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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <cmath>
#define MAX 15
using namespace std;
typedef pair<int,int> p;

bool contain(vector<int>,int);
int numberOne(int);

int main(void){
  int N;
  cin >> N;
  vector<p> v[MAX]; 
  for(int i=0;i<N;i++){
    int A;
    cin >> A;
    for(int n=0;n<A;n++){
      int x,y;
      cin >> x >> y;
      p tmp(x-1,y);
      v[i].push_back(tmp);
    }
  }
  int status = 0;
  int maxCount = pow(2,N);
  int max = 0;

  for(int status=1;status<maxCount;status++){
    int tmp = status;
    vector<int> right;
    bool contradict = true;
    for(int n=0;n<N;n++){
      if(tmp%2 == 1){
	right.push_back(n);
      }
      tmp = tmp >> 1;
    }
    //cout << "sta:" << status << endl;
    // rightには正直者が入っている
    for(int n=0;n<right.size();n++){
      //正直者の分だけやればいい
      //cout << right[n] << endl;
      vector<p> witness = v[right[n]];
      for(int m=0;m<witness.size();m++){
	p wit = witness[m];
	//正直者
	bool flag;
	if(wit.second == 1){
	  flag = contain(right,wit.first);
	}else{
	  //適当野郎
	  flag = contain(right,wit.first);
	  flag = !flag;
	}
	// 矛盾があったら
	if(!flag){
	  contradict = false;
	  //cout << status << endl;
	}
      }
    }
    if(contradict){
      int value = numberOne(status);
       if(value > max){
         max = value;
      }    
    }
  }
  cout << max << endl;
  return 0;
}


bool contain(vector<int> v,int num){
  for(int n=0;n<v.size();n++){
    if(num == v[n]){
      return true;
    }
  }
  return false;
}

int numberOne(int num){
  int sum=0;
  for(int i=0;i<MAX;i++){
    if(num%2 == 1){
      sum++;
    }
    num = num >> 1;
  }
  return sum;
}