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.*;

class Main{
	static int[] swi = new int[11];

	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] k = new int[m];
		int[][] s = new int[m][];
		for(int i = 0; i < m; i++){
			k[i] = sc.nextInt();
			s[i] = new int[k[i]];
			for(int j = 0; j < k[i]; j++){
				s[i][j] = sc.nextInt()-1;
			}
		}
		int[] p = new int[m];
		for(int i = 0; i < m ; i++){
			p[i] = sc.nextInt();
		}
		int ans = 0;
		for(int i = 0; i < Math.pow(2,n); i++){
			pra();
			/*for(int aaa : swi){
				System.out.print(aaa);
			}
			System.out.println();*/
			int ba = 0;
			int sumsum = 0;
			for(int j = 0; j < m; j++){
				int sum = 0;
				for(int l = 0; l < k[j]; l++){
					if(swi[s[j][l]] == 1){
						sum++;
					}
				}
				if(sum%2 == p[j]){
					sumsum++;
				}
			}
			if(sumsum == m){
				ans++;
			}
		}
		System.out.print(ans);
	}

	static void pra(){
		int idx = 0;
		while(true){
			if(swi[idx] == 0){
				swi[idx] = 1;
				break;
			}else{
				swi[idx] = 0;
				idx++;
			}
		}
	}
}
