. Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique MathSciNet:0775838
Code
def statistic(D): return floor(log(1+D.height(), 2))
Created
Jul 29, 2017 at 15:23 by Martin Rubey
Updated
Jun 17, 2021 at 10:55 by Martin Rubey
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