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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC147C
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());

            var persons = new Dictionary<int, Person>(N);
            for (var i = 1; i <= N; i++)
            {
                var p = new Person
                {
                    No = i,
                    IsTure = false
                };

                var A = int.Parse(Console.ReadLine());
                for (var j = 0; j < A; j++)
                {
                    var xy = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
                    var t = new Testimony
                    {
                        No = xy[0],
                        IsTrue = xy[1] == 1
                    };
                    p.Testimonies.Add(t);
                }
                persons.Add(p.No, p);
            }

            int ans = 0;
            foreach (var p in persons.Values)
            {
                p.IsTure = true;

                foreach (var t in p.Testimonies)
                    persons[t.No].IsTure = t.IsTrue;

                foreach (var p2 in persons.Values)
                {
                    if (p2.IsTure)
                    {
                        foreach (var t2 in p2.Testimonies)
                            persons[t2.No].IsTure = t2.IsTrue;
                    }
                }

                ans = Math.Max(ans, persons.Values.Count(x => x.IsTure));

                p.IsTure = false;
            }
        }
    }

    [System.Diagnostics.DebuggerDisplay("No={No}")]
    class Person
    {
        public int No { get; set; }
        public bool IsTure { get; set; }
        public List<Testimony> Testimonies { get; } = new List<Testimony>();
    }

    [System.Diagnostics.DebuggerDisplay("No={No}, {IsTrue}")]
    class Testimony
    {
        public int No { get; set; }
        public bool IsTrue { get; set; }
    }
}