- FindStat

Identifier
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Images
=>
            
              Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0005;cc-rep-3
            

            [1,0]=>[1,1,0,0]=>[1,1,0,0]=>[1,0,1,0]
[1,0,1,0]=>[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[1,0,1,1,0,0]
[1,1,0,0]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]
[1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]
[1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]
[1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0]
[1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]
[1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[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]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[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]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[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]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[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]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[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]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[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]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[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]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[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]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[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]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[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]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[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]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[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]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[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]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[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]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[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]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[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]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[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]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[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]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[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]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[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]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[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]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[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]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[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]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[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]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[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]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[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]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[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]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[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]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[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]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[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]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[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]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[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]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[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]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[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]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[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]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[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]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[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]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[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]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[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]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[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]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[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]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[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]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[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]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[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]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[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]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[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]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[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]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[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]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[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]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[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]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[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]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[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]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[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]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[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]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[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]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[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]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[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]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[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]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[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]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[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]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[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]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[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]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[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]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[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]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[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]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[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]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[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]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[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]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[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]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[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]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[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]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[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]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[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]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[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]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[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]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[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]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[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]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[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]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[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]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[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]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[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]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[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]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[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]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[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]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[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]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[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]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[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]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[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]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[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]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[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]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[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]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[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]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[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]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[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]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[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]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[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]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[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]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[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]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[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]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[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]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[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]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[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]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[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]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[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]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[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]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[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]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
          
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
Adin-Bagno-Roichman transformation
Description
The Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.