Identifier
  • Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
    St001067: Dyck paths ⟶ ℤ (values match St000932The number of occurrences of the pattern UDU in a Dyck path., St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless.)
Values
=>
Cc0005;cc-rep-0 Cc0005;cc-rep
[1,0]=>[1,0]=>0 [1,0,1,0]=>[1,1,0,0]=>0 [1,1,0,0]=>[1,0,1,0]=>1 [1,0,1,0,1,0]=>[1,1,1,0,0,0]=>0 [1,0,1,1,0,0]=>[1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>[1,1,0,1,0,0]=>1 [1,1,0,1,0,0]=>[1,1,0,0,1,0]=>0 [1,1,1,0,0,0]=>[1,0,1,0,1,0]=>2 [1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>1 [1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>2 [1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0]=>2 [1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>0 [1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>0 [1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>1 [1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>0 [1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>0 [1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>0 [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>0 [1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>1 [1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>0 [1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>1 [1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>1 [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]=>[1,1,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>0 [1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>0 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>1 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>1 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>0 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>0 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>0 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>4 [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1 [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>0 [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 [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>1 [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>0 [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>2 [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>0 [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>0 [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>0 [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>0 [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1 [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>0 [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>0 [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>1 [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>1 [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>0 [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2 [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>1 [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>1 [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>3 [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2 [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>4 [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1 [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1 [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>1 [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>0 [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>0 [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2 [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3 [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>4 [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2 [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>1 [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2 [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1 [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>4 [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>3 [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>3 [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>5 [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]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>0 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>0 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>0 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>0 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>0 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>0 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>0 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>0 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>0 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>0 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>0 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>0 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>0 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>0 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>0 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>0 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>0 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>0 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>0 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>0 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>0 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>0 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>0 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>0 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>0 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>0 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>0 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>0 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>0 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>0 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>0 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1 [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]=>2 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>0 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>0 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>0 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>0 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>0 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>0 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>0 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>0 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>4 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>4 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4 [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]=>6
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Description
The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.