import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
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;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CSwitches solver = new CSwitches();
        solver.solve(1, in, out);
        out.close();
    }

    static class CSwitches {
        public void solve(int testNumber, InputReader sc, OutputWriter out) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int ar[][] = new int[m][n];
            for (int i = 0; i < m; i++) {
                int k = sc.nextInt();
                for (int j = 0; j < k; j++) {
                    int s = sc.nextInt();
                    ar[i][s - 1] = 1;
                }
            }
            int p[] = new int[m];
            for (int i = 0; i < m; i++)
                p[i] = sc.nextInt();
            int ans = 0;
            for (int i = 0; i < (1 << n); i++) {
                int arr[] = new int[n];
                for (int j = 0; j < n; j++) {
                    int a = ((1 << j) & i);
                    if (a != 0)
                        arr[j] = 1;
                }
                int c = 0;
                for (int j = 0; j < m; j++) {
                    int on = 0;
                    for (int k = 0; k < n; k++) {
                        if (ar[j][k] == 1 && arr[k] == 1)
                            on++;
                    }
                    if (on % 2 == p[j])
                        c++;
                }
                if (c == m)
                    ans++;
            }
            out.println(ans);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}



Measured memory_bytes: 22868