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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
    static int[] arr;
    static ArrayList<HashMap<Integer, Integer>> dp = new ArrayList<>();
    static int n;
	public static void main (String[] args) {
    	Scanner sc = new Scanner(System.in);
    	n = sc.nextInt();
    	arr = new int[n * 3];
    	for (int i = 0; i < n * 3; i++) {
    	    arr[i] = sc.nextInt() - 1;
    	}
    	for (int i = 0; i < n; i++) {
    	    dp.add(new HashMap<>());
    	}
    	System.out.println(dfw(Math.min(arr[0], arr[1]),Math.max(arr[0], arr[1]), 0));
    }
    
    static int dfw(int first, int second, int idx) {
        int key = first * n + second;
        if (dp.get(idx).containsKey(key)) {
            return dp.get(idx).get(key);
        }
        if (idx == n - 1) {
            if (first == second && first == arr[3 * n - 1]) {
                return 1;
            } else {
                return 0;
            }
        }
        int[] tmp = new int[]{first, second, arr[idx * 3 + 2], arr[idx * 3 + 3], arr[idx * 3 + 4]};
        Arrays.sort(tmp);
        if (tmp[0] == tmp[1] && tmp[1] == tmp[2]) {
            int value = dfw(tmp[3], tmp[4], idx + 1) + 1;
            dp.get(idx).put(key, value);
            return value;
        }
        if (tmp[1] == tmp[2] && tmp[2] == tmp[3]) {
            int value = dfw(tmp[0], tmp[4], idx + 1) + 1;
            dp.get(idx).put(key, value);
            return value;
        }
        if (tmp[2] == tmp[3] && tmp[3] == tmp[4]) {
            int value = dfw(tmp[0], tmp[1], idx + 1) + 1;
            dp.get(idx).put(key, value);
            return value;
        }
        int value = 0;
        for (int i = 0; i < 4; i++) {
            for (int j = i + 1; j < 5; j++) {
                value = Math.max(value, dfw(tmp[i], tmp[j], idx + 1));
            }
        }
        dp.get(idx).put(key, value);
        return value;
    }
}