In the ancient lands of Granitus, two rival architects, Alicius and Bobius, are competing in a legendary contest. The plains are scattered with $$$N$$$ stone towers, each varying in height. The architects take turns with a unique challenge: in each turn, the player in turn must choose a positive integer $$$X$$$ and remove $$$X$$$ stones from each tower that still has stones. The chosen $$$X$$$ cannot exceed the number of stones in the shortest tower that still has stones remaining. A player loses the game when he cannot make a valid move.

Given $$$N$$$ towers of stones, determine which architect, Alicius or Bobius, will win if both play optimally. Alicius always takes the first turn.

Your task is to predict the winner of the game assuming optimal play by both competitors.