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Identifier
  • St000015: Dyck paths ⟶ ℤ (values match St000053The number of valleys of the Dyck path., St001068The number of torsionless simple modules in the linear Nakayama algebra corresponding to a Dyck path., St001169The number of simple modules with projective dimension at least two of the linear Nakayama algebra corresponding to a Dyck path.)
Values
=>
Cc0005;cc-rep
[1,0]=>1 [1,0,1,0]=>2 [1,1,0,0]=>1 [1,0,1,0,1,0]=>3 [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]=>1 [1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,0]=>2 [1,1,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,0]=>2 [1,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,0]=>4 [1,0,1,0,1,1,0,0,1,0]=>4 [1,0,1,0,1,1,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0]=>4 [1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0]=>4 [1,0,1,1,0,1,0,1,0,0]=>4 [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]=>2 [1,1,0,0,1,0,1,0,1,0]=>4 [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]=>2 [1,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0]=>4 [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]=>2 [1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0]=>2 [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]=>2 [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]=>2 [1,1,1,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0]=>1 [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]=>5 [1,0,1,0,1,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,0,1,0]=>5 [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]=>5 [1,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,0]=>4 [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]=>5 [1,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0]=>4 [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]=>4 [1,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0]=>3 [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]=>3 [1,0,1,1,1,1,1,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,0]=>4 [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]=>3 [1,1,0,0,1,1,0,1,0,0,1,0]=>4 [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]=>3 [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]=>3 [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]=>5 [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]=>4 [1,1,0,1,0,0,1,1,1,0,0,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0]=>5 [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]=>4 [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]=>4 [1,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,0]=>4 [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]=>4 [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]=>3 [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]=>4 [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]=>3 [1,1,0,1,1,1,0,0,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,1,0,0,0]=>3 [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]=>4 [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]=>3 [1,1,1,0,0,0,1,1,1,0,0,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,0]=>4 [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]=>4 [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]=>3 [1,1,1,0,0,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,1,0,0,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,0]=>4 [1,1,1,0,1,0,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,0]=>3 [1,1,1,0,1,0,1,0,0,0,1,0]=>4 [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]=>4 [1,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0,1,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0]=>3 [1,1,1,0,1,1,0,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,1,1,1,0,0,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,0]=>3 [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]=>3 [1,1,1,1,0,0,1,1,0,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,0]=>3 [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]=>3 [1,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,0]=>2 [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]=>2 [1,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,0]=>1 [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]=>6 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>5 [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]=>6 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>5 [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]=>6 [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]=>6 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5 [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]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>5 [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]=>5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>5 [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]=>3 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>5 [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]=>5 [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]=>5 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>5 [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]=>3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>5 [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]=>5 [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]=>6 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>5 [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]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>5 [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]=>5 [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]=>5 [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]=>5 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>5 [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]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5 [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]=>3 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>5 [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]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>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]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>5 [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]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>5 [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]=>5 [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]=>5 [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]=>3 [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]=>3 [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]=>3 [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]=>3 [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]=>3 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>3 [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]=>3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>5 [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]=>5 [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]=>5 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>5 [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]=>3 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>5 [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]=>3 [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]=>4 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>5 [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]=>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]=>3 [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]=>3 [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]=>3 [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]=>3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>3 [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]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>3 [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]=>6 [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]=>5 [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]=>5 [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]=>5 [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]=>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]=>3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>6 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>5 [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]=>4 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6 [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]=>5 [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]=>5 [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]=>5 [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]=>5 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>5 [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]=>5 [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]=>5 [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]=>3 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>5 [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]=>3 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>5 [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]=>5 [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]=>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]=>3 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>5 [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]=>4 [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]=>5 [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]=>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]=>3 [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]=>3 [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]=>3 [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]=>3 [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]=>3 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>3 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>3 [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]=>5 [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]=>3 [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]=>3 [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]=>3 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>3 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>5 [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]=>3 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>5 [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]=>5 [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]=>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]=>3 [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]=>3 [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]=>3 [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]=>3 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>3 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>3 [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]=>2 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>5 [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]=>3 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>5 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>5 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>5 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>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]=>3 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>5 [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]=>5 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>5 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>5 [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]=>5 [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]=>3 [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]=>3 [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]=>3 [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]=>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]=>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]=>3 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>3 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>3 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2 [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]=>3 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2 [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]=>3 [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]=>3 [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]=>3 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>3 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2 [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]=>3 [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]=>3 [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]=>3 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>3 [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]=>3 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2 [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]=>3 [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]=>3 [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]=>3 [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]=>3 [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]=>3 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>3 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>3 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>3 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>3 [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]=>3 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>3 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>3 [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]=>2 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>3 [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]=>3 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>3 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>3 [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]=>3 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>3 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>3 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2 [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]=>2 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1 [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]=>7 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>7 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>7 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>6 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>7 [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]=>6 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>7 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>7 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>6 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>6 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5 [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]=>6 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5 [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]=>5 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7 [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7 [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]=>7 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>7 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>5 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>5 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>5 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>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]=>5 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>5 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>5 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>7 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>6 [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]=>6 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>5 [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]=>6 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>5 [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]=>5 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>5 [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]=>6 [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4 [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]=>4 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>7 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6 [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]=>6 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>5 [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]=>5 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>6 [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]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>7 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>6 [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]=>6 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>7 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>7 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>5 [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]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4 [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]=>5 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>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]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>5 [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]=>5 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>5 [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]=>5 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>5 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>5 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4 [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]=>5 [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>4 [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]=>4 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>5 [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]=>5 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>5 [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]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>5 [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]=>5 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>5 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>5 [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]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>6 [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]=>6 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>5 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>4 [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]=>4 [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>5 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>5 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>5 [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]=>5 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>5 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>5 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>5 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>5 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>5 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4 [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]=>5 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>5 [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>5
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Description
The number of peaks of a Dyck path.
Code
def statistic(x):
    return x.number_of_peaks()
Created
Sep 27, 2011 at 19:32 by Chris Berg
Updated
Mar 12, 2026 at 18:10 by Nupur Jain