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 <vector>
#include <algorithm>
using namespace std;

int a[12][12],p[12];
int main()
{
    int n,m; cin>>n>>m;
    for (int i=1; i<=m; i++)
    {
    	int s; cin>>s;
    	for (int j=1; j<=s; j++)
    	{
    		int t; cin>>t;
    		a[i][t]=1;
		}
	}
	for (int i=1; i<=m; i++) cin>>p[i];
	
	int ans=0;
	for (int i=0; i< 1<<n; i++)
	{
		int che=1;
		for (int j=1; j<=m; j++)
		{
			int sum=0;
			for (int u=1; u<=n; u++)
			    if (i & 1<<(u-1) && a[j][u]) sum++;
			if((sum-p[j])%2) che=0;
		}
		if (che) ans++;
	}
	
	cout << ans;
 } 