Acontiguous subsequence of a list s is a subsequence made up of consecutive elements of s. for instance, if s is 5, 15, −30, 10, −5, 40, 10, then 15, −30, 10 is a contiguous subsequence but 5, 15, 40 is not. give a linear-time algorithm for the following task: input: a list of numbers, a1, a2, . . , an. output: the contiguous subsequence of maximum sum (a subsequence of length zero has sum zero). for the preceding example, the answer would be 10, −5, 40, 10, with a sum of 55. (hint: for each j ∈ {1, 2, . . , n}, consider contiguous subsequences ending exactly at position j.)