Winner Mindset

Gabe has a gambling addiction and a winner's mindset. He plays a game where the casino picks out one integer uniformly at random from the set $\{1,2,\dots,n+2\}$ on the $n$th round of the game. If he guesses the integer correctly, he wins. Gabe plays the game repeatedly until he wins. Let $N$ be the number of rounds that Gabe plays. Find $\mathbb{E}\left[ N \right]$. If this is infinite, enter $-1$.