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: Wrong Answer)

#include <cmath>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <vector>
using namespace std;
typedef long long int ll;
typedef vector<int> vi;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define Sort(a) sort(a.begin(), a.end())
const int INF = 1 << 30;
const ll MOD = 1000000007;
int N;
vector<vector<pair<int, int>>> answers;

int isValid(int bit) {
  int max = 0;
  for (int i = 0; i < N; i++) {
    if ((bit & (1 << i)) == 0) continue;

    max++;
    for (auto answer : answers[i]) {
      if ((bit & (1 << (answer.first - 1))) != 0 && answer.second == 0)
        return false;
      if ((bit & (1 << (answer.first - 1))) == 0 && answer.second == 1)
        return false;
    }
  }
  return max;
}

int main(void) {
  cin >> N;
  answers.resize(N);
  for (int i = 0; i < N; i++) {
    int A;
    cin >> A;
    answers[i].resize(A);
    for (int j = 0; j < A; j++) {
      cin >> answers[i][j].first >> answers[i][j].second;
    }
  }

  int max;
  for (int bit = 0; bit < (1 << N); bit++) {
    int val = isValid(bit);

    if (val > max) max = val;
  }
  cout << max << endl;
  return 0;
}