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.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] k = new int[M];
        int[][] s = new int[M][];
        for (int i = 0; i < k.length; i++) {
            k[i] = sc.nextInt();
            s[i] = new int[k[i]];
            for (int j = 0; j < s[i].length; j++) {
                s[i][j] = sc.nextInt();
            }
        }
        int[] p = new int[M];
        for (int i = 0; i < p.length; i++) {
            p[i] = sc.nextInt();
        }
        
        int res = 0;
        for (int bit = 0; bit < (1 << N); bit++) {
            boolean ok = true;
            for (int i = 0; i < k.length; i++) {
                int on_counter = 0;
                for (int j = 0; j < s[i].length; j++) {
                    if ((bit & (1 << (N - s[i][j]))) != 0) {
                        on_counter++;
                    }
                }
                if (on_counter % 2 != p[i]) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                res++;
            }
        }
        System.out.println(res);
        sc.close();
    }
}