Identifier
- St001187: Dyck paths ⟶ ℤ (values match St000024The number of double up and double down steps of a Dyck path., St000443The number of long tunnels of a Dyck path., St001007The number of simple modules with projective dimension one in the linear Nakayama algebra corresponding to a Dyck path., St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra.)
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>1
[1,1,0,0]=>2
[1,0,1,0,1,0]=>1
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>2
[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]=>3
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,0]=>3
[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]=>3
[1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>2
[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]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>3
[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]=>4
[1,0,1,1,1,1,0,0,0,0,1,0]=>4
[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]=>4
[1,0,1,1,1,1,0,1,0,0,0,0]=>4
[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]=>2
[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[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]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[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]=>4
[1,1,0,1,1,1,0,0,0,1,0,0]=>4
[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]=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,0]=>4
[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]=>5
[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[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]=>4
[1,1,1,0,0,1,1,0,0,1,0,0]=>4
[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]=>5
[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[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]=>3
[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]=>4
[1,1,1,0,1,1,0,0,0,0,1,0]=>4
[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]=>4
[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]=>5
[1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,0,0,1,0]=>4
[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]=>4
[1,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0,1,0]=>4
[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]=>4
[1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>5
[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]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[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]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[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]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>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]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[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]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[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]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[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]=>3
[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]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[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]=>4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4
[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]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3
[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]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4
[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]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[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]=>4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>5
[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]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4
[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]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[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]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[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]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[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]=>3
[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]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5
[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]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3
[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]=>4
[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]=>4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4
[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]=>4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[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]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[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]=>3
[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]=>4
[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]=>4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>4
[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]=>3
[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]=>4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4
[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]=>4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4
[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]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[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]=>3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[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]=>3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3
[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]=>4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[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]=>4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4
[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]=>5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[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]=>5
[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]=>5
[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]=>5
[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]=>6
[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]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4
[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]=>5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[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]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>4
[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]=>4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[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]=>4
[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]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4
[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]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[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]=>4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[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]=>4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>4
[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]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>5
[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]=>4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4
[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]=>5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>5
[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]=>5
[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]=>5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4
[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]=>5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>5
[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]=>6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4
[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]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>5
[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]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[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]=>4
[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]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[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]=>5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>5
[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]=>5
[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]=>6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5
[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]=>5
[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]=>5
[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]=>5
[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]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5
[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]=>5
[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]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[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]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[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]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[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]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4
[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]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[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]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[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]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[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]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3
[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]=>3
[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]=>4
[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]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>5
[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]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[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]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[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]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4
[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]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>4
[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]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[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]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[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]=>4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4
[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]=>4
[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]=>4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4
[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]=>4
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>5
[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]=>5
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>4
[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]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5
[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]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4
[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]=>4
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[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]=>4
[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]=>4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4
[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]=>5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4
[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]=>4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>5
[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]=>5
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>5
[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]=>5
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4
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Description
The number of simple modules of grade at least one in the linear Nakayama algebra corresponding to a Dyck path.
The grade of an $A$-module $M$ is $\inf\{i\ge 0\mid \operatorname{Ext}^i_A(M,A)\neq 0\}$.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
The grade of an $A$-module $M$ is $\inf\{i\ge 0\mid \operatorname{Ext}^i_A(M,A)\neq 0\}$.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
Code
gap('LoadPackage("QPA");')
import tempfile as _tf, os as _os
_gap_code = r"""
DeclareOperation("gradeofmodule",[IsList]);
InstallMethod(gradeofmodule, "for a representation of a quiver", [IsList],0,function(LIST)
local A, M, RegA, UT, g, i, temmi;
A := LIST[1];
M := LIST[2];
RegA := DirectSumOfQPAModules(IndecProjectiveModules(A));
g := GorensteinDimensionOfAlgebra(A,30);
temmi := [];
Append(temmi,[Size(HomOverAlgebra(M,RegA))]);
for i in [0..g-1] do Append(temmi,[Size(ExtOverAlgebra(NthSyzygy(M,i),RegA)[2])]);
od;
UT := Filtered([0..g],x->temmi[x+1]>0);
return(Minimum(UT));
end);
DeclareOperation("numbersimpleswithgradeatleastk",[IsList]);
InstallMethod(numbersimpleswithgradeatleastk, "for a representation of a quiver", [IsList],0,function(LIST)
local A, WW, k, simA;
A := LIST[1];
k := LIST[2];
simA := SimpleModules(A);
WW := Filtered(simA,x->gradeofmodule([A,x])>=k);
return(Size(WW));
end);
"""
with _tf.NamedTemporaryFile(mode="w", suffix=".g", delete=False, dir="/tmp") as _f:
_f.write('LoadPackage("QPA");;\n')
_f.write(_gap_code)
_tmp = _f.name
gap.eval('Read("' + _tmp + '");')
_os.unlink(_tmp)
def kupisch(D):
DR = D.reverse()
H = DR.heights()
return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]
def statistic(D):
K = kupisch(D)
A = gap.NakayamaAlgebra(gap.GF(3), K)
return ZZ(gap.numbersimpleswithgradeatleastk([A, 1]))
Created
May 11, 2018 at 23:40 by Rene Marczinzik
Updated
Mar 13, 2026 at 16:41 by Nupur Jain
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