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 sc = new Scanner(System.in);
		int n = sc.nextInt();
        int m = sc.nextInt();
		int [][] in = new int [m][n+1]; 
        int [] p = new int [m];
        int [] light = new int [n];
        int ans = 0;
        for(int i=0;i<m;i++){in[i][0] = sc.nextInt();
                             for(int j=1;j<=in[i][0];j++)
                             {in[i][j] = sc.nextInt();}
                            }
        for(int i=0;i<m;i++){p[i]=sc.nextInt();}      
        for(int i=0;i<Math.pow(2,n);i++){int count = 0;int b = i;for(int j=0;j<n;j++){light[j]=b%2;
                                                                       b/=2;}
                                         for(int j=0;j<m;j++){int count2 = 0;
                                           for(int k=1;k<=in[j][0];k++){if(light[in[j][k]-1]==1){count2++;}
                                                                       }
                                                             if(count2%2==p[j]){count++;}
                                                             }
                                        if(count==m){ans++;}}                        
		System.out.println(ans);
	}
}