Draws to beat a hidden uniform

Let $U \sim \text{Uniform}(0,1)$, and independently let $X_1, X_2, \dots \sim \text{Uniform}(0,1)$ be i.i.d. Define $N = \min\{\,n : X_n > U\,\}$, the first index whose draw exceeds $U$. Compute $\mathbb{E}[N]$ (enter $-1$ if it is infinite).