#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <numeric>
#include <queue>
#include <stack>
#include <map> 
#include <set>
#include <string>
#include <functional>
#include <list>
#include <random>
#include <time.h>
#include <iomanip>
#include <assert.h>
#include <numeric>
#define int long long
#define ll long long
#define double long double
#define mod 1000000007
#define MAXN (int)1e+5 * 2+1
#define LL_MAX 9223372036854775807	//ない環境用
#define LL_HALFMAX 9223372036854775807 / 2	//ない環境用
#define MIN -(9223372036854775807 / 2)
#define INF 9223372036854775807 / 2
#define REP(i,a,n) for(int i=(a); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define FOR(it,c) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define ALLOF(c) (c).begin(), (c).end()
#define REPS(i,x) for(int i=1;i<=(int)(x);i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RREPS(i,x) for(int i=((int)(x));i>0;i--)
#define repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define mp make_pair


using namespace std;

std::mt19937 mt((int)time(0));

int dx[4] = { 0, 1, 0, -1 }; // x軸方向への変位
int dy[4] = { 1, 0, -1, 0 }; // y軸方向への変位

using Weight = int;
using Flow = int;
struct Edge {
	int src, dst;
	Weight weight;
	Flow cap;
	Edge() : src(0), dst(0), weight(0) {}
	Edge(int s, int d, Weight w) : src(s), dst(d), weight(w) {}
};
using Edges = std::vector<Edge>;
using Graph = std::vector<Edges>;
using Array = std::vector<Weight>;
using Matrix = std::vector<Array>;

void add_edge(Graph &g, int a, int b, Weight w = 1) {
	g[a].emplace_back(a, b, w);
	g[b].emplace_back(b, a, w);
}
void add_arc(Graph &g, int a, int b, Weight w = 1) { g[a].emplace_back(a, b, w); }

struct uf_tree {
	std::vector<int> parent;
	int __size;
	uf_tree(int size_) : parent(size_, -1), __size(size_) {}
	void unite(int x, int y) {
		if ((x = find(x)) != (y = find(y))) {
			if (parent[y] < parent[x]) std::swap(x, y);
			parent[x] += parent[y];
			parent[y] = x;
			__size--;
		}
	}
	bool is_same(int x, int y) { return find(x) == find(y); }
	int find(int x) { return parent[x] < 0 ? x : parent[x] = find(parent[x]); }
	int size(int x) { return -parent[find(x)]; }
	int size() { return __size; }
};



//!!!問題をちゃんと読む!!!
//!!!問題をちゃんと読め!!!
//!!!問題は読みましたか？!!!

class rest {
public:
	string S;
	int P;
	int Num;
public:
	rest(string s, int p, int num) {
		S = s;
		P = p;
		Num = num;
	}
	bool operator<(const rest &another) const
	{
		if( S != another.S)return S < another.S;
		return P > another.P;

	};
};

int imos[1000000];

signed main() {
	int N, M;
	cin >> N >> M;
	vector<vector<int>> swi;
	rep(i, M) {
		int k;
		cin >> k;
		vector<int> kSwi;
		rep(j, k) {
			int s;
			cin >> s;
			kSwi.push_back(s);
		}
		swi.push_back(kSwi);
	}
	vector<int> p;
	rep(i, M) {
		int pin;
		cin >> pin;
		p.push_back(pin);
	}
	int ans = 0;
	rep(i, (1 << N)) {
		int s[100];
		rep(k, 100) s[k] = 0;
		rep(j, N) {
			int SwitchOn = i & 1 << j;
			if (SwitchOn) {
				s[j] = 1;
			}
		}
		//チェック
		int On = 0;
		rep(den, M) {
			int num = 0;
			auto v = swi[den];

			for (auto link : v) {
				if (s[link - 1]) {
					num++;
				}
			}
			if (num % 2 == p[den]) {
				On++;
			}
		}
		if (On == M) {
			ans++;
		}
	}
	cout << ans << "\n";



	return 0;
}

Measured memory_bytes: 256