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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;

namespace abc147
{
    class Program
    {
        static void Main(string[] args)
        {
            //Console.SetIn(new StreamReader("input.txt"));
            solve_abc147C();
        }

        public class Pair
        {
            public int x;
            public int y;
            public Pair(int x, int y)
            {
                this.x = x;
                this.y = y;
            }
        }
        public static void solve_abc147C()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            List<List<Pair>> pairs = new List<List<Pair>>();
            for (int tt = 0; tt < n; tt++)
            {
                int a = Convert.ToInt32(Console.ReadLine());
                List<Pair> p = new List<Pair>();
                for (int jj = 0; jj < a; jj++)
                {
                    int[] xy = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                    p.Add(new Pair(xy[0], xy[1]));
                }
                pairs.Add(p);
            }

            int cnt = 0;
            int cntFalse = 0;
            int[] used = new int[16];
            int[] used2 = new int[16];
            for (int i = 0; i < pairs.Count; i++)
            {
                for (int j = 0; j < pairs[i].Count; j++)
                {
                    List<Pair> p = pairs[pairs[i][j].x - 1];
                    for (int k = 0; k < p.Count; k++)
                    {
                        if (i + 1 == p[k].x && pairs[i][j].y == 1 && p[k].y == 1)
                        {
                            cnt++;
                        }
                        else if (i + 1 == p[k].x && pairs[i][j].y == 0 && p[k].y == 0)
                        {
                            cntFalse++;
                        }
                    }
                }
            }
            Console.WriteLine(Math.Max(1, cnt - cntFalse));
        }
        public static void solve_abc147B()
        {
            string s = Console.ReadLine();
            int min = 0;
            int i = 0;
            int j = s.Length - 1;
            while (i <= j)
            {
                if (s[i] != s[j])
                {
                    min++;
                }
                i++;
                j--;
            }
            Console.WriteLine(min);
        }

        public static void solve_abc147A()
        {
            int[] abc = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

            Console.WriteLine(abc[0] + abc[1] + abc[2] >= 22 ? "bust" : "win");
        }
    }
}