Let the page reference and the working set window be c c d b c e c e a d and 4, respectively. The initial working set at time $$t = 0$$ contains the pages {a, d, e}, where a was referenced at time $$t = 0, d$$ was referenced at time $$t = -1,$$ and $$e$$ was referenced at time $$t = -2.$$ Determine the total number of page faults and the average number of page frames used by computing the working set at each reference.