Prove that f is continuous at Xo, iff......?

Let f be a real-valued function with dom(f) R, prove that f is continuous at Xo iff, for every monotonic sequence (Xn) in dom(f) converging to Xo, we have limf(X)=f(Xo). (Hint: Theorem: Every sequence (Sn) has a monotonic subsequence.)