C# ulong URL Shortener

using System.Collections.Generic;
using System.Linq;
using System.Text;

/**
 * ShortURL: Bijective conversion between natural numbers (IDs) and short strings
 *
 * ShortURL.Encode() takes an ID and turns it into a short string
 * ShortURL.Decode() takes a short string and turns it into an ID
 *
 * Features:
 * + VERY large alphabet all composite numbers from 33-64 are included to find the shortest and nicest looking URL.
 * + Offensive words have been made very unlikely due to design.
 * + This allows for much more room (support for ULONG data type) at the expense of sometimes adding 1 letter for shorter numbers.
 * + This method guarantees the shortest URL at the expense of one digit, but this is often reversed and some long numbers can become extra short!
 * + Ultimate PRIVACY. Search space is enormous. Nobody will ever find anyone else's URL.
 * + Added extra char "." that is acceptable in URLs
 * + No extra DB lookups
 *
 * Example output:
 * 434433 <=> zfMn-
 * 1234 <=> w-x
 * 8989800 <=> gVXG.
 * 132 <=> pc_
 * 2 <=> _c
 * (ulong) 18446744073709551615 <=> dD5E.dbtn3-s
 * (long) 9223372036854775807 <=> iD-kBTykgmf8
 * (uint) 4294967295 <=> efGCg_s
 * (int) 2147483647 <=> nfhj.gy
 * (ushort) 65535 <=> t_zs
 * (byte) 255 <=> ie-
 */

public class ShortURL
{
    private static string Keys = "abcdeghijkmnpqrstuvwxyz23456789_"; // Do not change this string length. If you want to remove something, replace it with something else.
    private static string AllChars = "abcdefghjkmnpqrstvwxyzABCDE-_.FGHJKLMNPQRSTVWXYZ1234567890oOiIuU"; // Do not change this string length. If you want to remove something, replace it with something else.
    private static Dictionary<char, string> DAlphabet = new Dictionary<char, string>();

    static ShortURL() // Contains all composite numbers from 33-64
    {
        for (int i = 0; i < Keys.Length; i++)
            DAlphabet[ Keys[ i ] ] = new string(AllChars.Take(AllChars.Length - i).ToArray());
    }

    public static string Encode(ulong num)
    {
        ulong n = num;
        List<string> s = new List<string>();
        foreach (char t in Keys)
        {
            string A = DAlphabet[ t ];
            ulong B = (ulong)A.Length;
            var S = new StringBuilder();

            while (n > 0) // Because we use all composite numbers, we will find the shortest url possible here!
            {
                S.Insert(0, A.ElementAt((int)(n % B)));
                n = n / B;
            }
            n = num;
            S.Insert(0, t);
            s.Add(S.ToString());
        }
        
        // Prioritizes certain characters. Changing this will make your version unique.
        var sort = s.OrderBy(x => x.Length).ThenByDescending(x => x.Contains("_") || x.Contains("-") || x.Contains(".")).ThenByDescending(x => x.ToCharArray().Count(z => char.IsLower(z)));

        return sort.ToArray()[ 0 ];

    }

    public static ulong Decode(string str)
    {
        char c = str[ 0 ];
        string Alphabet = DAlphabet[ c ];
        ulong Base = (ulong)Alphabet.Length;
        str = str.Substring(1, str.Length - 1);
        ulong num = 0;
        for (var i = 0; i < str.Length; i++)
        {
            num = num * Base + (ulong)Alphabet.IndexOf(str.ElementAt(i));
        }
        return num;
    }

}