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.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(), m = sc.nextInt();
        int[][] s = new int[m][10];
        for (int i = 0; i < m; i++) {
            int k = sc.nextInt();
            for (int j = 0; j < k; j++) {
                s[i][j] = sc.nextInt();
            }
        }
        boolean[] is0 = new boolean[m];
        for (int i = 0; i < m; i++) {
            is0[i] = sc.nextInt() == 0;
        }

        int ans = 0;
        for (int switches = 0; switches < (1 << n); switches++) {//suicchizentansaku
            boolean flag = true;
            boolean[] isOn = new boolean[n];
            for (int i = 0; i < n; i++) {
                isOn[i] = ((switches >> i) & 1) == 1;
            }

            for (int i = 0; i < m; i++) {//denkyugoto

                int on = 0;
                for (int k : s[i]) {
                    if (k == 0) break;
                    if (isOn[k - 1]) on++;
                }
                if (is0[i] != (on % 2 == 0)) {
                    flag = false;
                }

            }

            if (flag) ans++;
        }
        System.out.println(ans);
    }
}