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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

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

public class Main{
    public static void main(String[] args) throws IOException{
        FastReader in = new FastReader();
        FastWriter out = new FastWriter();
        int p = in.nextInt();
        int ans = 0;
        while (p-- > 0){
            boolean good = true;
            int a = in.nextInt();
            int x, y;
            for (int i = 0; i < a; i++){
                x = in.nextInt();
                y = in.nextInt();
                if (y != 1){
                    good = false;
                }
            }
            if (good) ans++;
        }
        out.pl(ans);


        out.close();
    }
}
class FastReader{ 
    BufferedReader br; 
    StringTokenizer st; 
    public FastReader() { 
        br = new BufferedReader(new InputStreamReader(System.in)); 
    } 
    String next(){ 
        while (st == null || !st.hasMoreElements()) { 
            try{ 
                st = new StringTokenizer(br.readLine()); 
            }catch (IOException  e){ 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 
    int nextInt(){ 
        return Integer.parseInt(next()); 
    } 
    long nextLong(){ 
        return Long.parseLong(next()); 
    } 
    double nextDouble(){ 
      return Double.parseDouble(next()); 
    } 
    String nextLine(){ 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        } 
        catch (IOException e){ 
            e.printStackTrace(); 
        } 
        return str; 
    } 
}
class FastWriter{
    PrintWriter out;
    FastWriter(){
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	out.flush();
    }
    void pl(Object o){
        out.write(o.toString());
	    out.write("\n");
        out.flush();
    }
    void pl(){
        out.write("\n");
    }
    void p(Object o){
        out.write(o.toString());
    }
    void close(){
        out.flush();
        out.close();
    }  
}