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, K[10], s[10][10], p[10], ans = 0;
	cin >> N >> M;
	for (int i = 0; i < M; i++) {
		cin >> K[i];
		for (int j = 0; j < K[i]; j++) {
			cin >> s[i][j];
			s[i][j]--;
		}
	}
	for (int i = 0; i < M; i++) cin >> p[i];
	for (int i = 0; i < pow(2, N); i++) {
		int X[10], I = i;
		for (int j = 0; j < N; j++) {
			X[j] = I % 2;
			I /= 2;
		}
		for (int j = 0; j < M; j++) {
			int z = 0;
			for (int k = 0; k < K[j]; k++) {
				if (X[s[j][k]]) z++;
			}
			if (z % 2 != p[j]) goto NEXT;
		}
		ans++;
	NEXT:;
	}
	cout << ans;
}