(7.13) Given two sequences S1 and S2 on a alphabet set , and a scoring function f:, the local alignment problem is to find a subsequence S1 from S1 and a subsequence S2 from S2 such that the score obtained by aligning S1 and S2 is the highest, among all possible subsequences of S1 and S2. Use the dynamic programming strategy to design an algorithm of O(nm) time or better for this problem, where n and m denote the lengths of S1 and S2 respectively