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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

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

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

            list.add(l);
        }

        int[] p = new int[m];

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

        int count = 0;
        for (int i = 0 ; i < Math.pow(2, n) ; i++) {
            boolean flg = true;
            int[] b = new int[10];
            int temp = i;
            int index = 0;
            while (temp > 0) {
                b[index] = temp % 2;
                temp /= 2;
                index++;
            }
            for (int j = 0 ; j < m ; j++) {
                int d = 0;
                for (int k = 0 ; k < list.get(j).size() ; k++) {
                    if (b[list.get(j).get(k) - 1] == 1) d++;
                }
                if (d % 2 != p[j]) {
                    flg = false;
                }
            }
            if (flg) count++;
        }

        System.out.println(count);

    }

}