Let $Y_1,...,Y_n$~Ber(p). Determine if $\hat{p_2}^2=\bar{Y}^2$ is a consistent estimator of $p^2$.

Question

Let $Y_1,...,Y_n$~Ber(p). Determine if $\hat{p_2}^2=\bar{Y}^2$ is a consistent estimator of $p^2$.So, first I tried to see if $\hat{p_2}^2$ was unbiased.
It follows $E(\hat{p_2}^2)=E(\bar{Y}^2)=Var(\bar{Y})+[E(\bar{Y})]^2=\frac{p(1-p)}{n}+p^2$. Therefore,$Bias(\hat{p_2}^2)=\frac{p(1-p)}{n}$. Now, I want to show consistency. Thus, I will show that the MSE converges to $0$ as n tends to infinity. The $MSE=Bias^2 +Var(\hat{p_2}^2)$. It is clear that $Bias^2=[\frac{p(1-p)}{n}]^2.$ We can rewrite $MSE=[\frac{p(1-p)}{n}]^2+Var(\bar{Y}^2)$. Now, this is the part I am having difficulty with. How can I solve for $Var(\bar{Y}^2)$.