475.When the Sequence Stops Falling

Let $X_1, X_2, \dots$ be IID with a continuous distribution, and let $N$ be the first index $n$ such that $X_1 \ge X_2 \ge \cdots \ge X_{n-1}$ but $X_{n-1} < X_n$ — the time the sequence first stops decreasing. Find $E[N]$.