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.*;
public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		
		int ans = 0;
		int n = scan.nextInt();
		int m = scan.nextInt();
		int p[] = new int [m];
		List<Integer>[] button = new ArrayList[n];
		for(int i=0;i<n;i++) {
			button[i] = new ArrayList<>();
		}
		
		for(int i=0;i<m;i++) {
			int k = scan.nextInt();
			for(int j=0;j<k;j++) {
				int s = scan.nextInt()-1;
				button[s].add(i);
			}
		}
		
		
		for(int i=0;i<m;i++) {
			p[i] = scan.nextInt();
		}
		
		for(int i=0;i<(1<<n);i++) {
			int on[] = new int[m];
			boolean check = true;
			for(int j=0;j<n;j++) {
				if((1 & i>>j)==1) {
					for(int l : button[j]) {
						on[l] += 1;
					}
				}
			}
			
			
			for(int j=0;j<m;j++) {
				if(on[j]%2 != p[j]) {
					check = false;
					break;
				}
			}
			
			if(check) {
				ans += 1;
			}
		}
		
		System.out.println(ans);
		
		
		
	}	
}
 