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.ArrayList;
import java.util.List;
import java.util.Scanner;

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

        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        int[] k = new int[m];
        List<List<Integer>> sw = new ArrayList<>();
        int[] p = new int[m];
        for(int i=0;i<m;i++){
            k[i] = Integer.parseInt(sc.next());
            sw.add(new ArrayList<>());
            for(int j=0;j<k[i];j++){
                sw.get(i).add(Integer.parseInt(sc.next())-1);
            }
        }
        for(int i=0;i<m;i++){
            p[i] = Integer.parseInt(sc.next());
        }
        sc.close();
        int temp;
        int count = 0;
        boolean flag = true;
        int res = 0;
        for(int i=0;i<1<<n;i++){
            flag = true;
            for(int j=0;j<m;j++){
                count = 0;
                for(int l=0;l<k[j];l++){
                    temp = sw.get(j).get(l);
                    if(((i>>temp) & 1)==1){
                        count++;
                    }
                }
                if(count%2!=p[j]){
                    flag = false;
                    break;
                }
            }
            if(flag){
                res++;
            }

        }
        System.out.println(res);
    }
}