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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

  public static void main(String[] args) throws Exception {
    try (final var stdin = new InputStreamReader(System.in);
         final var br = new BufferedReader(stdin)) {
      final var nm = br.readLine().split(" ");
      final var n = Integer.parseInt(nm[0]);
      final var m = Integer.parseInt(nm[1]);
      final var s = new String[m];
      for (int i = 0; i < s.length; i++) {
        final var stringBuilder = new StringBuilder();
        stringBuilder.append("0".repeat(n));
        Arrays.stream(br.readLine().split(" "))
          .skip(1)
          .forEach((idx) -> stringBuilder
            .replace(Integer.parseInt(idx) - 1, Integer.parseInt(idx), "1"));

        s[i] = stringBuilder.toString();
      }

      final var p = Arrays.stream(br.readLine().split(" "))
        .mapToInt(Integer::parseInt)
        .toArray();

      var size = 0;
      for (int i = 0; i < Math.pow(2, n); i++) {
        var ok = true;
        for (int j = 0; j < m; j++) {
          final var bin = Integer.toBinaryString(Integer.parseInt(s[j], 2) & i)
            .toCharArray();

          var countOne = 0;
          for (char c : bin) {
            if (c == '1') {
              countOne++;
            }
          }

          ok &= countOne % 2 == p[j];
        }

        if (ok) {
          size++;
        }
      }

      System.out.println(size);
    }
  }
}
