import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
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;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int N = in.nextInt();
            int M = in.nextInt();

            int[] switches = new int[N];
            for (int i = 0; i < M; i++) {
                int p = (1 << i);
                int k = in.nextInt();
                for (int j = 0; j < k; j++)
                    switches[in.nextInt() - 1] |= p;
            }
            int expected = 0;
            for (int i = 0; i < M; i++) {
                if (in.nextInt() == 1)
                    expected |= (1 << i);
            }

            int count = 0;
            int lim = (int) Math.pow(2, N);
            for (int i = 0; i < lim; i++) {
                int ans = 0;
                for (int j = 0; j < N; j++) {
                    if ((i & (1 << j)) != 0)
                        ans ^= switches[j];
                }
                if (ans == expected)
                    count++;
            }
            out.println(count);
        }

    }

    static class FastScanner {
        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int bufPointer;
        private int bufLength;

        public FastScanner(InputStream in) {
            this.in = in;
            this.bufPointer = 0;
            this.bufLength = 0;
        }

        private int readByte() {
            if (bufPointer >= bufLength) {
                if (bufLength == -1)
                    throw new InputMismatchException();

                bufPointer = 0;
                try {
                    bufLength = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (bufLength <= 0)
                    return -1;
            }
            return buffer[bufPointer++];
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int nextInt() {
            int n = 0;

            int b = readByte();
            while (isSpaceChar(b))
                b = readByte();

            boolean minus = (b == '-');
            if (minus)
                b = readByte();

            while (b >= '0' && b <= '9') {
                n *= 10;
                n += b - '0';
                b = readByte();
            }

            if (!isSpaceChar(b))
                throw new NumberFormatException();

            return minus ? -n : n;
        }

    }
}



Measured memory_bytes: 23380