Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
St000383: 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]=>1
[1,1,0,1,0,0]=>[3]=>3
[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]=>1
[1,0,1,1,0,1,0,0]=>[1,3]=>3
[1,0,1,1,1,0,0,0]=>[1,3]=>3
[1,1,0,0,1,0,1,0]=>[2,1,1]=>1
[1,1,0,0,1,1,0,0]=>[2,2]=>2
[1,1,0,1,0,0,1,0]=>[3,1]=>1
[1,1,0,1,0,1,0,0]=>[4]=>4
[1,1,0,1,1,0,0,0]=>[4]=>4
[1,1,1,0,0,0,1,0]=>[3,1]=>1
[1,1,1,0,0,1,0,0]=>[4]=>4
[1,1,1,0,1,0,0,0]=>[4]=>4
[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]=>1
[1,0,1,0,1,1,0,1,0,0]=>[1,1,3]=>3
[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]=>1
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>2
[1,0,1,1,0,1,0,0,1,0]=>[1,3,1]=>1
[1,0,1,1,0,1,0,1,0,0]=>[1,4]=>4
[1,0,1,1,0,1,1,0,0,0]=>[1,4]=>4
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>1
[1,0,1,1,1,0,0,1,0,0]=>[1,4]=>4
[1,0,1,1,1,0,1,0,0,0]=>[1,4]=>4
[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]=>1
[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]=>1
[1,1,0,0,1,1,0,1,0,0]=>[2,3]=>3
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>3
[1,1,0,1,0,0,1,0,1,0]=>[3,1,1]=>1
[1,1,0,1,0,0,1,1,0,0]=>[3,2]=>2
[1,1,0,1,0,1,0,0,1,0]=>[4,1]=>1
[1,1,0,1,0,1,0,1,0,0]=>[5]=>5
[1,1,0,1,0,1,1,0,0,0]=>[5]=>5
[1,1,0,1,1,0,0,0,1,0]=>[4,1]=>1
[1,1,0,1,1,0,0,1,0,0]=>[5]=>5
[1,1,0,1,1,0,1,0,0,0]=>[5]=>5
[1,1,0,1,1,1,0,0,0,0]=>[5]=>5
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>1
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>2
[1,1,1,0,0,1,0,0,1,0]=>[4,1]=>1
[1,1,1,0,0,1,0,1,0,0]=>[5]=>5
[1,1,1,0,0,1,1,0,0,0]=>[5]=>5
[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>1
[1,1,1,0,1,0,0,1,0,0]=>[5]=>5
[1,1,1,0,1,0,1,0,0,0]=>[5]=>5
[1,1,1,0,1,1,0,0,0,0]=>[5]=>5
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>1
[1,1,1,1,0,0,0,1,0,0]=>[5]=>5
[1,1,1,1,0,0,1,0,0,0]=>[5]=>5
[1,1,1,1,0,1,0,0,0,0]=>[5]=>5
[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]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,3]=>3
[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]=>1
[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]=>[1,1,3,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,4]=>4
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,4]=>4
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,4]=>4
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,4]=>4
[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]=>1
[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]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3]=>3
[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]=>[1,3,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,4,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,5]=>5
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,5]=>5
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,4,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,5]=>5
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,5]=>5
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,5]=>5
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>2
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,5]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,5]=>5
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5]=>5
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,5]=>5
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,5]=>5
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5]=>5
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5]=>5
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5]=>5
[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]=>1
[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]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3]=>3
[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]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>2
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4]=>4
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4]=>4
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4]=>4
[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]=>[3,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,2]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,3]=>3
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3]=>3
[1,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,2]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>[6]=>6
[1,1,0,1,0,1,0,1,1,0,0,0]=>[6]=>6
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>[6]=>6
[1,1,0,1,0,1,1,0,1,0,0,0]=>[6]=>6
[1,1,0,1,0,1,1,1,0,0,0,0]=>[6]=>6
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,2]=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>[6]=>6
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6]=>6
[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[6]=>6
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6]=>6
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6]=>6
[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>[6]=>6
[1,1,0,1,1,1,0,0,1,0,0,0]=>[6]=>6
[1,1,0,1,1,1,0,1,0,0,0,0]=>[6]=>6
[1,1,0,1,1,1,1,0,0,0,0,0]=>[6]=>6
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>2
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3]=>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]=>[4,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,2]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>[6]=>6
[1,1,1,0,0,1,0,1,1,0,0,0]=>[6]=>6
[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>[6]=>6
[1,1,1,0,0,1,1,0,1,0,0,0]=>[6]=>6
[1,1,1,0,0,1,1,1,0,0,0,0]=>[6]=>6
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6]=>6
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6]=>6
[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6]=>6
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6]=>6
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6]=>6
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>[6]=>6
[1,1,1,0,1,1,0,0,1,0,0,0]=>[6]=>6
[1,1,1,0,1,1,0,1,0,0,0,0]=>[6]=>6
[1,1,1,0,1,1,1,0,0,0,0,0]=>[6]=>6
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>[6]=>6
[1,1,1,1,0,0,0,1,1,0,0,0]=>[6]=>6
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>[6]=>6
[1,1,1,1,0,0,1,0,1,0,0,0]=>[6]=>6
[1,1,1,1,0,0,1,1,0,0,0,0]=>[6]=>6
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>[6]=>6
[1,1,1,1,0,1,0,0,1,0,0,0]=>[6]=>6
[1,1,1,1,0,1,0,1,0,0,0,0]=>[6]=>6
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6]=>6
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[6]=>6
[1,1,1,1,1,0,0,0,1,0,0,0]=>[6]=>6
[1,1,1,1,1,0,0,1,0,0,0,0]=>[6]=>6
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6]=>6
[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]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,3]=>3
[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]=>1
[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]=>[1,1,1,3,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,4]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,4]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,4]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,4]=>4
[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]=>1
[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]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,3]=>3
[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]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,3,2]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,5]=>5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,5]=>5
[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]=>1
[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]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,3]=>3
[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]=>1
[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]=>[1,2,3,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4]=>4
[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]=>[1,3,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,3]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,3]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,6]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,2]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,3]=>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]=>[1,4,1,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,2]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6]=>6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6]=>6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6]=>6
[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]=>1
[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]=>1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,3]=>3
[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]=>1
[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]=>[2,1,3,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,4]=>4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,4]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4]=>4
[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]=>1
[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]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,3]=>3
[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]=>[2,3,1,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,2]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5]=>5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5]=>5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5]=>5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5]=>5
[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]=>[3,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4]=>4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4]=>4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4]=>4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,3]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,3]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,2]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7]=>7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7]=>7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7]=>7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7]=>7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7]=>7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[7]=>7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7]=>7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[7]=>7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[7]=>7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[7]=>7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,2]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7]=>7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7]=>7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7]=>7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[7]=>7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7]=>7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7]=>7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7]=>7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7]=>7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[7]=>7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[7]=>7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7]=>7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[7]=>7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7]=>7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[7]=>7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7]=>7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[7]=>7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7]=>7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[7]=>7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7]=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7]=>7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[7]=>7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7]=>7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7]=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7]=>7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[7]=>7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[7]=>7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[7]=>7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[7]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]=>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]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4]=>4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4]=>4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4]=>4
[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]=>[4,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,3]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,3]=>3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7]=>7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[7]=>7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7]=>7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[7]=>7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[7]=>7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7]=>7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7]=>7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7]=>7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[7]=>7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[7]=>7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7]=>7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[7]=>7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[7]=>7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[7]=>7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,3]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,3]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7]=>7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[7]=>7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7]=>7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7]=>7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7]=>7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[7]=>7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7]=>7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7]=>7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7]=>7
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7]=>7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7]=>7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7]=>7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7]=>7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[7]=>7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7]=>7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7]=>7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7]=>7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7]=>7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7]=>7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7]=>7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7]=>7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7]=>7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7]=>7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7]=>7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7]=>7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7]=>7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7]=>7
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[7]=>7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7]=>7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[7]=>7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7]=>7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7]=>7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[7]=>7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7]=>7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7]=>7
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7]=>7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7]=>7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7]=>7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7]=>7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7]=>7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7]=>7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7]=>7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7]=>7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7]=>7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7]=>7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7]=>7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7]=>7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7]=>7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7]=>7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7]=>7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7]=>7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7]=>7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7]=>7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7]=>7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[7]=>7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7]=>7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7]=>7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7]=>7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7]=>7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7]=>7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7]=>7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7]=>7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7]=>7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7]=>7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7]=>7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7]=>7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7]=>7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7]=>7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7]=>7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7]=>7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7]=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7]=>7
[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
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,3,2]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,4]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,4]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,4]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,4]=>4
[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]=>1
[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]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,3]=>3
[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]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,2]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]=>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]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7]=>7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,3,1]=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,3]=>3
[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]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,2]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,3]=>3
[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]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>4
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>4
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]=>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]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>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]=>[5,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8]=>8
[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]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[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
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,10]=>10
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>8
[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
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,10]=>10
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]=>1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>1
[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]=>1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]=>1
[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]=>1
[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
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,2,1,1]=>1
[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]=>2
[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]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,4,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,9]=>9
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,5]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,5]=>5
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,5]=>5
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,5]=>5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,4,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,6,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,7,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,7,1]=>1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10]=>10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,4,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,6,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,7,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,3,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,10]=>10
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,4,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,2,4,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,6,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,1]=>1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,7,1]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,5,1,2]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]=>9
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,6,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,4,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,8]=>8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,8]=>8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,5]=>5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,5]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,6,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,8]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,8]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,6,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,6,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,7,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,3,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,1,1,2,1]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]=>2
[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
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,6]=>6
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,6]=>6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,4]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,4,4]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,6]=>6
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,6]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,8,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,6,1,2]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,6,1,2]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,5]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,10]=>10
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,7,1]=>1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,10]=>10
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,10]=>10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,6,2]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,8,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,8,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,9]=>9
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>10
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,4,4]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,2,2,4]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>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]=>[6,6]=>6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[6,6]=>6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,6]=>6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[6,6]=>6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,6,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,7,1]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,5,2,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,8]=>8
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[10,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[10,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,7,1]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,7,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,7,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,9]=>9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,6,2]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,9]=>9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,8]=>8
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,6,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,8]=>8
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,4,1,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,5]=>5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,2,1,4]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,3,5]=>5
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,6]=>6
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,6]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,8]=>8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,6,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,4]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,7,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,8,1]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,5,3,1]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,5,5]=>5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,3,5]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,5,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,7,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,8]=>8
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,8]=>8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,3]=>3
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,8]=>8
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,9]=>9
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,8]=>8
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Description
The last part of an integer composition.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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