UMVUE of the parameter of a double exponential density

Let $X_1,…,X_n$ ($n>2$) be a random sample from a population with probability density function

$$f(x|\theta)=\frac\theta2e^{-\theta|x|},\quad-\infty<x<\infty, \theta>0.$$

Then a uniformly minimum variance unbiased estimator of $\theta$ is