Suppose you have n rooms that you would like to connect in a communication network in one of the dormitories of Flash University. You have modeled the problem using a connected, undirected graph, G, where each of the n vertices in G is a room and each of the m edges in G is a possible connection that you can form by running a cable between the rooms represented by the end vertices of that edge. In this case, however, there are only two kinds of cables that you may possibly use, a 12-foot cable, which costs $10 and is sufficient to connect some pairs of rooms, and a 50-foot cable, which costs $30 and can be used to connect pairs of rooms that are farther apart. Describe an algorithm for finding a minimum-cost spanning tree for G in O(n + m) time.