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 <iostream>
#include <queue>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <cctype>

using namespace std;

#define REP(i,n) for(ll (i) = (0); (i) < (n); ++i)
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define ALL(v) v.begin(),v.end()
#define Decimal fixed << setprecision(20)
#define SHOWP(x) cerr<<"["<<(x).FI<<", "<<(x).SE<<"]";
#define SHOWX(x) cerr<<#x<<": "<<x<<endl;
#define SHOWVEC(v, e) REP(i, e) cerr << (v[i]) << ' '; cerr << endl;
#define SHOW2D(a, h, w) REP(i, h){REP(j, w)cerr<<setw(3)<<(a[i][j])<<' ';cerr<<endl;}
constexpr int INF = 1100000000;
constexpr long long LLINF = 1100000000000000000LL;
constexpr long long MOD = 1000000007;

typedef long long ll;
typedef pair<ll, ll> P;


int main()
{
  int N, M;
  cin >> N >> M;
  vector<vector<int>> v(M);
  REP(i, M) {
    int k; cin >> k;
    REP(j, k) {
      int s; cin >> s;
      v[i].PB(s - 1);
    }
  }
  vector<int> p(M);
  REP(i, M) cin >> p[i];

  int ans = 0;
  REP(b, 1 << N) {
    vector<int> u(M);
    int cnt = 0;
    REP(i, M) {
      int pt = 0;
      for (auto& s : v[i]) pt += (b >> s) & 1;
      if (pt % 2 == p[i]) cnt++;
    }
    if (cnt == M) ans++;
  }
  cout << ans << endl;
  return 0;
}