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 {
    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        List<Integer>[] list = new List[m];
        int[] pArr = new int[m];


        for (int i = 0; i < m; i++) {
            list[i] = new ArrayList<Integer>();
            int k = sc.nextInt();
            for (int j = 0; j < k; j++) {
                list[i].add(sc.nextInt());
            }
        }
        for (int i = 0; i < m; i++) {
            pArr[i] = sc.nextInt();
        }


        int count = 0;
        String format = "%0" + n + "d";
//        debug(format);
        for (int i = 0; i < Math.pow(2, n); i++) {
            String bin = String.format(format, Integer.parseInt(Integer.toBinaryString(i)));
//            debug(bin);
            boolean isValid = true;
            for (int j = 0; j < m; j++) {
                int sum = 0;
//                debug(list[j]);
                for (int k : list[j]) {
                    sum += bin.charAt(k - 1) == '1' ? 1 : 0;
                }
                if (sum % 2 != pArr[j]) isValid = false;
            }
            if (isValid) count++;
        }
        System.out.println(count);


//        System.out.println(sum / (n * Math.pow(2, indexMax)));
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
