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>
#include<queue>
#include<string>
#include<stack>
#include<algorithm>
#include<cstring>
#include<map>
using namespace std;
int sta=0;
int sw[20];
int n,m;
int dfs(int k,int i)
{
	if(i==n+1)return sta==k?1:0;
	return dfs(k^sw[i],i+1)+dfs(k,i+1);
}
int main()
{
	cin>>n>>m;
	for(int i=1;i<=m;i++)
	{
		int k;cin>>k;
		for(int j=1;j<=n;j++)
			sw[j]<<=1;
		while(k--)
		{
			int c;
			cin>>c;
			sw[c]+=1;
		}
	}
	int mi[20];
	mi[0]=1;
	for(int j=1;j<=m;j++)
	{
		cin>>mi[j];
	}
	for(int j=1;j<=m;j++)
	{
		sta<<=1;
		sta+=mi[j];
	}
	cout<<dfs(0,1);
	return 0;
}