# Problem Description
This is a digital clock mirroring problem where:
- Input is a time string in "xx:xx" format (24-hour format)
- The time needs to be transformed by mirroring it horizontally
- We need to determine if the resulting mirrored time is valid
- The function should return true if the mirrored result is a valid time, false otherwise

# Visual Facts
1. The image shows four examples of time mirroring:
   - "05:11" → "11:20" (Valid time)
   - "47:11" → "11:□□" (Invalid number for 7 and 4)
   - "69:30" → "0□:□□" (Invalid number for 3, 6 and 9)
   - "08:20" → "05:80" (Invalid time)

2. The mirroring operation is performed across a vertical axis
3. Each digit is displayed in seven-segment display format
4. The colon ":" remains in the same position after mirroring
5. The image marks invalid results with red boxes around problematic digits
6. Only one example is marked as "Valid Time"

# Visual Patterns
1. Digit Mirroring Rules:
   - 0 mirrors to 0
   - 1 mirrors to 1
   - 2 mirrors to 5
   - 5 mirrors to 2
   - 8 mirrors to 8
   - The other digits become invalid when mirrored

2. Time Validity Rules:
   - Hours must be between 00-23
   - Minutes must be between 00-59
   - Any result containing invalid digits or exceeding these ranges makes the entire time invalid

3. Transformation Pattern:
   - The first two digits become the last two digits in reverse
   - The last two digits become the first two digits in reverse
   - Each individual digit is mirrored according to the mirroring rules

4. Invalidation Conditions:
   - Numbers containing digits that don't have valid mirror images
   - Times where mirrored hours exceed 23
   - Times where mirrored minutes exceed 59

# Solution
def solution(input_s: str) -> bool:
    """
    Determines if the input string represents a valid time for the operations.

    Args:
        input_s: A string in "HH:MM" format (e.g. "10:53") representing a time.

    Returns:
        bool: True if the time is valid for the operations, False otherwise.
    """
    # Define the mapping of digits for mirroring
    mirror_map = {
        '0': '0',
        '1': '1',
        '2': '5',
        '5': '2',
        '8': '8'
    }

    # Split the input time into hours and minutes
    hours, minutes = input_s.split(":")

    # Check if all characters are valid for mirroring
    if any(char not in mirror_map for char in hours + minutes):
        return False

    # Mirror the hours and minutes
    mirrored_hours = mirror_map[minutes[1]] + mirror_map[minutes[0]]
    mirrored_minutes = mirror_map[hours[1]] + mirror_map[hours[0]]

    # Convert mirrored values to integers
    try:
        mirrored_hours = int(mirrored_hours)
        mirrored_minutes = int(mirrored_minutes)
    except ValueError:
        return False

    # Check if the mirrored time is valid
    if 0 <= mirrored_hours < 24 and 0 <= mirrored_minutes < 60:
        return True

    return False


# Test Script
def test():
    test_cases = [
        # Valid cases
        ("05:01", True),
        ("00:00", True),
        ("11:11", True),
        ("08:20", False),
        ("02:58", False),
        ("12:34", False),
        ("06:45", False),
        ("13:37", False),
        ("24:00", False), 
        ("00:60", False),
    ]

    for i, (input_s, expected_output) in enumerate(test_cases):
        try:
            output = solution(input_s)
        except Exception as e:
            error_message = (
                f"An exception occurred while running the test case:\n"
                f"`input_s`: {input_s}\n\n"
                f"Exception: '{str(e)}'"
            )
            assert False, error_message

        if output != expected_output:
            error_message = (
                f"The following Test Case failed:\n"
                f"`input_s`: {input_s}\n\n"
                f"Actual Output: {output}\n"
                f"Expected Output: {expected_output}"
            )
            assert False, error_message

test()