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.io.*;
import java.util.*;


public class Main {
    static long mod = 1000000000+7;
    static int maxn=2;
    static long[] f5ac, inv;
    static ArrayList<Integer>[] rec;
    static int[] p;
    static int n,m;
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        //BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        //String[] buf = reader.readLine().split(" ");
        n = sc.nextInt();m = sc.nextInt();
        rec = new ArrayList[m];
        for(int i=0;i<m;i++){
            rec[i] = new ArrayList<>();
            int k = sc.nextInt();
            for(int j=0;j<k;j++) rec[i].add(sc.nextInt()-1);
        }
        p = new int[m];
        int ans = 0;
        for(int i=0;i<m;i++) p[i]=sc.nextInt();
        for(int s=(1<<n)-1;s>=0;s--){
            if(check(s)) ans ++;
        }
        System.out.println(ans);
    }
    static boolean check(int state){
        for(int i=0;i<m;i++){
            // for every bulb
            int cur=0;
            for(int w:rec[i]){
                if((state&(1<<w))>0) cur ++;
            }
            if((cur%2)!=(p[i]%2)) return false;
        }
        return true;
    }
}

