Long tail distributions

Question

I have just started to study sub-exponential distributions. I wonder how to prove this statement : Let $X_1,\dots,X_n$ are independent random variables with distributions $F_1,\dots,F_n$ respectively. Suppose $F_1,\dots,F_n$ are all long tailed. Then, the distribution of $\max(X_1,\dots,X_n)$ is long tailed.