def roadsAndLibraries(n, c_lib, c_road, cities):
    # If library cost is less than or equal to road cost, build a library in each city
    if c_lib <= c_road:
        return c_lib * n
    
    # Initialize disjoint set (union-find) structures
    root = list(range(n + 1))
    rank = [0] * (n + 1)
    
    def find_root(i):
        if root[i] != i:
            root[i] = find_root(root[i])  # Path compression
        return root[i]
    
    def union(a, b):
        i, j = find_root(a), find_root(b)
        if i != j:
            # Union by rank
            if rank[i] > rank[j]:
                root[j] = i
            elif rank[i] < rank[j]:
                root[i] = j
            else:
                root[j] = i
                rank[i] += 1
    
    # Union all connected cities
    for a, b in cities:
        union(a, b)
    
    # Count connected components
    k = sum(1 for city in range(1, n + 1) if root[city] == city)
    
    # Calculate total cost: one library per component + roads for remaining cities
    return c_lib * k + c_road * (n - k)