using System;

public class Program

{

    public static void Main()

    {

        var rng = new Random();

        for (int i=0; i<100; i++)

        {

            var n = i;

            Console.WriteLine(string.Format("NID {0} {1} {2}", n, ToNID(n), FromNID(ToNID(n))));

        }

    }

    private const string NID_CHRS = "HQWKZCXPGSVTBLRMNJFD";

    private const int NID_BASE = 20;

    private const int NID_MIN = 1337;

    public static string ToNID(int n)

    {

        var s = "";

        n += NID_MIN;

        var sum = 0;

        do

        {

            var ci = n % NID_BASE;

            s = NID_CHRS[ci] + s;

            n /= NID_BASE;

            sum += ci;

        }

        while (n > 0);

        s = NID_CHRS[sum % NID_BASE] + s;

        return s;

    }

    public static int FromNID(string s)

    {

        s = s.Trim().ToUpperInvariant();

        if (s.Length < 1)

        {

            throw new Exception("Empty ID");

        }

        var n = 0;

        var sum = 0;

        for (int i = 1; i < s.Length; i++)

        {

            var c = s[i];

            var ci = NID_CHRS.IndexOf(c);

            var r = 1;

            for (int j = s.Length - i - 1; j > 0 ; j--)

                r *= NID_BASE;

            n += r * ci;

            sum += ci;

        }

        n -= NID_MIN;

        if (sum < 0)

        {

            throw new Exception("Invalid ID");

        }

        if (s[0] != NID_CHRS[sum % NID_BASE])

        {

            throw new Exception("Invalid ID");

        }

        return n;

    }

}