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 = sc.nextInt();
        int m = sc.nextInt();
        List<List<Integer>> sw = new ArrayList<>();
        for (int i = 0; i < m; ++i) sw.add(new ArrayList<>());

        for (int i = 0; i < m; ++i) {
            int k = sc.nextInt();
            for (int j = 0; j < k; ++j) {
                sw.get(i).add(sc.nextInt() - 1);
            }
        }

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

        int res = 0;
        for (int bit = 0; bit < (1<<n); ++bit) {
            boolean flag = true;
            for (int i = 0; i < m; ++i) {
                int cnt = 0;
                for (Integer id : sw.get(i)) {
                    if ((bit & (1<<id)) != 0) ++cnt;
                }
                if (cnt % 2 != p[i]) flag = false;
            }
            if (flag) ++res;
        }

        System.out.println(res);
    }
}