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: Runtime Error)

import copy
import itertools
n = int(input())
a = list(map(int,input().split()))
dp1 = [[0]*(n+1) for i in range(n+1)]
f = copy.deepcopy(dp1)
for k in list(itertools.permutations(a[0:5])):
  x = k[2]==k[3] and k[2]==k[4]
  dp1[k[0]][k[1]] = int(x)
  f[k[0]][k[1]] = 1
dp2 = copy.deepcopy(dp1)
x = 0
for i in range(1,n-1):
  p,q,r = sorted(a[(3*i+2):(3*i+5)])
  if p==r:
    x += 1
  elif p==q:
    for j in range(n):
      if f[j+1][p] == 1:
        dp2[j+1][r] = dp1[j+1][p] + 1
        dp2[r][j+1] = dp1[j+1][p] + 1
        f[j+1][r],dp2[r][j+1] = 1,1
      if f[r][r] == 1:
        dp2[p][p] = dp1[r][r] + 1
        f[p][p] = 1
  elif q==r:
    for j in range(n):
      if f[j+1][q] == 1:
        dp2[j+1][p] = dp1[j+1][q] + 1
        dp2[p][j+1] = dp1[j+1][q] + 1
        f[j+1][p],dp2[p][j+1] = 1,1
      if f[p][p] == 1:
        dp2[q][q] = dp1[p][p] + 1
        f[q][q] = 1
  else:
    if f[r][r] == 1:
      dp2[p][q] = dp1[r][r] + 1
      f[p][q] = 1
    if f[p][p] == 1:
      dp2[q][r] = dp1[p][p] + 1
      f[q][r] = 1
    if f[p][p] == 1:
      dp2[q][r] = dp1[p][p] + 1
      f[q][r] = 1
  dp1 = copy.deepcopy(dp2)
if f[a[-1]][a[-1]] == 1:
  dp1[a[-1]][a[-1]] += 1
print(x+max(sum(dp1,[])))