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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {

	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String str[] = br.readLine().split(" ");

		int n = Integer.parseInt(str[0]);
		int m = Integer.parseInt(str[1]);

		ArrayList<ArrayList<Integer>> list = new ArrayList<>();

		for (int i = 0; i < m; i++) {
			list.add(new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			str = br.readLine().split(" ");
			int k = Integer.parseInt(str[0]);
			for (int j = 1; j <= k; j++) {
				list.get(i).add(Integer.parseInt(str[j]) - 1);
			}
		}

		str = br.readLine().split(" ");

		int p[] = new int[m];
		for (int i = 0; i < m; i++) {
			p[i] = Integer.parseInt(str[i]);
		}

		int ans = 0;
		for (int i = 0; i < (1 << n); i++) {
			int swi[] = new int[m];
			for (int j = 0; j < n; j++) {
				if ((i & (1 << j)) != 0) {
					for (int k = 0; k < m; k++) {
						if (list.get(k).contains(j)) {
							swi[k]++;
						}
					}
				}
			}

			boolean flag = false;
			for (int j = 0; j < m; j++) {
				if (swi[j] % 2 != p[j]) {
					flag = true;
					break;
				}
			}

			if (!flag) {
				ans++;
			}
		}
		System.out.println(ans);
	}
}