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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main{

    static int n;
    static int[] hu=new int[15];

    static int[][] a=new int[15][15];

    static boolean dfs(int i){
        for(int j=0;j<n;j++){
            if(a[i][j]>-1&&hu[j]<0){
                hu[j]=a[i][j];
                if(i!=j&&a[i][j]==1&&!dfs(j)){
                    return false;
                }
            }else if(hu[j]>-1&&hu[j]!=a[i][j]){
                return false;
            }
        }
        return true;
    }
    public static void main(String[] args)throws Exception{
        Scanner sc=new Scanner(System.in);
        n=sc.nextInt();
        int inp=0;
        for(int i=0;i<n;i++){
            Arrays.fill(a[i],-1);
            a[i][i]=1;
            inp=sc.nextInt();
            for(int j=0;j<inp;j++){
                a[i][sc.nextInt()-1]=sc.nextInt();
            }
        }
        Queue<Integer> q=new ArrayDeque<>();
        int ans=0,count=0;
        boolean flag=true;
        for(int bit=0;bit<(1<<n);bit++){
            Arrays.fill(hu,-1);
            count=0;
            flag=true;
            for(int i=0;i<n;i++){
                if((bit&(1<<i))>0){
                    q.add(i);
                }
            }
            while(q.peek()!=null){
                int l=q.remove();
                if((flag=dfs(l))==false){
                    q.clear();
                    break;
                }
            }
            if(flag){
                for(int j=0;j<n;j++){
                    if(hu[j]==1)count++;
                }
            }
            ans=Math.max(ans,count);
        }
        System.out.println(ans);
    }
}