def roadsAndLibraries(n, c_lib, c_road, cities):
    # if libraries are cheaper we dont need to build roads
    if c_lib < c_road:
        return c_lib * n
    visited = [0] * n
    transport_stack = []
    cities_map = defaultdict(set)
    islands = 0
    # create a graph of road destinations
    # add both ways for bidirectional paths
    for i in cities:
        cities_map[i[0]-1].add(i[1]-1)
        cities_map[i[1]-1].add(i[0]-1)
    # iterate over the list of road edges
    for city in cities_map:
        if visited[city]:
            continue
        # if we have never been at this city before it is a new island
        islands += 1
        transport_stack.append(city)
        # travel the path of the road
        # if we find a new city add it to the stack
        while transport_stack:
            new_destination = transport_stack.pop(-1)
            if not visited[new_destination]:
                visited[new_destination] = 1
                if new_destination in cities_map:
                    for destination in cities_map[new_destination]:
                        if not visited[destination]:
                            transport_stack.append(destination)
		# if we nevered visited after looking at all the roads then it must be an island 
    islands += n - sum(visited)
    roads = n - islands
    # we need 1 road per city and 1 library per island
    result = (roads * c_road) + (c_lib * islands)
    return result