#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
// define
const int INF = 1 << 24;
#define endl "\n"
#ifdef LOCAL
#define lout cerr
#else
ostream devnull(0);
#define lout devnull
#endif
#define AMULET                                                                 \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
// rep
// Inspired by:
// https://github.com/kurokoji/.cpp-Template/blob/master/template/template2.cpp
#define GET_MACRO(_1, _2, _3, _4, NAME, ...) NAME
#define rep(...)                                                               \
  GET_MACRO(__VA_ARGS__, rep4, rep3, rep2, rep1)                               \
  (__VA_ARGS__)
#define rep1(n) rep2(_, n)
#define rep2(i, n) rep3(i, 0, n)
#define rep3(i, a, n) rep4(i, a, n, 1)
#define rep4(i, a, n, d) rep5(i, a, n, d, <)
#define rep5(i, a, n, d, o)                                                    \
  for(auto i = decltype(n)(a), i##_len = (n); i o i##_len; i += (d))

#define rrep(...)                                                              \
  GET_MACRO(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)                           \
  (__VA_ARGS__)
#define rrep1(a) rrep2(_, a)
#define rrep2(i, a) rrep3(i, a, 0)
#define rrep3(i, a, n) rrep4(i, a, n, -1)
#define rrep4(i, a, n, d) rep5(i, (a)-1, n, d, >=)

#define repc(...)                                                              \
  GET_MACRO(__VA_ARGS__, repc4, repc3, repc2, repc1)                           \
  (__VA_ARGS__)
#define repc1(n) repc2(_, n)
#define repc2(i, n) repc3(i, 0, n)
#define repc3(i, a, n) repc4(i, a, n, 1)
#define repc4(i, a, n, d) rep5(i, a, n, d, <=)

#define dump(x) lout << #x << " = " << x << endl;
// alias
typedef long long ll;
typedef long long lint;
typedef pair<int, int> pii;
typedef pair<lint, lint> pll;
// func
template <class C> inline void vcin(C &c);
template <class C, class D> inline void vcin(C &c, D &d);
template <class C> inline void vcout(const C &c, const string separate = "\n");
template <class T = int> inline T in();
template <class T> inline bool chmin(T &a, T b);
template <class T> inline bool chmax(T &a, T b);
// http://beet-aizu.hatenablog.com/entry/2018/04/08/145516
template <typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

void solve() {
  int n, m;
  cin >> n >> m;

  vector<int> t(m);

  rep(i, m) {
    int ki;
    cin >> ki;
    rep(ki) {
      int si;
      cin >> si;
      t[i] |= (1 << (si - 1));
    }
  }
  vector<int> p(m);
  vcin(p);

  lint ans = 0;

  rep(j, 1 << n) {
    bool flag = true;
    rep(i, m) {
      if(__builtin_popcount(j & t[i]) % 2 != p[i]) {
        flag = false;
        break;
      }
    }
    if(flag)
      ans++;
  }

  cout << ans << endl;
}

signed main() {
  AMULET
  solve();
  return 0;
}

template <class C> inline void vcin(C &c) {
  for(auto &&a : c) { cin >> a; }
}

template <class C, class D> inline void vcin(C &c, D &d) {
  for(auto it1 = c.begin(), it2 = d.begin(); it1 != c.end() && it2 != d.end();
      it1++, it2++) {
    cin >> *it1 >> *it2;
  }
}
template <class C> inline void vcout(const C &c, const string separate) {
  for(auto it = c.begin(); it != c.end(); it++) {
    if(it != c.begin())
      cout << separate;
    cout << *it;
  }
}
template <class T = int> inline T in() {
  T x;
  cin >> x;
  return (x);
}
template <class T> inline bool chmin(T &a, T b) {
  if(a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if(a < b) {
    a = b;
    return true;
  }
  return false;
}


Measured memory_bytes: 256