The shortest common supersequence for a pair of sequences X and Y is the shortest sequence for which both X and Y are subsequences. Specifically, given two sequences X = {x1, . . . , xm} and Y = {y1, ..., yn}, a sequence U = {u1, . . . , uk} is a common supersequence of X and Y if items can be removed from U to produce X and Y . Give an O(mn) dynamic programming algorithm to find the shortest common supersequence of sequences X and Y .