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.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] light = new int[m];
		int[] p = new int[m];
		
		for(int i = 0; i < m; i++){
		    int k = sc.nextInt();
		    for(int j = 0; j < k; j++){
		        int s = sc.nextInt();
		        light[i] |= 1<<(s-1); 
		    }
		}
		for(int i = 0; i < m; i++){
		    p[i] = sc.nextInt();
		}
		// 計算
		int result = 0;
		for(int i = 0; i < 1<<n; i++){
		    int temp = 0;
		    for(int j = 0; j < m; j++){
		        if(Integer.bitCount(i & light[j])%2 == p[j]){
		            temp++;
		            continue;
		        }
		        break;
		    }
		    if(temp == m) result++;
		}
		
		// 出力
		System.out.println(result);
	}
}