MLE and MOM for piecewise uniform

Let $0.2, 1.2, 1.4, 0.3, 0.9, 0.7$ be the observed values of a random sample of size $6$ from a continuous distribution with the probability density function $$f(x)=\begin{cases} 1, & 0 < x \le \frac{1}{2} \ \frac{1}{2\theta-1}, & \frac{1}{2} < x \le \theta \ 0, & \text{otherwise,} \end{cases}$$ where $\theta > \frac{1}{2}$ is unknown. Then the maximum likelihood estimate and the method of moments estimate of $\theta$, respectively, are