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>
using namespace std;
int n,m,p[20][20],ans=0;
bool k[20],pp[20];
void dfs(int u){
	if(u>n){
		for(int i=1;i<=m;i++){
			int tmp=0;
			for(int j=1;j<=p[i][0];j++) tmp+=k[p[i][j]];
			if(tmp%2!=pp[i]) return;
		}
		ans++;
		return;
	}
	k[u]=0;
	dfs(u+1);
	k[u]=1;
	dfs(u+1);
}
int main(){
	scanf("%d %d",&n,&m);
	for(int i=1;i<=m;i++){
		scanf("%d",&p[i][0]);
		for(int j=1;j<=p[i][0];j++) scanf("%d",&p[i][j]);
	}
	for(int i=1;i<=m;i++) scanf("%d",&pp[i]);
	dfs(1);
	printf("%d\n",ans);
}