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)

N = int(input())
A = list(map(int, input().split()))
A.append(0)
A.append(0)

ans = 0
doubles = set()
singles = set()
if A[0] == A[1]:
  doubles.add(A[0])
  singles.add(A[0])
else:
  singles.add(A[0])
  singles.add(A[1])
  
for i in range(0, N):
  a = A[2+3*i] 
  b = A[2+3*i+1]
  c = A[2+3*i+2]
  #print(ans, doubles, singles, a, b, c)
  if a == b == c:
    ans += 1
    continue
  d = None
  if a == b or b == c:
    d = b
  if  c == a:
    d = a
  #print(d)
  if d == None:
    match = False
    for x in (a, b, c):
      if x in doubles:
        match = True
        break
    if match:
      doubles.clear()
      singles.remove(x)
      for x2 in (a, b, c):
        if x2 != x:
          singles.add(x2)
      
      ans += 1
      continue
    else:
      for x in (a, b, c):
        singles.add(x)
  else:
    for x in (a, b, c):
      if x != d:
        s = x
    if d in singles:
      if s in singles:
        doubles.add(s)
      if d in doubles:
        #print('d in doubles')
        doubles.clear()
        if s in singles:
          doubles.add(s)
        singles.add(s)
        ans+=1
        continue
      else:
        doubles.clear()
        if s in singles:
          doubles.add(s)
        singles.remove(d)
        singles.add(s)
        ans += 1
        continue
        
    if s in doubles:
        doubles.clear()
        singles.remove(s)
        singles.add(d)
        doubles.add(d)
        ans+=1
        continue
    if s in singles:
        doubles.add(s)
        singles.add(s)
    else:
        singles.add(s)
    singles.add(d)
    doubles.add(d)
#print(doubles)
print(ans)