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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_176
{
    class F
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] array = ReadInts();

            int[,] dp = new int[n + 1, n + 1];
            for(int i = 0; i <= n; i++)
            {
                for(int j = 0; j <= n; j++)
                {
                    dp[i, j] = int.MinValue;
                }
            }

            int res = 0;
            int greedy = 0;
            for (int i = 2; i < array.Length; i += 3)
            {
                int[,] nextDp = new int[n + 1, n + 1];
                if (i + 1 == array.Length)
                {
                    nextDp[array[i], array[i]] = dp[array[i], array[i]] + 1;
                    res = Max(res, nextDp[array[i], array[i]]);
                }
                else
                {
                    if (array[i] == array[i + 1] && array[i] == array[i + 2])
                    {
                        greedy++;
                    }
                    else if (array[i] == array[i + 1] && array[i] != array[i + 2])
                    {
                        for (int j = 1; j <= n; j++)
                        {
                            int next = Max(Max(dp[array[i], j], dp[j, array[i]]) + 1,
                                Max(dp[array[i + 2], j], dp[j, array[i + 2]]));
                            nextDp[array[i + 2], j] = next;
                            nextDp[j, array[i + 2]] = next;
                            res = Max(res, next);
                        }
                    }
                    else if (array[i + 1] == array[i + 2] && array[i + 1] != array[i])
                    {
                        for (int j = 1; j <= n; j++)
                        {
                            int next = Max(Max(dp[array[i + 1], j], dp[j, array[i + 1]]) + 1,
                                Max(dp[array[i], j], dp[j, array[i]]));
                            nextDp[array[i], j] = next;
                            nextDp[j, array[i]] = next;
                            res = Max(res, next);
                        }
                    }
                    else if (array[i + 2] == array[i] && array[i + 2] != array[i + 1])
                    {
                        for (int j = 1; j <= n; j++)
                        {
                            int next = Max(Max(dp[array[i + 2], j], dp[j, array[i + 2]]) + 1,
                                Max(dp[array[i + 1], j], dp[j, array[i + 1]]));
                            nextDp[array[i + 1], j] = next;
                            nextDp[j, array[i + 1]] = next;
                            res = Max(res, next);
                        }
                    }
                    else
                    {
                        int next = Max(dp[array[i], array[i]] + 1,
                            Max(dp[array[i + 1], array[i + 2]], dp[array[i + 2], array[i + 1]]));
                        nextDp[array[i + 1], array[i + 2]] = next;
                        nextDp[array[i + 2], array[i + 1]] = next;
                        res = Max(res, next);

                        next = Max(dp[array[i + 1], array[i + 1]] + 1,
                            Max(dp[array[i + 2], array[i]], dp[array[i], array[i + 2]]));
                        nextDp[array[i + 2], array[i]] = next;
                        nextDp[array[i], array[i + 2]] = next;
                        res = Max(res, next);

                        next = Max(dp[array[i + 2], array[i + 2]] + 1,
                            Max(dp[array[i], array[i + 1]], dp[array[i + 1], array[i]]));
                        nextDp[array[i], array[i + 1]] = next;
                        nextDp[array[i + 1], array[i]] = next;
                        res = Max(res, next);
                    }
                }
                dp = nextDp;
            }

            WriteLine(res + greedy);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}