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 <bits/stdc++.h>
using namespace std;

int N;
vector<vector<pair<int, int>>> xy;

bool JUDGE(int bit){
    for(int i = 0; i < N; i++){
        if(!(bit & (1 << i))) continue;
        for(pair<int, int> v : xy[i]){
            if(!(bit & (1 << v.first)) && v.second == 1) return false;
            else if(bit & (1 << v.first) && v.second == 0) return false;
        }
    }
    return true;
}

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

    int res = 0;
    for(int bit = 0; bit < (1 << N); bit++){
        if(JUDGE(bit)){
            int count = 0;
            for(int i = 0; i < N; i++){
                if(bit & (1 << i)) count++; 
            }
            res = max(res, count);
        }
    }
    cout << res << endl;
}