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;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var personCount = int.Parse(Console.ReadLine());

            var persons = new List<Person>();

            for (int i = 1; i <= personCount; i++)
            {
                var testCount = int.Parse(Console.ReadLine());

                var tests = new List<Test>();

                for (int ti = 0; ti < testCount; ti++)
                {
                    var vals = Console.ReadLine().Split(' ');
                    var target = int.Parse(vals[0]);
                    var isHonest = int.Parse(vals[1]) == 1;
                    tests.Add(new Test(target, isHonest));
                }

                persons.Add(new Person(i, tests.ToArray()));
            }

            //unkind = 0人
            if (IsAllowed(persons, new int[0]))
            {
                Console.WriteLine(personCount);
                return;
            }

            for (int unkindCount = 1; unkindCount <= personCount; unkindCount++)
            {
                foreach (var combi in EnumerateCombination(Enumerable.Range(1, personCount), unkindCount))
                {
                    if (IsAllowed(persons, combi))
                    {
                        Console.WriteLine(personCount - unkindCount);
                        return;
                    }
                }
            }

            Console.WriteLine(0);
        }


        private static bool IsAllowed(IEnumerable<Person> all, int[] unkindNumbers)
        {
            var kateiList = all.Select(p => new PersonIf(p, !unkindNumbers.Contains(p.Number))).ToArray();

            return IsAllCollect(kateiList);
        }

        private static bool IsAllCollect(PersonIf[] kateiList)
        {
            foreach (var katei in kateiList)
            {
                if (!katei.MaybeHonest) continue;

                foreach (var test in katei.Person.Tests)
                {
                    var target = kateiList.Single(k => k.Person.Number == test.Number);
                    if (test.IsHonest)
                    {
                        if (target.MaybeHonest) continue;

                        return false;
                    }
                    else
                    {
                        if (target.MaybeHonest) return false;
                    }
                }
            }

            return true;
        }


        private static IEnumerable<int[]> EnumerateCombination(IEnumerable<int> all, int count)
        {
            if (count == 0)
            {
                yield break;
            }
            if (count == 1)
            {
                foreach (var n in all)
                {
                    yield return new[] { n };
                }
                yield break;
            }

            foreach (var n in all)
            {
                var leftside = new int[] { n };

                var unused = all.SkipWhile(e => e != n).Skip(1).ToList();

                foreach (var rightside in EnumerateCombination(unused, count - 1))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }

        }
    }

    class PersonIf
    {
        public Person Person { get; }

        public bool MaybeHonest { get; set; }

        public PersonIf(Person person, bool maybeHonest)
        {
            this.Person = person;
            this.MaybeHonest = maybeHonest;
        }
    }

    class Person
    {
        public int Number { get; }
        public Test[] Tests { get; }

        public Person(int number, Test[] tests)
        {
            if (number < 1 || 15 < number) throw new ArgumentOutOfRangeException(nameof(number));

            this.Number = number;
            this.Tests = tests;
        }
    }

    class Test
    {

        public int Number { get; }
        public bool IsHonest { get; }
        public Test(int number, bool isHonest)
        {
            this.Number = number;
            this.IsHonest = isHonest;
        }
    }
}