def format_time(time: str) -> str:
    """
    Convert Yale API times to 24-hour, full format.

    Parameters
    ----------
    time:
        A time from the Yale API 'meeting_html' field.

    Returns
    -------
    time:
        formatted time
    """
    time_stripped = time[:-2]

    if ":" in time_stripped:

        hour = time_stripped.split(":")[0]
        minute = time_stripped.split(":")[1]

    else:

        hour = time_stripped
        minute = "00"

    hour_num = int(hour)

    if time[-2:] == "am" and hour_num == 12:
        hour_num = 0

    elif time[-2:] == "pm" and 1 <= hour_num <= 11:
        hour_num = hour_num + 12

    hour = str(hour_num)

    return hour + ":" + minute