A group of 2n 1 routers are interconnected in a centralized binary tree, with a router at each tree node. Router i communicates with router u by sending a message to the root of the tree. The root then sends the message back down to v. Derive an expression for the average number of hops per message for a router to communicate with another router. You do not have to simplify the expression derived. Hint. Use the height of a router from the root the tree.