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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i=0;i < (n); ++i)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;
typedef vector<int> V;
typedef pair<int,int> P;
typedef vector<vector<int>> Graph;

int main() {
    int ans = 0;
    int n;
    cin >> n;
    vector<vector<P>> v(n);
    rep(i,n){
        int a;
        cin >> a;
        rep(j,a){
            int x,y;
            cin >> x >> y;
            x--;
            v[i].push_back(make_pair(x,y));
        }
    }
    for(int bit=0;bit<(1<<n);bit++){
        bool flag = true;
        for(int i=0;i<n;i++){
            if(bit&(1<<i)){
                for(auto j : v[i]){
                    if(!((j.second==1&&(bit&(1<<j.first)))||(j.second==0&&!(bit&(1<<j.first))))) flag = false;
                }
            }
        }
        if(flag) ans = max(ans,__builtin_popcount(bit));
    }
    cout << ans << endl;
}