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.ArrayList;
    import java.util.List;
    import java.util.Scanner;
     
    public class Main {
        public static void main(String[] args) {
            Scanner sc = new Scanner(System.in);
            int N = sc.nextInt();
            int M = sc.nextInt();
            List<List<Integer>> s = new ArrayList<>(M);
            for(int i = 0; i < M; i++) {
                int k = sc.nextInt();
                List<Integer> l  = new ArrayList<>();
                for(int j = 0; j < k; j++) {
                    l.add(sc.nextInt() - 1);
                }
                s.add(l);
            }
            List<Integer> p = new ArrayList<>();
            for(int i = 0; i < M; i++) {
                p.add(sc.nextInt());
            }
     
            long res = 0;
            for(int bit = 0; bit < (1 << N); bit++) {
                boolean ok = true;
                for(int i = 0; i < M; i++) {
                    int count = 0;
                    for(int t : s.get(i)) {
                        if(((bit >> t) & 1) == 1) count++;
                    }
                    if(count % 2 != p.get(i)) {
                        ok = false;
                        break;
                    }
                }
                if(ok) res++;
            }
            System.out.println(res);
        }
    }