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-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string[] str = Console.ReadLine().Split();
		int[]A = new int[3*N];
		int[]M = new int[N];
		for(var i=0;i<3*N;i++){
			A[i] = int.Parse(str[i]);
			M[A[i]-1] = i;
		}
		if(N==1){
			Console.WriteLine("1");
		} else {
			var list = new List<int>();
          	int ans = 0;
			int[]C = new int[N];
			for(var i=0;i<2;i++){
              	bool flag = true;
              	for(var j=0;j<list.Count;j++){
                  	if(list[j]==A[i]-1){
                      	flag = false;
                    }
                }
              	if(flag){
					list.Add(A[i]-1);
                }
				C[A[i]-1]++;
			}
			int[]K = new int[N];
			for(var j=0;j<N-1;j++){
				for(var i=0;i<3;i++){
                  	bool flag2 = true;
              		for(var k=0;k<list.Count;k++){
                  		if(list[k]==A[i]-1){
                      		flag2 = false;
	                    }
     	           }
     	         	if(flag2){
						list.Add(A[i+j*3+2]-1);
            	    }
					C[A[i+j*3+2]-1]++;
				}
				list.Sort((x,y)=>(C[y]-C[x]));
                  //for(var k=0;k<list.Count;k++){
                  //    Console.Error.Write(list[k]+"-"+C[list[k]]+" ");
                  //}
                  //Console.Error.WriteLine();
              	int ct = 0;
				if(C[list[0]]==3){
					ans++;
					list.RemoveAt(0);
                  	ct += 3;
				}
				list.Sort((x,y)=>(M[y]*1000-C[y]-(M[x]*1000-C[x])));
				while(ct < 3 && list.Count>0){
					int a = list[0];
                  	//Console.Error.WriteLine(a);
					if(ct==2 && C[a]==2){
						M[a] = 10000;
						C[a] = 1;
						break;
					} else {
						M[a] = 10000;
						ct += C[a];
						C[a] = 0;
						list.RemoveAt(0);
					}
				}
			}
              	bool flag3 = true;
              	for(var j=0;j<list.Count;j++){
                  	if(list[j]==A[3*N-1]-1){
                      	flag3 = false;
                    }
                }
              	if(flag3){
                  	list.Add(A[3*N-1]-1);
                }
                C[A[3*N-1]-1]++;
                  //for(var k=0;k<list.Count;k++){
                  //    Console.Error.Write(list[k]+"-"+C[list[k]]+" ");
                  //}
                  //Console.Error.WriteLine();
			if(C[list[0]]==3){
				ans++;
			}
			Console.WriteLine(ans);
		}
	}
}