Identifier
-
Mp00120:
Dyck paths
—Lalanne-Kreweras involution⟶
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]=>[1,1,0,0,1,0]=>0
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>1
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>1
[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]=>[1,1,1,0,0,0,1,0]=>0
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>0
[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>2
[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]=>[1,1,1,1,0,0,0,0,1,0]=>0
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>0
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>0
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>0
[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>0
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>2
[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]=>[1,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>3
[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]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>0
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>0
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>0
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>0
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>0
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>0
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>0
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>0
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>[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]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[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]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[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]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[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]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[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]=>2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5
[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
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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