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: Wrong Answer)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h> //C++の機能を「全て」読み込むための命令
#define rep(i,n) for(int i=0; i<(n); ++i)
#define cout(x) cout<<x<<endl
#define all(v) v.begin(), v.end()
using namespace std;
using ll = long long;
using P = pair<int,int>;
using vi = vector<int>;
using Mat = vector<vector<int>>;


int main(){
    int n;
    cin >> n;
    vi a(n);
    Mat x(n),y(n);
    rep(i,n){
        cin >> a[i];
        rep(j,a[i]){
            int x_,y_;
            cin >> x_ >> y_;
            x[i].push_back(x_);
            y[i].push_back(y_);
        } 
    }

    int max_honest = 0; 
    for(int t=0; t<(1<<n); ++t){
        bitset<16> s(t);
        int num_honest = 0;
        bool can = true;
        rep(i,n){//N人を検証
            rep(j,a[i]){//一人当たりの証言
                //正直者だと仮定した人の証言検証
                if(s.test(i)&&(s.test(x[i][j]-1)!= y[i][j])){
                    can = false;
                    break;
                }
                //嘘つきだと仮定した人の証言検証
                if(!(s.test(i))&&(s.test(x[i][j]-1) == y[i][j])){
                    can = false;
                    break;
                }
            }
            if(can && s.test(i)) num_honest += 1;
            if(can==false) break;
        }
        if(can && num_honest>max_honest) max_honest = num_honest;
    }
    cout(max_honest);
    
    return 0;
}