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();
		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); // & And  | Or ^  Xor ~  Not(ビット反転)
			}
			s[i] = allS;
		}
		for(int i = 0 ; i < m  ; i++) {
			p[i] = sc.nextInt();
		}
		for (int i = 0; i < 1 << n ; i++) {
			boolean flag = true;
			for(int j = 0 ; j < m ; j++) {
				int k = s[j] & i;
				if(Integer.bitCount(k) % 2 != p[j]) {
					flag = false;
					continue;
					}
			}
			if(flag)
				num++;
		}

		sc.close();
			System.out.println(num);


	}

}
