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<stdio.h>
#include<math.h>
int m,n,k[1001],a[101][101],mt[101],p[101],sum=0;
bool mark;
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		scanf("%d",&k[i]);
		for(int j=1;j<=k[i];j++) scanf("%d",&a[i][j]);
	}
	for(int i=1;i<=m;i++) scanf("%d",&p[i]);
	for(int i=1;i<=pow(2,n);i++){
		mark=true;
		for(int j=1;j<=m;j++){
			for(int pp=1;pp<=k[j];pp++)
				if(i&(1<<(a[j][pp]-1))) mt[j]++;
			if(mt[j]%2!=p[j]) {
				mark=false;break;
			}
		}
		if(mark) {
			sum++;
			//printf("%d  ",i);
		}
		for(int j=1;j<=m;j++) mt[j]=0;
	}
	printf("%d",sum);
}