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[][] s=new int[m][];
		for(int i=0;i<m;i++){
			int ki=sc.nextInt();
			s[i]=new int[ki];
			for(int j=0;j<ki;j++){
				s[i][j]=sc.nextInt()-1;
			}
		}
		int[] p=new int[m];
		for(int i=0;i<m;i++){
			p[i]=sc.nextInt();
		}
		
		int r=0;
		loop:
		for(int f=0;f<(1<<n);f++){
			for(int i=0;i<m;i++){
				int c=0;
				for(int j=0;j<s[i].length;j++){
					if((f&(1<<s[i][j]))>0)
						c++;
				}
				if(c%2!=p[i])
					continue loop;
			}
			r++;
		}
		System.out.println(r);
			

	}
}