Defeating Monsters

You are playing a computer game. In the current level of the game, you have to fight $N$ monsters. The monsters will appear in order from $1$ to $N$, that is, the $i^{th}$ monster will appear after the $(i-1)^{th}$ monster. As soon as a monster appears: - You must fight with the newly appeared monster, leaving aside any other monster you were fighting with. - If you manage to kill the monster