How do I compute, in O(n) time, a convex hull of a set of points which are sorted by x-coordinate?

I read about algorithms to compute convex hulls. Most of them take O(n*log(n)) time, where n is the number of input points.

Let S = {p_1, p_2, ..., p_n} be a set of points which are sorted by x-coordinates, that is, p_1.x <= p_2.x <= ... <= p_n.x.

I have to describe an algorithm that computes the convex hull of S, CH(S), in O(n) time. Additionally, I also have to analyze the running time of the algorithm.