Simultaneous Nim

Chef is a famous Nim player. He has his own set of N heaps, and the i-th heap contains Ai stones. What is so special about this set is that with this set of stones Chef always wins when he's moving second. Chef's friends don't know the math behind the game at all, but the fact that Chef is playing with the same set of stones all the time seems suspicious to them. To prove that he's a really good