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 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        int sum = 0;
        int[][] numlist = new int[m][n+1];
        List<Integer> plist = new ArrayList<>();
        for(int i=0;i<m;i++){
            int k = in.nextInt();
            numlist[i][0]=k;
            for(int j=0;j<k;j++){
                numlist[i][j+1] = in.nextInt();
            }
        }
        for(int i=0;i<m;i++)
            plist.add(in.nextInt());

        for(int i=0;i< 1<<n;i++){
            int att = 0,z=0;
            for(int j=0;j<m;j++){
                att = 0;
               for(int k=0;k<numlist[j][0];k++){
                   z = numlist[j][k+1]-1;
                   att ^= (i>>z & 1);
               }
               if(att != plist.get(j))  break;
               else if(j==m-1){
                   sum++;
               }
            }
        }
        System.out.println(sum);
    }
}
