- FindStat

Identifier
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
Images
=>
            
              Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2
            

            [1,0]=>[1,1,0,0]=>[1,0,1,0]
[1,0,1,0]=>[1,1,0,1,0,0]=>[1,0,1,0,1,0]
[1,1,0,0]=>[1,1,1,0,0,0]=>[1,0,1,1,0,0]
[1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]
[1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]
[1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0]
[1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
          
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.