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.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		Map<Integer, Set> lists = new HashMap<>();
		for (int i = 1; i <= M; i++) {
			int kn = sc.nextInt();
			Set<Integer> set = new HashSet<>();
			for (int j = 1; j <= kn; j++) {
				set.add(sc.nextInt());
			}
			lists.put(i, set);
		}
		Map<Integer, Integer> pMap = new HashMap<>();
		for (int i = 1; i <= M; i++) {
			pMap.put(i, sc.nextInt());
		}
		sc.close();
		int max = (int) Math.pow(2, (double) N);
		int ans = 0;
		for (int i = 0; i < max; i++) {
			String binary = Integer.toBinaryString(i);
			int len = binary.length();
			Map<Integer, Integer> ls = new HashMap<>();
			for (int k = 1; k <= M; k++) {
				ls.put(k, 0);
			}
			for (int j = 1; j <= len; j++) {
				for (int k = 1; k <= M; k++) {
					int tmp = ls.get(k);
					if (binary.charAt(len - j) == '1') {
						if (lists.get(k).contains(j)) {
							ls.put(k, tmp + 1);
						}
					}
				}
			}
			boolean bl = true;
			for (int k = 1; k <= M; k++) {
				if (ls.get(k) % 2 != pMap.get(k)) {
					bl = false;
				}
			}
			if (bl) {
				ans++;
			}

		}
		System.out.println(ans);
	}
}