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>
using namespace std;
typedef long long ll;

int main()
{
  int n;
  cin >> n;
  int xy[15][15];
  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      xy[i][j] = -1;
    }
  }

  for (int i = 0; i < n; i++)
  {
    int a;
    cin >> a;
    for (int j = 0; j < a; j++)
    {
      int x, y;
      cin >> x >> y;
      --x;
      xy[i][x] = y;
    }
  }
  int ans = 0;
  for (int i = 0; i < (1 << n); i++)
  {
    vector<int> d(n);
    for (int j = 0; j < n; j++)
    {
      if (i >> j & 1)
      {
        d[j] = 1;
      }
    }
    int flg = 1;
    for (int j = 0; j < n; j++)
    {
      if (d[j])
      {
        for (int k = 0; k < n; k++)
        {
          if (xy[j][k] == -1)
          {
            continue;
          }
          if (xy[j][k] != d[k])
          {
            flg = 0;
          }
        }
      }
    }
    if (flg)
    {
      ans = max(ans, __builtin_popcount(i));
    }
  }
  cout << ans << endl;
}