import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws Exception {
        try (Reader r = new Reader(System.in)) {
            int N = r.i();
            int M = r.i();
            int[][] S = new int[M][];
            for (int i = 0; i < M; i++) {
                int k = r.i();
                S[i] = new int[k];
                for (int j = 0; j < k; j++) {
                    S[i][j] = r.i() - 1;
                }
            }
            int[] P = r.ia();

            int ans = 0;
            for (int s = 0; s < Math.pow(2, N); s++) {
                boolean ok = true;
                for (int i = 0; i < M; i++) {
                    int q = 0;
                    for (int j = 0; j < S[i].length; j++) {
                        q += (s & (1 << S[i][j])) >> S[i][j];
                    }

                    if (q % 2 != P[i]) {
                        ok = false;
                        break;
                    }
                }

                if (ok) {
                    ans++;
                }
            }

            System.out.println(ans);
        }
    }

    public static class Reader implements AutoCloseable {

        private BufferedReader br;

        private String[] buf;

        private int bufidx = -1;

        public Reader(InputStream in) {
            this.br = new BufferedReader(new InputStreamReader(in));
        }

        @Override
        public void close() throws Exception {
            br.close();
        }

        private void readBuf() throws IOException {
            if (bufidx == -1 || bufidx == buf.length) {
                buf = br.readLine().split(" ");
                bufidx = 0;
            }
        }

        public String s() throws IOException {
            readBuf();
            return buf[bufidx++];
        }

        public int i() throws IOException {
            return Integer.parseInt(s());
        }

        public long l() throws IOException {
            return Long.parseLong(s());
        }

        public double d() throws IOException {
            return Double.parseDouble(s());
        }

        public String[] sa() throws IOException {
            readBuf();
            if (bufidx != 0) {
                throw new RuntimeException("illegal read");
            }
            bufidx = -1;
            return buf;
        }

        public int[] ia() throws IOException {
            String[] sa = sa();
            int[] ia = new int[sa.length];
            for (int i = 0; i < sa.length; i++) {
                ia[i] = Integer.parseInt(sa[i]);
            }
            return ia;
        }

        public long[] la() throws IOException {
            String[] sa = sa();
            long[] la = new long[sa.length];
            for (int i = 0; i < sa.length; i++) {
                la[i] = Long.parseLong(sa[i]);
            }
            return la;
        }

        public double[] da() throws IOException {
            String[] sa = sa();
            double[] da = new double[sa.length];
            for (int i = 0; i < sa.length; i++) {
                da[i] = Double.parseDouble(sa[i]);
            }
            return da;
        }

        public int[][] im(int N) throws IOException {
            int[][] im = new int[N][];
            for (int i = 0; i < N; i++) {
                im[i] = ia();
            }
            return im;
        }

        public long[][] lm(int N) throws IOException {
            long[][] lm = new long[N][];
            for (int i = 0; i < N; i++) {
                lm[i] = la();
            }
            return lm;
        }

        public double[][] dm(int N) throws IOException {
            double[][] dm = new double[N][];
            for (int i = 0; i < N; i++) {
                dm[i] = da();
            }
            return dm;
        }

    }

}


Measured memory_bytes: 23252