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();//スイッチ
    int m = sc.nextInt();//電球
    int[] ak = new int[m];//電球に繋がっているスイッチの個数
    int[][] sw = new int[m][n];//電球mに接続しているスイッチの情報
    int[] ju = new int[m]; //電球に繋がっているスイッチ%2が配列内の値の時点灯
    int ans = 0;//条件合致数

    for(int i=0; i<m; i++){
      ak[i] = sc.nextInt();//電球i+1に繋がっているスイッチ個数
      for(int j=0; j<ak[i]; j++){
        sw[i][j] = sc.nextInt(); //繋がるスイッチ番号入力
      }
    }

    for(int k=0; k<m;k++){
      ju[k] = sc.nextInt();//1or0を入力
    }

    for(int i=0; i< (1<<n); i++){//スイッチの全ビット探索
      int[] swon = new int[m];//電球に繋がっているonの数
      for(int j=0; j<n;j++){//jビット左論理シフト

        if((1&i>>j)==1){//スイッチj+1がonかoffか
          for(int k=0; k<m;k++){//k+1=電球番号
            for(int l=0; l<ak[k];l++){
              if(sw[k][l]==j+1){
                swon[k] = swon[k] + 1;
              }
            }
          }

        }

      }
      // for(int p=0; p<m;p++){
      //   System.out.println("*"+swon[p]);
      // }
      //全ての電球が点灯したかの判定
      boolean judge = false;
      int count=0;
      for(int p=0;p<m;p++){
        if(swon[p]%2 == ju[p]){
          count +=1;
        }
      }
      if(count==m){
        ans += 1;
      }


    }

    System.out.println(ans);


  }
}