import re

_VALUE_MAP = [
    (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"),
]

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

_CANONICAL_PATTERN = re.compile(
    r"^M{0,3}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$"
)


def int_to_roman(n):
    if not isinstance(n, int) or isinstance(n, bool) or n < 1 or n > 3999:
        raise ValueError("integer out of range (1..3999)")
    result = []
    for value, symbol in _VALUE_MAP:
        while n >= value:
            result.append(symbol)
            n -= value
    return "".join(result)


def roman_to_int(s):
    if not isinstance(s, str) or not s:
        raise ValueError("empty or invalid Roman numeral")
    if not _CANONICAL_PATTERN.match(s):
        raise ValueError("malformed or non-canonical Roman numeral")
    total = 0
    prev = 0
    for ch in reversed(s):
        value = _ROMAN_VALUES[ch]
        if value < prev:
            total -= value
        else:
            total += value
            prev = value
    return total