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.Linq;

namespace CSharp
{
    class Program
    {
        static void Main()
        {
            var N = int.Parse(Console.ReadLine());

            var A = new int[N];
            var xy = new int[N][][];
            for (int i = 0; i < N; i++)
            {
                A[i] = int.Parse(Console.ReadLine());
                xy[i] = new int[A[i]][];
                for (int j = 0; j < A[i]; j++)
                {
                    xy[i][j] = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                }
            }

            var result = 0;
            for (int i = (int)(Math.Pow(2, N) - 1); i >= 0; i--)
            {
                var flag = true;
                var str = Convert.ToString(i, 2).PadRight(N, '0');

                for (int j = 0; j < N; j++)
                {
                    if (str[j] == '0')
                    {
                        continue;
                    }
                    for (int k = 0; k < A[j]; k++)
                    {
                        if (xy[j][k][1] != str[xy[j][k][0] - 1] - '0')
                        {
                            flag = false;
                            break;
                        }
                    }
                    for (int k = 0; k < N; k++)
                    {
                        if (str[k] == '0')
                        {
                            continue;
                        }
                        for (int l = 0; l < A[k]; l++)
                        {
                            if (xy[k][l][0] == j + 1 && xy[k][l][1] == 0)
                            {
                                flag = false;
                                break;
                            }
                        }
                        if (!flag)
                        {
                            break;
                        }
                    }
                    if (!flag)
                    {
                        break;
                    }
                }
                if (flag)
                {
                    if (str.Count(x => x == '1') > result)
                    {
                        result = str.Count(x => x == '1');
                    }
                    break;
                }
            }
            Console.WriteLine(result);
        }
    }
}