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.Scanner;

class Main {
  public static void main(String[] args) {
    Scanner stdIn = new Scanner(System.in);
    int n = stdIn.nextInt();
    int m = stdIn.nextInt();
    int[] s = new int[m];
    int[] p = new int[m];

    for(int i=0; i<m; i++) {
      int k = stdIn.nextInt();
      for(int j=0; j<k; j++) {
        int a = stdIn.nextInt();
        s[i] += Math.pow(2,a-1);
      }
    }

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

    int N = (int)Math.pow(2,n);


    int ans = 0;
    for(int i=0; i<N; i++) {
      int flag = 1;
        for(int j=0; j<m; j++) {
          int cnt = i&s[j];
          int bits = 0;
          while(cnt != 0) {
            if((cnt&1) == 1) { bits++; }
            cnt >>>= 1;
          }
          if(bits%2 != p[j]) {
            flag = 0;
            break;
          }
        }
      if(flag == 1) { ans++; }
    }

    System.out.println(ans);
  }
}
