- FindStat

Identifier
Mp00123: Dyck paths —Barnabei-Castronuovo involution⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00228: Dyck paths —reflect parallelogram polyomino⟶ Dyck paths
Images
=>
            
              Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0005;cc-rep-3
            

            [1,0]=>[1,0]=>[1,0]=>[1,0]
[1,0,1,0]=>[1,0,1,0]=>[1,1,0,0]=>[1,0,1,0]
[1,1,0,0]=>[1,1,0,0]=>[1,0,1,0]=>[1,1,0,0]
[1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,1,0,1,0,0]=>[1,0,1,0,1,0]
[1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[1,1,0,1,0,0]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[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]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[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]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
          
Map
Barnabei-Castronuovo involution
Description
The Barnabei-Castronuovo Schützenberger involution on Dyck paths.
The image of a Dyck path is obtained by reversing the canonical decompositions of the two halves of the Dyck path. More precisely, let $D_1, 1, D_2, 1, \dots$ be the canonical decomposition of the first half, then the canonical decomposition of the first half of the image is $\dots, 1, D_2, 1, D_1$.
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
Map
reflect parallelogram polyomino
Description
Reflect the corresponding parallelogram polyomino, such that the first column becomes the first row.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.