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
/*
ID: wangjun30
TASK:
LANG: C++
*/
#include<iostream>
using namespace std;
int b[20];
int rl[20][20];
int k[20];
int p[20];
int main(){
	int n,m,ans=0;
	cin>>n>>m;
	for(int i=1;i<=m;i++){
		cin>>k[i];
		for(int j=1;j<=k[i];j++)
			cin>>rl[i][j];
	}
	for(int i=1;i<=m;i++)
		cin>>p[i];
	while(b[0]==0){
		int j=n;
		for(int i=1;i<=m;i++){
			int sum=0;
			for(int j=1;j<=k[i];j++)
				sum+=b[rl[i][j]];
			if(sum%2!=p[i])
				goto End;
		}
		ans++;
		End:;
		while(b[j]==1)
			b[j]=0,j--;
		b[j]=1;
	}
	cout<<ans;
	return 0;
}