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,ans;
int a[17][17],p[17],vis[17];
bool check(){
	for(int i=1;i<=m;++i){
		int tmp=0;
		for(int j=1;j<=a[i][0];++j)
			if(vis[a[i][j]]){
				tmp++;
				tmp%=2;
			}
		if(tmp!=p[i])
            return 0;
	}
	return 1;
}
void dfs(int x){
	if(x==n+1){
		if(check())
            ans++;
		return ;
	}
	for(int i=x+1;i<=n+1;++i){
		vis[i]=1;
		dfs(i);
		vis[i]=0;
	}
}
int main() {
	cin>>n>>m;
	for(int i=1;i<=m;++i){
		cin>>a[i][0];
		for(int j=1;j<=a[i][0];++j)
			cin>>a[i][j];
	}
	for(int i=1;i<=m;++i)
		cin>>p[i];
	dfs(0);
	cout<<ans;
}
