contiguous 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 an algorithm for the following task:

Input: A list of numbers, a$1,$ a$2,...,$ an$.$

Output: The maximum sum of a contiguous subsequence $($a subsequence of length zero has sum zero$).$ The choice of selecting no elements is allowed.