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<vector<int>> s;
vector<int> p;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin >> n >> m;
	s.resize(m);
	for(int i=0; i<m; ++i){
		int k;
		cin >> k;
		s[i].resize(k);
		for(auto &j:s[i]) cin >> j;
	}
	p.resize(m);
	for(auto &i:p) cin >> i;
	int ans = 0;
	for(int i=0; i<(1<<n); ++i){
		bool f = true;
		for(int j=0; j<m; ++j){
			int t = 0;
			for(size_t k=0; k<s[j].size(); ++k){
				if((i>>(s[j][k]-1))&1) ++t;
			}
			if(t % 2 != p[j] % 2){
				f = false;
				break;
			}
		}
		if(f) ++ans;
	}
	cout << ans << "\n";
}