A group of herbalists has decided to move to a new village on the boundary of a huge forest.
The arrangement of houses and paths in the village turned out to be a major problem: Many of the herbalists are friends and want to visit each other often, so they want to have a path between their houses. However the herbalists are also known for quarreling with everyone else. To avoid the chance of meeting with someone they do not like, it is required that no two paths intersect - there should be no crossroads in the village (And of course also no other means of crossing; overpasses spoil the scenery and underpasses destroy the root systems of precious herbs.) . Each herbalist also wants to be able to visit the forest, of course without having to cross any path - i.e., it is also necessary to make it possible to get from each house to "infinity" without crossing a path.
You are given a description of the relationships between herbalists. Your task is to decide whether such an ideal village can be built.