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>
using namespace std;

int n, m, k[11], s[11], t, p[11], ans;
bool f;

int numberOfSetBits(int i){
	if (i <= 1) return i;
	else return numberOfSetBits(i >> 1) + (i % 2);
}

int main(){
	cin >> n >> m;
	for (int i = 0; i < m; ++i){
		cin >> k[i];
		s[i] = 0;
		for (int j = 0; j < k[i]; ++j){
			cin >> t;
			s[i] += (1 << (t-1));
		}
	}
	for (int i = 0; i < m; ++i) cin >> p[i];

	ans = 0;
	for (int i = 0; i < (1 << n); ++i){
		f = true;
		for (int j = 0; j < m; ++j){
			if (numberOfSetBits(s[j] & i) % 2 != p[j]){
				f = false;
				break;
			}
		}
		if (f) ans++;
	}
	cout << ans;
}