Problem 1 [20]: Given a collection S = {S, S2, ..., Sk} of k = 0(1) strings with total length Si = n, design an O(n)-time algorithm to return the number of distinct strings that occur as substrings of exactly two elements of S. For example, for S = {abaabb, abba, bbaaa}, the algorithm should return 5 (the sought set of strings is {ab, abb, bba, aa, baa}). Write the pseudo-code of your solution (excluding construction of structures introduced in lectures), prove its correctness, and analyze its complexity.