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.Arrays;
import java.util.Scanner;

public class Main {
    int n, m;
    int[][] ss;
    int[] ks;
    int[] ps;
    void run() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt(); m = sc.nextInt();

        ss = new int[m][];
        ks = new int[m];
        ps = new int[m];
        for (int i = 0; i < m; i++) {
            ks[i] = sc.nextInt();
            ss[i] = new int[ks[i]];
            for (int j = 0; j < ks[i]; j++) {
                ss[i][j] = sc.nextInt() - 1;
            }
        }

        for (int i = 0; i < m; i++) {
            ps[i] = sc.nextInt();
        }

        int cnt = 0;
        for (int S = 0; S < (1 << n); S++) {
            if (check(S)) cnt++;
        }
        System.out.println(cnt);
    }

    boolean check(int S) {
        for (int i = 0; i < m; i++) {
            int cnt = 0;
            for (int j = 0; j < ks[i]; j++) {
                cnt += (S & (1 << ss[i][j])) > 0 ? 1 : 0;
            }
            if (cnt % 2 != ps[i]) return false;
        }
        return true;
    }

    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
