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;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    static class CHonestOrUnkind2
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var list = new List<List<Tuple<int, int>>>();

            for (int i = 0; i < n; i++)
            {
                var a = int.Parse(Console.ReadLine());
                list.Add(new List<Tuple<int, int>>());
                for (int j = 0; j < a; j++)
                {
                    var xy = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();                    
                    list[i].Add(Tuple.Create(xy[0]- 1, xy[1]));
                }
            }

            int honestCount = 0;
            int maxHonestCount = 0;
            for (int bit = 0; bit < (1 << n); bit++)
            {
                honestCount = 0;

                if (!IsHonest(bit, list)) { continue; }

                for (int i = 0; i < n; i++)
                {
                    if ((bit & (1 << i)) > 0) { honestCount++; }
                }

                maxHonestCount = Math.Max(maxHonestCount, honestCount);
            }
            
            Console.WriteLine(maxHonestCount);
            Console.ReadLine();
        }

        static bool IsHonest(int bit, List<List<Tuple<int, int>>> list)
        {
            for (int i = 0; i < list.Count; i++)
            {
                // Number"i" is honest? Unkind is skip.
                if ((bit & (1 << i)) == 0) { continue; }

                foreach (var item in list[i])
                {
                    // Evidence is honest, but temp is unkind.
                    if (item.Item2 == 1 && (bit & (1 << item.Item1)) == 0)
                    {
                        // Exists unkind in bit.
                        return false;
                    }
                    // Evidence is unkind, but temp is honest.
                    if (item.Item2 == 0 && (bit & (1 << item.Item1)) > 0)
                    {
                        // Exists unkind in bit.
                        return false;
                    }
                }
            }

            // Not exists unkind in bit.
            return true;
        }
    }
}