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

namespace c
{
    class Program
    {
        public static readonly long INF = 999999999999;
        public static readonly long MOD = 1000000007;

        static void Main(string[] args)
        {
            var n = Scanner.IntScan()[0];
            var xy = new List<List<int[]>>();

            for(var i = 0; i < n; i++)
            {
                var a = Scanner.IntScan()[0];
                var z = new List<int[]>();
                for(var j = 0; j < a; j++)
                {
                    z.Add(Scanner.IntScan());
                }
                xy.Add(z);
            }
            var res = 0;
            for(var bit = 0; bit < (1 << n); bit++)
            {
                var sum = 0;
                var ok = true;
                for (var i = 0; i < n; i++)
                {
                    if((bit&(1<<i)) == (1 << i))
                    {
                        foreach(var a in xy[i])
                        {
                            if((bit&(1<<(a[0]-1))) == (a[1] << (a[0] - 1)))
                            {
                                sum++;
                            }
                            else
                            {
                                ok = false;
                            }
                        }
                    }
                }
                if(ok) if (res < sum) res = sum;
            }
            Console.WriteLine(res);
        }
    }

    public class Scanner
    {
        public static string[] Scan() => Console.ReadLine().Split(' ');
        public static int[] IntScan() => Array.ConvertAll(Scan(), int.Parse);
        public static long[] LongScan() => Array.ConvertAll(Scan(), long.Parse);
        public static string[][] Scan(int n) => Enumerable.Repeat(0, n).Select(_ => Scan()).ToArray();
        public static int[][] IntScan(int n) => Enumerable.Repeat(0, n).Select(_ => IntScan()).ToArray();
        public static long[][] LongScan(int n) => Enumerable.Repeat(0, n).Select(_ => LongScan()).ToArray();

    }

    public class Ex
    {
        public static bool Chmin(ref int a, int b) { if (a > b) { a = b; return true; } return false; }
        public static bool Chmin(ref long a, long b) { if (a > b) { a = b; return true; } return false; }
        public static bool Chmax(ref int a, int b) { if (a < b) { a = b; return true; } return false; }
        public static bool Chmax(ref long a, long b) { if (a < b) { a = b; return true; } return false; }
        public static int[] SubArr(int[] arr, int begin, int n) { int[] a = new int[arr.Length]; Array.Copy(arr, begin, a, 0, n); return a; }
    }
}