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 {

    private static int N;
    private static int M;
    private static int[][] s;
    private static int[] p;

    private static void read() {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        s = new int[M][];
        for (int m = 0; m < M; m += 1) {
            int k = sc.nextInt();
            int[] sm = new int[k];
            for (int ki = 0; ki < k; ki += 1) {
                sm[ki] = sc.nextInt();
            }
            s[m] = sm;
        }
        p = new int[M];
        for (int m = 0; m < M; m += 1) {
            p[m] = sc.nextInt();
        }
    }

    public static void main(String[] args) {
        read();

        int cnt = 0;
        for (int bit = 0; bit < (1 << N); bit += 1) {
            List<Integer> switches = new LinkedList<>();
            for (int s = 0; s < N; s += 1) {
                if ((bit & (1 << s)) != 0) {
                    switches.add(s + 1);
                }
            }
            cnt += isOn(switches);
        }

        System.out.println(cnt);
    }

    private static int isOn(List<Integer> switches) {
        for (int m = 0; m < M; m += 1) {
            int cnt = 0;
            for (int s : s[m]) {
                cnt += switches.contains(s) ? 1 : 0;
            }
            if (cnt % 2 != p[m]) {
                return 0;
            }
        }
        return 1;
    }

}

