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 { //atcoder ABC128C -

	public static void main(String[] args) {
		Scanner seer = new Scanner(System.in);
		int n = seer.nextInt();
		int m = seer.nextInt();
		ArrayList<Integer>[] bs = new ArrayList[m];
		for(int i = 0; i < m; i++){
			int k = seer.nextInt();
			bs[i] = new ArrayList<>();
			for(int j = 0; j < k; j++){
				bs[i].add(seer.nextInt()-1);
			}
		}
		int[] ps = new int[m];
		for(int i = 0; i < m; i++){
			ps[i] = seer.nextInt();
		}
		int res = 0;
		for(int mask = 0; mask < (1 << n); mask++){
			boolean add = true;
			for(int i = 0; i < m; i++){
				int comp = 0;
				for(int k: bs[i]){
					if((mask & (1 << k)) > 0){
						comp++;
					}
				}
				if(comp % 2 != ps[i]){
					add = false;
				}
			}
			if(add) res++;
		}
		System.out.println(res);
	}
}
