You are planning to attend a music and arts festival that hosts multiple events that you are interested in, but many of these events may (partially) overlap. Assume that you get some value v_i from attending an event i, but you get this value only if you are there for the whole duration of the event; you get no value if you have to miss part of it. Given such a set of events, E, your goal is to choose a non-overlapping set of events, , to attend, aiming to maximize your total value. More formally, for each event you have a start time s_i and a finish time f_i and you want to design an algorithm that runs in time O(n log n), where n is the total number of events, and the output of the algorithm is a set such that for any two events we have or (no overlap) and the total value is maximized. Provide detailed pseudocode for your proposed algorithm (you can use sorting as a subroutine), as well as an explanation regarding why it works and why its running time is indeed O(n log n).