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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt();
		int M = in.nextInt();
		ArrayList<ArrayList<Integer>> s = new ArrayList<>();
		for (int i = 0; i < M; i++) {
			int k = in.nextInt();
			ArrayList<Integer> si = new ArrayList<>();
			for (int j = 0; j < k; j++) {
				si.add(in.nextInt() - 1);
			}
			s.add(si);
		}
		int[] p = new int[M];
		for (int i = 0; i < M; i++) {
			p[i] = in.nextInt();

		}
		int ans = 0;
		for (int i = 0; i < (1 << N); i++) {
			boolean isOk = true;
			for (int j = 0; j < M; j++) {
				int count = 0;
				for (Integer sw : s.get(j)) {
					if ((i & (1 << sw)) != 0) {
						count++;
					}
				}
				count %= 2;
				if (count != p[j]) {
					isOk = false;
				}
			}
			if (isOk) {
				++ans;
			}
		}
		System.out.println(ans);
		in.close();
	}
}