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;

struct StExpr
{
  StExpr() : m_nPerson(0), m_nAttr(0) { }

  int m_nPerson;
  int m_nAttr;
};

void fnInput(vector<vector<StExpr>>& rvvoExpr)
{
  int nPersonSiz;
  cin >> nPersonSiz;
  rvvoExpr.resize(nPersonSiz + 1);

  for (int i = 1; i < rvvoExpr.size(); i++)
  {
    int nAttrSiz;
    cin >> nAttrSiz;
    rvvoExpr[i].resize(nAttrSiz);

    for (int j = 0; j < rvvoExpr[i].size(); j++)
      cin >> rvvoExpr[i][j].m_nPerson >> rvvoExpr[i][j].m_nAttr;
  }
}
 
int fnHonestCheck(const vector<vector<StExpr>>& cnrvvoExpr, 
                  const vector<int>& cnrvnHonest, int nMan)
{
  if (cnrvnHonest[nMan])               // Honest
  {
    for (int j = 0; j < cnrvvoExpr[nMan].size(); j++)
      if (cnrvvoExpr[nMan][j].m_nAttr  !=
          cnrvnHonest[ cnrvvoExpr[nMan][j].m_nPerson ] )
        return 0;

    return 1;
  }
  else                                 // UnKind
  {
    for (int j = 0; j < cnrvvoExpr[nMan].size(); j++)
      if (cnrvvoExpr[nMan][j].m_nAttr  !=
          cnrvnHonest[ cnrvvoExpr[nMan][j].m_nPerson ] )
        return 1;

    return 0;
  }
}
  
int fnMaxHonestGet(const vector<vector<StExpr>>& cnrvvoExpr)
{
  vector<int> vnHonest(cnrvvoExpr.size());
  int nMaxHonestCnt = 0;
  
  for (int n = 1; n < ( 1 << (cnrvvoExpr.size() - 1) ); n++)
  {
    int nHonestCnt = 0;

    for (int i = 0; i < cnrvvoExpr.size() - 1; i++)
      if (n & (1 << i))
      {
        vnHonest[i + 1] = 1;           // Honest
        nHonestCnt++;
      }
      else
        vnHonest[i + 1] = 0;           // UnKind

    bool bReslt = true;
    for (int nMan = 1; nMan < vnHonest.size(); nMan++)
      if (!fnHonestCheck(cnrvvoExpr, vnHonest, nMan))
      {
        bReslt = false;
        break;
      }

    if (bReslt) nMaxHonestCnt = max(nMaxHonestCnt, nHonestCnt);
  }
  return nMaxHonestCnt;
}

int main()
{
  vector<vector<StExpr>> vvoExpr;

  fnInput(vvoExpr);
  cout << fnMaxHonestGet(vvoExpr) << endl;

  return 0;
}