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 {
	Scanner sc = new Scanner(System.in);
	
	public static void main(String[] args) {
		Main m = new Main();
		m.run();
	}
	
	void run() {
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int k[] = new int[m];
		
		for(int i = 0; i < m;i++) {
			int kn = sc.nextInt();
			for(int j =0 ; j < kn; j++) {
				k[i] |= (1 << (sc.nextInt()-1));
			}
		}
		
		int p[] = new int[m];
		for(int i =0 ; i < m; i++) {
			p[i] = sc.nextInt();
		}
		
		int  count=0;
		for(int i = 0; i < 1<<n;i++) {
			boolean flag = true;
			for(int j = 0; j< m;j++) {				
//				System.out.println(m + " " +k[j]+" " + i+ " " +Integer.bitCount((k[j] & i)));
				flag = flag && (p[j] == Integer.bitCount((k[j] & i))%2 );
			}
			if(flag) {
//				System.out.println(i);
				count++;
			}
		}
		
		System.out.println(count);
		
	}
}
