Identifier
Images
=>
Cc0005;cc-rep-0
[]=>[]
[1,0]=>[1]
[1,0,1,0]=>[1,1]
[1,1,0,0]=>[2]
[1,0,1,0,1,0]=>[1,1,1]
[1,0,1,1,0,0]=>[1,2]
[1,1,0,0,1,0]=>[2,1]
[1,1,0,1,0,0]=>[2,1]
[1,1,1,0,0,0]=>[3]
[1,0,1,0,1,0,1,0]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[1,1,2]
[1,0,1,1,0,0,1,0]=>[1,2,1]
[1,0,1,1,0,1,0,0]=>[1,2,1]
[1,0,1,1,1,0,0,0]=>[1,3]
[1,1,0,0,1,0,1,0]=>[2,1,1]
[1,1,0,0,1,1,0,0]=>[2,2]
[1,1,0,1,0,0,1,0]=>[2,1,1]
[1,1,0,1,0,1,0,0]=>[2,1,1]
[1,1,0,1,1,0,0,0]=>[2,2]
[1,1,1,0,0,0,1,0]=>[3,1]
[1,1,1,0,0,1,0,0]=>[3,1]
[1,1,1,0,1,0,0,0]=>[3,1]
[1,1,1,1,0,0,0,0]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]
[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]
[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]
[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]
[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]
[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]
[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]
[1,1,0,1,1,1,0,0,0,0]=>[2,3]
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]
[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]
[1,1,1,0,0,1,1,0,0,0]=>[3,2]
[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]
[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]
[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]
[1,1,1,0,1,1,0,0,0,0]=>[3,2]
[1,1,1,1,0,0,0,0,1,0]=>[4,1]
[1,1,1,1,0,0,0,1,0,0]=>[4,1]
[1,1,1,1,0,0,1,0,0,0]=>[4,1]
[1,1,1,1,0,1,0,0,0,0]=>[4,1]
[1,1,1,1,1,0,0,0,0,0]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,3,1]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,3]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[5,2,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,4,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,5,2,1]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,4]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[5,2,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[4,3,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,5,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,5,2,1]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,5,1,2]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,3,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[6,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[4,2,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,6,2]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,4,2,2]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[4,3,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,2,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,4,3,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,5,1,2]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,5,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,4,2,1,1]
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,1,3]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,5,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,4,2,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,2,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,4,2,2]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,3,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,6,1]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,5,1]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,5,2]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,6,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[5,2,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[3,4,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,3,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,1,2,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[6,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,1,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,6,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,4,2,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,4,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,5,3]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,2]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,6,1]
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,1,4]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,4,3]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,5,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,3]
[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]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,4]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,1,2,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,1,2,1,2]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,1,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,5]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,2,4]
[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]
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,1,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,1,2,4]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,4,2]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,1,4,2]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,6]
[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]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,1,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2,3]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,3,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,2,3,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,3,2]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,5]
[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]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,1,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,1,2]
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,1,2,1]
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,1,3]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,1,3,1]
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,1,4]
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,2,2,1,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,2,3,1,1]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,5]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,1,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,1,3]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,4,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,4,3]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[2,4,1,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,2,1]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,4,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,5,2]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,5,2]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,5,2]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,5,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,6,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,6,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]
[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]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,3,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,3,2]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,1,2]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,2,1,3]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2,2]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,2,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,3,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,4,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,1,1]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,5,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,5,1]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,5,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,6]
[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]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,4]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,3,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,1,2,2]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,1,3,1]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,3,1]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,1,2,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,4,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,4,1]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,5]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[3,2,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2,2]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,1,2]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,1,2]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[3,2,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[3,2,3,1]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,4]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[3,3,1,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[3,3,2,1]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[3,3,1,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,1,2]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[3,3,2,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[3,3,2,1]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[3,4,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[3,4,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[3,4,2]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,4,2]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[3,4,1,1]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,4,1,1]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,5,1]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,5,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,1,3,1]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,2,3]
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,2,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2]
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,3,2]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,4,1]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,4,1]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,2,2]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,2,2]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,3,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,4,1]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,4,1]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,4,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,3,1]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,2]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,3,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,1,3,1]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,2,1,2]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,2,1,2]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,2,2,1]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[4,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[4,3,2]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,3,2]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,3,2]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[4,3,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,4,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[4,4,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,4,1]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,4,1]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,4,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,1,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[5,2,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,2,2]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,4]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,2,2]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,2,1,1]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,2,2]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,1,2,1]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,1,2,1]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,2,1,1]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[5,2,2]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[5,2,1,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,2,1,1]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,2,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,3,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,4]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[6,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[6,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]
[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]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,4,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,3,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,3,1,2]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,3,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,1,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,5,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,3,2,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,1,2]
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,5,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,3,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,1,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,5,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,2]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,5,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,3,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,6,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,3,3,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,6,1]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,5,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,2,1,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,2,3]
[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]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,3,2]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,2,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,3,3]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,5,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,1,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,1,3]
[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]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,2,4,1]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]
[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]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,5,2]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]
[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]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,1,5]
[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]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,3,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]
[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]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,5,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]
[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]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]
[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]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]
[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]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,2,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,2,3,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,2,3,2]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,4,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,5,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,6,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,2,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,1,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,4,2]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[4,2,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,4,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,3,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,5,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,2,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[6,1,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,6,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,1,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,2,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,1,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,2,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,3,1,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,1,2,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,2,5]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,2,4]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,2,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,1]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,1,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,3,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,1,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,4,1,1,2]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,4,1,2]
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,4,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[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]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,1,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,5,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,5,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,4,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,5,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,5,1,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,2,1,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,1,4]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,1,4]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,2,4,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,2,4,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[4,2,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,2,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[4,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[2,3,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,1,4,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,3,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,1,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,4]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,2,4,1]
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,1,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,1,3,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,1,4,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,4,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,3,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,3,2]
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,4,3]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,4,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,4,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,2,3,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,1,2,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,5,3]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,2,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,6,2]
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,1,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,4,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,2,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]
[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]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,2,3,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,5,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,4,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,5,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[6,2,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,4,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[3,3,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,1,2,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,5,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,4,3]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,4,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,1,3]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,1,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,3,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,1,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,3,1,2]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,1,2,2]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,5,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,4,2]
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,3,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,5,1,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,5,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,4,1,2]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,3,3,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,1,3,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,3,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,3,1,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,4,1,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,1,2,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,1,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,4,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,3,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,2,1,3]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,3]
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,1,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,5,1,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,1,3]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,1,4]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,1,2,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,2,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,1,2,2]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,1,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,4,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,1,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,1,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,1,4,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,1,3,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,1,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,1,3]
[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]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[3,2,1,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,1,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,4,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,2,3,2]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,2,3,1,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,3,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,2,3,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,2,3,1]
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,2,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,1,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,1,2]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,4,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,3,1,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,3,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,1,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,2,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,3,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,2,3,1,2]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,3,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,2,1,3]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,1,2,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,1,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,3,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,3,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,1,2,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,2,2]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,1,2,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,1,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,3,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,5,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,1,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,3,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2,1,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,1,2,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[2,5,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,3,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,4,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,1,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,1,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[4,2,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,2,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,5,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,4,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,1,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,2,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,2,3,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,1,3]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,3,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,5,1,1]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,1,4]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,3,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2,2]
[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]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,1,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,2,3,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,4,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,1,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,1,4,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,2,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[2,3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,3,2]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,1,3]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[4,2,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[2,3,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,3,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,2]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,5,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,1,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,1,2,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,2,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,1,2,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[7,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,8,1]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,7,2]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[6,3,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,8,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,7,1,1]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,6,3]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[6,2,1,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,4,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,8,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,7,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,7,2]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,6,2,1]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,5,4]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,1,2,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[4,5,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,8,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,7,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,6,2,1]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,1,2]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,5]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[7,2,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[6,3,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,6,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,8,1]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,7,2]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,5,2,2]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,8,1]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,5,3,1]
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,5,1,3]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,1,2]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,7,1]
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,6,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,8]
[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,4]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,4,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,3,1,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,5]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,3,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,1,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,1,1,2]
[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,1,1,2,1,1]
[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]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,1,1,2,1]
[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]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]
[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,4,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,3,1,1,1]
[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]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,4,2,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,6,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,4,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,5,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,6,2]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,7,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,1,3]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,1,3,1,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,2,3]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,4,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1,1]
[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]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,6,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,1,3]
[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]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,1,3,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,1,4]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,7]
[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]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,2,1,2,1]
[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]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,3,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,4,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,6,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,6,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,1,2,1]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,5,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,4]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,4,3]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,6,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,4,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,4,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4,2]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,5,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,1,1,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,3,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[6,1,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[6,1,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,1,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[7,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,1,1,2]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,1,1,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1,1]
[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]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,1,2]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,3]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,4]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,5]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,6]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,7]
[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,2,1,1,1]
[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]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,6,1,1]
[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]
[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]
[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]
[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]
[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]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,2,1]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,7]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,1,6]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,1,2,1,1]
[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]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,3,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[8,2]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,3]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[7,3]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,4]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,4]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,3,1,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,3,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,2,1,2,1]
[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]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,3,3,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,1,1,1]
[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]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,2,1]
[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]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,1,3,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,1,4,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,2,1,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,2,1]
[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]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,2,2,1,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,3,1,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,1,1,2,1]
[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]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[2,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[2,3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,4,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,3,1,1,1]
[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]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[3,2,2,1,1,1]
[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]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[4,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[7,2,1]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,7,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[7,2,1]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,7,1]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,5,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[8,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,5,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,7,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[7,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[8,2]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[4,5,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[2,6,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,1,4,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1,1]
[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]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,1,2]
[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,1,1,3,1]
[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]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1,1,1]
[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]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,2]
[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]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1,1]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,5,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,1,1,3]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,1,4]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,1,5]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,5]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,6]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,7]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,7,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[3,6,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[4,5,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[5,4,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[6,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1,1,1]
[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]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,1]
[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,1,1,2,1]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,5]
[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]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,1,4]
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,1,5]
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,1,6]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]
[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]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,1,1,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,1,2,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,2,1,1,1]
[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]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,1,1,1,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,1,1,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,2,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,2,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,2,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,2,1,1,1,1]
[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]
[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]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[2,5,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,1,4,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[3,1,4,1,1]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,1,3,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,2,1]
[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]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,1,1,1]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,7,2]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,3,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[6,4]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,1,1,2,1]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,4,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,3,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,5,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[8,1,1]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[6,3,1]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,4,1]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,6,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1,1]
[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]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,2,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,3,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,1,2,1]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,6,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,1,3,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,2,3,1,1,1]
[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]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[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]
[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]
[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]
[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]
[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]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,2,2,2,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,6,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,1,2]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,1,1,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,3,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,2,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,2,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,3,1,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,3,1,2,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,7,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,1,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,1,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,1,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,3,1,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,1,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,1,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,3,1,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,3,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,1,2,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,2,1,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,4,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,4,1,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,3,1,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,3,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,3,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,1,2,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,2,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,3,2,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,5,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,4,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,1,1,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,3,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,3,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,2,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,3,1,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,1,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,3,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,2,1]
[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]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1,1]
[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]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,1,1,3,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,1,3,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1,1,1]
[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]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,1,1,2,2]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,1,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[6,2,2]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[4,1,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,1,1,2,1,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[4,1,3,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[4,3,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0]=>[7,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,6,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[3,6,1]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[7,2,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[6,3,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,4,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,1,1,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[2,6,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,1,1,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2,2]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,5,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,4,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,3,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,2,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[2,6,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,1,1,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,3,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,4,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,1,1,2]
[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]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,2,3,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,3,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,1,4,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,2,4,1,1,1]
[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]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,2,2,1,2]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,1,3,1,2]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,2,3,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,2,1,2,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,2,1,1,3]
[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]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,2,2,1,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,2,1,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,3,1,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,2,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,3,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,2,3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,4,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,2,3,1,1,2]
[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]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,2,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,3,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,1,4,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,4,1,1,1]
[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]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[4,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,1,1,2,1]
[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]
[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]
[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]
[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]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,2,1,2,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[2,6,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,7,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,6,2]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,6]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,1,4]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,1,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,1,2]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[6,2,2]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[6,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,2,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[3,4,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,2,1]
[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]
[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]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,3,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,2,1,1,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]
[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]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,1,2]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[3,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[2,3,2,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,4,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1,2,1]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,2,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[2,2,3,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,3,3,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,3,1,2,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,2,4,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,5,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,1,2,1,1]
[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]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,2,2,3,1]
[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]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,1,3,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,1,4,1,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,1,4,1,1]
[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]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,3,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,3,2,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,4,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,1,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,1,3,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,2,2,3,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,3,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,2,4,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,4,1,1]
[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]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,1,3,1,1,1]
[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]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,1,1,4]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,4,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,4,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,4,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[2,3,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,2,1]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[2,3,2,1,2]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,3,2]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[2,2,2,1,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,3]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,2,3,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[2,5,1,2]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,2,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[2,4,1,2,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[2,2,3,2,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,1,3,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,3,3]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,4,2]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,1,1,3,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,1,1,2,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,2,1,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,2,1,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,1,1,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[4,3,1,2]
[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]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,2,1,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[3,3,1,1,2]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[4,3,1,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,2,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[4,4,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[4,2,1,2,1]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[4,3,2,1]
[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]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[3,2,1,3,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,2,1,1,1]
[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]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,1,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,2,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[3,3,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,1,2,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,1,3,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,1,3,2]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,1,1,2,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2,1,2]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,2,1]
[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]
[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,1,1,2,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[7,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[6,3,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,1]
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,5,1]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,2,1,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,1,2,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,2,3,1,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,1,1,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,3,1,1,1]
[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]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,2,1,1,1]
[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]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,2,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,4,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,1,3,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,2,2,1,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,1,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,2,2,1,2]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,3,1,1,2]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,1,2,1,2]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,3,2,1,1,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,1,1,2]
[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]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[2,1,3,1,1,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,2,1,2,1,2]
[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]
[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]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,1,1,2]
[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]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,1,1,2]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[4,4,2]
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,2,3]
[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,1,1,2,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1,1]
[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]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,2,1,1,1]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,3,3,1]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[3,3,1,1,2]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,1,1,3,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,1,3,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,1,4]
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,5,1,1]
[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,1,1,2]
[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]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,1,2]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,1,1,2,1]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,1,2]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,1,1,3]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,4,2,1,1,1]
[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]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1,1]
[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]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,1,1,3,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,3,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[2,4,1,2,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,5,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,3,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[3,3,1,1,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[4,1,2,1,2]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,6]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,4,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,1,1,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[7,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,4,4,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,3,5,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,6,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2,2]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,3,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,1,1,2,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,7,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,7,1]
[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]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,1,2,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,6,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,2,1,1,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,5,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,2,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,2,3,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,3,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[4,3,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[6,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,2,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,2,3,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,4,3,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,4,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,3,4,1,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,2,1,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[3,3,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,1,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,3,3,1,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,5,1,1,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,2,1,2,1,1,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,2,2]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,4,1,2,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[3,3,1,1,2]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,1,3,2]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,1,2,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,1,1,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,3,2,1,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,1,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,2,3,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,1,4,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,2,3,2]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,1,4,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,2,1,4,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,1,4,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,2,1,3,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,1,4,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,2,1,3,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,4,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,1,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[2,4,1,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,1,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,1,2,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,1,4,1,2]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,1,3,1,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,3,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,3,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,1,3,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,1,1,3,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,1,2,2]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,1,3,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,3,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,2,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[2,5,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,2,4,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[2,2,2,3,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,2,3,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,2,4,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,2,5,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,3,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,4,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,2,4,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,4,1,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,3,1]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,1,3]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2]
[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]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,2,6]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,2,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,2,1,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,1,3,2,1]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,2,2,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,3,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,2,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,4,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,2,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,1,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,2,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,2,1,1,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,2,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,2,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,2,1,3,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,3,2,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,4,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,1,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,4,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,1,1,2]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[5,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,4,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,1,2,2]
[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]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,1,2,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,1,2,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,1,2,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,1,2,2]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[3,6,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,1,1,2]
[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]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,2,3,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,2,4,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,3,2,1,2,1]
[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]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,2,1]
[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]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,1,2,1]
[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]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,1,3,1,1,1]
[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]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[3,2,2,1,1,1]
[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]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[4,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,1,1,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,9,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[8,2,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,9,1]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,8,2]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,9,1]
[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]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,7,3]
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,6,4]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,5,5]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,4,6]
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,3,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,4,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,5,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,1,1,1,2]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[9,2]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,9]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,2,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,8,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[8,1,1,1]
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,6,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,6,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,6,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,2,2,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,3,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,9,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,1,5]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,1,1,1,2,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[8,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,1,1,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[2,1,1,4,2,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,2,4,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,1,1,1,2]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[8,3]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,3,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[9,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2,8,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,2,1]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[10,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,1,1,1,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,1,1,1,1,2]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,8,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,7,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,6,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[5,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,4,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[7,3,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[8,2,1]
[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,7,1,1]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,6,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,5,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,1,1,1,2]
[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]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,8]
[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,7]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,6]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[6,5]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[7,4]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[8,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[9,2]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,1,1,1,2]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,1,1,1,3,1]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,1,1,3,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,1,1,3,1,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,1,3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[10,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,1,1,1,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,1,1,1,3,1]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,1,1,3,1,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,1,3,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[9,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,2,1,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,1,1,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,2,1,1,1,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,1,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,1,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[2,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,1,1,1,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,1,1,1,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,8,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,7,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,1,1,1,2]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,5,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,5]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,5,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,2,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,4,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[7,4]
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[6,5]
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[5,6]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[4,7]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,10,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,2,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,2,2,3,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,2,3,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,2,3,2,1,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,2,4,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,1,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,3,2,1,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,4,1,1,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,3,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,3,3,1,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,1,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,4,2,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,1,2,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,3,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,1,3,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,3,1,4,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,3,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,1,1,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,3,2,2,1,2,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,3,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,1,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,1,1,1,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,3,2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,3,2,3,1,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,3,1,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,3,3,2,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,3,4,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,1,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,4,1,3,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,1,2,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,1,1,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,4,2,2,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,4,3,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,1,2,2,3,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,2,3,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,1,2,3,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[2,1,2,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,3,1,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,1,3,2,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,1,4,1,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,1,3,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,1,3,3,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,1,4,1,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,1,4,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,5,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,2,1,2,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,3,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,1,3,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,2,1,4,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,1,1,2,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,1,3,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,1,1,4,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,3,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,1,2,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,2,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,1,3,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,1,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,1,1,1,3,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[2,2,2,2,1,2,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,2,3,1,1,2,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,1,2,1,2,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1,1,2,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,1,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,2,2,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,3,1,1,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,2,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,1,2,1,2,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,2,1,1,2,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[3,3,1,1,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1,1,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,2,1,1,1,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,1,1,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[2,2,2,3,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[2,2,3,1,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[2,2,3,2,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[2,2,4,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[2,3,1,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[2,3,1,3,1,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[2,3,2,1,2,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[2,3,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[2,3,3,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[2,4,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,5,1,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,4,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,3,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,2,1,2,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[3,3,1,1,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,1,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[3,2,2,2,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[3,2,3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,2,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[3,3,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,2,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[4,2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[4,3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[11,1]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,10]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1,1,1]
[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]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,2,2,2]
[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]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,1,2,2]
[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]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,1,1,2,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,3,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,1,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,2,1,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,4,1,1,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,1,1,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,3,1,1,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,3,3,1,1,2]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,3,1,1,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,2,1,1,2]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,2,1,1,2]
[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]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,2,1,1,1,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,2,1,1,2]
[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]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,1,1,1,1,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,1,1,2]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,1,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,3,1,2]
[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]
[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]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,3,1,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,3,1,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,2,1,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,3,1,2,1,2]
[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]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,1,1,2,1,2]
[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]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,3,2,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,1,2,2,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,2,2,1,2]
[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]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,4,1,1]
[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]
[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]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,3,1,1]
[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]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,1,1,3,1,1]
[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]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,3,3,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,2,3,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,2,3,1,1]
[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]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,2,2,1,1]
[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]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,1,1,2,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,2,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,2,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,4,3,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,3,3,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,2,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,5,2,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,4,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,2,2,1,1]
[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]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,1,2,2,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,2,1,2,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,2,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,2,3,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,3,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,4,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,4,2,1,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,3,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,3,3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,3,2,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,5,1,1,1,1]
[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]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,2,5,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,1,5,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,1,4,1,1,1]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,4,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,1,1,2,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,2,3,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,2,3,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,1,3,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,3,1,1,3,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,1,1,3,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,1,1,1,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1,3,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,1,3,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,2,1,3,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,2,1,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,4,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,3,1,2,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,3,1,2,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,3,1,2,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,2,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,1,2,1,2,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,1,1,2,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,2,1,1,2,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,2,1,2,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,3,2,1,2,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,1,1,1,2,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,5,1,1,2,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,1,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[4,1,1,3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1,3,2,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,2,2,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,3,1,2,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,1,2,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,1,1,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,3,2,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,3,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,3,2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,1,3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,2,3,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,4,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,2,1,3,2,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,3,1,3,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,2,1,1,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,2,3,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[1,3,3,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,1,4,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,4,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,2,2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,3,2,1,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,3,1,3,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,4,1,3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,2,1,2,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,1,2,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,2,1,1,4,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,1,1,4,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,2,3,1,1,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,3,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,1,4,1,1,2]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,5,1,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,2,2,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,3,2,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,1,3,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,3,3,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[1,4,3,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,2,1,4,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,3,1,4,1,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,1,1,1,2]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,5,1,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,2,4,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,3,4,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,2,1,5,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,5,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,2,2,2,1,2]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,3,2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,1,3,2,1,2]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,2,3,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,4,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,3,1,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,1,2,1,2]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,2,3,1,2,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,3,3,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,2,1,4,1,2,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,4,1,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,2,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2,1,2,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1,2,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,3,1,2,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,3,1,2,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,2,2,1,1,3]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,2,1,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3,1,1,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1,1,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,3,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,2,2,1,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,2,2,1,1,3]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,1,2,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,1,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,2,1,2,1,3]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,1,1,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,1,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,1,1,3,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,2,2,2,1,2]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,1,3,2,1,2]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,2,3,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,3,1,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,3,1,2,1,2]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,3,1,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,3,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,4,1,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,2,4,1,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,2,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,2,2,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,3,2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,1,3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,2,3,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[1,4,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,2,1,3,2,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,3,1,3,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,2,1,1,2]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,2,3,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,3,3,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,2,1,4,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,2,4,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,2,2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,3,2,1,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,2,3,1,3,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,2,1,2,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,1,2,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,2,1,1,4,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,1,1,4,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,2,3,1,1,2]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,3,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,2,1,4,1,1,2]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,1,1,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,5,1,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,2,2,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[1,3,2,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,1,3,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,2,3,3,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,4,3,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,2,1,4,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,3,1,4,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,1,1,1,2]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,5,1,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,2,4,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,3,4,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,1,5,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,5,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[3,1,4,2,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2,2,1,2]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,2,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,3,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,2,2,1,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,2,2,1,2,1]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[5,2,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,2,2,3,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,2,2,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,2,3,2,1,2,1]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[4,3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,4,2,1,2,1]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[3,4,2,1,1,1]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[2,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,2,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,2,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,1,2,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,1,3,3,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1,3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,1,3,3,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,1,3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,2,2,3,2,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,3,3,2,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,1,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,2,4,2,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,2,3,1,2,1]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[4,2,3,1,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,3,3,1,2,1]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[3,3,3,1,1,1]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[2,4,3,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,3,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,2,4,1,2,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,4,1,2,1]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[3,2,4,1,1,1]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,4,1,1,1,1]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[2,2,5,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,5,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,1,2,2,1]
[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]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,1,1,2,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,3,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,4,1,2,2,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[3,4,1,2,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,5,1,2,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[3,4,1,1,2,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[3,4,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,1,1,2,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,1,3,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,1,1,2,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,1,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[5,1,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,1,1,1,1,2,1]
[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]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,2,1,2,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,1,1,2,4,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1,2,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,1,2,4,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,1,2,3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,3,1,4,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,3,1,3,2,1]
[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]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,1,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,2,1,4,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,1,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,2,2,2,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,3,2,3,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,2,3,3,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[3,1,3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[3,3,1,3,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[2,4,1,3,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,3,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,2,2,4,1,1]
[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]
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,3,1,4,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,1,1,4,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,2,1,4,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,2,2,1]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[4,2,2,2,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,2,2,1]
[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]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[2,4,2,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,2,2,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,2,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,2,3,2,2,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[3,1,3,2,2,1]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[3,2,3,2,1,1]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[2,3,3,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[3,1,3,2,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[2,2,4,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[2,1,4,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[3,3,1,2,2,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[3,3,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[2,4,1,2,2,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[2,4,1,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,1,2,1,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,2,1,2,1]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,2,2,3,2,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,1,2,3,2,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,3,1,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,1,3,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,3,2,1,1]
[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]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[2,3,2,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[3,1,2,3,1,1,1]
[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]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[2,1,3,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,3,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,3,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,3,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,3,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[2,2,2,4,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,1,2,4,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,3,1,4,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,1,5,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,1,5,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,3,3,2,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,2,4,1]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[2,3,3,1,2,1]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,2,2,3]
[1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,1,1]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,2,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,2,1,3,1]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[2,3,3,2,1,1]
[1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,1,2]
[1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[2,3,2,2,1,2]
[1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[2,3,5,2]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,3,2,1,2,2]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,3,3,3,1]
[1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[2,2,2,1,3,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,2,2,1,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,2,2,1,4,1]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,1,2,1,2]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,1,3,2]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[2,4,2,1,2,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[2,4,2,1,3]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[2,2,3,1,1,2,1]
[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]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[2,5,1,2,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,4,2,1,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,4,2,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,4,1,2,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0]=>[2,2,3,2,1,1,1]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0]=>[2,5,2,1,2]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[2,5,2,1,1,1]
[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[2,4,4,2]
[1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,5,1,2,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,4,2,3,1]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[2,2,4,1,1,2]
[1,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[2,2,4,2,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,4,1,3,2]
[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]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,2,1]
[1,1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0]=>[2,4,2,1,2,1]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0]=>[2,2,5,2,1]
[1,1,0,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0]=>[2,4,1,2,2,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[3,1,3,3,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,1,3,2,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,3,4,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,1,3,2,1,2]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,1,3,3,2]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[3,1,2,2,1,2,1]
[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]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,4,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[3,1,5,1,2]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[3,1,4,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[3,1,2,4,2]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[3,1,4,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,1,3,3]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,1,1,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,1,1,4,2]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,1,2,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,1,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,1,3,3]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,2,1,4,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,2,1,2,3,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,1,1,3,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,2,1,1,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,3,1,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,3,1,2,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,2,1,1,1,3,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,2,1,1,1,2,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,2,1,3,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,2,1,2,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,3,1,1,3,1]
[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]
[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]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[4,2,2,1,1,2]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,1,1,2]
[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]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,1,2]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2,1,1,2]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,3,1,2]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,2,1,1,1,2]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[3,3,1,1,1,1,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,1,2,1,2]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,2,1,1,1,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,4,2,1,2]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,1,1,2]
[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]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0]=>[4,3,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[4,2,4,1,1]
[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]
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,2,2,3,1]
[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]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,4,2,1,1]
[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]
[1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[4,3,2,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[4,4,1,2,1]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0]=>[4,2,2,1,2,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0]=>[4,5,2,1]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[4,2,1,2,2,1]
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[4,3,3,1,1]
[1,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[3,2,1,3,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[3,2,1,4,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[3,2,1,2,1,2,1]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[3,2,1,3,2,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,2,1,2,1,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[5,2,1,3,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1,1,3,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,1,2,1,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[5,2,1,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,4,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[3,3,2,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,2,1,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,2,1]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[6,1,2,1,1,1]
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[5,2,3,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[3,4,1,1,2,1]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[3,4,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[5,1,3,2,1]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[3,3,2,1,2,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[7,1,2,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[5,2,1,2,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[3,5,2,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[5,1,2,2,1,1]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[2,2,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[2,2,2,3,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[2,2,3,1,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[2,2,3,2,1,1,1]
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0]=>[2,2,4,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,3,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,2,1,2,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[2,3,2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,3,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[2,4,1,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,4,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,5,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,1,3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[3,1,4,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,3,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,1,1,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[3,2,2,1,2,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,1,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,1,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[3,2,2,2,1,1,1]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[3,2,3,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[3,3,1,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,3,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,3,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[4,2,1,2,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,3,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,1,1,1,1,1]
[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]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,2,2,3,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,2,3,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,2,4,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,3,1,1,1]
[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]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,4,1,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,3,2,2,1,1,1]
[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]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,4,1,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,4,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,5,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,2,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,1,2,3,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,3,1,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,1,3,2,1,1,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,2,1,4,1,1,1,1]
[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]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,1,2,3,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,3,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,1,3,2,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,1,4,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,1,1,2,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,3,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,3,1,1,1]
[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]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,3,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,1,1,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,3,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,2,2,1,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1,2,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,1,2,1,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,1,1,1,2,1,1]
[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]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1,2,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,2,1,2,1,1]
[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]
[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]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,1,1,2,1,1]
[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]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,2,2,2,1,2]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,2,2,3,1,1,2]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,1,2,1,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,3,2,1,1,2]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,2,4,1,1,1,2]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,1,2,2,1,2]
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,3,1,3,1,1,2]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,3,2,1,2,1,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,1,2,1,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,3,2,2,1,1,2]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,3,3,1,1,1,2]
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2,1,1,2]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,4,2,1,1,1,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,1,2,2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[2,1,2,3,1,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,1,3,1,2,1,2]
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[2,1,3,2,1,1,2]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[2,1,4,1,1,1,2]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,3,1,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2,2,1,2]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,3,1,1,2]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[2,2,2,1,2,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,1,2,1,2]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,1,2,1,2,1,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,1,2,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,1,2,1,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,1,1,2]
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,2,3,1,1,1,2]
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2,1,1,2]
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0]=>[2,3,2,1,1,1,2]
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0]=>[2,4,1,1,1,1,2]
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[3,1,2,2,1,1,2]
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,3,1,1,1,2]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2,1,1,2]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2,1,1,2]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0]=>[3,2,2,1,1,1,2]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[3,3,1,1,1,1,2]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,1,1,1,2]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,1,1,1,1,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[11,1]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[10,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,1,1,1,1,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,3,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,3,2,1,2,1,1]
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[2,5,3,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,4,1,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,2,1,2,3,1,1]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,2,1,4,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[2,2,3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[2,4,1,2,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,2,3,1,1,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,2,2,1,2,2,1]
[1,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[2,4,3,2,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[2,4,1,1,1,2,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,1,2,1,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,3,1,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[4,5,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,1,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,3,2,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,1,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,2,1,2,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1,3,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[6,1,1,3,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,2,1,1,3,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,3,2,3,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,3,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,2,1,2,1,1,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]=>[6,3,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[6,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,1,4,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0]=>[3,3,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,2,1,2,2,1,1]
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[5,3,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,1,1,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,2,3,3,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,2,5,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,2,2,3,2,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,2,4,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,4,3,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,4,2,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,4,1,1,3,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,3,1,2,3,1]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,4,3,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,6,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,3,3,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,5,1,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,2,2,1,2,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,4,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,2,1,2,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,4,3,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,3,1,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,1,1,2,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,3,1,1,4,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,2,2,3,1]
[1,0,1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,1,2,4,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,2,3,1]
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[3,3,4,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,1,1,2,3,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,1,1,4,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,2,1,2,3,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,2,1,4,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,3,1,2,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,2,2,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,3,1,1,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,1,3,2,1,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[2,1,2,3,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[3,3,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,1,1,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,2,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,1,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,3,1,1,1,2]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,2,1,2,1,2]
[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0]=>[1,5,3,1,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,1,1,1,1,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2,1,1,2]
[1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,1,2,3,1,2]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,2,1,4,1,1,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,2,1,1,2]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,1,2,1,1,2]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,1,1,2,2]
[1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,2,1,2,2,2]
[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,4,3,2,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,1,1,1,2,2]
[1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,1,2,1,2,2]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,3,1,2]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[3,5,1,1,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2,1,1,2]
[1,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,2,3,2,2]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[3,4,1,2,2]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,3,1,1,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,1,2,1,2,2]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,3,1,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2,1,2,2]
[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[3,3,1,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,1,1,3,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,2,1,1,3,2]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[2,3,2,3,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,1,2,3,2]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[3,3,1,1,1,1,2]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2,1,1,2]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[5,3,1,1,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,1,1,1,1,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[2,1,2,3,1,1,2]
[1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[2,1,4,1,1,1,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0]=>[2,3,2,1,1,1,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,2,1,1,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,2,1,2,2,1,2]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0]=>[4,3,2,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,1,2,1,2]
[1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[3,1,2,1,2,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,2,1,4,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,1,1,4]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,1,4,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,2,2,1,4]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,1,4,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,1,2,3]
[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]
[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]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,1,2,3]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,1,2,1,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,2,2,1,4]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,3,2,1,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,1,1,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,1,2,3]
[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]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[5,1,3,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,2,2,1,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[5,1,1,3,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,2,2,1,4]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,3,1,1,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1,3,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[5,1,1,3,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,4,1,3,1,1]
[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]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,1,1,3,1,1]
[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]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3,1,3]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,2,1,4]
[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]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,2,1,2]
[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]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,2,1,4]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3,1,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,1,2,1,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1,3,1]
[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]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1,3,1]
[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]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[2,1,5,1,1,2]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[3,1,5,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,1,2,4,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,1,5,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,1,2,4,1,2]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,1,5,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,2,1,5,1,1]
[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]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,1,5,1,1]
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,2,1,4,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,1,5,1,1]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,2,1,4,1,2]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[3,1,5,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,4,1,2,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1,2,1]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[2,4,1,2,2,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,2,1,2,1]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2,1,2]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,2,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1,2,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[2,4,1,2,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,2,1,2,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,4,1,2,1,2]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,2,1,2,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,1,2,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,1,2,1]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[2,1,4,2,2,1]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[2,1,4,2,2,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,1,2,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,1,2,1]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[2,1,4,2,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[2,1,4,2,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,5,1,2,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,5,1,2,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,3,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,3,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,2,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,3,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,2,2,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,3,1,1]
[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]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,2,2,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,3,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[4,2,1,2,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,3,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[4,2,1,2,2,1]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,3,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,2,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,2,1,3,1]
[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]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1,3,1]
[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]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1,3,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,1,2,1,2,2]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,2,1,2,2]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,1,2,1,2,1]
[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]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,2,1,2,1]
[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]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,2,1,2,2]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3,1,1,3]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,3,1,1,1]
[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]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,1,3,1,1]
[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]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[4,2,1,1,3,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,2,1,3,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,1,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,3,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2,2,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,1,1,3,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2,2,1,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,1,1,1,3,1]
[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]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[3,2,1,2,1,3]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,1,2,2,2]
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,3,1,2,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,1,2,2,1,2]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,1,2,1,2,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,1,2,1,3]
[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]
[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]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,1,2,1,3]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,3,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,1,2,2,1,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,3,1,2,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,1,2,2,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,2,1,3,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[11,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,2,2,3,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,2,3,2,2,1]
[1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,4,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,3,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,3,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,3,2,3,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,4,1,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,2,2,1,4,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,2,1,2,4,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,1,2,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,1,3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,1,2,1,4,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,1,3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,1,3,2,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,2,2,2,3,1]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,3,3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,3,1,2,3,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,2,3,3,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,2,4,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,2,1,2,2,3,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,1,3,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,2,1,2,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,1,1,2,3,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,2,4,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,4,1,3,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,1,1,4,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,4,1,3,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,2,2,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,1,1,2,3,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,1,1,3,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,1,2,1,4,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,1,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,1,1,2,2,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,1,3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,2,1,2,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,1,1,4,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,2,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,1,3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,1,1,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,1,1,2,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,1,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,1,1,2,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,1,1,2,3,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,2,2,1,1,3,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,1,1,3,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,2,1,1,3,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,1,1,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,2,2,2,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,2,3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,2,3,1,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,2,2,1,4,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,3,1,2,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,2,1,3,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,2,2,1,3,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,3,2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,1,2,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,2,1,2,3,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,2,2,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,1,2,2,2,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,1,3,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,2,2,1,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,2,1,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,1,2,1,3,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,1,2,1,3,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1,2,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,1,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,1,1,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,3,2,2,1,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,2,3,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,1,2,1,2,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,3,1,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,2,3,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[2,1,1,4,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,3,1,2,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,4,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,4,1,2,2,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,4,1,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,4,1,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1,2,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,2,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,1,1,1,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,1,1,1,2,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,5,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,2,2,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,2,2,3,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,2,2,4,1,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,2,1,2,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,1,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,2,3,3,1,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,2,4,1,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,2,4,2,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,5,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,1,3,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,3,1,4,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,3,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,4,1,1,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,3,2,2,1,2,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,3,3,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,1,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,1,1,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,2,2,3,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,3,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,1,2,3,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,1,2,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,1,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,1,3,2,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,1,4,1,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,2,1,2,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,1,2,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,3,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[2,2,2,3,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,2,3,1,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[2,2,3,2,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[2,2,4,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,3,1,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,2,1,2,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[2,3,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,3,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[2,4,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[3,1,2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[3,1,2,3,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[3,1,3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,1,4,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,1,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,3,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,2,1,2,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[3,3,1,1,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,2,1,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,1,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[3,2,2,2,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[3,2,3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,2,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[3,3,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[3,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[4,1,3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,2,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[4,2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[4,3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,1,1,1,1,1,1]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
Send a Dyck path to the composition of sizes of its rises.
Properties
surjective, graded
Sage code
def mapping(D): return D.rise_composition()
Weight
26
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
Apr 04, 2022 at 13:54 by Tilman Möller
searching the database
Sorry, this map was not found in the database.