#include <bits/stdc++.h>
using namespace std;

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
    return '"' + s + '"';
}

string to_string(const char* s) {
    return to_string((string) s);
}

string to_string(bool b) {
     return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
    bool first = true;
    string res = "{";
    for (int i = 0; i < static_cast<int>(v.size()); i++) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(v[i]);
    }
    res += "}";
    return res;
}

template <size_t N>
string to_string(bitset<N> v) {
    string res = "";
    for (size_t i = 0; i < N; i++) {
        res += static_cast<char>('0' + v[i]);
    }
    return res;
}

template <typename A>
string to_string(A v) {
    if(v.size() >= 100) {
        return "Too big container";
    }

    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
    return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
    return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

#define rep(i,n) for (int i = 0; i < n; ++i)
#define rep1(i,n) for (int i = 1; i <= n; ++i)
#define reps(i,s,n) for (int i = s; i < n; ++i)
#define all(c) begin(c),end(c)
template<typename T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
typedef long long ll;
typedef long double ld;
typedef pair<int,int> PINT;
typedef pair<ll,ll> PLL;
const long long MOD = 1e9+7;
#define precout() cout << std::fixed << std::setprecision(20);
#define print(a) cout << a << endl;
const int INFI = (1 << 30) - 1;
const long long INFLL = (1LL << 62) - 1;
template<typename T> void printv(vector<T>&v) {
    int n = v.size() - 1;
    rep(i, n) cout << v[i] << " ";
    cout << v.back() << endl;
}
const int dy[4] = { 0, 1, 0, -1 };
const int dx[4] = { 1, 0, -1, 0 };
double deg2rad(double deg) { return deg * M_PI / 180; }
double rad2deg(double rad) { return rad * 180 / M_PI; }

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N,M; cin >> N >> M;
    vector<vector<int>> S(M);
    rep(i, M) {
        int k; cin >> k;
        rep(j, k) {
            int s; cin >> s; --s;
            S[i].push_back(s);
        }
    }

    vector<int> P(M);
    rep(i, M) cin >> P[i];

    int ans = 0;
    for(int bit = 0; bit < (1 << N); ++bit) {
        vector<bool> onS(N, 0);
        rep(i, N) {
            if(bit & (1 << i)) {
                onS[i] = 1;
            }
        }

        int onCnt = 0;
        rep(i, M) {
            int cnt = 0;
            rep(j, S[i].size()) {
                if(onS[S[i][j]]) ++cnt;
            }
            if((cnt % 2) == P[i]) ++onCnt;
        }

        if(onCnt == M) ++ans;
    }

    print(ans);
}


Measured memory_bytes: 3660