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 sc = new Scanner(System.in);
    int N = sc.nextInt();
    int M = sc.nextInt();
    int s[][]= new int[M][N];
    int tmp=0;
    int p[] = new int[M];
    for(int i=0;i<M;i++){
      tmp=sc.nextInt();
      for(int j=0;j<tmp;j++){
        s[i][j]=sc.nextInt();
      }
    }
    for(int i=0;i<M;i++){
      p[i]=sc.nextInt();
    }
    int answer =0;
    int tmps=0;
    boolean allRight=true;
    boolean r[] = new boolean[M];
    for(int i=0;i<M;i++){
      r[i]=false;
    }
    for(int i=0;i<(1<<N);i++){
      for(int j=0;j<M;j++){
        for(int k=0;k<N;k++){
          if((i>>s[j][k])%2==1){//s[j][k]のスイッチが今おささってるか判定
            tmps++;
          }
        }
        if(tmps%2==p[j]){//j番目の電球はOK
          r[j]=true;
          tmps=0;
        }
      }
      //電球なめて全部光ってたら答えをインクリメント
      for(int l=0;l<M;l++){
        if(!r[l]){
          allRight=false;
          break;
        }
      }
 //     System.out.println(i);
 //     System.out.println(allRight);
      if(allRight){
      answer++;
      }
      allRight=true;
      for(int m=0;m<M;m++){//それぞれ初期値に戻す
        r[m]=false;
      }
      tmps=0;
    }

    System.out.println(answer);
  }
  


  
}
