from collections import defaultdict
    
    def find_cheryls_birthday(possible_dates):
        # Parse the dates into month and day
        dates = [date.split() for date in possible_dates]
        months = [month for month, day in dates]
        days = [day for month, day in dates]
    
        # Step 1: Albert knows the month and says he doesn't know the birthday
        # and that Bernard doesn't know either. This implies the month has no unique days.
        month_counts = defaultdict(int)
        day_counts = defaultdict(int)
        for month, day in dates:
            month_counts[month] += 1
            day_counts[day] += 1
    
        # Months with all days appearing more than once
        possible_months = [month for month in month_counts if all(day_counts[day] > 1 for m, day in dates if m == month)]
        filtered_dates = [date for date in dates if date[0] in possible_months]
    
        # Step 2: Bernard knows the day and now knows the birthday
        # This means the day is unique in the filtered dates
        filtered_days = defaultdict(int)
        for month, day in filtered_dates:
            filtered_days[day] += 1
        possible_days = [day for day in filtered_days if filtered_days[day] == 1]
        filtered_dates = [date for date in filtered_dates if date[1] in possible_days]
    
        # Step 3: Albert now knows the birthday, so the month must be unique in remaining dates
        possible_months = defaultdict(int)
        for month, day in filtered_dates:
            possible_months[month] += 1
        final_dates = [date for date in filtered_dates if possible_months[date[0]] == 1]
    
        # Convert back to original format
        return ' '.join(final_dates[0]) if final_dates else "No unique solution found."
    
    # Example usage:
    possible_dates = [
        "May 15", "May 16", "May 19",
        "June 17", "June 18",
        "July 14", "July 16",
        "August 14", "August 15", "August 17"
    ]
    
    birthday = find_cheryls_birthday(possible_dates)
    print(f"Cheryl's Birthday is on {birthday}.")