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 int n;
	public static int m;
	public static int[][] cs;
	public static int[] ps;
    public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		m = sc.nextInt();
		cs = new int[m][n];
		for(int i=0; i<m; i++){
			int k = sc.nextInt();
			for(int j=0; j<k; j++){
				cs[i][j] = sc.nextInt();
			}
		}
		ps = new int[m];
		for(int i=0; i<m; i++){
			ps[i] = sc.nextInt();
		}
		int ans = bitSearch(n);
		System.out.println(ans);
	}

	static int bitSearch(int n) {
		int ans = 0;
		for (int i = 0; i < (Math.pow(2, n)); i++) {
			boolean[] flags = new boolean[n];
			for (int j = 0; j < n; j++) {
				if ((1 & i >> j) == 1) {
					flags[j] = true;
				} else {
					flags[j] = false;
				}
			}
			boolean flag=true;
			for(int j=0; j<cs.length; j++){
				int count = 0;
				for(int k: cs[j]){
					if(k != 0 && flags[k-1]) count++;
				}
				if(count%2!=ps[j]) flag=false; 
			}
			if(flag) ans++;
		}
		return ans;
	}
}
