Identifier
-
Mp00103:
Dyck paths
—peeling map⟶
Dyck paths
St000998: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0005;cc-rep
[1,0]=>[1,0]=>2
[1,0,1,0]=>[1,0,1,0]=>3
[1,1,0,0]=>[1,0,1,0]=>3
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>4
[1,0,1,1,0,0]=>[1,0,1,0,1,0]=>4
[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]=>4
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0]=>5
[1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>6
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>6
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>7
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[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]=>8
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>7
[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]=>7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[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]=>8
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>8
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Description
Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path.
Map
peeling map
Description
Send a Dyck path to its peeled Dyck path.
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