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 java.lang.*;

class Lamp{
    List<Integer> validSwitch;
    int p;
    public Lamp(List<Integer> validSwitch, int p){
        this.validSwitch = validSwitch;
        this.p = p;
    }
    boolean lighted(long switchSet){
        int cur=p;
        for(int s:validSwitch){
            if((switchSet & (1<<s))!=0) cur++;
        }
        return cur%2==0;
    }
}

public class Main {
    static int popCount(long bits){
        bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
        bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
        bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
        bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
        return (int)((bits & 0x0000ffff) + (bits >>16 & 0x0000ffff));
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        Lamp[] lamp = new Lamp[M];
        List<Integer>[] validSwitch = new ArrayList[M];
        for(int m=0; m<M; m++){
            int K = sc.nextInt();
            validSwitch[m] = new ArrayList<>(K);
            for(int k=0; k<K; k++) validSwitch[m].add(sc.nextInt()-1);
        }
        for(int m=0; m<M; m++) lamp[m] = new Lamp(validSwitch[m], sc.nextInt());

        long ans=0;
        for(long s=0; s<(1<<N); s++){
            boolean allLight = true;
            for(Lamp l: lamp) if(!l.lighted(s)) allLight=false;
            if(allLight) ans++;
        }
        System.out.println(ans);
    }
}