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 <cstdio>
#include <vector>
#define N 15
using namespace std;

int n, m, k, c, ans, p[N];
vector<int> s[N];
int main()
{
	int i, j, x, t;
	cin >> n >> m;
	for (i = 0; i < m; i++) {
		scanf("%d", &k);
		for (j = 0; j < k; j++) {
			scanf("%d", &t);
			s[i].push_back(t - 1);
		}
	}
	for (i = 0; i < m; i++) scanf("%d", &p[i]);
	for (x = 0; x < 1 << n; x++) {
		for (i = 0; i < m; i++) {
			c = 0;
			for (j = 0; j < s[i].size(); j++) {
				if (x & (1 << s[i][j])) c++;
			}
			if (c % 2 != p[i]) break;
		}
		if (i == m) ans++;
	}
    cout << ans << endl;
    return 0;
}