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>
using namespace std;
int main(){
	int n,m,sum=0;
	cin>>n>>m;
	int a[m+1],b[m+1],c[m+1][10005];
	for(int i=1;i<=m;i++){
		cin>>a[i];
		for(int j=1;j<=a[i];j++){
			cin>>c[i][j];
		}
	}
	for(int i=1;i<=m;i++){
		cin>>b[i];
	}
	int g[100005]={0},j=n;
	while(g[0]==0){
		bool false_true=true;
		for(int k=1;k<=m;k++){
			int s=0;
			for(int l=1;l<=a[k];l++){
				if(g[c[k][l]]){
					s++;
				}
			}
			if(s%2!=b[k]){
				false_true=false;
			}
		}
		if(false_true==true){
			sum++;
		}
		j=n;
		while(g[j]==1) j--;
		g[j]++;
		for(int i=j+1;i<=n;i++){
			g[i]=0;
		}
	}
	cout<<sum;
}