Under the assumption of the Neyman-Pearson Lemma, for a simple hypothesis test $H_0: \theta=\theta_0$ vs $H_1: \theta=\theta_1$, if the likelihood ratio $\Lambda(x) = L(\theta_0|x)/L(\theta_1|x)$ is a strictly monotonic function of a sufficient statistic $T(x)$, what can be said about the rejection region?