from collections import defaultdict, deque

def roadsAndLibraries(n, c_lib, c_road, cities):
    """
    Cost 1 : one lib in each city
    Formula: c_lib * n
    
    Cost 2 : one lib per group of connected cities + connecting roads
    Formula: c_lib * k + c_road * (n - k), where k is number of groups
    
    If c_lib <= c_road, Cost 1 is lower; otherwise, Cost 2 is.
    """
    # Return Cost 1
    if c_lib <= c_road:
        return c_lib * n


    # Calculate Cost 2 below:
    
    # Initialize number of groups
    k = 0
    
    # Record direct connections for each city
    connections = defaultdict(set)
    for a, b in cities:
        connections[a].add(b)
        connections[b].add(a)
    
    # Track visited cities
    visited = [False] * (n + 1)
    
    # Identify connected components (groups of cities)
    for city in range(1, n + 1):
        if visited[city]:
            continue
        
        # Start a new group
        visited[city] = True
        k += 1
        
        # BFS to mark all cities in this group
        dq = deque([city])
        while dq:
            curr_city = dq.popleft()
            for linked_city in connections[curr_city]:
                if not visited[linked_city]:
                    visited[linked_city] = True
                    dq.append(linked_city)
                    
    # Return Cost 2
    return c_lib * k + c_road * (n - k)