Identifier
- St000659: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0,1,0]=>0
[1,1,0,0]=>1
[1,0,1,0,1,0]=>0
[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]=>0
[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]=>1
[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0]=>2
[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]=>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]=>0
[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]=>1
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>2
[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]=>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]=>2
[1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0]=>2
[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]=>1
[1,1,1,0,0,0,1,1,0,0]=>2
[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]=>2
[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]=>2
[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]=>0
[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]=>1
[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]=>2
[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]=>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]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>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]=>2
[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]=>1
[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]=>1
[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]=>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]=>2
[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]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0]=>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]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>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]=>2
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[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]=>1
[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]=>1
[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]=>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]=>2
[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]=>2
[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]=>2
[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]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>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]=>1
[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]=>2
[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]=>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]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>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]=>2
[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]=>1
[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]=>1
[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]=>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]=>2
[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]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>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]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>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]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>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]=>2
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[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]=>1
[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]=>1
[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]=>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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>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]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>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]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>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]=>2
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>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]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[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]=>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]=>1
[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]=>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]=>2
[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]=>2
[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]=>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]=>1
[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]=>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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>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]=>1
[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]=>2
[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]=>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]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[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]=>2
[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]=>1
[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]=>1
[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]=>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]=>2
[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]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>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]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[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]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[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]=>2
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[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]=>1
[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]=>1
[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]=>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]=>2
[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]=>2
[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]=>2
[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]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>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]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[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]=>3
[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]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[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]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[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]=>2
[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]=>2
[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]=>2
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3
[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]=>3
[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]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[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]=>1
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>1
[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]=>1
[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]=>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]=>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]=>1
[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]=>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]=>2
[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
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[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]=>1
[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]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[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]=>1
[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]=>1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[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]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[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]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>3
[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]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[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]=>2
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Description
The number of rises of length at least 2 of a Dyck path.
Code
def statistic(D): return sum( 1 for i in D.rise_composition() if i >= 2 )
Created
Nov 30, 2016 at 20:07 by Christian Stump
Updated
Nov 30, 2016 at 20:07 by Christian Stump
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