The transportation ministry has just decided to pay $80$ companies to repair $2400$ roads. These roads connects $100$ cities. Each road is between two cities and there is at most one road between any two cities. Each company must repair exactly $30$ roads, and each road is repaired by exactly one company. For a company to repair a road, it is necessary for the company to set up stations at the both cities on its endpoints. Prove that there are at least $8$ companies stationed at one city.