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 {
	

	static int[] ps;
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int[][] connections = new int[n][m];

		ps = new int[m];
		int ans = 0;

		for(int i = 0; i < m ; i++) {
			int k = sc.nextInt();
			for(int j = 0; j<k ; j++) {
				int s = sc.nextInt() - 1 ;
				connections[s][i] = 1;
			}
		}
		
		for(int i = 0; i < m ; i++) {
			
			ps[i] = sc.nextInt();
		}
		
		double NUM = Math.pow(2, (double)n);
		for(int i=0;i<NUM;i++) {

			ans += isOn(m,n,i,connections);
		}
		

		System.out.println(ans);

	}
	
	public static int isOn(int m, int n, int NUM, int[][] connections) {
		for(int j=0;j<m;j++) {
			int count = 0;
			for(int k=0;k<n;k++) {
				count += connections[k][j] * (NUM / (int)Math.pow(2,k) % 2);
			}
			if((count % 2) != ps[j]) {
				return 0;
			}
			
		}
		return 1;
	}
}