Exercise 4.2. Given a sequence of n numbers, a1,,an, we want to find the longest subsequence of (not necessarily consecutive) decreasing values. For example, for the sequence a=(10,6,9,22,3,2,7,5), a possible (but not unique) solution is (10,9,7,5) of length 4. Formulate a dynamic programming algorithm that solves this problem. What is the running time of the algorithm? Is this a polynomial in the input size