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>
#include <vector>

using namespace std;

int N,M;
vector<int> s[15];
int p[15];
int ans;

inline bool judge(int state)
{
	int cnt=0;
	for (int i=1; i<=M; i++)
	{
		int tmp=0;
		for (int j=0; j<s[i].size(); j++) if (state>>(N-s[i][j])&1) tmp++;
		if (tmp%2==p[i]) cnt++;
	}
	return cnt==M;
}

int main()
{
	cin >> N >> M;
	for (int i=1; i<=M; i++)
	{
		int k;
		for (cin >> k; k--; )
		{
			int tmp;
			cin >> tmp;
			s[i].push_back(tmp);
		}
	}
	for (int i=1; i<=M; i++) cin >> p[i];
	for (int i=0; i<(1<<N); i++) if (judge(i)) ans++;
	cout << ans;
	return 0;
}