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;

public static class Program
{
    public static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var listA = new List<List<int[]>>();
        for (int i = 0; i < n; i++)
        {
            var a = int.Parse(Console.ReadLine());
            listA.Add(new List<int[]>(Enumerable.Range(0, a)
                .Select(x => Console.ReadLine().Split(' ')
                .Select(y => int.Parse(y)).ToArray())));
        }
        var max = 0;
        for (int i = 0; i < Math.Pow(2, n); i++)
        {
            var ary = new bool[n];
            for (int j = 0; j < n; j++)
            {
                var y = (i >> j) & 1;
                ary[j] = y == 1;
            }
            var katei = ary.Select((val, idx) => new { Index = idx, Value = val })
                .Where(x => x.Value).Select(x => x.Index).ToArray();
            if (katei.Length == 0)
            {
                continue;
            }
            if (ary.Check(katei.Select(x => listA[x]).ToList()))
            {
                max = katei.Length > max ? katei.Length : max;
            }
        }
        Console.WriteLine(max);
    }

    public static bool Check(this bool[] ary, List<List<int[]>> listA)
    {
        foreach (var syougen in listA)
        {
            foreach (var item in syougen)
            {
                if (item[1] == 1)
                {
                    if (!ary[item[0] - 1])
                    {
                        return false;
                    }
                }
                else
                {
                    if (ary[item[0] - 1])
                    {
                        return false;
                    }
                }
            }
        }
        return true;
    }
}