Program.cs

using System.Text.RegularExpressions;

Regex RomanRgx = new(@"^(?=.)M{0,3}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$", RegexOptions.Compiled | RegexOptions.IgnoreCase);
Dictionary<char, int> Map = new()
{
    {'I', 1}, {'V', 5}, {'X', 10}, {'L', 50},
    {'C', 100}, {'D', 500}, {'M', 1000}
};

while (true)
{
    Console.WriteLine("Enter values separated by spaces:");
    string? inputLine = Console.ReadLine();

    if (string.IsNullOrWhiteSpace(inputLine))
    {
        Console.WriteLine("No input provided. Exiting...");
        return;
    }

    inputLine = inputLine.Replace("\"", "").Replace(",", " ");

    List<string> mixedInputs = inputLine.Split(' ', StringSplitOptions.RemoveEmptyEntries).ToList();

    var (validItems, rejected) = testfunc(mixedInputs);

    Console.WriteLine("\nSorted values:");
    Console.WriteLine(string.Join(" ", validItems));

    Console.WriteLine("\nRejected values:");
    Console.WriteLine(rejected.Any() ? string.Join(" ", rejected) : "None");
}


(List<string> sorted, List<string> rejected) testfunc(IEnumerable<string> inputs)
{
    var validList = new List<(string original, int value, bool isRoman)>();
    var rejectedList = new List<string>();

    foreach (var input in inputs)
    {
        if (IsValidInt(input, out int intValue))
        {
            validList.Add((input, intValue, false));
        }
        else if (IsValidRm(input, out int romanValue))
        {
            validList.Add((input, romanValue, true));
        }
        else
        {
            rejectedList.Add(input);
        }
    }

    var sorted = validList
        .OrderBy(x => x.value)
        .Select(x => x.isRoman ? $"{x.original}({x.value})" : x.original)
        .ToList();

    return (sorted, rejectedList);
}

bool IsValidInt(string input, out int value)
{
    if (int.TryParse(input, out value))
    {
        if (value >= 1 && value <= 3999) return true;
    }
    return false;
}

bool IsValidRm(string input, out int value)
{
    value = 0;
    if (!RomanRgx.IsMatch(input)) return false;

    value = RmToInt(input);
    return value >= 1 && value <= 3999;
}

int RmToInt(string roman)
{
    roman = roman.ToUpper();
    int total = 0;
    int prevValue = 0;
    
    for (int i = roman.Length - 1; i >= 0; i--)
    {
        var current = Map[roman[i]];
        if (current < prevValue)
            total -= current;
        else
            total += current;
        prevValue = current;
    }
    return total;
}