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<math.h>
using namespace std;
int main()
{
	int N, M, K[10], P[10], s[10][10];
	int i, j, k;
	int ans = 0,sw,ch;
	cin >> N >> M;
	for (i = 0; i < M; i++) {
		cin >> K[i];
		for (j = 0; j < K[i]; j++) {
			cin >> s[i][j];
		}
	}
  
	for (i = 0; i < M; i++) cin >> P[i];
	for (i = 0; i < pow(2,N); i++) {
		ch = 1;
		for (j = 0; j < M; j++) {
			sw = 0;
			for (k = 0; k < K[j]; k++) {
				if ((i / (int)pow(2, s[j][k] - 1)) % 2) sw++;
			}
			if (sw % 2 != P[j]) ch = 0;
		}
		ans += ch;
	}
	cout << ans << endl;
}