MLE in an exponential-of-exponential model

Let $X_{1},X_{2},…,X_{n}$ be a random sample of size $n$ $(n\ge 1)$ from a distribution with the probability density function $f(x)=\dfrac{1}{2\beta^{3}}e^{3x-\frac{e^{x}}{\beta}}$, $x\in\mathbb{R}$, where $\beta>0$ is an unknown parameter. Which one of the following is a maximum likelihood estimator of $\beta$?