Power of a test for a difference of normal means

Let $X_1,X_2,X_3,X_4$ be a random sample from $N(\theta_1,\sigma^2)$ distribution and $Y_1,Y_2,Y_3,Y_4$ be a random sample from $N(\theta_2,\sigma^2)$ distribution, where $\theta_1,\theta_2\in(-\infty,\infty)$ and $\sigma>0$. Further suppose that the two random samples are independent. For testing the null hypothesis $H_0:\theta_1=\theta_2$ against the alternative hypothesis $H_1:\theta_1>\theta_2$, suppose that a test $\psi$ rejects $H_0$ if and only if $\sum_{i=1}^4X_i>\sum_{j=1}^4Y_j$. The power of the test $\psi$ at $\theta_1=1+\sqrt2$, $\theta_2=1$ and $\sigma^2=4$ is