NJIT decides to introduce its own coinage with three different types of coins: 1 cent, 5 cent, and 8 cents. We would like to know what is the minimum number of coins we can use if we pay for an item worth n cents. Give an efficient algorithm that if given n as input, it prints as output the minimum set of coins that has value exactly n. Analyze the time and space requirements of your algorithm. Prove its correctness. For example, you can pay an item worth 40 cents by giving five 8-cent coins; other alternatives is eight 5-cent coints, or forty 1-cent coins, or say four 8-cent, one 5-cent and three 1-centcoins.