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 <iostream>
#include <vector>
#include <bitset>

using namespace std;

int main(){
	int N=0, M=0;
	cin >> N >> M;

	vector<unsigned int> s(M, 0);
	unsigned int p;

	for(int i=0; i<M; i++){
		int k;
		cin >> k;
		for(int j=0; j<k; j++){
			int l;
			cin >> l;
			l--;
			s[i]|=(1<<l);
		}
	}

	for(int i=0; i<M; i++){
		int k;
		cin >> k;
		p|=(k<<i);
	}

	int r=0;
	for(int i=0; i<(1<<N); i++){
		int f=1;
		for(int j=0; j<M; j++){
			if(((p&(1<<j))>>j)!=(__builtin_popcount(i&s[j])&(1))){
				f=0; break;
			}
		}
		r+=f;
	}

	cout << r << endl;

	return 0;

}
