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>
using namespace std;
int k[15],p[15],s[15][15];
int main ()
{
	int n,m,i,j,k1;
	scanf("%d%d",&n,&m);
	for(i=1;i<=m;++i)
	{
		scanf("%d",&k[i]);
		for(j=1;j<=k[i];++j)
		  scanf("%d",&s[i][j]);
	}
	for(i=1;i<=m;++i)
	  for(j=1;j<=k[i];++j) s[i][j]--;
	for(i=1;i<=m;++i) scanf("%d",&p[i]);
	int ans=0;
	for(i=0;i<(1<<n);++i)
	{
		int b1=0;
		for(j=1;j<=m;++j)
		{
			int sum=0;
			for(k1=1;k1<=k[j];++k1)
			  if(((i>>s[j][k1])&1)==1) sum++;
			sum%=2;
			if(sum!=p[j]) 
			{
				b1=1;
				break;
			} 
		}
		if(b1==0) ans++;
	}
	printf("%d",ans);
}