from collections import defaultdict

def build_graph(w, e, connections):
    # Initialize an empty graph
    graph = defaultdict(list)
    
    # Add all western stations to the graph
    for i in range(w):
        graph[i] = []
    
    # Add all eastern stations to the graph
    for i in range(w, w+e):
        graph[i] = []
    
    # Add connections to the graph
    for u, v in connections:
        graph[u].append(v)
        graph[v].append(u)
    
    return graph

def bfs(graph, start):
    # Initialize visited array and queue for BFS
    visited = [False] * len(graph)
    queue = []
    
    # Mark start as visited and add to queue
    visited[start] = True
    queue.append(start)
    
    # Initialize distance array
    dist = [0] * len(graph)
    
    while queue:
        # Dequeue a vertex from queue
        s = queue.pop(0)
        
        # Get all adjacent vertices of the dequeued vertex s
        # If adjacent vertex is not visited yet, then mark it visited
        # and enqueue it in the queue
        for i in graph[s]:
            if not visited[i]:
                visited[i] = True
                queue.append(i)
                
                # Update the distance of the adjacent vertex
                dist[i] = dist[s] + 1
    
    return dist

def get_average_distance(w, e, connections):
    # Build the graph
    graph = build_graph(w, e, connections)
    
    # Initialize variables for minimum and maximum distances
    min_dist = float('inf')
    max_dist = -1
    
    # Iterate over all possible pairs of start and end vertices
    for start in range(w):
        dist = bfs(graph, start)
        for end in range(w, w+e):
            if dist[end] > max_dist:
                max_dist = dist[end]
            if dist[end] < min_dist:
                min_dist = dist[end]
    
    # Calculate the average distance and return it
    total_dist = sum([sum(bfs(graph, i)) for i in range(w)])
    avg_dist = total_dist / (w*(w-1) + e*(e-1) + 2*w*e)
    
    return avg_dist, min_dist, max_dist

# Example usage
w = 4
e = 3
connections = [(0,4), (1,5), (2,6), (4,5), (5,6)]
avg_dist, min_dist, max_dist = get_average_distance(w, e, connections)
print("Average distance:", avg_dist)
print("Minimum distance:", min_dist)
print("Maximum distance:", max_dist)