Most powerful test between two symmetric densities

Let $X_1,X_2,…,X_n$ be a random sample from a continuous distribution with the probability density function $f(x)$. To test the hypothesis

$$H_0:f(x)=\frac1{\sqrt\pi}e^{-x^2},-\infty<x<\infty \text{ against } H_1:f(x)=e^{-2|x|},-\infty<x<\infty,$$

the rejection region of the most powerful size $\alpha$ test is of the form, for some $c>0$,