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
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		Map<Integer,List<Integer>> s = new HashMap<>();
		for(int i=0;i<m;i++) {
			List<Integer> list = new ArrayList<>();
			int k = in.nextInt();
			for(int j=0;j<k;j++) {
				list.add(in.nextInt()-1);
			}
			s.put(i, list);
		}
		int[] p = new int[m];
		for(int i=0;i<m;i++) {
			p[i] = in.nextInt();
		}
		int ans = 0;
		int max = 1<<n;
		for(int i=0;i<max;i++) {
			int[] s_tmp = new int[n];
			for(int j=0;j<n;j++) {
				s_tmp[j] = (i>>j)&1;
			}
			boolean fail = false;
			for(int idx : s.keySet()) {
				int count = 0;
				for(int idx2 : s.get(idx)) {
					count += s_tmp[idx2];
				}
				if(count%2!=p[idx]) {
					fail = true;
					break;
				}
			}
			if(fail) continue;
			else ans++;
		}
		System.out.println(ans);
		in.close();
	}

}
