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.Scanner;

public 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();
			for (int j = 0; j < ki; j ++) {
				S[i] += 1 << (sc.nextInt() - 1);
				//System.out.println(Integer.toBinaryString(S[i]));
			}
		}
	    
	    
	    int p [] = new int [M];
	    for (int i = 0; i < M; i++) {
	    	p[i]=sc.nextInt();
	    }
	    
	    sc.close();
	    
	    long ans = 0;
	    for (int i = 0; i < Math.pow(2,N); i++) {
	    	boolean ok = true;
			for (int j = 0; j < M; j++) {
				if (Integer.bitCount(S[j] & i) % 2 != p[j]) {
					ok = false;
					break;
				}
			}
			if (ok) 
				ans ++; 
	    	
	    }
	    System.out.println(ans);
	    
	}

}
