Identifier
- St000394: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>0
[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]=>2
[1,1,1,0,0,0]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,0,0]=>3
[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]=>2
[1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0]=>3
[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]=>3
[1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,0,0,0]=>4
[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]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[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]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[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]=>5
[1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>4
[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]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,1,1,0,0,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,1,0,1,1,0,0,0,0]=>6
[1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,1,0,1,1,1,0,0,1,0,0,0]=>6
[1,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,0,1,0,1,1,0,0,0]=>5
[1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,1,1,0,0,1,1,0,1,0,0,0]=>6
[1,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,1,0,0]=>5
[1,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,1,1,0,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,1,1,0,1,1,0,0,0,0,1,0]=>5
[1,1,1,0,1,1,0,0,0,1,0,0]=>6
[1,1,1,0,1,1,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,0,1,0,0,0,0]=>8
[1,1,1,0,1,1,1,0,0,0,0,0]=>6
[1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,1,1,1,0,0,1,0,0,1,0,0]=>6
[1,1,1,1,0,0,1,0,1,0,0,0]=>7
[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,1,1,1,0,1,0,0,0,1,0,0]=>7
[1,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,0]=>5
[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]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[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]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4
[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]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4
[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]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4
[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]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5
[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]=>5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[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]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>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]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>9
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>11
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>10
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>9
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>11
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[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]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[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]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4
[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]=>5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4
[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]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[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]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4
[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]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>7
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[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]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[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]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>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]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>5
[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]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>8
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>6
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>9
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>4
[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]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>6
[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]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>9
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>8
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>10
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>10
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>10
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>11
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>12
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>10
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>8
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>12
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[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]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>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]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>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]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4
[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]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>7
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>7
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>6
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>7
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>10
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>10
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>11
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>9
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>6
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>10
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>7
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>6
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>7
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>9
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>9
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>12
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>7
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>10
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>11
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>13
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>10
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>12
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>9
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>6
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>9
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>11
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>13
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>9
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>10
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>11
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>8
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>7
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>7
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>10
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>7
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>6
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>12
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>11
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>11
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>12
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>10
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>9
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>11
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>10
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>11
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>13
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>11
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>10
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>11
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>9
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>11
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>10
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>10
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>11
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>9
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>9
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>10
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>12
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>11
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>13
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>14
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>12
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>11
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>13
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>10
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>7
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>10
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>11
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>12
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>10
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>11
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>12
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>13
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>14
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>11
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>9
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>10
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>11
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>12
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>7
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>7
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>5
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>11
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>11
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>9
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>9
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>11
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>12
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>10
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>10
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>12
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>11
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>12
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>10
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>11
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>13
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>12
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>13
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>14
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>15
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>12
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>13
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>14
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>11
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>9
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>11
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>10
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>12
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>13
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>11
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>13
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>14
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>15
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>10
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>11
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>13
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>7
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>7
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>7
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>10
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>9
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>7
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>9
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>10
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>11
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>10
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>13
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>11
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>9
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>10
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>11
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>12
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>11
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>13
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>14
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>12
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>12
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>13
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>14
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>15
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>16
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>13
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>11
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>12
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>13
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>14
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>10
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>11
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>11
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>12
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>12
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>13
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>14
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>12
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>11
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>11
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>11
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>10
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>10
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>13
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>13
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>16
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>11
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>11
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>10
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>10
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>13
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>13
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>10
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>11
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>12
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>10
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>12
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>14
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>13
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>16
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>11
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>16
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>11
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>12
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>13
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>13
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>13
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>15
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>15
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>18
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>16
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>12
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>15
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>16
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>12
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>17
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>14
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>17
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>14
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>12
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>16
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>12
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>17
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>12
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>15
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>13
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>18
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>13
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>11
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>12
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>10
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>11
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>9
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>11
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>13
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>8
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>9
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>8
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>10
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>7
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>7
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>14
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>13
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>13
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>18
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>20
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>13
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>13
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>12
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>15
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>18
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>21
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>21
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>19
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>19
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>19
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>19
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>15
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>14
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>13
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>11
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>15
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>11
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>20
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>11
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>13
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>15
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>17
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>19
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>21
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>11
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>13
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>14
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>12
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>19
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>19
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>13
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>16
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>15
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>14
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>14
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>13
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>14
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>14
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>12
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>12
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>14
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>14
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>14
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>11
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>10
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>11
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>10
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>10
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>11
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>14
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>14
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>13
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>14
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>14
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>12
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>12
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>12
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>14
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>13
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>14
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>20
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>14
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>14
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>14
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>25
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>10
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>16
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>15
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]=>11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>10
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>25
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>25
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>17
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>17
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>18
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>17
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>17
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>13
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>15
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>18
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>9
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>20
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]=>12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>20
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>20
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>19
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>20
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>20
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>18
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>18
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>18
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>18
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>20
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>20
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>19
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>20
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>20
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>17
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>17
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>16
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>17
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>17
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>17
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>17
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>17
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>17
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>20
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>20
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>19
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>20
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>20
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>18
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>18
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>18
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>18
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>20
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>20
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>19
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>20
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>20
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>16
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>16
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>15
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>16
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>16
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>14
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>16
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>16
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>15
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>16
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>16
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>14
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>13
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>14
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>14
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>14
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>14
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>14
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>16
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>16
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>15
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>16
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>16
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>14
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>14
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>14
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>16
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>15
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>16
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>16
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>20
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>20
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>19
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>20
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>20
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>18
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>18
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>18
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>18
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>20
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>20
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>19
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>20
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>20
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>17
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>17
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>16
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>17
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>16
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>16
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>16
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>16
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>17
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>17
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>16
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>17
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>17
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>20
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>20
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>19
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>20
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>20
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>18
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>18
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>18
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>18
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>20
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>20
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>19
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>20
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>20
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>11
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>15
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]=>17
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>42
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>12
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>13
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]=>14
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]=>63
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>28
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>21
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>42
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>12
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]=>15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>15
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]=>171
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]=>27
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Description
The sum of the heights of the peaks of a Dyck path minus the number of peaks.
References
[1] Feinberg, G., Lee, K.-H. Homogeneous representations of Type A KLR-algebras and Dyck paths arXiv:1505.04075
[2] Cheng, S.-E., Elizalde, S., Kasraoui, A., Sagan, B. Inversion polynomials for 321-avoiding permutations arXiv:1112.6014
[2] Cheng, S.-E., Elizalde, S., Kasraoui, A., Sagan, B. Inversion polynomials for 321-avoiding permutations arXiv:1112.6014
Code
def statistic(D): heights = D.heights() return sum(heights[i+1]-1 for i in D.peaks())
Created
Feb 17, 2016 at 20:41 by Christian Stump
Updated
Dec 30, 2023 at 12:12 by Martin Rubey
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