Write a program that implements the FIFO, LRU, and optimal $($OPT$)$ page$-$replacement algorithms presented in Section $10\mathrm{.}4.$ Have your program initially generate a random page$-$reference string where page numbers range from $0$ to $9.$ Apply the random page$-$reference string to each algorithm, and record the number of page faults incurred by each algorithm. Pass the number of page frames to the program at startup.