Distribution of the Mid-Range for Uniform Samples

Let $X_1, \ldots, X_n$ be iid $\operatorname{Uniform}(0,1)$ with $n \ge 2$. The mid-range is defined as $M = \frac{X_{(1)} + X_{(n)}}{2}$. Using the joint density of $(X_{(1)}, X_{(n)})$, derive the PDF of $M$.