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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys

sys.setrecursionlimit(500005)
stdin = sys.stdin

ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().strip()


n = ni()
a = na()

dp = [[-99999999] * (n+1) for _ in range(n+1)]
dp[a[0]][a[1]] = 0

dprow = [-99999999] * (n+1)
dpcol = [-99999999] * (n+1)
dprow[a[0]] = 0
dpcol[a[1]] = 0

margin = 0
for i in range(2, 3*n-2, 3):
    if a[i] == a[i+1] and a[i+1] == a[i+2]:
        margin += 1
    else:
        q = []
        for j in (a[i], a[i+1], a[i+2]):
            for k in (a[i], a[i+1], a[i+2]):
                b = [j, k, a[i], a[i+1], a[i+2]]
                b.sort()
                if b[0] == b[2]:
                    q.append((b[3], b[4], dp[j][k] + 1))
                if b[1] == b[3]:
                    q.append((b[0], b[4], dp[j][k] + 1))
                if b[2] == b[4]:
                    q.append((b[0], b[1], dp[j][k] + 1))
        for j in range(n+1):
            for k in (a[i], a[i + 1], a[i + 2]):
                q.append((j, k, dprow[j]))
                q.append((k, j, dpcol[j]))
        mx = max(dprow)
        for jj in range(i, i+3):
            for kk in range(jj+1, i+3):
                q.append((a[jj], a[kk], mx))
        for u in q:
            dp[u[0]][u[1]] = max(dp[u[0]][u[1]], u[2])
            dprow[u[0]] = max(dprow[u[0]], u[2])
            dpcol[u[1]] = max(dpcol[u[1]], u[2])

ans = max(*dprow, dp[a[-1]][a[-1]] + 1)

print(ans+margin)