Young naturalist Bill studies ants in school. His ants feed on plant-louses that live on apple trees. Each ant colony needs its own apple tree to feed itself.Bill has a map with coordinates of n
ant colonies and n
apple trees. He knows that ants travel from their colony to their feeding places and back using chemically tagged routes. The routes cannot intersect each other or ants will get confused and get to the wrong colony or tree, thus spurring a war between colonies.Bill would like to connect each ant colony to a single apple tree so that all n
routes are non-intersecting straight lines. In this problem such connection is always possible. Your task is to write a program that finds such connection.