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.*;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.next());
    int m = Integer.parseInt(sc.next());
    int[] k = new int[m];
    int[][] s = new int[m][];
    int[] p = new int[m];
    for(int i=0;i<m;i++){
      k[i] = Integer.parseInt(sc.next());
      s[i] = new int[k[i]];
      for(int j=0;j<k[i];j++){
        s[i][j] = Integer.parseInt(sc.next())-1;
      }
    }
    for(int i=0;i<m;i++){
      p[i] = Integer.parseInt(sc.next());
    }
    int res = 0;
    outer:for(int i=0;i<(1<<n);i++){
      for(int j=0;j<m;j++){
        int count = 0;
        for(int l=0;l<k[j];l++){
          if(((i>>s[j][l]) & 1)==1){
            count++;
          }
        }
        if(count%2!=p[j]){
          continue outer;
        }
      }
      res++;
    }
    System.out.println(res);
    
  }
}
