Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
St000657: Integer compositions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>1
[1,0,1,0]=>[1,1]=>1
[1,1,0,0]=>[2]=>2
[1,0,1,0,1,0]=>[1,1,1]=>1
[1,0,1,1,0,0]=>[1,2]=>1
[1,1,0,0,1,0]=>[2,1]=>1
[1,1,0,1,0,0]=>[2,1]=>1
[1,1,1,0,0,0]=>[3]=>3
[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>1
[1,0,1,0,1,1,0,0]=>[1,1,2]=>1
[1,0,1,1,0,0,1,0]=>[1,2,1]=>1
[1,0,1,1,0,1,0,0]=>[1,2,1]=>1
[1,0,1,1,1,0,0,0]=>[1,3]=>1
[1,1,0,0,1,0,1,0]=>[2,1,1]=>1
[1,1,0,0,1,1,0,0]=>[2,2]=>2
[1,1,0,1,0,0,1,0]=>[2,1,1]=>1
[1,1,0,1,0,1,0,0]=>[2,1,1]=>1
[1,1,0,1,1,0,0,0]=>[2,2]=>2
[1,1,1,0,0,0,1,0]=>[3,1]=>1
[1,1,1,0,0,1,0,0]=>[3,1]=>1
[1,1,1,0,1,0,0,0]=>[3,1]=>1
[1,1,1,1,0,0,0,0]=>[4]=>4
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>1
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>1
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>1
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>1
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>1
[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>1
[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>1
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>1
[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>1
[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>1
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>1
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>1
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>1
[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>1
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>2
[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>1
[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>1
[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>1
[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>1
[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>1
[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>2
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>1
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>2
[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>1
[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>1
[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>2
[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>1
[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>1
[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>1
[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>2
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>1
[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>1
[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>1
[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>1
[1,1,1,1,1,0,0,0,0,0]=>[5]=>5
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>1
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>2
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]=>1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]=>1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,3,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,3]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[5,2,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,4,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]=>1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,5,2,1]=>1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,4]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[4,3,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,5,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,5,2,1]=>1
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,5,1,2]=>1
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,3,1]=>1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[4,2,2,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,6,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,6,2]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,4,2,2]=>1
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,1]=>1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]=>2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,6]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[4,3,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,2,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1,1]=>1
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,4,3,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,5,1,2]=>1
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,5,2,1]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,4,2,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,1,3]=>1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]=>1
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,5,1]=>1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,4,2,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,2,2]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,4,2,2]=>1
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,3,1,1]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,6,1]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,5,1]=>1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,6,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[3,4,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,3,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,1,2,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[6,1,2]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,1,2]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[4,3,2]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,4,2,1,1]=>1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,4,2,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,5,3]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,2]=>1
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,1,1]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,6,1]=>1
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,1,4]=>1
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,4,3]=>2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,5,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,3]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,1,2,2]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,1,2,2]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,4]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,1,2,1,2]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,1,2,1,2]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,1,2,3]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,1,4,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,1,4,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,4,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,5]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,1,2]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,2,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,2,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,2,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,2,4]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,1,3]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,1,2]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,1,2,2,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,1,2,2,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,1,2,4]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,4,2]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,4,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,1,4,2]=>1
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,4,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1,4,1,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,5,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,5,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,5,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,5,1]=>1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,6]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,2,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,1,3,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,2,1,2]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2,3]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,3,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,2,3,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,3,2]=>2
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,5]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,1,4]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,1,2]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,1,2,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,1,3]=>1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,1,3,1]=>1
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,1,4]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,2,2,1,2]=>1
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,2,3,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,5]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,1,2,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,2,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,3,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,2,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,1,3]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,4,3]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,4,3]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[2,4,1,2]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,2,1]=>1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,4,3]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,5,2]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,5,2]=>2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,5,2]=>2
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,5,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,5,2]=>2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,6,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,6,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,6,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,6,1]=>1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,6,1]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,3,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,3,2]=>1
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]=>1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2,2]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2,2]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,1,2]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,2,1,3]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2,2]=>2
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,2,4]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,4,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2]=>2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,5,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,5,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,5,1]=>1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,6]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,4]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,3,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,4]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,3]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,1,2,2]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,1,3,1]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,3,1]=>1
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,1,4]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,1,2,2,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,3,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,3,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,1,3,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,3,1,1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,4,1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,4,1]=>1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,5]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[3,2,1,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,2,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2,2]=>2
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2,2]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,1,2]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,1,2]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[3,2,2,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[3,2,3,1]=>1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,4]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[3,3,1,2]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[3,3,2,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[3,3,1,2]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,1,2]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[3,3,2,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[3,3,2,1]=>1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[3,4,2]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[3,4,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[3,4,2]=>2
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,4,2]=>2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[3,4,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,4,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,5,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,5,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[3,5,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,5,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,5,1]=>1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,5,1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]=>3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,1,3,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,2,3]=>2
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,2,3]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2]=>2
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,3,2]=>2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,4,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,2]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,2,2]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,2,2]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,3,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,3,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,2]=>1
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,3,1]=>1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,1,3,1]=>1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,2,1,2]=>1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,2,1,2]=>1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,2,2,1]=>1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[4,2,3]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[4,3,2]=>2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,3,2]=>2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,3,2]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[4,3,2]=>2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,4,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,5]=>4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]=>4
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,1,1,2]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,2,2]=>2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,4]=>4
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,1,1,2]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,2,2]=>2
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,2,2]=>2
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,1,2]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,1,2]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,1,2]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[5,2,2]=>2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,2,2]=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,3,1]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,4]=>4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,3]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[6,3]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[6,3]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,3]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,2]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[7,2]=>2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[7,2]=>2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[7,2]=>2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,4,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,4,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,3,2]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,4,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,3,2,1,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,4,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,3,1,2]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]=>1
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,3,2,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,1,2,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,5,1,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,3,2,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,1,2]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,5,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,3,1,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,1,2,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,5,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,2]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,5,1,1]=>1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]=>1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,3,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,6,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,3,3,1]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,6,1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,5,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,2,1,2]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,2,3]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,3,2]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1,2,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,2,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2,2]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,2,4]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,3,2,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,3,3]=>1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,5,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,1,2,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,1,3]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,2,4,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,5,2]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,2]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,2,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,1,5]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,2,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,3,1,1,1]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]=>1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,1,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,5,3]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]=>1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,1,2]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,2,1,2]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,2,3]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,2,3,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,2,3,2]=>2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,5]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,4,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,5,1,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,5,2]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,6,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,1,2]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,2]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]=>1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,2,3]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,1,3]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,4,1,1]=>1
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,5]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,4,2]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[4,2,3]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,4,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,3,1]=>1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,5,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,2,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[6,1,2]=>1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,6,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>1
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,5,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,2,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,1,2]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,1,2,2]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,2,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,2,3,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,2,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,1,3,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,3,1,2]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,1,2,2]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,2,5]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,2,4]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,2,3]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,2]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,1,2]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,1,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,2,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,1]=>1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,1,2]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,3,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,1,2,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,2,2,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,4,1,1,2]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,4,1,2]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,4,2]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,1,2]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,5,2]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,4,2]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,5,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,4,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>2
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,5,1]=>1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,5,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,2,1,3]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,1,2,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,1,4]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,1,4]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,2,4,1]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,2,4,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,1,3,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[4,2,1,2]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[4,2,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[2,3,2,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,1,4,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,3,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,2,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,2,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,1,2,2]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,4]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,5,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,2,3,1]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,2,4,1]=>1
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,1,5]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,1,3,2]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,1,4,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,2,2,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,4,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,3,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,3,2]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,4,3]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,4,2]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,4,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,2,3,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,1,2,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,5,3]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,3,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,2,3]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,2]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,6,2]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,1,3]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,2]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2,2]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,2,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2,2]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,2,2,2]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,2,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,4,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,2,3,1]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,5,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,4,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,5,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[6,2,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,4,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,2,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,1,2,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,5,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,4,3]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]=>2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,3,3,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3,2,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,2,3,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,3,2,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,2,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,2,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,2,2,2,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,2,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,4,1]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,4,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,1,3]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,3,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1,3,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,1,2,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,3,2,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,3,1,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,2,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,1,2,2]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2,2]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,2,2,2]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,3,1,2]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,1,2,2]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,5,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,4]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,2,1,2]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,4,2]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,3,2]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,5,1,2]=>1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,5,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,5,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,4,1,2]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,3,3,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,3,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,1,3,2]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,3,2,2]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,3,1,2]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,2,2,2]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,3,1,2]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,4,1,2]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,1,2,2]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,1,2]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,4,1,2]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,2,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,2,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,2,1]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,2,1,3]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,3]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,1,3]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,5,1,2]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,1,3]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,1,4]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,1,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,4,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,2,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,2,2]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,1,2,2]=>1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,1,2,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,4,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,1,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,1,2,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,1,2]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,1,4,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,1,3,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1,2,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,1,3]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,1,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,1,2]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[3,2,1,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,2,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,2,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,2,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,1,2,1]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,4,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2,2]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2,2]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2,2]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,2,3,2]=>2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,3,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,2,3,1,2]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,3,2]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,2,3,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,2,3,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,2,2]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,2,2,2]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,1,2]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,1,2]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,2,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,4,2,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,3,1,2]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,3,1,2]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,1,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,1,2,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,2,2]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,1,3,2]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,3,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2,2]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,2,1,2,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,2,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,2,3,1,2]=>1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,3,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,2,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,2,1,3]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,1,2,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,3,2,1]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,3,2,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,1,2,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,1,2,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,1,2]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,1,3]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,3,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,2,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2,2]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,1,2,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,3,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,2,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,3,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,2,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,3,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,1,2,2]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,1,2,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,3,1,1]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,5,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,1,3,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,2,1]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,3,2,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2,1,2]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,1,2,2]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[2,5,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,3,1,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,4,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,2,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,1,2]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,1,2,2]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[4,2,1,2]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,2,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,1,3,1,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,4,2,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,1,3,2,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,2,3,2]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,2,3,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,1,3]=>1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,3,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,5,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,1,4]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,3,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,2,2,2,2]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2,2]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1,2,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,2,3,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,4,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,4,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,1,2,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,1,3,1]=>1
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,1,4,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,2,3]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[2,3,2,1,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,3,2]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,2,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,1,3,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,2,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,1,3]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[4,2,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[2,3,2,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,1,2,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,2,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,2,3]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,2]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,5,2]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,1,2,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,1,2]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,1,2,2]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,2,2]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,1,2,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,4,2,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>1
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Description
The smallest part of an integer composition.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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