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);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[][] kk =new int[m][n];
		for(int i=0;  i<m; i++){
			int k=sc.nextInt();
			for(int j=0;j<k; j++){
				int s = sc.nextInt()-1;
				kk[i][s]=1;
			}
		}
		int[] p=new int[m];
		for(int i=0; i<m; i++){
			p[i]= sc.nextInt();
		}
		boolean oi=true;
		long ans=0;
		for(int i=0; i<Math.pow(2,n); i++){
			for(int j=0; j<m; j++){
				int count=0;
				oi=true;
				for(int k=0; k<n; k++){
					if(kk[j][k]==1 && ((i>>k)&1)==1){
						count++;
					}
				}
				if(count%2!=p[j]){
					oi=false;
					break;
				}
			}
			if(oi){
				ans++;
			}
		}
		System.out.println(ans);
	}
}
