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>
#define rep(i,n) for (int i = 0; i < (n); i++)
using namespace std;
typedef long long ll;
//using pint = pair<int,int>;
typedef pair<int,int> pint;

int n;
vector<vector<pint> > v;

bool judge(int bit){
    for(int i = 0; i < n; i++){
        if(!(bit & (1<<i)))continue;
        for(pint xy : v[i]){
            int x = xy.first;
            int y = xy.second;
            if(y==1 && !(bit&(1<<x)))return false;
            if(y==0 &&  (bit&(1<<x)))return false;
        }
    }
    return true;
}

int main(){
    cin >> n;
    v.resize(n);
    for(int i = 0; i < n; i++){
        int a; cin >> a;
        v[i].resize(a);
        for(int j = 0; j < a; j++){
            cin >> v[i][j].first >> v[i][j].second;
            --v[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;
}