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<algorithm>
#define int long long
using namespace std;
typedef pair<int,int> P;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define INF 1000000000000

int MOD=1000000007;
int modpow(int a,int x){
  if(a<0)a+=MOD;
  int ans=1;
  while(x>0){
    if(x&1) ans=ans*a%MOD;
      a=a*a%MOD;
      x>>=1;
  }
  return ans;
}

int gyaku(int n){
    return modpow(n,MOD-2);
}
////////////////////////////////////////////////////////////
signed main() {
  int n;
  cin>>n;
  vector<vector<int>>x(n,vector<int>(0));
  vector<vector<int>>y(n,vector<int>(0));
  rep(i,n){
    int t;
    cin>>t;
    rep(j,t){
      int tx,ty;
      cin>>tx>>ty;
      tx--;
      x[i].push_back(tx);
      y[i].push_back(ty);
    }
  }
  int ans=0;
  for(int bit=0;bit<(1<<n);++bit){
    int count=0;
    int tb=bit;
    while(tb>0){
      if(tb&1)count++;
      tb/=2;
    }
    bool b=1;
    rep(i,n){
      if(bit&(1<<i)){
      rep(j,x[i].size()){
        if(bit&(1<<x[i][j]) && y[i][j]==0){b=0;}
        if(!(bit&(1<<x[i][j])) && y[i][j]==1){b=0;}
      }
    }
  }
    if(b){ans=max(ans,count);}
  }
  cout<<ans<<endl;
}