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
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc = new Scanner(System.in);
		int n =sc.nextInt();
		int m = sc.nextInt();
		List<Integer>[] adj = new ArrayList[m];
		for(int i=0;i<m;++i){
			 adj[i] = new ArrayList<>();
			 int k = sc.nextInt();
			 for(int j=0;j<k;++j){
			 	int s = sc.nextInt()-1;
			 	adj[i].add(s);
			 }
		}
		int[] p = new int[m];
		for(int i=0;i<m;++i) p[i] = sc.nextInt();
		int ans = 0;
		for(int i = 0; i < (1<<n); ++i){
			boolean light = true;
			
			for (int j=0;j<m;++j){
				int on = 0;
				
				for(int bulb : adj[j])
				if(((i>>bulb)&1) == 1) ++on;
				
				on%=2;
				if(on!=p[j]) light = false;
				
			}
			
			if(light) ++ans;
			
		}
		
		System.out.println(ans);
 	}
}