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 n, m;
vector<int> sw[14];
int p[14];
int ans = 0;
void can(int state){
	int ret = 0;
	for(int i = 0;i<m;i++){
		int cnt = 0;
		for(int j : sw[i]){
			if((1<<j)&state)	cnt++;
		}
		if(cnt % 2 == p[i])
		ret += (1<<i);
	}
	if(ret == (1<<m)-1)	ans++;
}
int main() {
	cin>>n>>m;
	for(int i = 0;i<m;i++)
	{
		int t;
		cin>>t;
		int q;
		while(t--){
			cin>>q;
			sw[i].push_back(--q);
		}
	}
	for(int i = 0;i<m;i++)	cin>>p[i];
	for(int i = 0; i<(1<<n);i++)
		can(i);
	cout<<ans;
	return 0;
}