_VALUES = [
    (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"),
]

_CHAR_VALUES = {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}


def int_to_roman(n):
    if not isinstance(n, int) or isinstance(n, bool):
        raise ValueError("n must be an integer in the range 1..3999")
    if n < 1 or n > 3999:
        raise ValueError("n must be in the range 1..3999")
    parts = []
    remaining = n
    for value, symbol in _VALUES:
        while remaining >= value:
            parts.append(symbol)
            remaining -= value
    return "".join(parts)


def roman_to_int(s):
    if not isinstance(s, str) or not s:
        raise ValueError("input must be a non-empty Roman numeral string")
    for ch in s:
        if ch not in _CHAR_VALUES:
            raise ValueError("invalid character in Roman numeral: %r" % ch)
    total = 0
    i = 0
    length = len(s)
    while i < length:
        value = _CHAR_VALUES[s[i]]
        if i + 1 < length and _CHAR_VALUES[s[i + 1]] > value:
            total += _CHAR_VALUES[s[i + 1]] - value
            i += 2
        else:
            total += value
            i += 1
    if total < 1 or total > 3999 or int_to_roman(total) != s:
        raise ValueError("not a canonical Roman numeral: %r" % s)
    return total