Let S = {a1, a2, a3, a4, a5} be a set of five distinct memory addresses (each address is 32 bit long). We say that a memory access sequence R is valid if the following conditions hold:

(a) R contains exactly 10 elements;

(b) Each element of R belongs to S;

(c) Each element of S appears in R at least one time. For example, R = (a1, a2, a1, a3, a1, a2, a1, a3, a4, a5) is a valid sequence.

(a) What is the minimum number of misses for any valid sequence R? Give an example of S and R that result in the minimum number of misses (use hexadecimal notation).

(b) What is the maximum number of misses that a valid sequence R might have? Give an example of S and R that result in the maximum number of misses (use hexadecimal notation).