As we all know, eating breakfast regularly is good for our health. As several new restaurants were opened in the campus, Miao decides that she will get up early and enjoy a nice breakfast every morning.
Noodles, porridge, bread, eggs... there are many kinds of food served in the morning. For each kind of food, there may be several dishes left, each contains different amount of sugar, fat and proteins. Of course, maybe for some kinds of food there are no dishes left, because Miao gets up late and the food of these kinds are sold out!
Miao will order some of the dishes left, and eat all of them without wasting. If Miao has totally uptake \(S\) grams of sugar, \(F\) grams of fat and \(P\) grams of proteins, she will have a happiness value of \(S\cdot F\cdot P\).
However, Miao would not order two dishes of the same kind, that is, she will order at most one dish for each kind of food.
Can you help Miao to calculate the maximum happiness value she can have?