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 arg[]){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		ArrayList<Integer>adj[]=new ArrayList[m];
		for(int i=0;i<m;i++)
			adj[i]=new ArrayList<>();
		for(int i=0;i<m;i++){
			int c=sc.nextInt();
			for(int j=0;j<c;j++)
				adj[i].add(sc.nextInt());
		}
		int cnt=0;
		ArrayList<Integer> stat=new ArrayList<>();
		for(int i=0;i<m;i++)
			stat.add(sc.nextInt());
		//System.out.println(stat);
		ArrayList<Integer> curr=new ArrayList<>();
		for(int i=0;i<(1<<n);i++){
			for(int j=0;j<n;j++)
				curr.add((i>>j)&1);
		//	System.out.println(curr);
			boolean v=true;
			for(int l=0;l<m;l++){
				int cc=0;
				for(Integer k:adj[l])
					cc+=curr.get(k-1);
				
				if(cc%2!=stat.get(l))
					v=false;
			}
			//System.out.println(cc);
			if(v)
				cnt++;
			//System.out.println(cnt);
			curr.clear();
		}
		System.out.println(cnt);
	}
}