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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Linq;
using System.Numerics;

namespace AtCoderWorkspace
{
    public class Solver
    {
        public void Solve()
        {
            var cin = new Scanner();
            var n = cin.nextInt();
            var personList = new List<List<Shougen>>();
            for (int i = 0; i < n; i++)
            {
                var shougenList = new List<Shougen>();
                var a = cin.nextInt();
                for (int j = 0; j < a; j++)
                {
                    var x = cin.nextInt();
                    var y = cin.nextInt();
                    shougenList.Add(new Shougen { person = x, say = y });
                }
                personList.Add(shougenList);
            }

            // 全員証言しないやつがいる
            foreach (var item in personList)
            {
                if (item.Count == 0)
                {
                    Console.WriteLine(n);
                    return;
                }
            }
            

            var honestyStack = new Stack<int>();
            var ansList = new List<int>();
            for (int i = 0; i < n; i++)
            {
                // 正直者セット
                var honestySet = new HashSet<int>();                

                var ans = 1;
                // i 人目を正直者と仮定する
                honestySet.Add(i + 1);
                var honesty = personList[i];
                foreach (var shougen in honesty)
                {
                    if(shougen.say == 1)
                    {
                        ans++;
                        honestyStack.Push(shougen.person);                        
                    }                    
                }                
                
                // 正直者の探索
                while(honestyStack.Count() > 0)
                {
                    // 信用できる証言
                    var honestyPerson = honestyStack.Pop();
                    honestySet.Add(honestyPerson);
                    
                    // 信頼できる人
                    var subHonesty = personList[honestyPerson-1];
                    
                    // 信頼できる人が言っている正直者を探索
                    foreach (var shougen in subHonesty)
                    {
                        if(shougen.say == 1)
                        {
                            if (honestySet.Contains(shougen.person)) continue;
                            ans++;
                            honestyStack.Push(shougen.person);
                        }
                        else
                        {
                            // 正直者と仮定した人が言う不親切な人なので、最初に仮定した人にたどり着いたら矛盾
                            if(shougen.person == i + 1)
                            {
                                honestyStack.Clear();
                                ans = 0;
                                break;
                            }
                        }
                    }               
                }
                
                ansList.Add(ans);
            }

            Console.WriteLine(ansList.Max());
        }
    }

    class Shougen
    {
        public int person { get; set; }
        public int say { get; set; }

    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public int[] DPArrayInt(int N, int ex)
        {
            int[] Array = new int[N+ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt();
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public long[] DPArrayLong(int N, int ex)
        {
            long[] Array = new long[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong();
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }   

    class Program
    {
        static void Main(string[] s) => new Solver().Solve();
    }
}