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;

public static class Bits
{
    public static int PopCount(int bits)
    {
        bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
        bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
        bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
        bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
        return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);
    }
}

public struct Person
{
    public int Honests;
    public int Unkinds;

    public Person(int honests, int unkinds)
    {
        Honests = honests;
        Unkinds = unkinds;
    }
}

public class Solution
{
    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        var persons = new Person[N];
        for (int i = 0; i < N; i++)
        {
            var A = int.Parse(Console.ReadLine());
            var honests = 0;
            var unkinds = 0;
            for (int j = 0; j < A; j++)
            {
                var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                var x = vals[0];
                var y = vals[1];
                if (y == 1)
                {
                    honests |= 1 << (x - 1);
                }
                else
                {
                    unkinds |= 1 << (x - 1);
                }
            }
            persons[i] = new Person(honests, unkinds);
        }

        var max = 0;
        var mask = (1 << N) - 1;
        for (int pattern = 0; pattern < (1 << N); pattern++)
        {
            bool ok = true;
            for (int i = 0; i < N; i++)
            {
                if (((1 << i) & pattern) == 0)
                {
                    continue;
                }
                var person = persons[i];
                if ((person.Honests & pattern) != person.Honests)
                {
                    ok = false;
                    break;
                }
                if ((person.Unkinds & (mask ^ pattern)) != person.Unkinds)
                {
                    ok = false;
                    break;
                }
            }
            if (ok)
            {
                max = Math.Max(Bits.PopCount(pattern), max);
            }
        }

        Console.WriteLine(max);
    }
}