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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define DEBUG if(0)
#define lli long long int
#define ldouble long double
using namespace std;

const int maxN = 6e3, maxX = 2e3 + 1; int n;
int arr[maxN];

unordered_map<int, int> memo[maxN][maxX];
int solve(int i = 0, int a = arr[0], int b = arr[1])
{
  if (i + 2 == n - 1) return a == b && b == arr[n - 1];

  // if (a > b) swap(a, b);
  if (memo[i][a].count(b)) return memo[i][a][b];

  arr[i] = a;
  arr[i + 1] = b;

  int ans = 0;
  for (int j = 0; j < 5; j++)
    for (int k = j + 1; k < 5; k++)
    {
      int other = 0, cnt = 0;
      for (int hehe = 0; hehe < 5; hehe++)
        if (hehe != j && hehe != k)
        {
          if (other == 0) other = arr[i + hehe];
          if (arr[i + hehe] == other)
            cnt++;
        }
      ans = max(ans, (cnt == 3) + solve(i + 3, arr[i + j], arr[i + k]));
    }

  return memo[i][a][b] = ans;
}

int main()
{
  int tt = 0;
  while (scanf("%d", &n) != EOF)
  {
    n = 3*n;
    for (int i = 0; i < n; i++) scanf("%d", &arr[i]);

    if (tt++)
      for (int i = 0; i < n; i++)
        for (int j = 0; j <= (n / 3); j++)
          memo[i][j].clear();
    int ans = solve();
    printf("%d\n", ans);
  }
  return 0;
}