Suppose that a random variable X has the Poisson distribution with unknown mean ( > 0). Show that the only unbiased estimator of e2

Suppose that a random variable X has the Poisson distribution with unknown mean λ (λ > 0). Show that the only unbiased estimator of e−2λ is the estimator δ(X) such that δ(X) = 1 if X is an even integer and δ(X) = −1 if X is an odd integer.