Problem:
Score : 300 points

Problem Statement

We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.

Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.

How many combinations of "on" and "off" states of the switches light all the bulbs?

Constraints

1 \leq N, M \leq 10

1 \leq k_i \leq N

1 \leq s_{ij} \leq N

s_{ia} \neq s_{ib} (a \neq b)

p_i is 0 or 1.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M

Output

Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.

Sample Input 1

2 2
2 1 2
1 2
0 1

Sample Output 1

1

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

There are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.

Sample Input 2

2 3
2 1 2
1 1
1 2
0 0 1

Sample Output 2

0

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an even number of switches that are "on" among the following: Switch 1.

Bulb 3 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

Switch 1 has to be "off" to light Bulb 2 and Switch 2 has to be "on" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.

Sample Input 3

5 2
3 1 2 5
2 2 3
1 0

Sample Output 3

8

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include "bits/stdc++.h"

using namespace std;
#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

#define int long long
#define ll long long
#define DBG 1
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define loop(n) rep(loop, (0), (n))
#define all(c) begin(c), end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9) + 7;
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
using pii = pair<int, int>;
// template<class T> ostream &operator<<(ostream &os,T &t){dump(t);return os;}
template <typename T, typename S>istream &operator>>(istream &is, pair<T, S> &p) { is >> p.first >> p.second; return is; }
//template <typename T, typename S>ostream &operator<<(ostream &os, pair<T, S> &p) {os << p.first << " " << p.second;return os;}

template <typename T> void printvv(const vector<vector<T>> &v) {
	cerr << endl;
	rep(i, 0, v.size()) rep(j, 0, v[i].size()) {
		if (typeid(v[i][j]).name() == typeid(INF).name() and v[i][j] == INF) {
			cerr << "INF";
		}
		else
			cerr << v[i][j];
		cerr << (j == v[i].size() - 1 ? '\n' : ' ');
	}
	cerr << endl;
}

#ifndef _DEBUG
#define printvv(...)
#endif
void YES(bool f) { cout << (f ? "YES" : "NO") << endl; }
void Yes(bool f) { cout << (f ? "Yes" : "No") << endl; }
template <class T, class U>bool chmin(T& a, U b) { if (a > b) { a = b; return true; }return false; }
template <class T, class U>bool chmax(T& a, U b) { if (a < b) { a = b; return true; }return false; }

signed main(signed argc, char *argv[]) {
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(12);

	int N, M; cin >> N >> M;
	vector<vector<int>>S(M);
	rep(i, 0, M) {
		int k; cin >> k;
		rep(j, 0, k) {
			int s; cin >> s;
			s--;
			S[i].eb(s);
		}
	}
	int ans = 0;
	vector<int>P(M); rep(i, 0, M) { cin >> P[i]; }
	rep(bits, 0, (1ll << N)) {
		int cnt = 0;
		vector<int>p(M);
		rep(i, 0, M) {
			int f = 0;
			for (auto s : S[i]) {
				if ((bits >> s) & 1) {
					p[i]++;
				}
			}
		}
		int f = 1;
		rep(i, 0, M) {
			if (P[i] % 2 != p[i] % 2) {
				f = 0;
			}
		}
		ans += f;
	}
	cout << ans << endl;

	return 0;
}