Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
St000381: 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]=>2
[1,1,0,0,1,0]=>[2,1]=>2
[1,1,0,1,0,0]=>[2,1]=>2
[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]=>2
[1,0,1,1,0,0,1,0]=>[1,2,1]=>2
[1,0,1,1,0,1,0,0]=>[1,2,1]=>2
[1,0,1,1,1,0,0,0]=>[1,3]=>3
[1,1,0,0,1,0,1,0]=>[2,1,1]=>2
[1,1,0,0,1,1,0,0]=>[2,2]=>2
[1,1,0,1,0,0,1,0]=>[2,1,1]=>2
[1,1,0,1,0,1,0,0]=>[2,1,1]=>2
[1,1,0,1,1,0,0,0]=>[2,2]=>2
[1,1,1,0,0,0,1,0]=>[3,1]=>3
[1,1,1,0,0,1,0,0]=>[3,1]=>3
[1,1,1,0,1,0,0,0]=>[3,1]=>3
[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]=>2
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>2
[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>2
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>3
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>2
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>2
[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>2
[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>2
[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>2
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>3
[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>3
[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>3
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>4
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>2
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>2
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>2
[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>2
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>3
[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>2
[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>2
[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>2
[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>2
[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>2
[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>3
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>3
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>3
[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>3
[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>3
[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>3
[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>3
[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>3
[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>3
[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>3
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>4
[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>4
[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>4
[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>4
[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]=>2
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>4
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>3
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>3
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>3
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>4
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>2
[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]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>2
[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]=>3
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>3
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>2
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>3
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>2
[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]=>3
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>3
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>3
[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]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>3
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>3
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>3
[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]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>3
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>3
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>3
[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]=>4
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>4
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>4
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>5
[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]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>6
[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]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]=>4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]=>2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]=>3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]=>3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]=>3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]=>3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>6
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>2
[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]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>2
[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]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>4
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]=>3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]=>2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>2
[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]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>2
[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]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]=>2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>2
[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]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]=>2
[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]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>5
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>4
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>4
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>4
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>4
[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]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>4
[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]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>4
[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]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>4
[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]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>7
[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]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]=>7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]=>7
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]=>6
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]=>7
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]=>6
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1]=>8
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,1,1]=>7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,3,1]=>5
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]=>7
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,8,1]=>8
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,3]=>5
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[7,1,1]=>7
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]=>6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[5,2,1,1]=>5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,4,1]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,7,1]=>7
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,8,1]=>8
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]=>6
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,5,2,1]=>5
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,7,1,1]=>7
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,4]=>4
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,1,1]=>7
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,1]=>5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[4,3,1,1]=>4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,5,1]=>5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,7,1]=>7
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,8,1]=>8
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,5,2,1]=>5
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,7,1,1]=>7
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,5,1,2]=>5
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,3,1]=>4
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,6,2,1]=>6
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1,1]=>8
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5]=>5
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1]=>7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[6,2,1]=>6
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[4,2,2,1]=>4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,6,1]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]=>7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,8,1]=>8
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,6,2]=>6
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1]=>5
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,7,1,1]=>7
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,6,2,1]=>6
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,4,2,2]=>4
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,1,2]=>6
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,1]=>4
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]=>7
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,6]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[4,3,1,1]=>4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,2,1,1]=>5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1,1]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,8,1]=>8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1,1]=>5
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,4,3,1]=>4
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,5,1,2]=>5
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,5,2,1]=>5
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,4,2,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,1,3]=>4
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]=>6
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,5,1]=>5
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,1]=>8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1,1]=>3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,4,2,1]=>4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,8,1]=>8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,2,2]=>5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1,1]=>5
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,5,3,1]=>5
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,4,2,2]=>4
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,3,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,6,1]=>6
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,5,1]=>5
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>5
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,6,1]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,1,1]=>6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[3,4,1,1]=>4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,3,1]=>5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,1,2,1]=>4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]=>5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[6,1,2]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,1,2]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[4,3,2]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,4,2,1,1]=>4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,1]=>4
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1]=>5
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,4,2,1,1]=>4
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,5,3]=>5
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,2]=>4
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]=>5
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,1,1]=>4
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,6,1]=>6
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,1,4]=>4
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,4,3]=>4
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,5,2]=>5
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,6,1]=>6
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,3]=>3
[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]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,1,2,2]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,1,2,2]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,4]=>4
[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]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,1,2,1,2]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]=>3
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,1,2,1,2]=>2
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,1,2,3]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,1,4,1]=>4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,1,4,1]=>4
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,4,1]=>4
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,5]=>5
[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]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,1,2]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1,2,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1,2,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,2,4]=>4
[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]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,1,3]=>3
[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]=>2
[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]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,1,2]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,1,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,1,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,1,2,4]=>4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,4,2]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,4,1,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,1,4,2]=>4
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,4,1,1]=>4
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1,4,1,1]=>4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,5,1]=>5
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,5,1]=>5
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,5,1]=>5
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,5,1]=>5
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,6]=>6
[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]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,2,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,1,3,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,2,1,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2,3]=>3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,3,1,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,2,3,1,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,3,2]=>3
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,5]=>5
[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]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,2,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,1,4]=>4
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,1,2]=>2
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,1,2,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,1,3]=>3
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,1,3,1]=>3
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,1,4]=>4
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,2,2,1,2]=>2
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,2,3,1,1]=>3
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,5]=>5
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,1,2,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,2,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,3,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,2,1]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,1,3]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,4,3]=>4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,4,3]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[2,4,1,2]=>4
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,2,1]=>4
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,4,3]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,5,2]=>5
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,5,2]=>5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,5,2]=>5
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,5,2]=>5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,5,1,1]=>5
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,5,2]=>5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,6,1]=>6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,6,1]=>6
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,6,1]=>6
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,6,1]=>6
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,6,1]=>6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]=>7
[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]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,3,1,1]=>3
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,3,2]=>3
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]=>4
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5]=>5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2,2]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2,2]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,1,2]=>3
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,2,1,3]=>3
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2,2]=>3
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,2,4]=>4
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,4,1,1]=>4
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,1,1]=>4
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2]=>4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,5,1]=>5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,5,1]=>5
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,5,1]=>5
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,6]=>6
[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]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,4]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,3,1,1]=>3
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]=>4
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5]=>5
[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]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,4]=>4
[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]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]=>3
[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]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,1,2]=>3
[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]=>3
[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]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,3]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,1,2,1,1]=>3
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,1,2,2]=>3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,1,3,1]=>3
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,3,1]=>3
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,1,4]=>4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,1,2,2,1]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,3,1,1]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,3,1,1]=>3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,1,3,1,1]=>3
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,3,1,1]=>3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,4,1]=>4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,4,1]=>4
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,5]=>5
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[3,2,1,2,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,2,1,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2,2]=>3
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2,2]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,1,2]=>3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,1,2]=>3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[3,2,2,1,1]=>3
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[3,2,3,1]=>3
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,4]=>4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[3,3,1,2]=>3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[3,3,2,1]=>3
[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]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,1,2]=>3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[3,3,2,1]=>3
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[3,3,2,1]=>3
[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]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[3,4,1,1]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[3,4,2]=>4
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,4,2]=>4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[3,4,1,1]=>4
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,4,1,1]=>4
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2]=>4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,5,1]=>5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,5,1]=>5
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[3,5,1]=>5
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,5,1]=>5
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,5,1]=>5
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,5,1]=>5
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]=>6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,1,3,1]=>4
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>4
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,2,3]=>4
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,2,3]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2]=>4
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,3,2]=>4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,4,1]=>4
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5]=>5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,2]=>4
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,2,2]=>4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,2,2]=>4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,3,1]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5]=>5
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,3,1]=>4
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,2]=>4
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,3,1]=>4
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,1,3,1]=>4
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,2,1,2]=>4
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,2,1,2]=>4
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,2,2,1]=>4
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[4,2,3]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[4,3,2]=>4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,3,2]=>4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,3,2]=>4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[4,3,2]=>4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,4,1]=>4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,5]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,1,1,2]=>5
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,2,2]=>5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,4]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,1,1,2]=>5
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,2,2]=>5
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,2,2]=>5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,1,2]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,1,2]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,1,2]=>5
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[5,2,2]=>5
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,2,2]=>5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,4]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,3]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[6,3]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[6,3]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,3]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,2]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[7,2]=>7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[7,2]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[7,2]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]=>7
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]=>8
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]=>1
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]=>4
[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]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,4,1]=>4
[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]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,4,1,1]=>4
[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]=>3
[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]=>3
[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]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,3,2]=>3
[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]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,4,1]=>4
[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]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,3,2,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,4,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1,1]=>4
[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]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,3,1,2]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]=>5
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,3,2,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,1,2,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,5,1,1]=>5
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,3,2,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1,1]=>4
[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]=>3
[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]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,1,2]=>3
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,5,1]=>5
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,3,1,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,1,2,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,5,1,1]=>5
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1,1]=>4
[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]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,2]=>3
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,5,1]=>5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,5,1,1]=>5
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]=>6
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,3,1,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,6,1,1]=>6
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,5,1]=>5
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,3,3,1]=>3
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,3,3,1,1]=>3
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,6,1]=>6
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,5,1,1]=>5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,1,3,1,1]=>3
[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]=>2
[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]=>2
[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]=>2
[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]=>3
[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]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,2,3]=>3
[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]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,3,2]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]=>4
[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]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2,2]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,2,4]=>4
[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]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,3,2,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,3,3]=>3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,5,1]=>5
[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]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,1,3]=>3
[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]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]=>2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,2,4,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]=>5
[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]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,5,2]=>5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>6
[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]=>2
[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]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>3
[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]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,1,5]=>5
[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]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,2,1,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,3,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]=>5
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]=>6
[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]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,5,3]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>6
[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]=>2
[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]=>2
[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]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]=>3
[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]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>4
[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]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]=>3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>5
[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]=>2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>5
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>6
[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]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,1,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,2,1,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,2,3]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,2,3,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,2,3,2]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,5]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,4,1,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,5,1,1]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,5,2]=>5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,6,1]=>6
[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]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,1,2]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>4
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]=>3
[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]=>4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]=>5
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,2,3]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,1,3]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,2,2]=>2
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,5,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2,2]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,4,4]=>4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,7,1]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,1,2,1,1]=>2
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]=>6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3,3]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,2,3]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,3,2,2]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,1,4]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,4,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>5
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,2]=>2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,1]=>10
[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]=>2
[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]=>2
[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]=>2
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[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]=>3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,5]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]=>3
[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]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>6
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>5
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>5
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1,1]=>5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>4
[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]=>3
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>4
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]=>4
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,5]=>5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,4,2]=>4
[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]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,4,1]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]=>6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]=>9
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,3,1]=>5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]=>9
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,5,1]=>5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]=>9
[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]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[6,1,2]=>6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,6,1]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>5
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,5,1]=>5
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,1,2]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,1,2,2]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,2,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,2,3,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,1,3,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,3,1,2]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,1,2,2]=>3
[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]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,1,1,2,1]=>4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,5,1,1,1,1]=>5
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,2,3,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,1,3,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[2,2,2,2,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,2,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,3,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,1,2,1]=>3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>2
[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]=>2
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,2,5]=>5
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,2,4]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,2,3]=>3
[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]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,1,2]=>4
[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]=>2
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,1,1]=>4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,2,1,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,1,1,1]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[8,1,1]=>8
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,7,1]=>7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,1]=>5
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,1,2]=>5
[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]=>3
[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]=>2
[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]=>3
[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]=>2
[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]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>2
[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]=>2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,1,1]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,4,1,1,2]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,4,1,2]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,4,2]=>4
[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]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,1,2]=>2
[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]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,5,2]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,4,2]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,5,1,1]=>5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,4,1,1]=>4
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,5,1]=>5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,5,1,1]=>5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]=>4
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,2,1,3]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,1,4]=>4
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,1,4]=>4
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>5
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,5]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,1,4]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,2,4,1]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,2,4,1]=>4
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,1,3,1]=>3
[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]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1,1]=>4
[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]=>2
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,1]=>8
[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]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>2
[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]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[4,2,1,2]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[4,2,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[2,3,2,1,1]=>3
[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]=>2
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,1]=>5
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,1,4,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,2,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,2,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,1,2,2]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,4]=>4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,5,1]=>5
[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]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,2,3,1]=>3
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,2,4,1]=>4
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,1,5]=>5
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,1,3,2]=>3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,1,4,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1,1]=>6
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]=>5
[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]=>2
[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]=>3
[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]=>2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,4,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,3,1,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>4
[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]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,3,2]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,2,2]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,4,3]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,4,2]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,4,1,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,2,3,1,1]=>3
[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]=>2
[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]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,1,2,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,5,3]=>5
[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]=>2
[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]=>2
[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]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,3,1]=>5
[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]=>2
[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]=>2
[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]=>3
[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]=>2
[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]=>3
[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]=>3
[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]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,2,3]=>4
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,2]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,6,2]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,1,3]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]=>4
[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]=>2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2,2]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,2,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2,2]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,2,2,2]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,2,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,4,1,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,1,1]=>4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,1,1,1]=>3
[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]=>2
[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]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]=>3
[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]=>3
[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]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,2,3,1]=>3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,5,1]=>5
[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]=>2
[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]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1,1]=>5
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,4,1,1,1]=>4
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>2
[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]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]=>2
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,5,1]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[6,2,1]=>6
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1,1]=>4
[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]=>3
[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]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,4,1,1]=>4
[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]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,1]=>5
[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]=>2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,5,1]=>5
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,4,3]=>4
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]=>4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,3,3,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3,2,1]=>3
[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]=>2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[8,1,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,1]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,2,3,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,3,2,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,2,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,2,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,2,2,2,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,2,1]=>2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,4,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,4,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,2,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,2,1]=>3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,1,3]=>4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>4
[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]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,3,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1,3,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>3
[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]=>2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,1,2,1,1]=>3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,3,2,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,3,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1,1]=>2
[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]=>2
[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]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,1,2,2]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2,2]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,3,1,2]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,1,2,2]=>3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,5,1]=>5
[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]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,4]=>4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]=>4
[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]=>2
[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]=>2
[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]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,4,2]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,3,2]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,1,1,2]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,5,1,2]=>5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,5,1,1]=>5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,5,1,1]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1,1]=>5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,4,1,2]=>4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,1,2]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,1,3]=>3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,3,3,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,3,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,1,3,2]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,3,2,2]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,3,1,2]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>4
[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]=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,1,1,1]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,2,2,2]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,3,1,2]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,4,1,2]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,1,2,2]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,1,2]=>3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,4,1,2]=>4
[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]=>3
[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]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1,1]=>3
[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]=>2
[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]=>2
[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]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,2,1,3]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,3]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]=>4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,1,3]=>3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,5,1,2]=>5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,1,3]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,1,4]=>4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,1,3,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,2,2,2]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,3,1,1,2,2]=>3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,1,1,1,2]=>4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,3,2,1,1,2]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2,3,1,2]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,3,1,2]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,2,1,2,1,2]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,3,2,1,2]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,2,2,1,2]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,4,1,1]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1,4,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,3,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,3,3,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,2,3,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,3,2,2,1,1]=>3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,1,2,1,1]=>4
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,4,1,1,1,1]=>4
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1]=>3
[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]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,1,3,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]=>4
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,1,1]=>4
[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]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,4,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,1,1,1,1]=>4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,2,1,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,2,2]=>3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,1,2,2]=>2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,1,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,4,1]=>4
[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]=>3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[8,1,1]=>8
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>4
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,1,2,1]=>4
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,1,2,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,1,2]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>3
[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]=>3
[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]=>2
[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]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[10,1]=>10
[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]=>2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>5
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]=>5
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]=>6
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,1,4,1]=>4
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,1,3,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,1,2,1]=>4
[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]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>3
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,1,2,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,1,1,2,1]=>4
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,1,1,1]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,1,1,3,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,1,1,2,1]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>3
[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]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,1,3]=>3
[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]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,1,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[3,2,1,2,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,2,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,2,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,2,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,2,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>3
[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]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,4,1,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,1]=>4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,7,1,1]=>7
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,8,1]=>8
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>3
[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]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2,2]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2,2]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,2,2]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,2,3,2]=>3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,3,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,2,3,1,2]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,3,2]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,2,3,1,1]=>3
[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]=>2
[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]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,2,3,1]=>3
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,2,2]=>4
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>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]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,1,2]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,2,1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,4,2,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]=>4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,3,1,2]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,1,2]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,1,1,2,1]=>4
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,2,3,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[2,2,2,2,1,1]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,1,2,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,1,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,1,1,4,1,1]=>4
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[3,1,2,4,1,1]=>4
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[3,3,2,2,1,1]=>3
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[3,2,2,3,1,1]=>3
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[2,2,3,3,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,1,3,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,1,1,3]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,3,1,2]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[4,3,1,2]=>4
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,1,1,2]=>3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[4,4,1,1]=>4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[3,2,1,2,1,1]=>3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[3,3,1,1,1,1]=>3
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,3,1,1,3]=>3
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0]=>[2,2,3,2,1,2]=>3
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,1,1,2,2]=>3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,3,1,1,1,2]=>4
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[4,2,1,2,1,2]=>4
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[3,3,2,1,1,2]=>3
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[4,3,1,2,1,1]=>4
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[4,4,1,1,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[4,2,1,3,1,1]=>4
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,1,2,1]=>3
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,1,2,1]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,2,2]=>3
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,1,3,2]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,3,2,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,2,1,2,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,2,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,2,3,1,2]=>3
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,3,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,2,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,2,1,3]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,1,3,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,1,2,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,3,2,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,3,2,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,1,2,1]=>3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,1,2,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,1,2]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,1,3]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,3,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,2,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2,2]=>2
[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]=>2
[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]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,3,1,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,2,1,1,1]=>4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,3,1,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,2,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,1,1,1]=>4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1,1]=>6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,2,1,1]=>2
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,2,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[3,3,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,2,1,2]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2,1,2]=>3
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[2,2,2,1,1,2]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,1,1,2]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,2,2,2,2,1,1]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,3,2,1,2,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,3,3,1,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,2,2,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,1,2,2,1,2,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,1,2,1,2,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1,2,1,1]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1,1,2,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>2
[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]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,2]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]=>4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,3,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,2,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,1,2,2]=>3
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,1,4]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,1,1,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,2,1,1,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]=>2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,1,2,1]=>3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1,1]=>4
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,3,1,1]=>3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,5,1,1,1]=>5
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,1,1]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,1,3,1]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,2,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,3,2,1,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,1]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2,1,2]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,1,2,2]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[2,5,1,1]=>5
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>2
[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]=>3
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,4,4,1]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,3,1,1]=>3
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,3,5,1]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,4,1,1]=>4
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,6,1]=>6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,2,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,1,2]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,1,2,2]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[4,2,1,2]=>4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]=>4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,2,1]=>2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,7,1]=>7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,1,3,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]=>5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,4,2,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1,1]=>4
[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]=>2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,1,3,2,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,2,3,2]=>3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2]=>4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,2,3,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,1,3]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,3,1]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,5,1,1]=>5
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,1,4]=>4
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,3,2,2,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,1,1,4]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,1,1,4]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,1,2,2,3]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,1,2,2,3]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,2,4,1,1]=>4
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,3,1,1]=>4
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,2,2,1,1,3]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,2,2,1,1,3]=>3
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>3
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,3,1,2]=>4
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,3,1,2]=>4
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[3,3,1,1,2,2]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,3,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,2,2,2,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2,2]=>2
[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]=>2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,1]=>8
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]=>5
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,2,3,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,4,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,4,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,1,2,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>3
[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]=>2
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,1,3,1]=>3
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,1,4,1]=>4
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,2,3]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[2,3,2,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,2,2]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,3,2]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,2,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,1,3,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,2,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,1,2,2,1]=>2
[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]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>5
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,1,3]=>5
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[4,2,1,1,1]=>4
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[2,3,2,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,1,2,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,2,1,1]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,2,3]=>4
[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]=>5
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,5,2]=>5
[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]=>2
[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]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,1,2]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,1,2,2]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,2,2]=>3
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,1,2,1]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1,1]=>3
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,3,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,4,2,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,1,1,2,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,2,3,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,2,2,2,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,2,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[3,3,1,1,1,1]=>3
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Description
The largest 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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