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();
        int m = sc.nextInt();
        int[][] S = new int[m][n];
        int[] P = new int[m];
        int ans = 0;
        for(int i = 0; i < m; i++) {
            int k = sc.nextInt();
            for(int j = 0; j < k; j++) S[i][j] = sc.nextInt();
        }
        for(int i = 0; i < m; i++) P[i] = sc.nextInt();

        for(int i = 0; i < (1 << n); i++) {
            int c1 = 0;
            for(int j = 0; j < m; j++) {
                int c2 = 0;
                for(int sft : S[j]) {
                    if(sft > 0) {
                         c2 += (i >> (n - sft)) & 1;
                    }
                }
                if(c2 % 2 == P[j]) c1++;
            }
            if(c1 == m) ans++;
        }
        System.out.println(ans);
    }
}
