Identifier
- St000685: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>1
[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]=>2
[1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[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]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>3
[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]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>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]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>3
[1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[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]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[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]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3
[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]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>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]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[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]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>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]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>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]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[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]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>4
[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]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3
[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]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[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]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[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]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4
[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]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>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]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>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]=>1
[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]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>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]=>3
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The dominant dimension of the linear Nakayama algebra corresponding to a Dyck path.
To every Dyck path there is a linear Nakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path. and on the Nakayama algebras page.
To every Dyck path there is a linear Nakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path. and on the Nakayama algebras page.
References
[1] Marczinzik, R. Upper bounds for the dominant dimension of Nakayama and related algebras arXiv:1605.09634
[2] wikipedia:Nakayama_algebra
[3] https://www.math.uni-bielefeld.de/~ringel/lectures/tachi/tachikawa/dominant.htm
[2] wikipedia:Nakayama_algebra
[3] https://www.math.uni-bielefeld.de/~ringel/lectures/tachi/tachikawa/dominant.htm
Code
def kupisch(D):
DR = D.reverse()
H = DR.heights()
return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]
def proj_to_inj_nak(L):
"""ProjToInjNak: for each j, collect all k in L where k >= L[(j-k) mod n], take minimum."""
n = len(L)
Liste_d = []
for j in range(1, n + 1):
candidates = []
for k in L:
r = (j - k) % n
if r == 0: r = n
if k >= L[r - 1]:
candidates.append(k)
Liste_d.append(min(candidates))
return Liste_d
def domdim_from_kupisch(L):
"""Dominant dimension of LNakayama algebra from Kupisch series."""
n = len(L)
Liste_d = proj_to_inj_nak(L)
List1 = set()
for i in range(1, n + 1):
r = i % n
if r == 0: r = n
s = (i + 1) % n
if s == 0: s = n
if Liste_d[s - 1] <= Liste_d[r - 1]:
List1.add(i - 1)
List2 = set()
for i in range(1, n + 1):
r = i % n
if r == 0: r = n
s = (i - 1) % n
if s == 0: s = n
if L[s - 1] <= L[r - 1]:
List2.add(i - 1)
List_not_in_List2 = [i for i in range(n) if i not in List2]
if not List_not_in_List2:
return n
List_for_dom = []
for j in List_not_in_List2:
List_for_dom.append([(j + L[j] - 1, L[j])])
def f(x, y):
c = (x - y) % n
if c == 0: c = n
z = (x + 1) % n
if z == 0: z = n
return (c, Liste_d[z - 1] - y)
for r_idx in range(len(List_for_dom)):
while True:
last = List_for_dom[r_idx][-1]
result = f(last[0], last[1])
if result[0] % n in List1:
List_for_dom[r_idx].append(result)
else:
break
temp2 = [len(lst) for lst in List_for_dom]
return min(temp2)
def statistic(D):
return domdim_from_kupisch(kupisch(D))
Created
Jan 10, 2017 at 14:50 by Rene Marczinzik
Updated
Mar 12, 2026 at 18:07 by Nupur Jain
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!