Suppose there are n people in a group, each aware of a scandal nobody else in the group knows about. These people communicate by telephone. When two people in the group talk, they share information about all scandals each knows about. For example, after the first call, two people each know about two scandals. The gossip problem asks for G (n), the minimum number of telephone calls that are needed for all n people to learn about all of the scandals. Prove that G(n) = 2n − 4 for n ≥ 4.