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 <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <cmath>
#include <limits>
#include <numeric>
#include <iomanip>
#include <cstdlib>
#include <iterator>
#include <functional>
#include <unordered_map>

using namespace std;

typedef unsigned                    ui;
typedef int                         si;
typedef long                        sl;
typedef long long                   ll;
typedef unsigned long long          ull;

#ifdef LOCALHOST
std::ifstream in("input.txt", std::ifstream::in);
#endif // LOCALHOST

#ifdef LOCALHOST
#define is in
#else
#define is cin
#endif // LOCALHOST

int answer = 0;
vector<vector<pair<int, int>>> t;
unordered_map<int, int> p;
vector<bool> a;

bool check() {
    unordered_map<int, int> f;
    for (int i = 0; i < t.size(); ++i) {
        for (int j = 0; j < t[i].size(); ++j) {
            if (a[i]) {
                const int person = t[i][j].first;
                const int fact = t[i][j].second;
                const auto found = f.find(person);

                if (a[person - 1] != fact) {
                    return false;
                }

                if (found != f.end()) {
                    if (found->second != fact) {
                        return false;
                    }
                } else {
                    f[person] = fact;
                }
            }
        }
    }

    return true;
}

void gen(int n, int i) {
    if (i == n) {
//        cout << "check: " << endl;
//        for (int i = 0; i < n; ++i) {
//            cout << a[i] << " ";
//        }
//        cout << endl;

        if (check()) {
//            cout << "TRUE" << endl;
            int cur_ans = 0;
            for (int i = 0; i < n; ++i) {
                if (a[i]) {
                    cur_ans += 1;
                }
            }

            answer = max(answer, cur_ans);
        }

        return;
    }

    a[i] = 0;
    gen(n, i + 1);
    a[i] = 1;
    gen(n, i + 1);
}

int main(int argc, char *argv[])
{
    std::ios_base::sync_with_stdio(false);

    ll n;
    cin >> n;

    for (int i = 0; i < n; ++i) {
        int c;
        cin >> c;

        vector<pair<int, int>> current;
        for (int j = 0; j < c; ++j) {
            int x, y;
            cin >> x >> y;

            current.emplace_back(x, y);
        }

        t.emplace_back(current);
    }

    a.resize(n);
    gen(n, 0);
/*
    for (int i = 0; i < n; ++i) {
        int c;
        cin >> c;

        vector<pair<int, int>> current;
        for (int j = 0; j < c; ++j) {
            int x, y;
            cin >> x >> y;

            if (y == 1) {
                p[x] += 1;
            }

            current.emplace_back(x, y);
        }

        t.emplace_back(current);
    }

    answer = n;
    for (int i = 1; i <= n; ++i) {
        if (p.count(i) > 0) {
            --answer;
        }
    }
    */

    cout << answer << endl;

    return 0;
}