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.*;

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

        int n = sc.nextInt();
        int m = sc.nextInt();
        int ans = 0;
        int[] lights = new int[m];
        int[] p = new int[m];

        for (int i = 0; i < m; i++) {
            int k = sc.nextInt();

            int state = 0;

            for (int j = 0; j < k; j++) {
                int s = sc.nextInt();

                state += (1 << (s - 1));
            }

            lights[i] = state;
        }

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

        for (int i = 0; i < (1 << n); i++) {
            boolean check = true;

            for (int j = 0; j < m; j++) {
                int cond = Integer.bitCount(i & lights[j]);

                if (cond % 2 != p[j]) {
                    check = false;
                    break;
                }
            }

            if (check) {
                ans++;
            }
        }

        System.out.println(ans);
    }
}