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 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();
            s[i] = new int[k[i]];
            for (int j=0;j<k[i];j++){
                s[i][j] = scanner.nextInt();
            }
        }
        int[] p = new int[m];
        for (int i=0;i<m;i++){
            p[i] = scanner.nextInt();
        }
        int countAnswer = 0;
        for (int i=0;i<Math.pow(2,n);i++){
            String str = Integer.toBinaryString(i);
            while (str.length()<n){
                str = "0" + str;
            }
            int count1 = 0;
            for (int j=0;j<m;j++){
                int count2 = 0;
                for (int a=0;a<n;a++){
                    boolean b = false;
                    for (int bo=0;bo<s[j].length&&!b;bo++){
                        if (s[j][bo]==a+1){
                            b = true;
                        }
                    }
                    if (str.charAt(a)=='1'&&b)count2++;
                }
                if (count2%2==p[j])count1++;
            }
            if (count1==m)countAnswer++;
        }
        System.out.println(countAnswer);
    }
}