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: Runtime Error)

#include <bits/stdc++.h>

#define rep(i, n) for(int i=0; i < n; i++)
#define reps(i, n) for(int i=1; i <= n; i++)
#define INF 1e9
#define ALL(v) v.begin(), v.end()

using namespace std;
using ll=long long;


int main(){
  int N,M,p;
  cin >> N >> M;
  int k[M];
  int ans =0;
  vector<vector<int>> stol(10);


  rep(i,M){
    cin >> k[i];
    rep(j,k[i]){
      int sw;
      cin >> sw;
      stol.at(sw).push_back(i+1);
      //cin >> s[i][j];
    }
  }

  //全部点灯条件
  bitset<10> lightall;
  rep(i,M){
    cin >> p;
    if(p)lightall.set(i);
  }

  rep(tmp,(1<<N)){
    bitset<10> s(tmp);
    bitset<10> light;
    //あるswitch pattern
    rep(i,N){
      if(s.test(i)){
        for(int l: stol.at(i+1))light.flip(l-1);
      }
    }
    if(light ==lightall)ans++;
  }
  cout << ans;
}