Expected Increase

Let $X_1,X_2,\dots$ be a sequence of IID random variables with some continuous PDF $f(x)$. Let $N$ be the time at which the sequence stops decreasing i.e. the first value $n$ such that $X_1 \geq X_2 \geq \dots \geq X_{n-1}$ but $X_{n-1} < X_{n}$. Find $\ln(\mathbb{E}[N])$.