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 s[][] = new int[m][n];
    int pat[] = new int[n];
    int k[] = new int[m];
    int p[] = new int[m];
    int ans = 0;

    for (int i=0; i<m; i++){
      k[i] = Integer.parseInt(sc.next());
      for(int j=0; j<k[i]; j++){
        s[i][j] = Integer.parseInt(sc.next());
      }
    }

    for(int i=0; i<m; i++){
      p[i] = Integer.parseInt(sc.next());
    }

    for(int i=0; i<Math.pow(2, n); i++){
      String bin = Integer.toBinaryString(i);
      
      if(bin.length() < n){
        for(int j=bin.length(); j<n; j++){
          bin = "0" + bin;
        }
      }
      
      //System.out.println(bin);
      
      for(int j=0; j<n; j++){
        pat[j] = Integer.parseInt(bin.substring(j,j+1));
      }
      
      int tdon = 0;
      for(int kk=0; kk<m; kk++){ // 電球
        int tson = 0;
        for(int ll=0; ll<k[kk]; ll++){ // スイッチ
          tson += pat[s[kk][ll]-1];
        }
        if(tson%2 == p[kk]) {
          tdon++;
        }
      }
      if(tdon == m){
        ans++;
      }
    }
    
    System.out.println(ans);
    
  }
}
