There are people having dinner at a grand hall. One of them is known to be sick, while the other are healthy. Each minute, each person talks to one other person in the room at random. There is no limit on how many times a person talks to another person. If one is sick and one is healthy, the healthy person is infected and becomes sick. Once a person becomes sick, they are assumed to be sick for the rest of the dinner. Find the minimum amount of time (in minutes) until every person in the hall becomes sick.