Suppose that n files having lengths L1, L2,, Ln are stored on a tape. If the files are stored in the order of i1, i2, ., in, then the time to retrieve file ik is Tk = E-1 Li,. The average retrieval time is defined as E-1 Tk. Design a greedy algorithm for determining the order of the n files on a tape so as to minimize the average retrieval time. Show that your algorithm is optimal by stating and proving the greedy choice property and the optimal substructure property.