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;
using System.Text;
using System.Threading.Tasks;

namespace CSharp_AtCoder
{
    
    class Person
    {
        public int n;
        public int[] x;
        public int[] y;
        public Person(int n, int[] x, int[] y)
        {
            this.n = n;
            this.x = x;
            this.y = y;
        }
    }

    class Program
    {

        static Person[] persons;

        static List<string> authenticity;
        static int N;

        static void SetBinaryList(string now, int length)
        {
            if (length >= N)
            {
                authenticity.Add(now);
                return;
            }

            SetBinaryList(now + "1", length + 1);
            SetBinaryList(now + "0", length + 1);
        }

        static int MaxNumber(string auth)
        {
            bool contradiction = false;
            int cnt_true = 0;

            for(int i = 0; i < N; i++)
            {
                if (auth[i] == '0') continue;

                for(int j = 0; j < persons[i].n; j++)
                {
                    int x = persons[i].x[j];
                    int y = persons[i].y[j];
                    if (int.Parse(auth[x].ToString()) != y)
                    {
                        contradiction = true;
                        break;
                    }
                }

                cnt_true++;

                if (contradiction) break;
            }


            if (contradiction) return 0;
            else return cnt_true;
        }

        static void Main(string[] args)
        {
            N = int.Parse(Console.ReadLine());

            persons = new Person[N];
            for(int i = 0; i < N; i++)
            { 
                int A = int.Parse(Console.ReadLine());
                int[] x = new int[A];
                int[] y = new int[A];
                for(int j = 0; j < A; j++)
                {
                    int[] xy = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                    x[j] = xy[0] - 1;
                    y[j] = xy[1];
                }
                persons[i] = new Person(A, x, y);
            }

            authenticity = new List<string>();
            SetBinaryList("", 0);

            int max = 0;
            foreach(var now_case in authenticity)
            {
                max = Math.Max(max, MaxNumber(now_case));
            }

            Console.WriteLine(max);
        }
    }
}