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 main() {
		int N, M;
		cin >> N >> M;
		vector<int> sw(N);
		for (int i = 0; i < M; i++) {
				int K;
				cin >> K;
				for (int j = 0; j < K; j++) {
						int s;
						cin >> s;
						s--;
						sw[s] |= 1<<i;
				}
		}

		int p = 0;
		for (int i = 0; i < M; i++) {
				int x;
				cin >> x;
				p |= x<<i;
		}

		int ans = 0;
		for (int s = 0; s < (1<<N); s++) {
				int t = 0;
				for (int i = 0; i < N; i++) {
						if (s>>i & 1) t ^= sw[i];
				}
				if (t == p) ans++;
		}

		cout << ans << endl;

		return 0;
}
