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

      int cnt = 0;
      for(int i = 0; i < (1<<n); i++) {
        int num = i;
        if(check(map, p, num))
          cnt++;
      }
      System.out.println(cnt);
  }

  private static boolean check(Map<Integer, List<Integer>> map, int[] pArr, int n) {
    for(Map.Entry<Integer, List<Integer>> entry : map.entrySet()) {
        int p = pArr[entry.getKey()];
        List<Integer> lights = entry.getValue();
        int cnt = 0;
        for(int lightIdx : lights) {
          if(((n >> lightIdx) & 1) == 1)
            cnt++;
        }
        if(cnt % 2 != p)
          return false;
    }
    return true;
  }
}