Cubes

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

public class Cubes
{
    private static HashSet<string> invalidCombs = new HashSet<string>();
    private static HashSet<string> combs = new HashSet<string>();
    private static string[, ,] cube;

    public static void Main()
    {
        string[] stickValues = Console.ReadLine().Split(' ');


        PermuteWithRepetitions(stickValues, 0, stickValues.Length - 1);

        Console.WriteLine(combs.Count);
    }

    private static void PermuteWithRepetitions(string[] stickValues, int start, int end)
    {
        AddCurrentCombinationToList(stickValues);

        for (int left = end - 1; left >= start; left--)
        {
            for (int right = left + 1; right <= end; right++)
            {
                if (stickValues[left] != stickValues[right])
                {
                    Swap(ref stickValues[left], ref stickValues[right]);
                    PermuteWithRepetitions(stickValues, left + 1, end);
                }
            }

            var firstElement = stickValues[left];
            for (int i = left; i <= end - 1; i++)
            {
                stickValues[i] = stickValues[i + 1];
            }

            stickValues[end] = firstElement;
        }
    }

    private static void AddCurrentCombinationToList(string[] currentCombination)
    {
        AssignCubeValues(currentCombination);
        RotateCube();

        if (!invalidCombs.Contains(string.Join("", currentCombination)))
        {
            combs.Add(string.Join("", currentCombination));
        }
    }

    private static void Swap<T>(ref T first, ref T second)
    {
        T oldFirst = first;
        first = second;
        second = oldFirst;
    }

    private static void AssignCubeValues(string[] stickValues)
    {
        cube = new string[3, 2, 2];
        int index = 0;
        for (int z = 0; z < cube.GetLength(2); z++)
        {
            for (int y = 0; y < cube.GetLength(1); y++)
            {
                for (int x = 0; x < cube.GetLength(0); x++)
                {
                    cube[x, y, z] = stickValues[index];
                    index++;
                }
            }
        }
    }

    private static void RotateCube()
    {
        for (int i = 0; i < 3; i++)
        {
            RotateByAxis(cube, 0, 0, 0);
            RotateByAxis(cube, 1, 0, 0);
            RotateByAxis(cube, 2, 0, 0);
            invalidCombs.Add(GetCurrentComb(cube));
        }
    }

    private static void RotateByAxis(string[, ,] cube, int x, int y, int z)
    {
        string oldValue = cube[x, y, z];
        cube[x, y, z] = cube[x, y, z + 1];
        cube[x, y, z + 1] = cube[x, y + 1, z + 1];
        cube[x, y + 1, z + 1] = cube[x, y + 1, z];
        cube[x, y + 1, z] = oldValue;
    }

    private static string GetCurrentComb(string[, ,] cube)
    {
        StringBuilder result = new StringBuilder();
        for (int z = 0; z < cube.GetLength(2); z++)
        {
            for (int y = 0; y < cube.GetLength(1); y++)
            {
                for (int x = 0; x < cube.GetLength(0); x++)
                {
                    result.Append(cube[x, y, z]);
                }
            }
        }

        return result.ToString();
    }
}