def int_to_roman(n):
    if type(n) is not int or n < 1 or n > 3999:
        raise ValueError("n must be an integer in the range 1..3999")
    pairs = (
        (1000, "M"),
        (900, "CM"),
        (500, "D"),
        (400, "CD"),
        (100, "C"),
        (90, "XC"),
        (50, "L"),
        (40, "XL"),
        (10, "X"),
        (9, "IX"),
        (5, "V"),
        (4, "IV"),
        (1, "I"),
    )
    parts = []
    for value, symbol in pairs:
        count, n = divmod(n, value)
        if count:
            parts.append(symbol * count)
    return "".join(parts)


def roman_to_int(s):
    if type(s) is not str or not s:
        raise ValueError("s must be a non-empty canonical Roman numeral string")
    values = {
        "I": 1,
        "V": 5,
        "X": 10,
        "L": 50,
        "C": 100,
        "D": 500,
        "M": 1000,
    }
    for ch in s:
        if ch not in values:
            raise ValueError("s must be a non-empty canonical Roman numeral string")
    total = 0
    i = 0
    length = len(s)
    while i < length:
        if i + 1 < length and values[s[i]] < values[s[i + 1]]:
            total += values[s[i + 1]] - values[s[i]]
            i += 2
        else:
            total += values[s[i]]
            i += 1
    if total < 1 or total > 3999 or int_to_roman(total) != s:
        raise ValueError("s must be a non-empty canonical Roman numeral string")
    return total