Problem 3. You are given an unsorted array A[1:n] of n distinct positive integers. Design an algorithm that in O(n+M) worst-case time, where M is the maximum possible integer within A finds the h-index of A. The h-index is defined as the maximum integer h such that A[1:n] has at least h indices whose entry is at least h. ( 25 points) Remember to separately write your algorithm (10 points), the proof of correctness ( 10 points), and runtime analysis ( 5 points). Example. For n=8 and A=[9,8,70,30,2,7,4,5] the correct answer is 5 (because the largest integer, h, such that h of the integers in A are at least h is 5 ). Bonus part. If instead of an O(n+M) worst-case time algorithm, you design an algorithm with worst-case runtime of O(n), i.e., with no dependence on M, you receive +5 extra credit points