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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define REP(i,a,b) for (int i = a; i < (b); ++i)
#define RREP(i,a,b) for (int i = a; i > (b); --i)
#define all(x) (x).begin(),(x).end()
#define YY cout << "Yes" << endl
#define NN cout << "No" << endl
const int INF = 1000000007;
typedef long long ll;
using namespace std;
using Graph = vector<vector<int>>;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }
ll lcm(ll a, ll b) { return (a * b) / gcd(a,b); }
int solve(){
  int n,m;
  cin>>n>>m;
  vector<vector<int>>v(m);
  vector<int>p(m);
  rep(i,m){
    int k;
    cin>>k;
    rep(j,k){
      int tmp;
      cin>>tmp;
      tmp--;
      v[i].push_back(tmp);
    }
  }
  rep(i,m)cin>>p[i];
  int ans=0;
  rep(i,(1<<n)){
    int tmp=0;
    rep(j,m){
      int cnt=0;
      rep(k,v[j].size()){
        if(i & (1<<v[j][k]))cnt++;
      }
      if(cnt%2==p[j])tmp++;
    }
    if(tmp==m)ans++;
  }
  cout<<ans<<endl;
  return 0;
}
int main(){
  // ios::sync_with_stdio(false);cin.tie(nullptr);
  // cout << fixed;cout << setprecision(16);
  solve();
  return 0;
}