Statistical Inference — joint sufficiency for normal mean and sd

Let $x_1,x_2,…,x_n$ be a random sample from a Normal distribution $N(\mu,\sigma^2)$. Suppose both $\mu$ and $\sigma$ are unknown. Which of the following are jointly sufficient statistic for $(\mu,\sigma)$? 1. $\{\sum_{i=1}^n x_i,\sum_{i=1}^n x_i^2\}$. 2. $\{\sum_{i=1}^n x_i,\sum_{i=1}^n(x_i-\bar x)^2\}$. 3. $\{\sum_{i=1}^n x_i^2,\sum_{i=1}^n(x_i-\bar x)^2\}$. Select the correct answer using the code given below: