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;
vector<int> G[16];
int n;
bool ok(int state){
    //cout<<state<<endl;
	for(int i=0;i<n;++i){
		if( ((1<<i)&state) > 0){
			for(int j=0;j<n;++j){
				if(G[i][j]!=-1){
					if(G[i][j]==0 && (state & (1<<j))!=0 ){
						return false;
					}
					if(G[i][j]==1 && (state & (1<<j))==0 ){
						return false;
					}					
				}
			}
		}
	}
	return true;
}
int main(){
	cin>>n;
	for(int i=0;i<n;++i){
		int Ai;cin>>Ai;
		G[i] = vector<int>(n,-1);
		for(int j=1;j<=Ai;++j){
			int num,honest;cin>>num>>honest;
			G[i][num-1] = honest;
		}
	}
    /*
    for(auto i:G){
      for(auto j:i){
        cout<<j<<" ";
      }
      cout<<endl;
    }
    */
	int res = 0;
	for(int state = 0;state < (1<<n);++state){
		if(ok(state)){
            //cout<<state<<endl;
			res = max(res,__builtin_popcount(state));
		}
	}
	cout<<res<<endl;
	return 0;
}