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 <stdio.h>
#include <algorithm>
#include <queue>
#include <functional>
using namespace std;
using ll = long long;

int n, m, mask[10], p[10], pm, cnt = 0;
void rec(int bits, int d) {
	if (d < 0) {
		cnt += bits == pm;
		return;
	}
	rec(bits, d - 1);
	rec(bits ^ mask[d], d - 1);
}
int main() {
	scanf("%d %d", &n, &m);
	for (int i = 0; i < m; i++) {
		int k, s;
		scanf("%d", &k);
		for (int j = 0; j < k; j++) {
			scanf("%d", &s);
			mask[s - 1] ^= (1 << i);
		}
	}
	for (int i = 0; i < m; i++) {
		scanf("%d", p + i);
		pm ^= p[i] << i;
	}
	rec(0, n - 1);
	printf("%d\n", cnt);
}