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, c, ans, s[15][15], p[15];
int main() {
	int i, j, t;
	cin>>n>>m;
	for(i=0; i<m; i++) {
		cin>>k;
		while(k--) {
			cin>>t;
			s[i][--t] = 1;
		}
	}
	for(i=0; i<m; i++) cin>>p[i];
	for(k=0; k<1<<n; k++) {
		for(i=0; i<m; i++) {
			c = 0;
			for(j=0; j<n; j++) {
				if(s[i][j] && (k>>j)&1) c++;
			}
			if(c%2 != p[i]) break;
		}
		if(i==m) ans++;
	}
	cout<<ans;
	return 0;
}