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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace C
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var n = int.Parse(Console.ReadLine());
            var maxHonest = 0;
            var testimony = new Tuple<int, int>[n][];
            for (var i = 0; i < n; i++)
            {
                var a = int.Parse(Console.ReadLine());
                testimony[i] = new Tuple<int, int>[a];
                for (var j = 0; j < a; j++)
                {
                    var xy = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                    testimony[i][j] = new Tuple<int, int>(xy[0] - 1, xy[1]);
                }
            }

            foreach (var bit in BitFullSearchEnumerable(n))
            {
                var honest = bit.Count(x => x);
                var valid = true;
                for (var i = 0; i < n; i++)
                {
                    if (bit[i])
                    {
                        for (var j = 0; j < testimony[i].Length; j++)
                        {
                            var target = testimony[i][j].Item1;
                            var isHonest = testimony[i][j].Item2 == 1;
                            if (bit[target] != isHonest)
                            {
                                valid = false;
                                break;
                            }
                        }
                    }
                }
                if (valid) maxHonest = Math.Max(maxHonest, honest);
            }
            Console.WriteLine(maxHonest);
        }

        static IEnumerable<bool[]> BitFullSearchEnumerable(int n)
        {
            if (n < 0) yield return new bool[0];
            for (var i = 0; i < Math.Pow(2, n); i++)
            {
                var array = new bool[n];
                for (var j = 0; j < n; j++)
                {
                    var right = (i >> j) & 1;
                    array[j] = right == 1;
                }
                yield return array;
            }
        }
    }
}