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 n, m;
int k[10];
int s[10][10];
int p[10];

int main(void){
	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];

	int res = 0;
	for(int i = 0; i < 1<<n; i++){
		bool flag = true;
		for(int j = 0; j < m; j++){
			int num = 0;
			for(int l = 0; l < k[j]; l++){
				if(i>>s[j][l] & 1) num++;
			}
			if(num % 2 != p[j]) flag = false;
		}

		if(flag) res++;
	}

	cout << res << endl;
	return 0;
}