Identifier
- St001038: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[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]=>2
[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]=>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]=>1
[1,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,0,0]=>2
[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]=>2
[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]=>1
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>3
[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]=>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]=>1
[1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>4
[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]=>1
[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]=>3
[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]=>2
[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]=>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]=>3
[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]=>3
[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]=>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]=>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]=>1
[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]=>1
[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]=>3
[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]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>4
[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]=>4
[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]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>3
[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]=>3
[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]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>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]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>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]=>2
[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]=>2
[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]=>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]=>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]=>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]=>1
[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]=>3
[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]=>2
[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>4
[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]=>5
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>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]=>1
[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]=>1
[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]=>3
[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]=>3
[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]=>4
[1,1,1,1,1,1,0,0,0,0,0,0]=>3
[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]=>2
[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]=>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]=>3
[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]=>3
[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]=>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]=>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]=>1
[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]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>4
[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]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>4
[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]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>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]=>2
[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]=>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]=>1
[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]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[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]=>2
[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]=>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]=>1
[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]=>1
[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]=>3
[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]=>2
[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]=>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]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[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]=>1
[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]=>5
[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]=>5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[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]=>3
[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]=>1
[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]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3
[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]=>1
[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]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>4
[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]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3
[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]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>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]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>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]=>2
[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]=>2
[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]=>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]=>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]=>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]=>1
[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]=>1
[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]=>1
[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]=>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]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>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]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>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]=>1
[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]=>1
[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]=>3
[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]=>2
[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]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>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]=>2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>4
[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]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[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]=>3
[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]=>3
[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]=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[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]=>3
[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]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[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]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>4
[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]=>4
[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]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[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]=>2
[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]=>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]=>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]=>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]=>1
[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]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>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]=>1
[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]=>1
[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]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>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]=>1
[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]=>1
[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]=>1
[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]=>3
[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]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4
[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]=>4
[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]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>3
[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]=>3
[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]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>4
[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]=>2
[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]=>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]=>3
[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]=>3
[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]=>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]=>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]=>1
[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]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[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]=>4
[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]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4
[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]=>4
[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]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[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]=>3
[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]=>2
[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]=>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]=>3
[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]=>3
[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]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[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]=>1
[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]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>4
[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]=>2
[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]=>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]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[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]=>3
[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]=>5
[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]=>2
[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]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>5
[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]=>5
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>3
[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]=>4
[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]=>1
[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]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3
[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]=>4
[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]=>4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>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]=>2
[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]=>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]=>1
[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]=>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]=>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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[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]=>2
[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]=>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]=>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]=>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]=>1
[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]=>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]=>1
[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]=>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]=>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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>3
[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]=>2
[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]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[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]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3
[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]=>1
[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]=>1
[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]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>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]=>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]=>3
[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]=>2
[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]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[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]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[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]=>2
[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]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[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]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[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]=>3
[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]=>5
[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]=>2
[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]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[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]=>3
[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]=>3
[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]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3
[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]=>2
[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]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>4
[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]=>4
[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]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>4
[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]=>4
[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]=>4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>3
[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]=>2
[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]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>4
[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]=>3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>3
[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]=>3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[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]=>5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>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]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
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Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
Code
def statistic(D): return min(ParallelogramPolyomino.from_dyck_word(D).heights())
Created
Nov 06, 2017 at 23:19 by Martin Rubey
Updated
Nov 06, 2017 at 23:19 by Martin Rubey
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