public class CheeseRolling
{
	int N;
	int[][] winner;
	long[][] cache;
	int[][] chooses;
	int[] nxt;
	long[] fact;

	boolean powerOf2(int x)
	{
		return (x & (x - 1)) == 0;
	}

	long[] f(int st)
	{
		if (cache[st] != null)
			return cache[st];
		if (powerOf2(st))
		{
			cache[st] = new long[N];
			for (int i = 0; i < N; i++) if (st == (1 << i))
			{
				cache[st][i] = 1;
				return cache[st];
			}
		}
		int cnt = Integer.bitCount(st) / 2;
		long[] ans = new long[N];
		for (int i = 0; i < nxt[cnt]; i++) if ((chooses[cnt][i] & st) == chooses[cnt][i])
		{
			long[] A = f(chooses[cnt][i]);
			long[] B = f(chooses[cnt][i] ^ st);
			for (int a = 0; a < N; a++)
			{
				for (int b = 0; b < N; b++)
				{
					ans[winner[a][b]] += A[a] * B[b];
				}
			}
		}
		return cache[st] = ans;
	}

	int choose(int n, int k)
	{
		return (int) (fact[n] / fact[k] / fact[n-k]);
	}

	public long[] waysToWin(String[] wins)
	{
		N = wins.length;
		fact = new long[N+1];
		fact[0] = 1;
		for (int i = 1; i <= N; i++)
			fact[i] = fact[i-1] * i;
		nxt = new int[N+1];
		chooses = new int[N+1][];
		for (int i = 0; i <= N; i++)
			chooses[i] = new int[choose(N, i)];
		winner = new int[N][N];
		for (int i = 0; i < N; i++)
			for (int j = 0; j < N; j++)
				winner[i][j] = wins[i].charAt(j) == 'Y' ? i : j;
		cache = new long[1 << N][];
		for (int i = 0; i < (1 << N); i++)
		{
			int cnt = Integer.bitCount(i);
			chooses[cnt][nxt[cnt]++] = i;
		}
		return f((1 << N) - 1);
	}
}