Bias and unbiasedness of $e^{2\bar X}$

Let $x_1,x_2,\dots,x_n$ be a random sample from $N(\theta,\sigma^{2})$ distribution, $\sigma^{2}$ is known, $\theta$ is unknown. Which of the following statements is/are correct?

I. The MLE of $e^{2\theta}$ is $e^{2\bar x}$ with bias $e^{\frac{2\sigma^2}{n}}-1$.

II. An unbiased estimator of $e^{2\theta}$ is $e^{2\bar x-\frac{2\sigma^2}{n}}$.