One hundred million cities lie on Planet MO. Initially, there are no air routes between any two cities. Now an airline company comes. It plans to establish 5050 two-way routes, each route connects two different cities, and no two routes connect the same two cities. The "degree" of a city is defined to be the number of routes departing from that city. The "benefit" of a route is the product of the "degrees" of the two cities it connects.
Find the maximum possible value of the sum of the benefits of these 5050 routes. combinatoricsgraph theoryChina