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 {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		// 整数の入力
		int n = sc.nextInt();
		int m = sc.nextInt();

		int[][] sk = new int[10][10];
		int[] k = new int[m];
		int[] p = new int[m];

		for(int i=0;i<m;i++){
			int k2 = sc.nextInt();
			k[i] = k2;
			for(int j=0;j<k2;j++){
				sk[i][j]=sc.nextInt();
			}
		}

		for(int s=0;s<m;s++){
			p[s]=sc.nextInt();
		}

		int num = (int)(Math.pow(2,n));
		int[] sw = new int[n];
		int ans = 0;

		for(int t=0;t<num;t++){
			int nnn = t;
			for(int u=0;u<n;u++){	//スイッチのオンオフ
				sw[u]=nnn%2;
				nnn/=2;
			}
			boolean flg = true;
			for(int v=0;v<m;v++){	//電球
				int count = 0;
				for(int w=0;w<k[v];w++){	//対応スイッチ
					count += sw[sk[v][w]-1];
				}
				if(count%2!=p[v]){
					flg=false;
					break;
				}
			}
			if(flg)ans++;
		}

		// 出力
		System.out.println(ans);
	}
}