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{
  static int n;
  static int m;
  static boolean[] sw;
  static int[][] a;
  static int[] p;
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    n=sc.nextInt();
    m=sc.nextInt();
    a=new int[m][];
    for(int i=0;i<m;i++){
      int k=sc.nextInt();
      a[i]=new int[k];
      for(int j=0;j<k;j++){
        a[i][j]=sc.nextInt()-1;
      }
    }
    p=new int[m];
    for(int i=0;i<m;i++){
      p[i]=sc.nextInt();
    }
    sw=new boolean[n];
    System.out.println(calc(0));
  }
  static int calc(int fixed){
    if(fixed<n){
      int res=0;
      res+=calc(fixed+1);
      sw[fixed]=true;
      res+=calc(fixed+1);
      sw[fixed]=false;
      return res;
    }
    for(int i=0;i<m;i++){
      int cnt=0;
      for(int j=0;j<a[i].length;j++){
        if(sw[a[i][j]]){
          cnt++;
        }
      }
      if((cnt&1)!=p[i]){
        return 0;
      }
    }
    return 1;
  }
}