Problem:
Score : 600 points

Problem Statement

We have 3N cards arranged in a row from left to right, where each card has an integer between 1 and N (inclusive) written on it. The integer written on the i-th card from the left is A_i.

You will do the following operation N-1 times:

Rearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain 1 point.

After these N-1 operations, if the integers written on the remaining three cards are all equal, you will gain 1 additional point.

Find the maximum number of points you can gain.

Constraints

1 \leq N \leq 2000

1 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_{3N}

Output

Print the maximum number of points you can gain.

Sample Input 1

2
1 2 1 2 2 1

Sample Output 1

2

Let us rearrange the five leftmost cards so that the integers written on the six cards will be 2\ 2\ 2\ 1\ 1\ 1 from left to right.

Then, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.

Now, the integers written on the remaining cards are 1\ 1\ 1.

Since these three cards have the same integer 1, we gain 1 more point.

In this way, we can gain 2 points - which is the maximum possible.

Sample Input 2

3
1 1 2 2 3 3 3 2 1

Sample Output 2

1

Sample Input 3

3
1 1 2 2 2 3 3 3 1

Sample Output 3

3

Solution in C# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

class MainClass {
  
  public static void Main (string[] args) {
    string n = Console.ReadLine();
    int[] inputs = Console.ReadLine().Split(' ').Select<string,int>(int.Parse).ToArray();
    // 22211
    // 76311
    // 10 9 8 1 1
    // 1 1 11
    int totalPoint = 0;
    if(inputs.Length < 3){
       Console.WriteLine("0");
       return;
    }
    int test = 0;
    for(int m = 0; m < inputs.Length; m ++){  
      int t = (m + 5) < inputs.Length ? m + 5 : inputs.Length - (m + 5);    
      for(int i = m; i < t; i ++ ){
        for(int j = i + 1; j < t; j++){
          if(inputs[i] < inputs[j]){
            int temp = inputs[i];
            inputs[i] = inputs[j];
            inputs[j] = temp;
          }
        }
      } 
      m+=2;
    }
    
    for(int i = 0; i < inputs.Length; i++ ){
      if((i + 2) < inputs.Length){
        if(inputs[i] == inputs[i + 1] && inputs[i + 1] == inputs[i + 2]){
          totalPoint+=1;
        }
        i+= 2;
      }
    }
    Console.WriteLine(totalPoint);
    
  }
}