Link is playing nim game with fried-chicken. If you don't know this game, here're the rules:
There are two players in this game, called Alice and Bob. The game starts with

piles of stones, the

-th pile contains

stones.
Alice and Bob take turns to play this game, Alice goes first. In each turn, the player should choose one pile of stones, and remove
)
stones from that pile. The player who can not operate loses.
Obviously, one of Alice and Bob has a winning strategy. If one player has a winning strategy, he or she wants to win in minimum turns. If one player will lose, he or she wants to lose in maximum turns.
Now, fried-chicken wonders, when both players uses the best strategy:
How many turns will take before the game ends?
How many kinds of operations can Alice do in the first turn under the restrictions above?