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 boolean[] bits;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int m=sc.nextInt();
        boolean[][] input=new boolean[m][n];
        bits=new boolean[n];
        int[] p=new int[m];
        int k;
        for(int i=0;i<m;i++){
          k=sc.nextInt();
          for(int j=0;j<k;j++){
            input[i][sc.nextInt()-1]=true;
          }
        }
        for(int i=0;i<m;i++){
          p[i]=sc.nextInt();
        }
        int tmp1;
        boolean tmp2;
        int ans=0;
        for(int i=0;i<Math.pow(2,n);i++){
          tmp2=true;
          for(int j=0;j<m;j++){
            tmp1=0;
            for(int l=0;l<n;l++){
              if(input[j][l]&&bits[l])tmp1++;
            }
            tmp2&=tmp1%2==p[j];
          }
          if(tmp2)ans++;
          if(i!=Math.pow(2,n)-1)update(0);
        }
        System.out.println(ans);

    }
    static void update(int pointer){
        if(!bits[pointer]){
            bits[pointer]=true;
        }else{
            bits[pointer]=false;
            update(pointer+1);
        }
    }
}
