#include <iostream>
#include <array>
#include <algorithm>
#include <map>
#include <vector>
#include <list>
#include <cmath>
#include <stack>
#include <queue>
#include <climits>
#include <string.h>
#include <cctype>
#include <set>

#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;
using namespace std;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }

// a と b の最大公約数を返す関数
long long GCD(long long a, long long b) {
	if (b == 0) return a;
	else return GCD(b, a % b);
}

long long gcd(long long a, long long b)
{
	if (a % b == 0)
	{
		return(b);
	}
	else
	{
		return(gcd(b, a % b));
	}
}

long long lcm(long long a, long long b)
{
	return a * b / gcd(a, b);
}

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
struct mint {
	ll x; // typedef long long ll;
	mint(ll x = 0) :x((x% mod + mod) % mod) {}
	mint operator-() const { return mint(-x); }
	mint& operator+=(const mint a) {
		if ((x += a.x) >= mod) x -= mod;
		return *this;
	}
	mint& operator-=(const mint a) {
		if ((x += mod - a.x) >= mod) x -= mod;
		return *this;
	}
	mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this; }
	mint operator+(const mint a) const { return mint(*this) += a; }
	mint operator-(const mint a) const { return mint(*this) -= a; }
	mint operator*(const mint a) const { return mint(*this) *= a; }
	mint pow(ll t) const {
		if (!t) return 1;
		mint a = pow(t >> 1);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}

	// for prime mod
	mint inv() const { return pow(mod - 2); }
	mint& operator/=(const mint a) { return *this *= a.inv(); }
	mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream& operator>>(istream& is, const mint& a) { return is >> a.x; }
ostream& operator<<(ostream& os, const mint& a) { return os << a.x; }

struct combination {
	vector<mint> fact, ifact;
	combination(int n) :fact(n + 1), ifact(n + 1) {
		fact[0] = 1;
		for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
		ifact[n] = fact[n].inv();
		for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
	}
	mint operator()(int n, int k) {
		if (k < 0 || k > n) return 0;
		return fact[n] * ifact[k] * ifact[n - k];
	}
} comb(2000005);

mint g(int r, int c) {
	return comb(r + c + 2, r + 1) - 1;
}

bool comp(int i, int j) {
	return i > j;
}

bool compare_by_b(pair<int, int> a, pair<int, int> b) {
	return a.second < b.second;
}

long tall[200000];
long long diff[200000];
vector<int> que;

// index が条件を満たすかどうか
bool isOK(int index, int key) {
	if (que[index] >= key) return true;
	else return false;
}

// 汎用的な二分探索のテンプレ
int binary_search(int key) {
	int left = -1; //「index = 0」が条件を満たすこともあるので、初期値は -1
	int right = (int)que.size(); // 「index = a.size()-1」が条件を満たさないこともあるので、初期値は a.size()

	/* どんな二分探索でもここの書き方を変えずにできる！ */
	while (right - left > 1) {
		int mid = left + (right - left) / 2;

		if (isOK(mid, key)) right = mid;
		else left = mid;
	}

	/* left は条件を満たさない最大の値、right は条件を満たす最小の値になっている */
	return right;
}

int n, m;
vector<int> s[10];
int p[10];
int sample[10];

bool check()
{

	for (int i = 0; i < m; i++)
	{
		int count = 0;
		for (int j = 0; j < s[i].size(); j++)
		{
			if (sample[s[i][j] - 1] == 1)
			{
				count++;
			}
		}
		if (count % 2 != p[i])
		{
			return false;
		}
	}
	return true;
}

int main()
{
	cin >> n >> m;
	for (int i = 0; i < m; i++)
	{
		int k;
		cin >> k;
		for (int j = 0; j < k; j++)
		{
			int tmp;
			cin >> tmp;
			s[i].push_back(tmp);
		}
	}

	for (int i = 0; i < m; i++)
	{
		cin >> p[i];
	}

	int count = 0;
	for (int i1 = 0; i1 < 2; i1++)
	{
		sample[0] = i1;
		if (n == 1)
		{
			if (check())
			{
				count++;
			}
			continue;
		}
		for (int i2 = 0; i2 < 2; i2++)
		{
			sample[1] = i2;
			if (n == 2)
			{
				if (check())
				{
					count++;
				}
				continue;
			}
			for (int i3 = 0; i3 < 2; i3++)
			{
				sample[2] = i3;
				if (n == 3)
				{
					if (check())
					{
						count++;
					}
					continue;
				}
				for (int i4 = 0; i4 < 2; i4++)
				{
					sample[3] = i4;
					if (n == 4)
					{
						if (check())
						{
							count++;
						}
						continue;
					}
					for (int i5 = 0; i5 < 2; i5++)
					{
						sample[4] = i5;
						if (n == 5)
						{
							if (check())
							{
								count++;
							}
							continue;
						}
						for (int i6 = 0; i6 < 2; i6++)
						{
							sample[5] = i6;
							if (n == 6)
							{
								if (check())
								{
									count++;
								}
								continue;
							}
							for (int i7 = 0; i7 < 2; i7++)
							{
								sample[6] = i7;
								if (n == 7)
								{
									if (check())
									{
										count++;
									}
									continue;
								}
								for (int i8 = 0; i8 < 2; i8++)
								{
									sample[7] = i8;
									if (n == 8)
									{
										if (check())
										{
											count++;
										}
										continue;
									}
									for (int i9 = 0; i9 < 2; i9++)
									{
										sample[8] = i9;
										if (n == 9)
										{
											if (check())
											{
												count++;
											}
											continue;
										}
										for (int i10 = 0; i10 < 2; i10++)
										{
											sample[9] = i10;
											if (check())
											{
												count++;
											}
										}
									}
								}
							}
						}
					}
				}
			}
		}
	}
	cout << count;
}


Measured memory_bytes: 31488