def int_to_roman(n):
    if not isinstance(n, int) or n < 1 or n > 3999:
        raise ValueError
    roman_numerals = [
        (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')
    ]
    result = ''
    for value, symbol in roman_numerals:
        while n >= value:
            result += symbol
            n -= value
    return result

def roman_to_int(s):
    if not s:
        raise ValueError
    roman_dict = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    total = 0
    prev = 0
    for char in reversed(s):
        if char not in roman_dict:
            raise ValueError
        curr = roman_dict[char]
        if curr < prev:
            total -= curr
        else:
            total += curr
        prev = curr
    if total < 1 or total > 3999:
        raise ValueError
    if int_to_roman(total) != s:
        raise ValueError
    return total