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{
    final static long mod = 1000000007;
    //
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        boolean[][] connection = new boolean[m][10];
        for(int i = 0; i < m; i++){
            int k = sc.nextInt();
            for(int j = 0; j < k; j++){
                connection[i][sc.nextInt() - 1] = true;
            }
        }
        int[] nums = new int[m];
        for(int i = 0; i < m; i++) nums[i] = sc.nextInt();
        int cnt = 0;
        for(int i = 0; i < (1 << n); i++){
            int on = 0;
            boolean[] swi = new boolean[10];
            for(int j = 0; j < 10; j++){
                if((i >> j & 1) == 1){
                    swi[j] = true;
                }
            }
            for(int j = 0; j < m; j++){
                int on_cnt = 0;
                for(int k = 0; k < 10; k++){
                    if(swi[k] && connection[j][k]) on_cnt++;
                }
                if(on_cnt % 2 == nums[j]) on++;
            }
            if(on == m) cnt++;
        }
        System.out.println(cnt);
    }
}