Statistical Inference — UMPU two-sided critical constants

Let $X_1,X_2,…,X_n$ be iid random variables with $N(\theta,1)$. The UMPU test of size $\alpha$ for testing $H_0:\theta=\theta_0$ against $H_1:\theta\ne\theta_0$ is given by $\varphi(x)=1$ if $\sum_{i=1}^n x_i<c_1$ or $\sum_{i=1}^n x_i>c_2$, and $0$ otherwise. What are the values $c_1$ and $c_2$?