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Identifier
  • St001007: 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., St001187The number of simple modules of grade at least 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 with projective dimension one in the linear Nakayama algebra corresponding to a Dyck path.
See St001011The number of simple modules with projective dimension two in the linear Nakayama algebra corresponding to a Dyck path., St001022The number of simple modules with projective dimension three in the linear Nakayama algebra corresponding to a Dyck path., and St001025The number of simple modules with projective dimension four in the linear Nakayama algebra corresponding to a Dyck path. for the number of simple modules with projective dimension two, three, and four respectively.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
Code
def count_pd1_simples(dyck_word):
    c = kupisch(dyck_word)
    n = len(c)

    count = 0
    for i in range(n):
        a, l = i, 1
        pd = 0

        while l < c[a] and pd < 1:
            a, l = a + l, c[a] - l
            pd += 1

        if pd == 1 and l == c[a]:
            count += 1

    return count

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):
    return count_pd1_simples(D)
Created
Oct 29, 2017 at 17:03 by Rene Marczinzik
Updated
Nov 06, 2026 at 17:12 by Christian Stump