#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
#include <iostream>
#include <random>
#include <unordered_map>
#include <unordered_set>
#include <immintrin.h>
#ifdef _MSC_VER
#include <ppl.h>
#endif

using namespace std;

//呪文
#define DUMPOUT cerr
#define dump(...) DUMPOUT<<"  ";DUMPOUT<<#__VA_ARGS__<<" :["<<__LINE__<<":"<<__FUNCTION__<<"]"<<endl;DUMPOUT<<"    ";dump_func(__VA_ARGS__)

typedef unsigned uint; typedef long long ll; typedef unsigned long long ull; typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef pair<double, double> pdd; typedef pair<string, string> pss;
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const pair<_KTy, _Ty>& m) { o << "{" << m.first << ", " << m.second << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const unordered_map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const vector<_Ty>& v) { if (v.empty()) { o << "{ }"; return o; } o << "{" << v.front(); for (auto itr = ++v.begin(); itr != v.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const unordered_set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; }	o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const stack<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } stack<_Ty> t(s); o << "{" << t.top(); t.pop(); while (!t.empty()) { o << ", " << t.top(); t.pop(); } o << "}";	return o; }
template <typename _Ty> ostream& operator << (ostream& o, const list<_Ty>& l) { if (l.empty()) { o << "{ }"; return o; } o << "{" << l.front(); for (auto itr = ++l.begin(); itr != l.end(); ++itr) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> istream& operator >> (istream& is, pair<_KTy, _Ty>& m) { is >> m.first >> m.second; return is; }
template <typename _Ty> istream& operator >> (istream& is, vector<_Ty>& v) { for (size_t i = 0; i < v.size(); i++) is >> v[i]; return is; }
namespace aux { // print tuple
    template<typename Ty, unsigned N, unsigned L> struct tp { static void print(ostream& os, const Ty& v) { os << get<N>(v) << ", "; tp<Ty, N + 1, L>::print(os, v); } };
    template<typename Ty, unsigned N> struct tp<Ty, N, N> { static void print(ostream& os, const Ty& v) { os << get<N>(v); } };
}
template<typename... Tys> ostream& operator<<(ostream& os, const tuple<Tys...>& t) { os << "{"; aux::tp<tuple<Tys...>, 0, sizeof...(Tys) - 1>::print(os, t); os << "}"; return os; }

template<typename A, size_t N, typename T> inline void Fill(A(&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }

void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) { DUMPOUT << head; if (sizeof...(Tail) == 0) { DUMPOUT << " "; } else { DUMPOUT << ", "; } dump_func(std::move(tail)...); }

template<typename Ty>Ty modpow(Ty n, Ty e, Ty m) { Ty result = 1; while (e > 0) { if (e & 1)result = (result*n) % m; e >>= 1; n = (n*n) % m; }return result; }


#define PI 3.14159265358979323846
#define EPS 1e-10
#define FOR(i,a,n) for(int i=(a);i<(n);++i)
#define REP(i,n)  FOR(i,0,n)
#define all(j) (j).begin(), (j).end()
#define SZ(j) ((int)(j).size())
#define fake false



#define int long long

signed main() {

    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    
    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);
    cin >> p;

    int ans = 0;
    // all switch
    for (int i = 0; i < (1 << N); i++) {
        vector<bool> on(N);
        for (int b = 0; b < N; b++) {
            if ((i >> b) & 1) on[b] = true;
            else on[b] = false;
        }

        int x = 0;
        for (int j = 0; j < M; j++) {
            // each lamp
            int numOn = 0;
            for (int k : S[j]) if (on[k]) numOn++;
            if (numOn % 2 == p[j]) x++;
        }
        if (x == M) ans++;
    }

    cout << ans << endl;

    return 0;
}


Measured memory_bytes: 256