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]=>[1,1,0,0,1,0]
[1,1,0,0,1,0]=>[1,1,0,1,0,0]
[1,1,0,1,0,0]=>[1,0,1,0,1,0]
[1,1,1,0,0,0]=>[1,0,1,1,0,0]
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0]
[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]=>[1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[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]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[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]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
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(only identities of compositions of up to three maps are shown)
Description
Rotate the associated triangulation counterclockwise.
Given a triangulation of the -gon, we obtain a binary tree by interpreting each face of the triangulation as an internal vertex. The children of a vertex are the vertices corresponding to adjacent faces that are further away from the root.
Traversing the tree in pre-order and recording upon first encounter every left edge as an up step and every right edge as a down step, we obtain a Dyck path of semilength .
Rotating the triangulation counterclockwise corresponds to this map.
Given a triangulation of the -gon, we obtain a binary tree by interpreting each face of the triangulation as an internal vertex. The children of a vertex are the vertices corresponding to adjacent faces that are further away from the root.
Traversing the tree in pre-order and recording upon first encounter every left edge as an up step and every right edge as a down step, we obtain a Dyck path of semilength .
Rotating the triangulation counterclockwise corresponds to this map.
Properties
bijective, graded
Sage code
def mapping(D):
H = DyckWord(D).heights()
z = H.count(0) - 1
p_dash = [i for i, h in enumerate(H) if not h]
D = list(D)
for j in p_dash[-2::-1]:
del D[j]
D = [1]*z + [0] + D
del D[-1]
return DyckWord(D)
Weight
26
Created
Sep 27, 2025 at 15:03 by Martin Rubey
Updated
Sep 27, 2025 at 15:03 by Martin Rubey
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