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;
import java.util.Arrays;
import java.util.List;

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]);

		int k[] = new int[m];
		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(" ");

			k[i] = Integer.parseInt(str[0]);

			for (int j = 1; j <= k[i]; j++) {
				list.get(i).add(Integer.parseInt(str[j]));
			}
		}

		int p[] = new int[m];
		str = br.readLine().split(" ");

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

		List<String> com = conbination(Arrays.asList(""), n);

		int ans = 0;
		for (int i = 0; i < com.size(); i++) {
			String swit[] = com.get(i).split("");
			boolean flag = false;

			for (int j = 0; j < m; j++) {
				int count = 0;
				for (int l = 0; l < k[j]; l++) {
					if (swit[list.get(j).get(l) - 1].equals("1")) {
						count++;
					}
				}

				if (count % 2 != p[j]) {
					flag = true;
					break;
				}
			}
			if (!flag)
				ans++;
		}
		System.out.println(ans);
	}

	public static List<String> conbination(List<String> binary, int count) {
		if (count <= 0)
			return binary;
		List<String> list = new ArrayList<String>(binary.size() * 2);
		for (String s : binary) {
			list.add(s + 0);
			list.add(s + 1);
		}
		return conbination(list, count - 1);
	}
}
