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

public class Test
{
    enum Player
    {
        None = -1,
        FirstPlayer = 0,
        SecondPlayer = 1
    };

    public static bool CheckWin(int n, IEnumerable<int> coinSequence)
    {
        if (coinSequence == null || coinSequence.Count() != 2 * n)
            throw new ArgumentException("coinSequence size must be equal 2*n");

        var forcePlayer = Player.None;
        var currentPlayer = Player.None;

        var playerCoins = new int[2] { n, 0 };
        var playerMoved = new int[2] { 0, 0 };
        var coinsOnDesk = 0;

        foreach (var coin in coinSequence)
        {
            currentPlayer = (Player)(coin == 1 ? 0 : 1);

            // force player
            {
                if (playerMoved[(int)currentPlayer] > n)
                {
                    switch (currentPlayer)
                    {
                        case Player.FirstPlayer: forcePlayer = Player.SecondPlayer; break;
                        case Player.SecondPlayer: forcePlayer = Player.FirstPlayer; break;
                        default: throw new Exception("Alg fail"); break;
                    }
                }

                if (forcePlayer != Player.None)
                    currentPlayer = forcePlayer;
            }

            switch (currentPlayer)
            {
                case Player.FirstPlayer:
                    if (playerCoins[0] != 0)
                    {
                        playerCoins[0]--;
                        coinsOnDesk++;
                    }
                    break;
                case Player.SecondPlayer:
                    if (coinsOnDesk != 0)
                    {
                        coinsOnDesk--;
                        playerCoins[1]++;
                    }
                    break;
                default: throw new Exception("Alg fail"); break;
            }

            playerMoved[(int)currentPlayer]++;
        }

        return (playerCoins[1] == n);
    }

    public static IEnumerable<IEnumerable<int>> GenerateCoins(int n)
    {
        if (n == 1)
        {
            yield return new int[] { 1 };
            yield return new int[] { 2 };
            yield break;
        }

        var smallerVariants = GenerateCoins(n - 1);
        foreach (var smallerVariant in smallerVariants)
        {
            yield return smallerVariant.Concat(new int[] { 1 });
            yield return smallerVariant.Concat(new int[] { 2 });
        }

        yield break;
    }

    public static int CountWinsSequences(int n)
    {
        return GenerateCoins(2 * n).Count(coinSequence => CheckWin(n, coinSequence));
    }

    public static void Main()
    {
        for (int n = 1; n <= 5; n++)
        {
            Console.WriteLine("n = {0}, wins = {1}", n, CountWinsSequences(n));
        }
    }
}