Identifier
- St001523: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>2
[1,1,0,0]=>2
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>3
[1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>4
[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]=>6
[1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>4
[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]=>6
[1,0,1,1,0,0,1,1,0,1,0,0]=>4
[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]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[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]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[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]=>3
[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>6
[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]=>4
[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]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0]=>4
[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]=>4
[1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,0]=>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]=>6
[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]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>4
[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]=>4
[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>4
[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]=>4
[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>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]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[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]=>6
[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0]=>3
[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]=>6
[1,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,1,0,0,0,0]=>4
[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]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[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]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,0]=>6
[1,1,1,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[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]=>4
[1,1,1,1,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[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]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[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]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>7
[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]=>4
[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]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>7
[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]=>4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3
[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]=>2
[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]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[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]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>7
[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]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[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]=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[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]=>4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[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]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>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]=>7
[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]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[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]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>7
[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]=>4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>5
[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]=>5
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[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]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[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]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>4
[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]=>7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[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]=>4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[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]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[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]=>7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[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]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[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]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>5
[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]=>4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>7
[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]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>3
[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]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[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]=>3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4
[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]=>7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3
[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]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>3
[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]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5
[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]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>6
[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]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>6
[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]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5
[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]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>6
[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]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4
[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]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>6
[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]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>6
[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]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>6
[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]=>8
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>6
[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]=>6
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>4
[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]=>6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[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]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[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]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>8
[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]=>5
[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]=>4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>8
[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]=>5
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[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]=>4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[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]=>6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[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]=>3
[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]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>8
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1
[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]=>6
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>8
[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]=>5
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>6
[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]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[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]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>8
[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]=>6
[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]=>3
[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]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4
[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]=>5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4
[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]=>6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[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]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[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]=>6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[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]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>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]=>6
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[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]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>3
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Description
The degree of symmetry of a Dyck path.
Given a Dyck path $D=(d_1,\dots,d_{2n})$, with $d_i\in\{0,1\}$, this is the number of positions $1\leq i\leq n$ such that $d_i = 1-d_{2n+1-i}$ and the initial height of the $i$-th step $\sum_{j < i} d_i$ equals the final height of the $(2n+1-i)$-th step.
Given a Dyck path $D=(d_1,\dots,d_{2n})$, with $d_i\in\{0,1\}$, this is the number of positions $1\leq i\leq n$ such that $d_i = 1-d_{2n+1-i}$ and the initial height of the $i$-th step $\sum_{j < i} d_i$ equals the final height of the $(2n+1-i)$-th step.
References
[1] Elizalde, S. The degree of symmetry of lattice paths arXiv:2002.12874
Code
def statistic(D): H1 = D.heights() H2 = D.reverse().heights() return sum(1 for i in range(D.semilength()) if H1[2*i] == H2[2*i] and H1[2*i+1] == H2[2*i+1])
Created
Mar 02, 2020 at 21:13 by Martin Rubey
Updated
Mar 05, 2020 at 14:11 by Martin Rubey
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