Identifier
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]
[1,0,1,0]=>[1,0,1,0]
[1,1,0,0]=>[1,0,1,0]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[1,0,1,1,0,0]=>[1,0,1,0,1,0]
[1,1,0,0,1,0]=>[1,0,1,0,1,0]
[1,1,0,1,0,0]=>[1,0,1,0,1,0]
[1,1,1,0,0,0]=>[1,0,1,0,1,0]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
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(only identities of compositions of up to three maps are shown)
Description
Send a Dyck path to its peeled Dyck path.
References
[1] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations MathSciNet:3153083
Properties
graded
Sage code
def mapping(D):
n = D.semilength()
area = D.to_area_sequence()
new_area = []
touch_sequences = []
touches = []
for i in range(n-1):
if area[i+1] == 0:
touches.append(i+1)
if len(touches) > 1:
touch_sequences.append(touches)
touches = []
elif area[i] == 0:
touches = []
new_area.append(0)
elif area[i+1] == 1:
new_area.append(0)
touches.append(i+1)
else:
new_area.append(area[i+1]-2)
new_area.append(0)
if area[n - 1] != 0:
touches.append(n)
if len(touches) > 1:
touch_sequences.append(touches)
return DyckWords().from_area_sequence(new_area)
Weight
51
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
May 11, 2021 at 15:01 by Martin Rubey
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