We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.

Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.

How many combinations of "on" and "off" states of the switches light all the bulbs?

Constraints

* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M


Output

Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.

Examples

Input

2 2
2 1 2
1 2
0 1


Output

1


Input

2 3
2 1 2
1 1
1 2
0 0 1


Output

0


Input

5 2
3 1 2 5
2 2 3
1 0


Output

8
#include <iostream>

using namespace std;

int n, m, k[15], s[15][15], p[15], ans;

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= m; i++)
	{
		cin >> k[i];
		for (int j = 1; j <= k[i];j++)
		{
			cin >> s[i][j];
		}
	}
	for (int i = 1; i <= m; i++) cin >> p[i];
	for (int i = 0; i < (1<<(n)); i++)
	{
		bool fl = 1;
		for (int j = 1; j <= m; j++)
		{
			int cnt = 0;
			for (int a = 1; a <= k[j]; a++)
			{
				if ((1<<(s[j][a]-1)) & i) cnt++;
			}
			if (cnt % 2 != p[j]) {fl = 0; break;}
		}
		if (fl) ans++;
	}
	cout << ans << endl;
	return 0;
}