Design an efficient algorithm that takes as input three sequences X, Y , and Z of length m, n, and p, respectively and returns the longest common subsequence of X, Y , and Z. Prove the correctness of your algorithm and analyze its worst-case running time.

Note that W is a common subsequence of X, Y , and Z if and only if W is a subsequence of X, W is a subsequence of Y , and W is a subsequence of Z.