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(), m = sc.nextInt();
		int[][] connect = new int[m][n];
		for (int i = 0; i < m; i++) {
			int l = sc.nextInt();
			for (int j = 0; j < l; j++) {
				connect[i][sc.nextInt()-1] = 1;
			}
		}
		int[] p = new int[m];
		for (int i = 0; i < m; i++) p[i] = sc.nextInt();
		int[] light; int count = 0; boolean flag;
		String format = "%".concat(String.valueOf(n)).concat("s");
		String s;
		for (int i = 0; i < 1<<n; i++) {
			s = String.format(format, Integer.toString(i,2)).replace(' ', '0');
			light = new int[m]; flag = true;
			for (int j = 0; j < n; j++) {
				if(s.charAt(j)=='1') {
					for (int k = 0; k < m; k++) {
						if(connect[k][j]==1)light[k]++;
					}
				}
			}
			for (int j = 0; j < m; j++) {
				if(light[j]%2!=p[j]) flag = false;
			}
			if(flag) count++;
		}
		System.out.println(count);
		sc.close();
	}
}