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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
vector<int>v[20];
int p[20];
int main()
{
	int ans=0;
	int n,m;cin>>n>>m;
	rep(i,m)
	{
		int a;
		scanf("%d",&a);
		rep(j,a)
		{
			int b;
			scanf("%d",&b);
			b--;
			v[i].push_back(b);
		}
	}
	rep(i,m)
	{
		scanf("%d",&p[i]);
	}
	rep(i,1<<n)
	{
		bool flag=true;
		rep(j,m)
		{
			int cnt=0;
			for(int m=0;m<v[j].size();m++)
			{
				int temp=v[j][m];
				if(i>>temp&1)
				cnt^=1;
			}
			if(cnt!=p[j])
				flag=false;
		}
		ans+=flag;
	}
	cout<<ans;
	return 0;
}