////////////////////////////////////////
///  tu3 pro-con template            ///
////////////////////////////////////////
#include "bits/stdc++.h"
using namespace std;

// -- typedefs -- //
#define EPS 1e-9
typedef long long llong;

// -- loop macros -- //
#define REP(i,n) for (auto i = decltype(n)(0); i < (n); i++)
#define RREP(i,n) for (auto i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (auto i = (s); i < (n); i++)
#define FORR(i,s,n) for (auto i = (n)-1; i >= (s); i--)
#define FORE(exp) for (auto && exp)
#define allof(c) c.begin(), c.end()
#define partof(c,s,e) c.begin() + (s), c.begin() + (e)

// -- functors -- //
#define PREDICATE(t,a,...) [&](const t & a) -> bool { return __VA_ARGS__; }
#define PRED(a,...) PREDICATE(auto,a,__VA_ARGS__)
#define COMPARISON(t,a,b,...) [&](const t & a, const t & b) -> bool { return __VA_ARGS__; }
#define COMP(a,b,...) COMPARISON(auto,a,b,__VA_ARGS__)
#define CONV1(a,...) [&](const auto & a) -> auto { return __VA_ARGS__; }
#define CONV2(a,b,...) [&](const auto & a, const auto & b) -> auto { return __VA_ARGS__; }
#define CONV3(a,b,c,...) [&](const auto & a, const auto & b, const auto & c) -> auto { return __VA_ARGS__; }

// -- I/O Helper -- //
struct _Reader { istream& cin; template <class T> _Reader operator ,(T& rhs) { cin >> rhs; return *this; } };
struct _Writer { ostream& cout; const char* delim{ " " }; bool f{ false }; template <class T> _Writer operator ,(const T& rhs) { cout << (f ? delim : "") << rhs; f = true; return *this; } };
#define READ(t,...) t __VA_ARGS__; (_Reader{cin}), __VA_ARGS__
#define WRITE(...) (_Writer{cout}), __VA_ARGS__, "\n"
#define WRITELN(...) (_Writer{cout, "\n"}), __VA_ARGS__, "\n"
#ifdef _DEBUG
#define DEBUG(...) (_Writer{cerr}), "DEBUG -> ", __VA_ARGS__, "\n"
#else
#define DEBUG(...)
#endif

// -- vevector -- //
template <class T> struct vevector : vector<vector<T>> { vevector(size_t n = 0, size_t m = 0, const T & initial = T()) : vector<vector<T>>(n, vector<T>(m, initial)) { } };
template <class T> struct vevevector : vector<vevector<T>> { vevevector(size_t n = 0, size_t m = 0, size_t l = 0, const T & initial = T()) : vector<vevector<T>>(n, vevector<T>(m, l, initial)) { } };
template <class T> struct vevevevector : vector<vevevector<T>> { vevevevector(size_t n = 0, size_t m = 0, size_t l = 0, size_t k = 0, const T & initial = T()) : vector<vevevector<T>>(n, vevevector<T>(m, l, k, initial)) { } };

namespace std {
	template <class T1, class T2> istream& operator >> (istream& in, pair<T1, T2>& p) { in >> p.first >> p.second; return in; }
	template <class T1, class T2> ostream& operator << (ostream& out, const pair<T1, T2>& p) { out << p.first << " " << p.second; return out; }
}

template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vector<T> readjag() { return read<T>(read<int>()); }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(readjag<T>()); return v; }

template <class T> struct iter_range_t { T beg, end; };
template <class T> iter_range_t<T> iter_range(T beg, T end) { return iter_range_t<T>{beg, end}; }
template <class T> ostream& operator << (ostream& out, iter_range_t<T> v) { if (v.beg != v.end) { out << *v.beg++; while (v.beg != v.end) { out << " " << *v.beg++; } } return out; }
template <class T> ostream& operator << (ostream& out, const vector<T>& v) { return out << iter_range(allof(v)); }

// -- etc -- //
template <class T> T infinity_value();
template <> int infinity_value<int>() { return int(1) << 28; }
template <> llong infinity_value<llong>() { return llong(1) << 60; }
template <> double infinity_value<double>() { return 1e+300 * 1e+300; }
#define INF(T) infinity_value<T>()

inline int sign_of(double x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }
template <class TInt> bool in_range(TInt val, TInt min, TInt max) { return val >= min && val < max; }
template <> bool in_range<double>(double val, double min, double max) { return val - min > -EPS && val - max < EPS; }
template <class TInt> bool in_range2d(TInt x, TInt y, TInt w, TInt h) { return x >= 0 && x < w && y >= 0 && y < h; }
vector<int> iotavn(int start, int count) { vector<int> r(count); iota(allof(r), start);	return r; }

//// start up ////
void solve();
int32_t main()
{
	//// for local debugging
	//freopen("input.txt", "right_", stdin);
	//freopen("output.txt", "w", stdout);

	//auto classic_table = ctype<char>::classic_table();
	//vector<ctype<char>::mask> ctable(classic_table, classic_table + ctype<char>::table_size);
	//ctable[':'] |= ctype_base::space; // as delimitor
	//ctable[','] |= ctype_base::space; // as delimitor
	//cin.imbue(locale(cin.getloc(), new ctype<char>(ctable.data())));

	cin.tie(nullptr);
	ios_base::sync_with_stdio(false);
	cout << fixed;
	cout << setprecision(std::numeric_limits<double>::max_digits10);

	solve();

	return 0;
}

////////////////////
/// template end ///
////////////////////

//// bit ////
typedef uint32_t uint;
typedef uint64_t ullong;
#ifdef _MSC_VER
#ifdef _WIN32
inline uint __builtin_ctz(uint x) { unsigned long r; _BitScanForward(&r, x); return r; }
inline uint __builtin_clz(uint x) { unsigned long r; _BitScanReverse(&r, x); return 31 - r; }
inline uint __builtin_ffs(uint x) { unsigned long r; return _BitScanForward(&r, x) ? r + 1 : 0; }
inline uint __builtin_popcount(uint x) { return __popcnt(x); }
#ifdef _WIN64
inline ullong __builtin_ctzll(ullong x) { unsigned long r; _BitScanForward64(&r, x); return r; }
inline ullong __builtin_clzll(ullong x) { unsigned long r; _BitScanReverse64(&r, x); return 63 - r; }
inline ullong __builtin_ffsll(ullong x) { unsigned long r; return _BitScanForward64(&r, x) ? r + 1 : 0; }
inline ullong __builtin_popcountll(ullong x) { return __popcnt64(x); }
#else
inline uint hidword(ullong x) { return static_cast<unsigned int>(x >> 32); }
inline uint lodword(ullong x) { return static_cast<unsigned int>(x & 0xFFFFFFFF); }
inline ullong __builtin_ctzll(ullong x) { return lodword(x) ? __builtin_ctz(lodword(x)) : __builtin_ctz(hidword(x)) + 32; }
inline ullong __builtin_clzll(ullong x) { return hidword(x) ? __builtin_clz(hidword(x)) : __builtin_clz(lodword(x)) + 32; }
inline ullong __builtin_ffsll(ullong x) { return lodword(x) ? __builtin_ffs(lodword(x)) : hidword(x) ? __builtin_ffs(hidword(x)) + 32 : 0; }
inline ullong __builtin_popcountll(ullong x) { return __builtin_popcount(lodword(x)) + __builtin_popcount(hidword(x)); }
#endif // _WIN64
#endif // _WIN32
#endif // _MSC_VER

void solve()
{
	READ(int, N, M);

	vector<int> swt;

	REP(i, M)
	{
		auto S = readjag<int>();
		int m = 0;
		FORE(s : S)
		{
			m |= 1 << (s - 1);
		}
		swt.push_back(m);
	}
	auto P = read<int>(M);

	llong ans = 0;
	REP(mask, 1 << N)
	{
		bool ok = true;
		REP(j, M)
		{
			ok &= (__builtin_popcount(swt[j] & mask) & 1) == P[j];
		}
		if (ok) ans++;
	}

	WRITE(ans);
}


Measured memory_bytes: 256