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 Microsoft.Win32;
using static System.Console;
 
 public static class Program
 {
     private static readonly long INF = long.MaxValue / 2;
     private static readonly int MOD = 1000000007;
 
     struct Pair<T, U> : IComparable<Pair<T, U>>
         where T : IComparable<T>
         where U : IComparable<U>
     {
         public T first;
         public U second;
         private bool CompWithFirst;
 
         public Pair(T f, U s, int comp)
         {
             first = f;
             second = s;
             CompWithFirst = comp == 1;
         }
 
         public int CompareTo(Pair<T, U> other)
         {
             return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
         }
     }
 
     public class PriorityQueue<T> where T : IComparable<T>
     {
 
         private List<T> Q;
         private readonly int r;
 
         public PriorityQueue(bool ascending)
         {
             if (ascending)
             {
                 r = 1;
             }
             else
             {
                 r = -1;
             }
 
             Q = new List<T>();
         }
 
 
         private void PushHeap(List<T> list, T item)
         {
             int n = list.Count();
             list.Add(item);
 
             while (n != 0)
             {
                 int pIndex = (n - 1) / 2;
 
                 if (list[n].CompareTo(list[pIndex]) * r > 0)
                 {
                     Swap(Q, n, pIndex);
                 }
                 else
                 {
                     break;
                 }
 
                 n = pIndex;
             }
         }
 
         private void PopHeap(List<T> list)
         {
             int n = list.Count() - 1;
             list[0] = list[n];
             list.RemoveAt(n);
 
             int cur = 0;
             int comp;
 
             while (2 * cur + 1 <= n - 1)
             {
                 int c1 = 2 * cur + 1;
                 int c2 = 2 * (cur + 1);
                 if (c1 == n - 1)
                 {
                     comp = c1;
                 }
                 else
                 {
 
                     comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                 }
 
                 if (list[cur].CompareTo(list[comp]) * r < 0)
                 {
                     Swap(Q, cur, comp);
                 }
                 else
                 {
                     break;
                 }
 
                 cur = comp;
             }
         }
 
         private void Swap(List<T> list, int a, int b)
         {
             T keep = list[a];
             list[a] = list[b];
             list[b] = keep;
         }
 
 
 
         public void Enqueue(T value)
         {
             PushHeap(Q, value);
         }
 
         public T Dequeue()
         {
             T ret = Q[0];
             PopHeap(Q);
             return ret;
         }
 
         public T Peek()
         {
             return Q[0];
         }
 
         public int CountItem()
         {
             return Q.Count();
         }
 
         public bool IsEmpty()
         {
             return !Q.Any();
         }
     }
 
     static long ModInv(long a, long m)
     {
         long b = m, u = 1, v = 0;
         while (b != 0)
         {
             long t = a / b;
             a -= t * b;
             long tmp = a;
             a = b;
             b = tmp;
             u -= t * v;
             tmp = u;
             u = v;
             v = tmp;
         }
 
         u %= m;
         if (u < 0) u += m;
         return u;
     }
 
     public static long CalcComb(long n, long m)
     {
         //条件チェック
         if (n < m) return 0;
         if (n < 0 || m < 0) return 0;
 
         //nＣm ＝ nＣm-1 ×（n-m+1）/ m 
 //         return CalcFact(n) / (CalcFact(m) * CalcFact(n - m));
         //MODで割ってbの逆元を求める
         return CalcFact(n) * ModInv((CalcFact(m) * CalcFact(n - m)) % MOD, MOD) % MOD;
     }
 
     /// <summary>
     /// 階乗を計算する。
     /// </summary>
     /// <param name="n">n</param>
     /// <returns>nの階乗（n!）</returns>
     public static long CalcFact(long n)
     {
         if (n <= 0)
         {
             return 1;
         }
 
         return n * CalcFact(n - 1) % MOD;
     }
 
 
     struct Pos
     {
         public int x;
         public int y;
 
         public Pos(int x, int y)
         {
             this.x = x;
             this.y = y;
         }
         
         public static Pos operator +(Pos p1, Pos p2)
         {
             var result = new Pos();
             result.x = p2.x + p1.x;
             result.y = p2.y + p1.y;
             return result;
         }
 
         public static Pos operator -(Pos p1, Pos p2)
         {
             var result = new Pos();
             result.x = p2.x - p1.x;
             result.y = p2.y - p1.y;
             return result;
         }
     }
     
     class Modular
     {
         private const int M = 1000000007;
         private long value;
 
         public Modular(long value)
         {
             this.value = value;
         }
 
         public static implicit operator Modular(long a)
         {
             var m = a % M;
             return new Modular((m < 0) ? m + M : m);
         }
 
         public static Modular operator +(Modular a, Modular b)
         {
             return a.value + b.value;
         }
 
         public static Modular operator -(Modular a, Modular b)
         {
             return a.value - b.value;
         }
 
         public static Modular operator *(Modular a, Modular b)
         {
             return a.value * b.value;
         }
 
         private static Modular Pow(Modular a, int n)
         {
             switch (n)
             {
                 case 0:
                     return 1;
                 case 1:
                     return a;
                 default:
                     var p = Pow(a, n / 2);
                     return p * p * Pow(a, n % 2);
             }
         }
 
         public static Modular operator /(Modular a, Modular b)
         {
             return a * Pow(b, M - 2);
         }
 
         private static readonly List<int> facs = new List<int> {1};
 
         private static Modular Fac(int n)
         {
             for (int i = facs.Count; i <= n; ++i)
             {
                 facs.Add((int) (Math.BigMul(facs.Last(), i) % M));
             }
 
             return facs[n];
         }
 
         public static Modular Ncr(int n, int r)
         {
             return (n < r) ? 0
                 : (n == r) ? 1
                 : Fac(n) / (Fac(r) * Fac(n - r));
         }
 
         public static explicit operator int(Modular a)
         {
             return (int) a.value;
         }
     }
     
     static class Permutation<T>
     {
         private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
         {
             int N = a.Length;
             if (N == 0)
             {
                 perms.Add(stack.Reverse().ToArray());
             }
             else
             {
                 var b = new T[N - 1];
                 Array.Copy(a, 1, b, 0, N - 1);
                 for (int i = 0; i < a.Length; ++i)
                 {
                     stack.Push(a[i]);
                     Search(perms, stack, b);
                     if (i < b.Length) { b[i] = a[i]; }
                     stack.Pop();
                 }
             }
         }
         public static IEnumerable<T[]> All(IEnumerable<T> src)
         {
             var perms = new List<T[]>();
             Search(perms, new Stack<T>(), src.ToArray());
             return perms;
         }
     }
 
     public static int ReadLineToInt()
     {
         return int.Parse(ReadLine());
     }
     
     public static long ReadLineToLong()
     {
         return long.Parse(ReadLine());
     }
     
     public static int[] ReadLineToInts()
     {
         return ReadLine().Split(' ').Select(int.Parse).ToArray();
     }
     
     static int nibunn(int[] array, int target)
     {
         int L = 0;
         int R = array.Length; 
             
         while(R - L > 1)
         {
             int mid = (R + L) / 2;
             if (array[mid] > target) L = mid;
             else R = mid;
         }
         return L;
     }


     struct Testmony
     {
         public int To;
         public int IsHonest;

         public Testmony(int to, int isHonest)
         {
             To = to;
             IsHonest = isHonest;
         }
     }
     
     public static void Main(string[] args)
     {
         int n = ReadLineToInt();
         var testmonies = new List<List<Testmony>>();

         for (int i = 0; i < n; i++)
         {
             int a = ReadLineToInt();
             testmonies.Add(new List<Testmony>());
             for (int j = 0; j < a; j++)
             {
                 int[] inputs = ReadLineToInts(); 
                 testmonies[i].Add(new Testmony(inputs[0], inputs[1]));
             }
         }
         
         //例 4人 0001 1111までの範囲を調べる
         int ans = 0;
         for (int bits = 1; bits < 1 << n; bits++)
         {
//             WriteLine(Convert.ToString(bits,2));
             bool ok = true;
             int counter = 0;
             for (int i = 0; i < n; i++)
             {

                 if ((bits & (1 << i)) == 0)
                 {
                     continue;
                 }

                 //真偽判定
                 for (int j = 0; j < testmonies[i].Count; j++)
                 {

                     if ((((bits >> (testmonies[i][j].To - 1)) & 1) ^ testmonies[i][j].IsHonest) == 1)
                     {
                         ok = false;
                     }
                 }

                 counter++;
             }

             if (ok)
             {
                 ans = Math.Max(ans, counter);
             }
         }

         WriteLine(ans);
     }
 }