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;

class Main {
	public static void main(String[] $) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		int[]s=new int[m];
		int[]p=new int[m];
		int num=0;
		for(int i=0;i<m;i++) {
			int allS=0;
			int k=sc.nextInt();
			for(int j=0;j<k;j++) {
				allS=allS |1<<(sc.nextInt()-1);
			}
			s[i]=allS;
		}
		for (int i=0;i<1<<n;i++) {
			boolean flag = true;
			for(int j=0;j<m;j++) {
				if(i==0)
					p[j]=sc.nextInt();
				int k=s[j]&i;
				if(Integer.bitCount(k)%2!=p[j]) {
					flag=false;
					continue;
					}
			}
			if(flag)
				num++;
		}
			System.out.println(num);
	}
}
