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>
#include<cstdio>
using namespace std;
int a[11][11],n,m,p[11];
bool check(int sta){
	for(int i=1;i<=m;i++){
		int cnt=0;
		for(int j=1;j<=a[i][0];j++){
			if(sta&(1<<(a[i][j]-1))){
				cnt++;
			}
		}
		if(cnt%2!=p[i])return 0;
	}
	return 1;
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		scanf("%d",&a[i][0]);
		for(int j=1;j<=a[i][0];j++)
			scanf("%d",&a[i][j]);
	}
	for(int i=1;i<=m;i++)
		scanf("%d",&p[i]);
	int sum=(1<<n)-1,ans=0;
	for(int sta=0;sta<=sum;sta++){
		if(check(sta))ans++;
	}
	printf("%d\n",ans);
	return 0;
}