- FindStat

Identifier
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00228: Dyck paths —reflect parallelogram polyomino⟶ Dyck paths
Images
=>
            
              Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2
            

            [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]=>[1,1,0,0]
[1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[1,0,1,0,1,0]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]
[1,1,0,1,0,0]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0]
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[1,1,0,1,0,0]
[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0]=>[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]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[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]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
          
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Map
reflect parallelogram polyomino
Description
Reflect the corresponding parallelogram polyomino, such that the first column becomes the first row.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.