Suppose there are n people in a group, each aware of a scandal no one 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, on the first call, two people share information, so by the end of the call, each of these people knows 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 the scandals. use mathematical induction to prove that g(n)< =2n-4 forn> =4.[hint: in the inductive step, have a new person call a particularperson at the start and at the end.]