The Last Sweet Game

Alice and Bob have just bought a total of n sweets from the sweet shop , and are going to eat them . Now , since both Alice and Bob are very kind ,they both want the other person to eat the last sweet. So , Alice and Bob decide to play a game. On each person's turn, they will eat k sweets such that k is a square number ( and $1 \leq k \leq$ number of leftover sweets ) . Given that Alice starts th