Suppose that you are given an unparenthesized mathematical expression containing n numbers, where the only operators are + and , as shown here: 4 + 3 2 5 + 1 6 + 7 You can change the value of the expression by adding parentheses in different positions. For example: 4 + 3 2 5 + 1 6 + 7 = 2 (4 + 3 (2 5)) + (1 6) + 7 = 12 (4 + (3 2)) (5 + 1) (6 + 7) = 14 For the purposes of this problem, we'll assume you can only put parentheses immediately before and immediately after a number, so that you couldn't interpret the expression multiplicatively as 4 + 3 (2) (5) + 1 6 + 7 = 36 Design an algorithm that, given an unparenthesized expression using only + and , determines the maximum possible value the expression can take when parentheses are added in. Your algorithm should run in time polynomial in n. Then: Describe your algorithm. Prove that your algorithm finds the maximum possible value the expression can take. Prove that your algorithm runs time polynomial in n.