There are 1000 people having dinner at a grand hall. One of them is known to be sick, while the other 999 are healthy. Each minute, each person talks to one other person in the room at random. However, as everyone is social, nobody talks to people they have previously talked to. In each pair, 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 maximum amount of time (in minutes) until every person in the hall becomes sick.
