Statement

Santa Claus is coming to town! In Venice, specifically. This city represents a challenge for Santa: in fact, it can be seen as a set of N small islands connected by K navigable canals. Each canal connects two islands and has a specific width: only a gondola which is narrower (or equally wide) than the canal is able to traverse it. Santa wants to build a network for gift dispatching by renting gondolas in some of the islands, so that every island can be reached by at least one gondola. Notice that if an island is not connected to other islands, Santa will still need to rent a gondola for that island: the presents need to be dispatched through the island by boat. As anyone that ever visited Venice knows, renting these boats can be quite expensive! You are given the description of every canal (width and islands connected), and a list of all the available gondola widths...