Identifier
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[]=>[]
[1,0]=>[1,0]
[1,0,1,0]=>[1,1,0,0]
[1,1,0,0]=>[1,0,1,0]
[1,0,1,0,1,0]=>[1,1,1,0,0,0]
[1,0,1,1,0,0]=>[1,1,0,1,0,0]
[1,1,0,0,1,0]=>[1,0,1,0,1,0]
[1,1,0,1,0,0]=>[1,0,1,1,0,0]
[1,1,1,0,0,0]=>[1,1,0,0,1,0]
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
The map that sends the Dyck path to a 321-avoiding permutation, then applies the Robinson-Schensted correspondence and finally interprets the first row of the insertion tableau and the second row of the recording tableau as up steps.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
References
[1] Knuth, D. E. The art of computer programming. Vol. 3 MathSciNet:3077154
[2] Krattenthaler, C. Permutations with restricted patterns and Dyck paths arXiv:math/0002200
[2] Krattenthaler, C. Permutations with restricted patterns and Dyck paths arXiv:math/0002200
Properties
bijective, graded
Sage code
def mapping(D): return from_pair_of_standard_tableaux(*RSK(to_321_avoiding_permutation(D))) def from_pair_of_standard_tableaux(P, Q): """ Return a Dyck path from a pair of SYT of the same shape with at most two rows. sage: all(from_pair_of_SYT(*D.to_pair_of_standard_tableaux()) == D for D in DyckWords(9)) True """ n = 2*P.size() D = [0]*(n) if not P: return DyckWord(D) for p in P[0]: D[p-1] = 1 if len(Q) == 2: for p in Q[1]: D[n-p] = 1 return DyckWord(D) def to_321_avoiding_permutation(P): n = (len(P)//2) a = P.rise_composition() A = [sum(a[:i+1]) for i in range(len(a))] d = P.reverse().rise_composition().reversed() D = [sum(d[:i]) for i in range(len(a))] pi = [None]*n rest = list(range(1, n+1)) for (e,f) in zip(A, D): pi[f] = e rest.remove(e) i = 0 for e in rest: while pi[i] is not None: i += 1 pi[i] = e return Permutation(pi)
Weight
40
Created
Jun 12, 2023 at 11:15 by Martin Rubey
Updated
Jun 12, 2023 at 11:15 by Martin Rubey
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