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;

public class Program {
	public static void Main() {
		var opinions = Enumerable.Range(0, int.Parse(Console.ReadLine()))
			.Select(_ => Enumerable.Range(0, int.Parse(Console.ReadLine()))
				.Select(__ => Console.ReadLine().Split(' '))
				.Where(x => x[1] == "1")
				.Select(x => int.Parse(x[0]) - 1)
				.ToArray())
			.ToArray();

		Console.WriteLine(Enumerable.Range(0, (int)Math.Pow(2, opinions.Length) - 1)
			.Select(flags => Convert.ToString(flags, 2)
				.Select((flag, index) => new { flag, index })
				.Where(x => x.flag == '1')
				.Select(x => x.index)
				.ToArray())
			.Where(honests => honests.All(honest => opinions[honest].All(x => honests.Contains(x))))
			.Max(x => x.Length));
	}
}