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();
    HashMap<Integer, ArrayList<Integer>> map = new HashMap<Integer, ArrayList<Integer>>();
    for(int i = 0; i < m; i++) {
      int k = sc.nextInt();
      ArrayList<Integer> list = new ArrayList<Integer>();
      for(int j = 0; j < k; j++) {
        int s = sc.nextInt();
        list.add(s - 1);
      }
      map.put(i, list);
    }
    int[] p = new int[m];
    for(int i = 0; i < m; i++) {
      p[i] = sc.nextInt();
    }

    int ans = 0;
    for(int i = 0; i < (int)Math.pow(2, n); i++) {
      int t = 1;
      for(int j = 0; j < m; j++) {
        ArrayList<Integer> list2 = map.get(j);
        int sum = 0;
        for(int k = 0; k < list2.size(); k++) {
          if((i & (1 << list2.get(k))) != 0) sum++;
        }
        if((sum % 2) != p[j]) t = 0;
      }
      if(t == 1) ans++;
    }
    System.out.println(ans);
  }
}