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.Linq;

class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        var evidences = new Tuple<int, int>[n][];

        // それぞれの証言を入力
        for(int i = 0; i < n; i++)
        {
            var evidenceNum = int.Parse(Console.ReadLine());
            evidences[i] = new Tuple<int, int>[evidenceNum];
            for (int j = 0; j < evidenceNum; j++)
            {
                var inputs = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                evidences[i][j] = new Tuple<int, int>(inputs[0], inputs[1]);
            }
        }

        var answer = 0;

        // bit全探索
        foreach(var personsData in BitFullSearch(n))
        {
            var isOK = true;
            for(int i = 0; i < n; i++)
            {
                // 真実を言う人(true)の言うことが正しいか調べる
                if (personsData[i])
                {
                    for (int k = 0; k < evidences[i].Length; k++)
                    {
                        var index = evidences[i][k].Item1;
                        var isTrueMan = evidences[i][k].Item2 == 1;
                        if (personsData[index-1] != isTrueMan)
                        {
                            isOK = false;
                            break;
                        }
                    }
                }
            }

            if (isOK)
            {
                var truePersonCount = personsData.Count(p => p);
                if (answer < truePersonCount) answer = truePersonCount;
            }
        }

        Console.WriteLine(answer);
    }


    public static IEnumerable<bool[]> BitFullSearch(int n)
    {
        if (n < 0) yield return new bool[] { };

        for(int i = 0; i < Math.Pow(2, n); i++)
        {
            var array = new bool[n];
            for(int j = 0; j < n; j++)
            {
                var firstDigit = (i >> j) & 1;
                if (firstDigit == 1) array[j] = true;
            }

            yield return array;
        }
    }
}