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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String[] nm = sc.nextLine().split(" ");
        int n = Integer.parseInt(nm[0]);// スイッチの種類
        int m = Integer.parseInt(nm[1]);// 電球の数

        List<List<Integer>> k = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            List<Integer> ele = new ArrayList<>();
            String[] a = sc.nextLine().split(" ");
            for (int j = 1; j < a.length; j++) {
                ele.add(Integer.valueOf(a[j]) - 1);
            }
            k.add(ele);
        }
        List<Integer> p = new ArrayList<>();
        for (String s : sc.nextLine().split(" ")) {
            p.add(Integer.valueOf(s));
        }

        int ans = 0;
        for (int i = 0; i < (Math.pow(2, n)); ++i) {
            boolean ok = true;
            for (int j = 0; j < m; ++j) {
                int c = 0;
                for (int id : k.get(j)) {
                    if ((1 & i >> id) == 1) {
                        ++c;
                    }
                }
                c %= 2;
                if (c != p.get(j)) {
                    ok = false;
                }
            }
            if (ok) {
                ++ans;
            }
        }
        System.out.println(ans);
    }
}