The government is picking a group of people to form a committee. For security reasons, these people are randomly picked from a pool. Suppose the pool forms a weird social network such that (i) there might be multiple connected components, and (ii) each connected component is complete (or a clique). What is the minimum number of people that the government needs to pick in order to make sure that in the selected group, there exists a subset of at least 5 people that are either all mutually connected or all mutually disconnected. Briefly justify your answer.