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
 *
 * @author KharYusuf
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CSwitches solver = new CSwitches();
        solver.solve(1, in, out);
        out.close();
    }

    static class CSwitches {
        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt(), m = s.nextInt(), a[][] = new int[m][n], p[] = new int[m], tot = 1 << n, k, ans = 0;
            boolean flag;
            for (int i = 0; i < m; i++) {
                k = s.nextInt();
                for (int j = 0; j < k; j++) {
                    a[i][s.nextInt() - 1] = 1;
                }
            }
            for (int i = 0; i < m; i++) {
                p[i] = s.nextInt();
            }
            for (int i = 0; i < tot; i++) {
                flag = true;
                for (int j = 0; j < m; j++) {
                    if (!check(a, p, j, i, n)) {
                        flag = false;
                        break;
                    }
                }
                if (flag) ans++;
            }
            w.println(ans);
        }

        boolean check(int[][] a, int[] p, int ind, int num, int n) {
            int on = 0;
            for (int i = 0; i < n; i++) {
                if (a[ind][i] == 1 && (num & 1) == 1) on++;
                num >>= 1;
            }
            return (on & 1) == p[ind];
        }

    }

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

        public FastReader(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 c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        }

    }
}



Measured memory_bytes: 25172