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 Ruby (2.3.3) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;

int main() {
  int n; cin >> n;
  vector<vector<int>> x(n), y(n);
  rep(i,n) {
    int a; cin >> a;
    x[i].resize(a);
    y[i].resize(a);
    rep(j,a) {
      cin >> x[i][j] >> y[i][j];
      x[i][j]--;
    }
  }
  int ans = 0;
  rep(bit,1<<n) {
    vector<bool> honest(n);
    rep(i,n) honest[i] = bit >> i & 1;
    bool ok = true;
    rep(i,n) if (honest[i]) {
      rep(j,x[i].size()) {
        if (honest[x[i][j]] && y[i][j] == 0) ok = false; 
        if (!honest[x[i][j]] && y[i][j] == 1) ok = false; 
      }
    }
    if (ok) ans = max(ans, __builtin_popcount(bit));
  }
  cout << ans << endl;
}