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.List;
import java.util.Scanner;


public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int m = scan.nextInt();

		List<Integer[]> list = new ArrayList<Integer[]>();
		for(int i = 0; i < m; i++) {
			int k = scan.nextInt();
			Integer[] sk = new Integer[k];
			for(int j = 0; j < k; j++) {
				sk[j] = scan.nextInt();
			}
			list.add(sk);
		}

		int[] p = new int[m];

		for(int i = 0; i < m; i++) {
			p[i] = scan.nextInt();
		}

		int ans = 0;
		for(int i = 0; i < 1 << n; i++) {
			boolean f = true;
			for(int k = 0; k < m; k++) {
				int res = 0;
				for(int l = 0; l < list.get(k).length; l++) {
					if((1 & i >> list.get(k)[l] - 1) == 1) {
						res++;
					}
				}
				if(res % 2 == p[k]) {

				}else {
					f= false;
					break;
				}
			}
			if(f) {
				ans++;
			}
		}

		System.out.println(ans);

	}
}