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;

int main(){
	int N,M;
	cin >> N >> M;
	vector<int> a(N);
	for(int i(0);i<M;++i){
		int k;
		cin >> k;
		for(int j(0);j<k;++j){
			int s;
			cin >> s;
			s--;
			a[s] |= 1 << i;
		}
	}
	int p(0);
	for(int i(0);i<M;++i){
		int x;
		cin >> x;
		p |= x << i;
	}
	int ans(0);
	for(int s(0);s<(1<<N);s++){
		int t(0);
		for(int i(0);i<N;++i){
			if(s>>i & 1){
				t ^= a[i];
			}
		}
		if(t == p){
			ans++;
		}
	}
	cout << ans << endl;
	return 0;
}