Question: Given a length-n array of integers A[1...n], we would like to find maximum sum which could be obtained by adding elements in a subsequence

Given a length-n array of integers A[1...n], we would like to find maximum sum which could be obtained by

Given a length-n array of integers A[1...n], 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 0 m n and indices 1

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