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();
    int totalPoint = 0;
    while(true){ 
      int k = inputs.Length >= 5 ? 5 : inputs.Length;      
      for(int m1 = 0; m1 < k; m1++){
        for(int m2 = m1 + 1; m2 < k; m2 ++){
          if(inputs[m1] <  inputs[m2]){
            int temp = inputs[m1];
            inputs[m1] = inputs[m2];
            inputs[m2] = temp;
          }   
        }
      } 
      if(inputs.Length < 3) break; 
      int index = inputs[0];
      bool check = false;
      for(int i = 0; i < 3; i++){
        if(index != inputs[0]){
          check = true;
        }
        for(int j = 0; j < inputs.Length - 1; j++){
          inputs[j] = inputs[j + 1];
        }
       Array.Resize(ref inputs, inputs.Length - 1);
      }  
      totalPoint += check ? 0 : 1;  
    }

    Console.WriteLine(totalPoint);
    
  }
}