class Solution{

	int mod = (int)(1e9 + 7);
	int mask;

	private:
	int MEM(int mask_j, vector<int> &a, vector<long long> &dp, int n)
	{
		if(mask_j > mask)
			return 0;
		
		if(mask_j == mask)
			return 1;
	 
		long long &ans = dp[mask_j];
	 
		if(ans!=-1)
			return (int)ans;
	 
		ans = 0;
	 
		int ind = __builtin_popcount(mask_j);
	 
		for(int j = 0; j < n; j++)
		{
			
			if(!((1<<j)&mask_j) and ((1<<j)&a[ind]))
			{
	 
				ans += 1LL*MEM(mask_j | (1<<j), a, dp, n);
	 
				if(ans>=mod)
					ans %= mod;
			}
			
		}
	 
		return (int)ans;
	}

	public:
	int numberOfWays(int n, vector<vector<char>> &mat)
	{
		
		vector<int> a(n, 0);
		for(int i = 0; i < n; i++)
		{
			for(int j = 0; j < n; j++)
			{
				
				if(mat[i][j] == '#')
					a[i] |= (1<<j);
			}
		}
	 
		mask = (1<<n)-1;

		vector<long long> dp(mask + 5, -1);
	 
		return MEM(0, a, dp, n);
	}

};