import java.io.*;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

        int n = in.nextInt();
        int m = in.nextInt();
        int[][] conSwi = new int[m][];
        for (int i = 0; i < m; i++) {
            int k = in.nextInt();
            conSwi[i] = in.nextIntArray(k);
        }
        int[] p = in.nextIntArray(m);
        int tot = 1 << n;
        int c = 0;
        for (int i = 0; i < tot; i++) {
            boolean plus = true;
            for (int j = 0; j < m; j++) {
                int num = 0;
                for (int k = 0; k < conSwi[j].length; k++) {
                    if ((i & (1 << (conSwi[j][k] - 1))) == 0) {
                        num++;
                    }
                }
                if (!((num & 1) == p[j])) {
                    plus = false;
                }
            }
            c = plus ? c + 1 : c;
        }
        out.println(c);
        out.close();
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public double[] nextDoubleArray(int n) {
            double[] arr = new double[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextDouble();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public char[] nextCharArray(int n) {
            char[] arr = nextLine().trim().replaceAll("\\s", "").toCharArray();
            return arr;
        }

        public String[] nextStringArray(int n) {
            String[] arr = new String[n];
            for (int i = 0; i < n; i++) {
                arr[i] = next();
            }
            return arr;
        }
    }
}


Measured memory_bytes: 21460