HINT: For i = 1 , . . . ,n, let S[i] be the max sum ending with A[i] while allowing size-1 gaps. Derive a recurrence for S[i] Problem 4. Max sum with 1-gaps Given a length- n array of integers A[1n], we would like to find maximum sum which could be obtained by adding elements in a subsequence of A if we are allowed to start anywhere in A but once we start, we can either take the element after the previously selected element or the one after, i.e, gaps of length at most 1 are allowed in the subsequence. More formally, given A find the maximum S such that there is an integer 0mn and indices 1i1<.