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.io.BufferedReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new java.io.InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());

        int N = Integer.parseInt(st.nextToken());
        int M = Integer.parseInt(st.nextToken());

        String[][] input_multiArray = new String[M][N];

        for(int i = 0; i < M; i++) {
            input_multiArray[i] = br.readLine().split(" ");
        }

        String[] p_array = br.readLine().split(" ");

        int ans = 0;

        for(int i = 0; i < (1<<N); i++) {

            boolean ableFlag = false;

            for(int j = 0; j < M; j++) {

                int onNum = 0;

                for(int k = 1; k <= Integer.parseInt(input_multiArray[j][0]); k++) {
                    if((i>>Integer.parseInt(input_multiArray[j][k])-1 & 1) == 1) {
                        onNum++;
                    }
                }

                if(onNum % 2 == Integer.parseInt(p_array[j])) {
                    ableFlag = true;
                } else {
                    ableFlag = false;
                    break;
                }
            }

            if(ableFlag) ans++;

        }

        pw.print(ans);
        br.close();
        pw.close();
    }
}