There once live a king who liked chess. He had a palace whose floor plan mimicked an 8x8 chessboard, with each of the 64 rooms having a door in each of its four walls. Originally, all the floors in all the rooms were painted white. Then the king ordered the flooors to be repainted so that they alternated like the squares of a chessboard. To do this, his painter had to walk through the palace repainting floors in ALL the rooms he visited. If he walked into a white room, he must repaint it black. If he walked into a black room, he must repainted white. The painter was allowed to exit the palace and reenter it at another door. What is the best way to execute the order? Namely, what is the path that painter should have to pain the least amount of times and have the chessboard pattern complete?