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 = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());

        Map<Integer, Set<Integer>> map = new HashMap<>();

        for (int i = 0; i < m; i++) {
            int k = Integer.parseInt(sc.next());

            Set<Integer> set = new HashSet<>();

            for (int j = 0; j < k; j++) {
                set.add(Integer.parseInt(sc.next()) - 1);
            }

            map.put(i, set);
        }

        List<Boolean> p = new ArrayList<>();

        for (int i = 0; i < m; i++) {
            p.add(Integer.parseInt(sc.next()) == 1);
        }

        int count = 0;

        for (int i = 0; i < Math.pow(2, n); i++) {
            boolean on = true;

            for (int j = 0; j < m; j++) {
                boolean sw = false;

                for (int k : map.get(j)) {
                    sw = sw ^ ((i & (int) Math.pow(2, k)) != 0);
                }

                if (sw != p.get(j)) on = false;
            }

            if (on) count++;
        }

        System.out.println(count);
    }
}