Maximize the NOSS

You are given a sequence of positive integers $a_1, a_2, \ldots, a_N$. You may change up to two elements of this sequence, each of them to any positive integer (not necessarily the same for two elements). Let's denote the resulting sequence by $b_1, b_2, \ldots, b_N$. Consider all $2^N$ subsequences of $b_1, b_2, \ldots, b_N$. For each subsequence, compute the sum of its elements ($0$ for the emp