Problem:
Score : 300 points

Problem Statement

There are N people numbered 1 to N. Each of them is either an honest person whose testimonies are always correct or an unkind person whose testimonies may be correct or not.

Person i gives A_i testimonies. The j-th testimony by Person i is represented by two integers x_{ij} and y_{ij}. If y_{ij} = 1, the testimony says Person x_{ij} is honest; if y_{ij} = 0, it says Person x_{ij} is unkind.

How many honest persons can be among those N people at most?

Constraints

All values in input are integers.

1 \leq N \leq 15

0 \leq A_i \leq N - 1

1 \leq x_{ij} \leq N

x_{ij} \neq i

x_{ij_1} \neq x_{ij_2} (j_1 \neq j_2)

y_{ij} = 0, 1

Input

Input is given from Standard Input in the following format:

N
A_1
x_{11} y_{11}
x_{12} y_{12}
:
x_{1A_1} y_{1A_1}
A_2
x_{21} y_{21}
x_{22} y_{22}
:
x_{2A_2} y_{2A_2}
:
A_N
x_{N1} y_{N1}
x_{N2} y_{N2}
:
x_{NA_N} y_{NA_N}

Output

Print the maximum possible number of honest persons among the N people.

Sample Input 1

3
1
2 1
1
1 1
1
2 0

Sample Output 1

2

If Person 1 and Person 2 are honest and Person 3 is unkind, we have two honest persons without inconsistencies, which is the maximum possible number of honest persons.

Sample Input 2

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

Sample Output 2

0

Assuming that one or more of them are honest immediately leads to a contradiction.

Sample Input 3

2
1
2 0
1
1 0

Sample Output 3

1

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <random>
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define rep1(i,n) for (int i = 1; i <= (n); ++i)

using namespace std;
using ll = long long;
using P = pair<int,int>;
using ull= unsigned long long;
const ll K_MAX=1e5+5;
const ll Lmax=ll(1e18);
const ll INF=1e9;
const int Bmax=2e5;

int main(){
  int n; cin>>n;
  int a,x,y;
  vector<vector<int>> g(n,vector<int>(n)); // g[i][j]: iの人の証言でjの人に関して．
  rep(i,n) rep(j,n) g[i][j]=-1;

  rep(i,n){//入力
    cin>>a;
    rep(j,a){
      cin>>x>>y;
      x--;
      g[i][x]=y;
    }
  }
  // 10の表記
  int ans=0;
  rep(i,1<<n){
    vector<int>d(n);
    int num=0;
    rep(j,n) if(i>>j&1){
      d[j]=1;
      num++;
    }else{
      d[j]=0;
    }
    bool ok=true;


    rep(j,n){
      if(d[j]==1){
        rep(k,n){
          if(g[j][k]==1 && d[k]==0){
            ok=false;
            break;
          }
          if(g[j][k]==0 && d[k]==1){
            ok=false;
            break;
         }
        }
      }

      if(!ok) break;
    }
    if(ok) ans=max(ans,num);



  }
  cout<<ans<<endl;




}