5. [10 pts] You are given a one-dimensional array that may contain both positive and negative integers. The goal is to find the sum of contiguous (ie. next to one another, in sequence) subarray of numbers which has the largest sum. For example, if the given array is -2,-5, 6, -2,-3,1,5, -6], then the maximum subarray, marked in boldface, has sum equal to 7. On problem set 3, we saw that this problem had an O(n log n) divide-and-conquer solution, but faster algorithms exist. Give an O(n) dynamic programming algorithm for this problem and argue for its correctness