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.Diagnostics;
using System.Linq;

namespace PaizaTest
{
    class Program
    {
        static int N;
        static int[] A = new int[20];
        //static Tuple<int, int>[] X = new Tuple<int, int>[20];
        //static Tuple<int, int>[] Y = new Tuple<int, int>[20];
        static int[][] X = new int[20][];
        static int[][] Y = new int[20][];

        static void Main(string[] args)
        {
            Solve();
        }

        static void Solve()
        {
            N = int.Parse(Console.ReadLine());
            for (int i = 1; i <= N; i++)
            {
                X[i] = new int[20];
                Y[i] = new int[20];
                var line = Console.ReadLine();
                A[i] = int.Parse(line);
                for (int j = 1; j <= A[i]; j++)
                {
                    var val = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
                    X[i][j] = val[0];
                    Y[i][j] = val[1];
                }
            }

            int ans = 0;
            for (int bits = 0; bits < (1 << N); bits++)
            {
                bool ok = true;
                for (int i = 1; i <= N; i++)
                {
                    if (((bits & (1 << (i - 1))) == 0)) continue;
                    for (int j = 1; j <= A[i]; j++)
                    {
                        if ((((bits >> (X[i][j] - 1)) & 1) ^ Y[i][j]) != 0)
                        {
                            ok = false;
                        }
                    }
                }
                if (ok)
                {
                    ans = Math.Max(ans, Counter(bits));
                }

            }
            Console.WriteLine(ans);
        }

        static int Counter(int x)
        {
            if (x == 0) return 0;
            return Counter(x >> 1) + (x & 1);
        }
    }
}