2. We will address the following problem: Given a sequence of whole numbers A= x , we are interested in finding an increasing subsequence of A, S={2,} with the property that the sum of the elements in the subsequence, x , is maximized. The increasing subsequences we are examining need not be contiguous, and may not be unique. For example, consider the sequence represented by the following array: A=[3.,1,5,7,8.4.12,2,10,6,14.1.9,5,13,3,11] A maximum-sum, increasing subsequence is [3,5,7,8,12,14), which has sum 49. Develop a recursive algorithm that finds the maximum sum of all increasing subsequences of a given sequence, A, as well as the subsequence that produces this maximum sum. (10 pts) KEY IDEA: Algorithm MaxSum( Input: Output