Identifier
-
Mp00122:
Dyck paths
—Elizalde-Deutsch bijection⟶
Dyck paths
St001036: Dyck paths ⟶ ℤ
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]=>0
[1,0,1,0,1,0]=>[1,1,0,0,1,0]=>1
[1,0,1,1,0,0]=>[1,1,0,1,0,0]=>0
[1,1,0,0,1,0]=>[1,1,1,0,0,0]=>0
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>1
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>0
[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0]=>0
[1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>0
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[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]=>[1,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>[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]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>[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]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>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]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[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]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>3
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
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Description
The number of inner corners of the parallelogram polyomino associated with the Dyck path.
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
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