CLT for the Bernoulli MLE

Let $\{Y_k\}_{k\ge 1}$ be a sequence of i.i.d. $\mathrm{Bin}(1,p)$ random variables, where $0<p<1$ is an unknown parameter. Let $\hat p_n$ be the maximum likelihood estimator of $p$ based on $Y_1,Y_2,…,Y_n$. It is claimed that: (I) $\dfrac{\hat p_n-p}{\sqrt{p(1-p)/n}}\xrightarrow{d} N(0,1)$ as $n\to\infty$. (II) $\dfrac{\hat p_n-p}{\sqrt{\hat p_n(1-\hat p_n)/n}}\xrightarrow{d} N(0,1)$ as $n\to\infty$. Which of the following statements is correct?