Sufficiency of $T$ and $S_0^2$

Let $x_1,x_2,\dots,x_n$ be a random sample from a normal $(\mu,\theta)$ and $\mu$ is known. Which of the following statements is/are correct?

I. $T=\sum_{i=1}^n(x_i-\mu)^2$ is sufficient statistic for $\theta$.

II. $S_0^2=\dfrac1n\sum_{i=1}^n(x_i-\mu)^2$ is sufficient statistic for $\theta$.