Once there was a king called XOR, he had a lot of land. Because of his name, he likes to play XOR games.

One day, he whimpered and wanted to establish N cities on that vast expanse of land, numbered 0, 1, 2..., N-1. He wanted to connect all the cities. If city A can reach City B through zero or one or several cities, then A and B are connected. The cost of repairing a road in City A and City B is the XOR value of number of City A and number of City B. This King XOR wanted to figure out the minimum cost for connecting all of the N cities.

Of course, like a fairy tale read as a child, there will be corresponding rewards after helping the king. If you help the king solve his problems, he will improve your ranking in the competition.