Puppy and Catchers

Today, puppy Tuzik is going to a new dog cinema. He has already left his home and just realised that he forgot his dog-collar! This is a real problem because the city is filled with catchers looking for stray dogs. A city where Tuzik lives in can be considered as an infinite grid, where each cell has exactly four neighbouring cells: those sharing a common side with the cell. Such a property of th