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 <bits/stdc++.h>
using namespace std;

int main()
{
	int n, m;
	cin >> n >> m;
	vector<vector<int>> ss(m);
	vector<int> ps(m);
	for (auto &s : ss)
	{
		int k;
		cin >> k;
		for (int i = 0; i < k; i++)
		{
			int x;
			cin >> x;
			s.emplace_back(x - 1);
		}
	}
	for (auto &p : ps)
	{
		cin >> p;
	}

	int ans = 0;
	for (int i = 0; i < (1 << n); i++)
	{
		bool f = true;
		for (int j = 0; j < m; j++)
		{
			int cnt = 0;
			for (int x : ss[j])
			{
				if ((i >> x) & 1)
				{
					cnt++;
				}
			}
			f &= (cnt % 2) == ps[j];
		}
		if (f)
		{
			ans++;
		}
	}

	cout << ans << endl;

	return 0;
}