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.*;

public class Main {
	Scanner sc = new Scanner(System.in);
	final int MOD = 1000000007;
	final int MAX = Integer.MAX_VALUE;
	final long LMAX = Long.MAX_VALUE;
		
	void doIt() {
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k[] = new int[n];
		for(int i = 0; i < m; i++) {
			int knum = sc.nextInt();
			for(int j = 0; j < knum; j++) {
				k[sc.nextInt() - 1] += (1 << i);
			}
		}
		int p = 0;
		for(int i = 0; i < m; i++) {
			p += sc.nextInt() << i; 
		}
		int cnt = 0;
		for(int i = 0; i < (1 << n); i++) {
			int check = 0;
			for(int j = 0; j < n; j++){
				if(((i >> j) & 1) == 1) {
					check ^= k[j];
				}
			}
			if(check == p) cnt++;
		}
		System.out.println(cnt);
	}

	
	public static void main(String[] args) {
		new Main().doIt();
	}
}
