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> 
using namespace std;
int n,m;
int num[11]={0};
int cnt=0;
vector <int>s[11]; 
bool p[11];
void dfs(int x)
{
	if(x==n+1)
	{
		for(int i=1;i<=m;i++)
			if(num[i]%2!=p[i])return ;
		cnt++;
		return ;
	}
	dfs(x+1);
	for(int i=0;i<s[x].size();i++)
	{
		num[s[x][i]]++;
	}
	dfs(x+1);
	for(int i=0;i<s[x].size();i++)
	{
		num[s[x][i]]--;
	}
}

int main()
{
	cin >> n >> m;
	int a,b;
	for(int i=1;i<=m;i++)
	{
		cin >> a;
		for(int j=1;j<=a;j++)
		{
			cin >> b;
			s[b].push_back(i);
		}
	}
	for(int i=1;i<=m;i++)
		cin >> p[i];
	dfs(1);
	cout << cnt;
	
	return 0;
}