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
//https://atcoder.jp/contests/abc128/tasks/abc128_c

import java.util.Scanner;
import java.util.ArrayList;

class Main{
    static int N,M;
    static ArrayList<ArrayList<Integer>> s = new ArrayList<>();
    static ArrayList<Integer> p = new ArrayList<>();
    static int[] a;
    static int ans = 0;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        for (int i=0;i<M;i++){
            int k = sc.nextInt();
            ArrayList<Integer> si = new ArrayList<>();
            for (int j=0;j<k;j++){
                si.add(sc.nextInt());
            }
            s.add(si);
        }
        for (int i=0;i<M;i++){
            p.add(sc.nextInt());
        }
        sc.close();
        a = new int[N];
        dfs(0);
        System.out.println(ans);
    }
    
    public static void dfs(int pos){
        if (pos==N){
            func();
        } else {
            a[pos] = 0;
            dfs(pos+1);
            a[pos] = 1;
            dfs(pos+1);
        }
    }

    public static void func(){
        int count = 0;
        for (int i=0;i<s.size();i++){
            int cnt1 = 0;
            for (Integer si:s.get(i)){
                if (a[si-1]==1){
                    cnt1++;
                }
            }
            if (cnt1%2==p.get(i)){
                count++;
            }
        }
        if (count==M){
            ans++;
        }
    }
}