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.*;
import java.util.stream.*;

public class Main {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int N = in.nextInt();
    int M = in.nextInt();
    int[][] s = new int[M][];
    for (int k = 0; k < M; k++) {
      s[k] = new int[in.nextInt()];
      for (int i = 0; i < s[k].length; i++) {
        s[k][i] = in.nextInt() - 1;
      }
    }
    int[] p = new int[M];
    for (int i = 0; i < M; i++) {
      p[i] = in.nextInt();
    }
    int ans = 0;
    for (int i = 0; i < Math.pow(2, N); i++) {
      int t = i;
      boolean[] on = new boolean[N];
      for (int j = 0; j < N; j++) {
        on[j] = t % 2 == 1;
        t /= 2;
      }
      boolean all = true;
      for (int k = 0; k < M; k++) {
        int cnt = 0;
        for (int j = 0; j < s[k].length; j++) {
          if (on[s[k][j]]) {
            cnt++;
          }
        }
        if (cnt % 2 != p[k]) {
          all = false;
        }
      }
      if (all) {
        ans++;
      }
    }
    System.out.println(ans);
  }
}