There are two kinds of professional actors: Mainstream actors (i.e., actors who will generally be a part of big-budget studio movies) and Indie actors (i.e., actors who will generally be a part of smaller, independent movies). Between any pair of actors, there may or may not be a rivalry. Suppose we have k actors and we have a list of r pairs of actors for which there are rivalries. Give an algorithm that determines whether it is possible to designate some of the actors as mainstream or indie such that each rivalry is between a mainstream actor and an indie actor. If it is possible to perform such a designation, your algorithm should produce it. The algorithm should run in O(k+r) time justify that this is true.