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;
typedef long long ll;
const int N=12e4;

int p;
int s[20];

int main(){
	ios::sync_with_stdio(0);
	int n,m;
	cin>>n>>m;
	for(int i=0,k;i<m;i++){
		cin>>k;
		for(int j=0,w;j<k;j++){
			cin>>w;
			s[w-1]|=(1<<i);
		}
	}
	for(int i=0,w;i<m;i++){
		cin>>w;
		p|=(w<<i);
	}
	int ans=0;
	for(int i=0;i<(1<<n);i++){
		int b=0;
		for(int j=0;j<n;j++)
			if(i>>j&1)b^=s[j];
		if(b==p)ans++;
	}
	cout<<ans;
	return 0;
}