from collections import defaultdict
    
    n = len(p)
    m = len(y)
    
    # Prepare events for cloud coverage
    cloud_start = []
    cloud_end = []
    for i in range(m):
        cloud_start.append((y[i] - r[i], i))
        cloud_end.append((y[i] + r[i], i))
    
    cloud_start.sort()
    cloud_end.sort()
    
    # Pair towns with their populations and sort by location
    towns = sorted([[x[i], p[i], -1] for i in range(n)], key=lambda t: t[0])
    
    active_clouds = set()
    cloud_start_i, cloud_end_i = 0, 0
    
    cloud_populations = defaultdict(int)
    free_population = 0
    
    for i in range(n):
        town_loc = towns[i][0]
        
        # Add clouds starting before or at town location
        while cloud_start_i < m and cloud_start[cloud_start_i][0] <= town_loc:
            active_clouds.add(cloud_start[cloud_start_i][1])
            cloud_start_i += 1
        
        # Remove clouds ending before town location
        while cloud_end_i < m and cloud_end[cloud_end_i][0] < town_loc:
            active_clouds.discard(cloud_end[cloud_end_i][1])
            cloud_end_i += 1
        
        if len(active_clouds) == 0:
            # Town is sunny
            free_population += towns[i][1]
        elif len(active_clouds) == 1:
            # Town covered by exactly one cloud
            c = next(iter(active_clouds))
            cloud_populations[c] += towns[i][1]
    
    # The maximum number of sunny people after removing one cloud
    max_cloud_pop = max(cloud_populations.values(), default=0)
    return free_population + max_cloud_pop