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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        struct SAYING
        {
            public int men;
            public int isLie;

        }


        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            List<SAYING>[] say = new List<SAYING>[N];
            for (int i = 0; i < N; i++)
            {
                say[i] = new List<SAYING>();
            }

            for (int i = 0; i < N; i++)
            {
                int num = int.Parse(Console.ReadLine());

                for (int j = 0; j < num; j++)
                {
                    string[] s0 = Console.ReadLine().Split(' ');

                    SAYING t;
                    t.men = int.Parse(s0[0]) - 1;
                    t.isLie = int.Parse(s0[1]);

                    say[i].Add(t);
                }
            }

            int ans = 0;
            int maxnum = (int)Math.Pow(2, N);
            for (int i = 0; i < maxnum; i++)
            {
                int localans = 0;
                bool valid = true;

                for (int j = 0; j < N; j++)
                {
                    int bit = 1 << j;

                    // 1＝正直者を検査
                    if(0 != (i & bit))
                    {
                        bool testOK = true;
                        foreach(SAYING st in say[j])
                        {
                            int bit2 = 1 << st.men;

                            if(
                                ((st.isLie == 0) && (0 != (i & bit2))) ||
                                ((st.isLie != 0) && (0 == (i & bit2)))
                                )
                            {
                                testOK = false;
                                break;
                            }
                        }

                        if(!testOK)
                        {
                            valid = false;
                            break;
                        }
                    }
                }

                if(valid)
                {
                    for (int j = 0; j < N; j++)
                    {
                        if(0 != (i & (1<<j)))
                        {
                            localans++;
                        }
                    }

                    ans = Math.Max(ans, localans);
                }
            }

            Console.WriteLine(ans);
        }
    }
}