import sys

# function to calculate the average path length before and after connecting a western and an eastern station
def calculate_average_path_length(W, E):
    # calculate average path length before connection
    avg_length_before = ((W-1)*(W-2)//2 + (E-1)*(E-2)//2) / (W+E-2)
    
    # create adjacency matrix for complete map after connection
    graph = [[sys.maxsize for j in range(W+E)] for i in range(W+E)]
    for i in range(W):
        for j in range(i+1, W):
            graph[i][j] = graph[j][i] = 1
    for i in range(E):
        for j in range(i+1, E):
            graph[i+W][j+W] = graph[j+W][i+W] = 1
    for i in range(W):
        for j in range(E):
            graph[i][j+W] = graph[j+W][i] = 2
    
    # use Floyd-Warshall algorithm to find shortest paths between all pairs of stations
    for k in range(W+E):
        for i in range(W+E):
            for j in range(W+E):
                graph[i][j] = min(graph[i][j], graph[i][k]+graph[k][j])
                
    # calculate average path length after connection
    total_length_after = sum([sum(graph[i]) for i in range(W+E)])
    avg_length_after = total_length_after / (W*E)
    
    # return the difference between the average path length after and before connection
    return avg_length_after - avg_length_before