Identifier
- St000645: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[]=>0
[1,0]=>0
[1,0,1,0]=>1
[1,1,0,0]=>0
[1,0,1,0,1,0]=>2
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,0]=>6
[1,1,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,0]=>3
[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]=>3
[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,0]=>7
[1,0,1,1,0,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,0]=>7
[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,1,0,0]=>6
[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]=>5
[1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,0,1,1,0,0]=>9
[1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,0]=>5
[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]=>8
[1,0,1,1,1,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0]=>7
[1,1,0,0,1,1,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0]=>9
[1,1,0,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,1,0,0,1,0]=>7
[1,1,0,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,1,0,0,1,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,0,1,1,0,0]=>6
[1,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[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]=>4
[1,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,0,1,1,0,0]=>8
[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[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]=>6
[1,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,0,0,0,1,0]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>6
[1,1,0,1,1,1,0,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,0]=>7
[1,1,1,0,0,0,1,1,1,0,0,0]=>9
[1,1,1,0,0,1,0,0,1,0,1,0]=>5
[1,1,1,0,0,1,0,0,1,1,0,0]=>6
[1,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,1,0,0,1,1,0,0,0,1,0]=>7
[1,1,1,0,0,1,1,0,0,1,0,0]=>6
[1,1,1,0,0,1,1,0,1,0,0,0]=>5
[1,1,1,0,0,1,1,1,0,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,0,1,1,0,0]=>7
[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]=>4
[1,1,1,0,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,0]=>6
[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]=>4
[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>9
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>7
[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]=>6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>7
[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]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>10
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>7
[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]=>6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>10
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>8
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6
[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]=>9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>8
[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]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>8
[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]=>6
[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]=>9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>8
[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]=>8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>8
[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]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>10
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>9
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>10
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>10
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>9
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>10
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>12
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>11
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>9
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>9
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>7
[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]=>5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>9
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>7
[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]=>7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>7
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>10
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>11
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>7
[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]=>9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>8
[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]=>8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>6
[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]=>6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>8
[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]=>6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>11
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>9
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>8
[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]=>6
[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]=>8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>8
[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]=>6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>7
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>9
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>10
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>9
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>8
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>12
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>11
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>10
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>12
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>7
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>7
[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]=>5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>10
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>8
[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]=>6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>9
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>10
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>7
[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]=>5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>8
[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]=>6
[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]=>8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[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]=>6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>10
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>8
[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]=>6
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>8
[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]=>6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>12
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>8
[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]=>9
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>8
[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]=>5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>8
[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]=>6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>6
[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]=>9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>3
[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]=>6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>10
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>8
[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]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>10
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>9
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>9
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>9
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>9
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>9
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>10
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>9
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>10
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>10
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>9
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>12
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>11
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>10
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>11
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>10
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>9
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>7
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>9
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>11
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>9
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>9
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>9
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>8
[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]=>7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>10
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>8
[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]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>9
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>12
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>11
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>13
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>9
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>11
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>9
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>10
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>9
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>11
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>9
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>9
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>9
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>7
[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]=>10
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>10
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>10
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>11
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>10
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>9
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>10
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>9
[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]=>7
[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]=>11
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>9
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>9
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>9
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>10
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>9
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>10
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>9
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>8
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>10
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>12
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>11
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>12
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>10
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>11
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>10
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>11
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>10
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>12
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>14
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>12
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>11
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>12
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>12
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>11
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>14
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>13
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>12
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>12
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>9
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>10
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>10
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>9
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>9
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>12
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>11
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>10
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>11
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>10
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>9
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>9
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>8
[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]=>7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>9
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>11
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>9
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>9
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>9
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>8
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>7
[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]=>10
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>9
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>8
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>9
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>12
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>11
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>11
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>10
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>10
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>9
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>11
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>9
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>9
[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]=>7
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>10
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>9
[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]=>7
[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]=>10
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>13
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>10
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>9
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>10
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>9
[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]=>9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>10
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>9
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>10
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>9
[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]=>7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>9
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>10
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>9
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>9
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>12
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>13
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>12
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>15
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>14
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>13
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>15
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>9
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>9
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>11
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>10
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>9
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>11
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>13
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>11
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>10
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>11
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>10
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>9
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>13
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>12
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>10
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>12
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>11
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>13
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>9
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>11
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>9
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>9
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>11
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>9
[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]=>9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>13
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>10
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>10
[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]=>8
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>10
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>7
[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]=>10
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>10
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>14
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>13
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>16
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>10
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>11
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>10
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>13
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>10
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>10
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>10
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>8
[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]=>12
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>11
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>10
[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]=>10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>10
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>13
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>10
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>10
[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]=>8
[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]=>10
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>11
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>10
[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]=>8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>11
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>15
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>11
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>11
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>10
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>9
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>11
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>10
[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]=>8
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>11
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>10
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>12
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>11
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>10
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>9
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>9
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>10
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>9
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>9
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>9
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>7
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>9
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>9
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>9
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>9
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>8
[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]=>7
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>10
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8
[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]=>7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>9
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>10
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>9
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>9
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>11
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>11
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>10
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>10
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>13
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>11
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>9
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>9
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>11
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>10
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>9
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>10
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>10
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>9
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>10
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>10
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>9
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>10
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>9
[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]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>11
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>10
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>9
[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]=>8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>11
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>11
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>13
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>15
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>11
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>11
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>10
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>10
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>13
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>12
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>11
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>11
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>11
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>10
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>11
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>11
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>10
[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]=>9
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>12
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>11
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10
[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]=>9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>13
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>16
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>13
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>12
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>14
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>13
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>12
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>11
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>13
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>12
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>11
[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]=>10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>15
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>14
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>12
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>11
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>12
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>9
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>9
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>7
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>11
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>9
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>11
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>10
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>9
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>10
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>11
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>9
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>11
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>8
[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]=>6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>8
[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]=>8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>6
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>9
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>8
[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]=>9
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>9
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>9
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>10
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>6
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>9
[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]=>6
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>10
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>10
[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]=>8
[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]=>12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>10
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>10
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>11
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>10
[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]=>10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>10
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>8
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>6
[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]=>6
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>6
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>9
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>11
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>12
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>11
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>7
[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]=>7
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>7
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>6
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>6
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>14
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>9
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>12
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>8
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>7
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>11
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>10
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>9
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>11
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>11
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>16
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>13
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>15
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>10
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>6
[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]=>6
[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]=>8
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>10
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>10
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>7
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>10
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>12
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>12
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>9
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>10
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>11
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>11
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>13
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>8
[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]=>6
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>7
[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]=>7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>7
[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]=>7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>6
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>11
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>6
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>7
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>6
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>10
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>6
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>7
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>7
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>7
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>7
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>13
[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]=>7
[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]=>8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>6
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>7
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>6
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>10
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>9
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>7
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>13
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>16
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>6
[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]=>6
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>9
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>10
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>12
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>10
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>11
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>6
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>7
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>6
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>6
[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]=>8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>7
[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]=>13
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>7
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>6
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>7
[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]=>6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>12
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>6
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>8
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>6
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>7
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>9
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>7
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>15
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>10
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>9
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>9
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>10
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>7
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>9
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>10
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>9
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>7
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>11
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>12
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>10
[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]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>5
[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]=>7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>8
[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]=>8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>13
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>14
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>14
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>14
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>13
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>13
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>14
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>14
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>12
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>7
[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]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>7
[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]=>8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>7
[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]=>7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>7
[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]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>9
[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]=>12
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>12
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>8
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>6
[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]=>6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>7
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>8
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>10
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>9
[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]=>10
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>11
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>11
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>11
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>11
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>12
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>14
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>11
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>14
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>14
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>18
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>14
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>18
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>14
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>18
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>20
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>20
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>18
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>9
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>13
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>16
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>17
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>16
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>10
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>11
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>11
[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]=>11
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>16
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>17
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>17
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>13
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>16
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>16
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>10
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>10
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>10
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>10
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>14
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>14
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>12
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>13
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>13
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>11
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>12
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>13
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>13
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>10
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>16
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>15
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>15
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>10
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>13
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>16
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>16
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>21
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>24
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>25
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>24
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>9
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>21
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>9
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>9
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>10
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>9
[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]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>8
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>8
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>8
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>8
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>16
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>16
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>16
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>14
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>14
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>14
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>14
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>15
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>10
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>11
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>11
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>11
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>11
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>13
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>13
[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]=>12
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>12
[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]=>12
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>12
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>10
[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]=>13
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>13
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>12
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>15
[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]=>12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>13
[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]=>10
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>12
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>12
[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]=>12
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>12
[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]=>13
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>13
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>11
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>11
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>11
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>10
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>9
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>9
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>10
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>9
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>18
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>18
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>11
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>11
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>12
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>13
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>13
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>13
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>13
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>15
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>15
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>14
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>14
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>14
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>15
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>14
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>14
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>13
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>14
[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]=>16
[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]=>15
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>18
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>14
[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]=>16
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>17
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>15
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>15
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>15
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>15
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>16
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>15
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>15
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>16
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>17
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>17
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>16
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>15
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>15
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>16
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>15
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>15
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>12
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>13
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>14
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>14
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>15
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>17
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>17
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>17
[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]=>18
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>17
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>18
[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]=>15
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>18
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>18
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>20
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>15
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>15
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>16
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>16
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>20
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>15
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>15
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>18
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>15
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>12
[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]=>18
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>17
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>18
[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]=>17
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>17
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>15
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>14
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>14
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>13
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>15
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>15
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>16
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>15
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>15
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>16
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>17
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>17
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>16
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>15
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>15
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>16
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>15
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>15
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>15
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>15
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>17
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>16
[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]=>18
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>15
[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]=>16
[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]=>14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>13
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>14
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>14
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>15
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>14
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>14
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>14
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>15
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>15
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>13
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>13
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>13
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>13
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>12
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>10
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>10
[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]=>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]=>12
[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]=>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]=>13
[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]=>14
[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]=>14
[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]=>15
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Description
The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between.
For a Dyck path $D = D_1 \cdots D_{2n}$ with peaks in positions $i_1 < \ldots < i_k$ and valleys in positions $j_1 < \ldots < j_{k-1}$, this statistic is given by
$$ \sum_{a=1}^{k-1} (j_a-i_a)(i_{a+1}-j_a) $$
For a Dyck path $D = D_1 \cdots D_{2n}$ with peaks in positions $i_1 < \ldots < i_k$ and valleys in positions $j_1 < \ldots < j_{k-1}$, this statistic is given by
$$ \sum_{a=1}^{k-1} (j_a-i_a)(i_{a+1}-j_a) $$
Code
def statistic(D): I = D.peaks() J = D.valleys() return sum( (J[a]-I[a])*(I[a+1]-J[a]) for a in range(len(J)) )
Created
Nov 10, 2016 at 11:59 by Christian Stump
Updated
Apr 12, 2023 at 15:53 by Martin Rubey
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