A young engineer designs a simple cipher based on Shannon's concept of a "product cipher". The ciphertext output, y, is generated by applying an affine cipher to the plaintext, x, to produce an intermediate result, z, and then applying another affine cipher to the immediate result, z, to produce the ciphertext output, y. This is represented mathematically as follows: z = a_1*x + b_1 mod n y = a_2 * z + b_2 mod n The pairs (a_1, b_1) and (a_2, b_2) form the key. (a) Determine an expression for the number of distinct mappings from plaintext to ciphertext in terms of n. (b) Comment on the usefulness of the approach used in the cipher