def normalize_interval(interval: int) -> int:
    """Return a normalized interval.

    Normalized intervals:
       1: Monthly   (every month)
       3: Quarterly (every three months)
       6: Biannual  (two times a year)
      12: Annual    (once a year)
    """

    if interval < 1 or interval > 12:
        raise ValueError("interval must be within 1-12-month range")

    # start (exclusive) / end (inclusive)
    normalized_intervals = {
        1: (0, 1),
        3: (1, 3),
        6: (3, 6),
        12: (6, 12)
    }

    for normalized_interval, (start, end) in normalized_intervals.items():
        if start < interval <= end:
            return normalized_interval

    assert False