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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		StringBuilder sb = new StringBuilder();
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[][] light = new int[m][n];
		int k, s;
		for (int i = 0; i < m; i++) {
			k = sc.nextInt();
			for (int j = 0; j < k; j++) {
				s = sc.nextInt() - 1;
				light[i][s]++;
			}
		}
		int[] p = new int[m];
		for (int i = 0; i < m; i++) {
			p[i] = sc.nextInt();
		}
		int t, d, idx, cnt, ans = 0;
		int[] sw;
		boolean ok;
		for (int i = 0; i < Math.pow(2, n); i++) {
			t = i;
			d = 512;
			idx = 9;
			sw = new int[n];
			while (t != 0) {
				if (t >= d) {
					t = t - d;
					sw[idx]++;
				}
				d = d / 2;
				idx--;
			}
			ok = true;
			for (int j = 0; j < m; j++) {
				cnt = 0;
				for (int l = 0; l < n; l++) {
					if (sw[l] == light[j][l] && sw[l] == 1) {
						cnt++;
					}
				}
				if (cnt % 2 == p[j]) {

				} else {
					ok = false;
					break;
				}
			}
			if (ok) {
				ans++;
			}
		}
		System.out.println(ans);
	}
}