Chef and the Feast

Chef has prepared a feast with N dishes for you. You like Chef's cooking, and so you want to eat all the dishes he has prepared for you. You are also given an array A of size N, where Ai represents the happiness you get by eating the i-th dish.You will eat all the dishes in a series of steps. In each step, you pick a non empty subset of the remaining dishes and eat them. The happiness you get from