Sufficient statistics for a Bernoulli parameter

Let $x_1,x_2,\dots,x_n$ be a random sample from a Bernoulli population with parameter $p$, where $0<p<1$. Which of the following is/are sufficient statistic(s) for $p$?

I. $\dfrac1n\sum_{i=1}^n x_i$

II. $\dfrac1n\sum_{i=1}^n(x_i-\bar x)^2$

III. $\sum_{i=1}^n x_i$