MLE of a two-sided power density

Let $X_1,X_2,…,X_n$ be a random sample of size $n$ ($\ge 2$) from a population having probability density function $f(x;\theta) = \begin{cases} \theta(2x)^{\theta-1} & \text{if } 0 < x \le \frac12 \ \theta(2-2x)^{\theta-1} & \text{if } \frac12 < x \le 1 \ 0 & \text{otherwise,} \end{cases}$ where $\theta > 0$ is an unknown parameter. Then which one of the following is a maximum likelihood estimator of $\theta$?