Running Maximum

Given a sequence of values ${a_k}_(k=1)^n$ , the running maxima are the sequence of values ${max(a_1,...,a_k)}_(k=1)^n$ . So, for example, given a sequence , the running maxima are . The unique values of the running maximum are sometimes known as high-water marks, so the high water marks for the above sequence are , which occur at , 2, 3, 4, and 8.