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.Diagnostics;
using System.Linq;

namespace ConsoleApp6
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var As = new List<A>();
            for (int i = 0; i < N; i++)
            {
                var a = new A();
                var shougenCount = int.Parse(Console.ReadLine());
                for (int j = 0; j < shougenCount; j++)
                {
                    var xy = Console.ReadLine().Split(' ');
                    a.Shougens.Add(new Shougen
                    {
                        X = int.Parse(xy[0]),
                        Y = int.Parse(xy[1]) == 1,
                    });
                }

                As.Add(a);
            }

            var patterns = Get(N).ToList();
            var valids = patterns.Where(x => IsValid(As, x));

            if (!valids.Any())
            {
                Debug.WriteLine(0);
                Console.WriteLine(0);
            }
            var max = valids.Max(x => x.Count(y => y));
            Debug.WriteLine(max);
            Console.WriteLine(max);
        }

        private static bool IsValid(List<A> As, List<bool> pattern)
        {
            foreach (var a in As.Select((a, i) => new { A = a, Index = i }))
            {
                // 信用しないので無視
                if (pattern[a.Index] == false) continue;

                // 矛盾するかどうかの判定
                if (a.A.Shougens.Any(x => pattern[x.X - 1] != x.Y))
                {
                    return false;
                }
            }

            return true;
        }

        private static IEnumerable<List<bool>> Get(int n)
        {
            for (int i = 0; i < Math.Pow(2, n); i++)
            {
                yield return Convert.ToString(i, 2).PadLeft(n, '0').Select(x => x == '1').ToList();
            }
        }

        class A
        {
            public List<Shougen> Shougens { get; set; } = new List<Shougen>();
        }
        class Shougen
        {
            public int X { get; set; }
            public bool Y { get; set; }
        }
    }
}