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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt(),m=sc.nextInt();
		int[] k=new int[m];
		int[][] s=new int[m][n];
		int[] p=new int[m];
		int[] sum=new int[m];
		int count=0;
		boolean flag=true;

		for(int i=0;i<m;i++) {
			k[i]=sc.nextInt();
			for(int j=0;j<k[i];j++) {
				s[i][j]=sc.nextInt();
			}
		}
		for(int i=0;i<m;i++) {
			p[i]=sc.nextInt();
		}
		for(int i=0;i<Math.pow(2, n);i++) {
			int[] status = new int[n];
			for(int j=0;j<n;j++) {//iを2進数にした場合にどこの桁が1になっているか判定し、1の場合はstatusに代入
				if((1&i>>j)==1) {
					status[j]=1;
				}
			}
			for(int h=0;h<m;h++) {
				for(int j=0;j<k[h];j++) {
					if(status[s[h][j]-1]==1)sum[h]++;
				}
			}
			//System.out.println("stauts"+Arrays.toString(status));
			//System.out.println("sum"+Arrays.toString(sum));
			for(int h=0;h<m;h++) {
				if(p[h]!=sum[h]%2)flag=false;
			}
			if(flag)count++;
			flag=true;
			Arrays.fill(sum, 0);
		}
		System.out.println(count);

	}
}

