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) {

		Solve s= new Solve();
		s.solve();

	}
}


class Solve{


	 public void solve() {
		 Scanner sc = new Scanner(System.in) ;
		 int N = sc.nextInt();
		 int M = sc.nextInt();
		 int[] a = new int[N];
		 int p=0;
		 int res=0;
		 for(int i = 0;i<M;i++) {
			 int k;
			 k=sc.nextInt();
			 for(int j = 0;j<k;j++) {
				 int s=sc.nextInt();
				 s--;
				 a[s]|=1<<i;
			 }
		 }
		 for(int i =0;i<M;i++) {
			 int x=sc.nextInt();
			 p |= x<<i;
		 }
		 
		 for(int j = 0;j<Math.pow(2, N);j++) {
			 int t = 0;
			 for(int i = 0;i<N;i++) {
				 if((j>>i&1)==1) {
					 t ^= a[i];
				 }
			 }
			 if(t==p) {
				 res++;
			 }
		 }
		 System.out.println(res);
	 }
}