using System;

using System.Linq;

public class Program

{   

    public static void Main()

    {

        string masterKey = "03694";

        var ownerKeys =

            from a in GetOwnerDigits(GetKeyDigit(masterKey, 1))

            from b in GetOwnerDigits(GetKeyDigit(masterKey, 2))

            from c in GetOwnerDigits(GetKeyDigit(masterKey, 3))

            from d in GetOwnerDigits(GetKeyDigit(masterKey, 4))

            from e in GetOwnerDigits(GetKeyDigit(masterKey, 5))

            select $"{a}{b}{c}{d}{e}";

        // neighbors should only have a distance between 2 and 6

        ownerKeys = ownerKeys

            .Where(k => IsBetween(Math.Abs(GetKeyDigit(k, 1) - GetKeyDigit(k, 2)), 2, 6))

            .Where(k => IsBetween(Math.Abs(GetKeyDigit(k, 2) - GetKeyDigit(k, 3)), 2, 6))

            .Where(k => IsBetween(Math.Abs(GetKeyDigit(k, 3) - GetKeyDigit(k, 4)), 2, 6))

            .Where(k => IsBetween(Math.Abs(GetKeyDigit(k, 4) - GetKeyDigit(k, 5)), 2, 6));

        Console.WriteLine($"{ownerKeys.Count()} keys found:");

        foreach(string key in ownerKeys)

            Console.WriteLine(key);

    }

    private static int GetKeyDigit(string key, int position)

    {

        return int.Parse((key[position - 1]).ToString());

    }

    private static int[] GetOwnerDigits(int digit)

    {

        return Enumerable.Range(0, 10).Where(x => x % 2 == digit % 2 && x != digit).ToArray();

    }

    public static bool IsBetween(int value, int minimum, int maximum)

    {

        return value >= minimum && value <= maximum;

    }

}