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 scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int m = scanner.nextInt();
		int[] k = new int[m];
		int[] s = new int[m];
		for (int i = 0; i < m; i++) {
			k[i] = scanner.nextInt();
			for (int j = 0; j < k[i]; j++) {
				s[i]= s[i] | (1<<(scanner.nextInt()-1));
			}
		}
		int[] p = new int[m];
		for (int i = 0; i < m; i++) {
			p[i] = scanner.nextInt();
		}
		
		// ① 全組み合わせをbit表現で展開するループ
		int count = 0;
		for (int i = 0; i < (1<<n); i++) {
			boolean ok = true;
			for (int mi = 0; mi < m; mi++) {
				// ② bitを順番に走査するループ
				
				int ons = s[mi] & i;
				int oncount = 0;
				for (int j = 0; j < n; j++) {
					if ((1 & ons>>j) == 1) {
						oncount++;
					}
				}
				if ((oncount % 2) != p[mi]) {
					ok = false;
					break;
				}
			}
			if (ok) {
				count++;
			}
		}
		System.out.println(count);

	}
}
