Add 1 or 2 Game

Alice and Bob play a game. There is an integer $X$, which is initially $0$. On their turn, Alice or Bob can choose to increment $X$ by either $1$ or $2$. The game ends as soon as $X \ge N$ holds. When the game ends, Bob wins the game if $X = N$, otherwise Alice wins the game. Alice goes first, and the players alternate turns. If both players play optimally, predict the winner. ### Input -