import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C solver = new C();
        solver.solve(1, in, out);
        out.close();
    }

    static class C {
        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int N = in.Int();
            int M = in.Int();
            int[] sw = new int[M];
            for (int i = 0; i < M; i++) {
                int k = in.Int();
                for (int s : in.Int(k)) {
                    sw[i] += (1 << (s - 1));
                }
            }
            int[] p = in.Int(M);

            int ans = 0;
            int max = (int) Math.pow(2, N);
            for (int i = 0; i <= max; i++) {
                boolean f = true;
                for (int j = 0; j < M; j++) {
                    if (Integer.bitCount(i & sw[j]) % 2 != p[j]) {
                        f = false;
                    }
                }
                if (f) ans++;
            }
            out.println(ans);
        }

    }

    static class MyScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public MyScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int Int() {
            return Integer.parseInt(next());
        }

        public int[] Int(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = Int();
            }
            return a;
        }

    }
}

