#include <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <array>
#include <vector>
#include <deque>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <queue>
#include <bitset>
#include <tuple>
#include <cmath>
#include <complex>
#include <algorithm>
#include <utility>
#include <regex>
#include <cstdint>
#include <numeric>
#include <functional>
#include <cassert>

using namespace std;
using ll  = long long;
using ull = unsigned long long;

namespace utils{
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
    template<class T, class Compare> using p_queue = priority_queue<T, vector<T>, Compare>;
    template<class T> using min_queue = p_queue<T, greater<T>>;
    template<class T> using max_queue = p_queue<T, less<T>>;

    template<class T> inline bool UPMIN(T& X, const T& A){ if(X > A) {X = A; return true;} return false; }
    template<class T> inline bool UPMAX(T& X, const T& A){ if(X < A) {X = A; return true;} return false; }

    template<class T>
    vector<T> VEC(int n, T t){
        return vector<T>(n, t);
    }
    template<class ...Ts>
    auto VEC(int n, Ts ... ts){
        return vector<decltype(VEC(ts...))>(n, VEC(ts...));
    }

    template <class S, class T>
    istream& operator>>(istream& is, tuple<S, T>& t){
        return is >> get<0>(t) >> get<1>(t);
    }

    template <class S, class T, class U>
    istream& operator>>(istream& is, tuple<S, T, U>& t){
        return is >> get<0>(t) >> get<1>(t) >> get<2>(t);
    }

    template <class S, class T>
    ostream& operator<<(ostream& os, const tuple<S, T>& t){
        return os << get<0>(t) << ' ' <<  get<1>(t);
    }

    template <class S, class T, class U>
    ostream& operator<<(ostream& os, const tuple<S, T, U>& t){
        return os << get<0>(t) << ' ' <<  get<1>(t) << ' ' <<  get<2>(t);
    }

    template<class T>
    istream& operator>>(istream& is, vector<T>& v){
        for (auto &&x : v) { is >> x; } return is;
    }

    template<class T>
    ostream& operator<<(ostream& os, const vector<T>& v){
        auto p = v.begin();
        assert(p != v.end());
        os << *p++;
        while(p != v.end()){
            os << ' ' << *p++;
        }
        return os ;
    }

    template<class T>
    ostream& operator<<(ostream& os, const vector<vector<T>>& v){
        auto p = v.begin();
        assert(p != v.end());
        os << *p++;
        while(p != v.end()){
            os << '\n' << *p++;
        }
        return os;
    }

    template<class ...Ts>
    ostream& operator<<(ostream& os, const vector<tuple<Ts...>>& v){
        auto p = v.begin();
        assert(p != v.end());
        os << *p++;
        while(p != v.end()){
            os << '\n' << *p++;
        }
        return os;
    }

    constexpr long long INFLL   = 1'000'000'000'000'000'000ll;
    constexpr int       INF     = 1'000'000'000;
    constexpr double    PI      = 3.14'159'265'358'973;
    constexpr double    EPS     = 1e-10;
}
using namespace utils;


class solver{
    istream& is;
    ostream& os;

public:
    solver(istream& I, ostream& O) :is(I), os(O) {}
    ll N, M;
    vector<unsigned> swi;
    unsigned req;
    bool input() {
        N = M = 0;
        is >> N >> M;
        swi.resize(N);
        unsigned b = 1;
        for (int i = 0; i < M; ++i) {
            int k; is >> k;
            for (int j = 0; j < k; ++j) {
                int s; is >> s;
                swi[s-1] |= b;
            } // end j
            b <<= 1u;
        } // end i
        req = 0;
        b = 1;
        for (int i = 0; i < M; ++i) {
            unsigned p; is >> p;
            if(p) req |= b;
            b <<= 1u;
        } // end i

        return !!is;
    }

    int dfs(int d, unsigned now){
        if(d >= N) return now == req;
        return dfs(d+1, now) + dfs(d+1, now ^ swi[d]);
    }

    void run();
};

int main(int argc, char *argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(16) << scientific;
#ifdef XELMH
    string test_cases = "test_C.txt";
    cerr << test_cases << " -->" << endl;
    auto fs = fstream(test_cases, fstream::in);
    int loop = 0;
    while(fs) {
        loop++;
        cout << '#' << loop << "#------\n";
        solver(fs, cout).run();
    }
    if(loop <= 1) {
        cout << "===" << endl;
        while(cin) solver(cin, cout).run();
    }
#else
    solver(cin, cout).run();
#endif
    return 0;
}


void solver::run(){
    if(!input()) return;
    os << dfs(0,0u) << endl;
}


Measured memory_bytes: 256