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<iostream>
#include<vector>
#include<algorithm>
#define rep(i,n) for(int i = 0; i < (n); i++)
using namespace std;

int main()
{
    int n, ans = 0;
    cin>>n;
    vector<vector<int>>who(n,vector<int>());
    vector<vector<int>>TorF(n,vector<int>());
    vector<vector<int>>copy_TorF(n,vector<int>());
    vector<int>number(n);
    rep(i,n){
        cin>>number[i];
        who[i].resize(number[i]);
        TorF[i].resize(number[i]);
        copy_TorF[i].resize(number[i]);
        rep(j,number[i]){
            cin>>who[i][j]>>TorF[i][j];
        }
    }

    rep(s,1<<n){
        int how_many = 0;
        bool ok = true;
        vector<int>which(n);
        rep(i,n){
            rep(j,number[i]){
                copy_TorF[i][j] = TorF[i][j]; 
            }
        }

        rep(i,n){
            if(s>>i&1) which[i] = 1;
        }
        rep(i,n){
            rep(j,number[i]){
                if(which[i]){
                    if(copy_TorF[i][j] ^ which[who[i][j]-1]) ok = false;
                }
            }
        }
        if(ok){
            rep(i,n){
                if(which[i]) how_many++;
            }
        }
        ans = max(ans,how_many);
    }
    cout<<ans<<endl;
    return 0;
}