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 scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[][] s = new int[m][n];
        for(int i = 0; i < m; i++){
            int k = scanner.nextInt();
            for(int j = 0; j < k; j++){
                int tmp = scanner.nextInt();
                s[i][tmp-1]++;
            }
        }
        int[] p = new int[m];
        for(int i = 0; i < m; i++){
            p[i] = scanner.nextInt();
        }
        int total = 0;
        for(int i = 0; i < Math.pow(2,n); i++){
            int[] ans = new int[m];
            for(int j = 0; j < n; j++){
                if ((1&i>>j) == 1) {
                    int index = 0;
                    for(int l = 0; l < m; l++){
                        ans[l] += s[l][j];
                    }
                }
            }
            int count = 0;
            for(int l = 0; l < m; l++){
                //System.out.print(ans[l]);
                if(ans[l]%2 == p[l]){count++;}
            }
            if(count == m){total++;}
        }
        System.out.println(total);
    }
}