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>
#define rep(i,n) for(int i=0; i<(int)(n); i++)

using namespace std;

int main(){
	int N, M;
	cin >> N >> M;
	int k[15];
	int s[15][15];
    int p[15];
	rep(i,M){
		cin >> k[i];
		rep(j,k[i]){
			cin >> s[i][j];
			s[i][j]--;
		}
	}
	rep(i,M) cin >> p[i];
	int ans=0;
	for(int bit=0; bit<(1<<N); bit++){
		int num=0;
		rep(i,M){
			int sum=0;
			rep(j,k[i]){
				if(bit&(1<<s[i][j])) sum++;
			}
			if(sum%2==p[i]) num++;
		}
		if(num==M) ans++;
	}
	cout << ans << endl;
	
	return 0;
}