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();
    boolean[][] b = new boolean[m][n];
    int[] p = new int[m];
    int ans = 0;

    for(int i = 0; i < m; i++){
      int k = sc.nextInt();
      for(int j = 0; j < k; j++){
        int s = sc.nextInt();
        b[i][s - 1] = true;
      }
    }

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

    for(int i = 0; i < (1 << n); i++){
      int tmp2 = 0;
      for(int l = 0; l < m; l++){
        int tmp = 0;
        for(int j = 0; j < n; j++){
          if(((1 & i >> j) == 1) && (b[l][j] == true)){
            tmp += 1;
          }
        }
        if(tmp % 2 == p[l]){
          tmp2 += 1;
        }
      }
      if(tmp2 == m){
        ans += 1;
      }
    }

    System.out.println(ans);
  }
}
