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.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) throws Exception {
        try (BufferedInputStream in = new BufferedInputStream(System.in);
             PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out))) {

            Scanner sc = new Scanner(in);

            int n = sc.nextInt();
            int m = sc.nextInt();

            ArrayList[] l = new ArrayList[m];
            for (int i = 0; i < m; i++) {
                int cnt = sc.nextInt();
                l[i] = new ArrayList();
                for (int j = 0; j < cnt; j++) l[i].add(sc.nextInt() - 1);
            }

            int[] p = new int[m];
            for (int i = 0; i < p.length; i++) p[i] = sc.nextInt();

            int ret = 0;
            for (int st = 0; st < 1 << n; st++) {
                int lighted = 0;
                for (int i = 0; i < l.length; i++) {
                    ArrayList<Integer> wiring = l[i];

                    int acc = 0;
                    for (Integer w : wiring) {
                        acc = (acc + (st >>> w & 1)) % 2;
                    }

                    if (acc == p[i]) lighted++;
                }

                if (lighted == m) ret++;
            }

            out.println(ret);
        }
    }
    
}
