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 AC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var hou = new List<int[]>[N];
            for (int i = 0; i < N; i++)
            {
                var A = ReadInt();
                hou[i] = new List<int[]>();
                for (int j = 0; j < A; j++)
                {
                    hou[i].Add(ReadArrayInt());
                }
            }
            var ans = 0;
            var max = 1 << N;
            for (int i = 1; i < max; i++)
            {
                var cnt = 0;
                var suc = true;
                for (int j = 0; j < N; j++)
                {
                    if ((i & 1 << j) != 1 << j) continue;
                    for (int k = 0; k < hou[j].Count(); k++)
                    {
                        var chk = hou[j][k][0] - 1;
                        if (hou[j][k][1] == 1)
                        {
                            if ((i & 1 << chk) != 1 << chk)
                            {
                                suc = false;
                                break;
                            }
                        }
                        else
                        {
                            if ((i & 1 << chk) == 1 << chk)
                            {
                                suc = false;
                                break;
                            }
                        }
                    }
                    if (!suc) break;
                    cnt++;
                }
                if (suc) ans = cnt > ans ? cnt : ans;
            }

            Console.WriteLine(ans);
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}