Identifier
  • Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
    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 with grade at least one in the corresponding Nakayama algebra., St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra.)
Values
=>
Cc0005;cc-rep-0 Cc0005;cc-rep
[1,0]=>[1,0]=>1 [1,0,1,0]=>[1,1,0,0]=>2 [1,1,0,0]=>[1,0,1,0]=>1 [1,0,1,0,1,0]=>[1,1,1,0,0,0]=>3 [1,0,1,1,0,0]=>[1,1,0,1,0,0]=>2 [1,1,0,0,1,0]=>[1,1,0,0,1,0]=>2 [1,1,0,1,0,0]=>[1,0,1,1,0,0]=>2 [1,1,1,0,0,0]=>[1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0]=>3 [1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0]=>3 [1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>2 [1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,1,0,0,0]=>[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]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>6 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>6 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>6 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>5 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>5 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>4 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>4 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>5 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>5 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>5 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>5 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>5 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>6 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>5 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[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]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>6 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>6 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>5 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>5 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>5 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>5 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>5 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>5 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>5 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[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]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>5 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>5 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>5 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>4 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>5 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[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]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>5 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[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]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>5 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>5 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>4 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>4 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>4 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>4 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
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Description
Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.