Statistical Inference — unbiasedness of an indicator-based binomial estimator

Let $x_1, x_2, x_3, …, x_m$ denote a random sample from a binomial $B(n, p)$ distribution. Define a statistic $u = \begin{cases}\frac{1}{2n}, & \text{if } x_1 + x_2 = 1 \ 0, & \text{otherwise}\end{cases}$. Which of the following statements is/are correct? I. $u$ is an unbiased estimator of $\frac{p(1-p)}{n}$. II. $u$ is a uniformly minimum variance unbiased estimator of $p$. III. $\sum_{i=1}^{m}x_i$ is a complete sufficient statistic for $p$. Select the answer using the code given below.