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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

N = gets.to_i
S = gets.split.map(&:to_i)

dp1 = Array.new(N + 1, -100_000_000)
dp2 = Array.new(N + 1){ Array.new(N + 1, -100_000_000) }
S[0,2].sort.tap do |x,y|
  dp1[x] = dp1[y] = dp1[0] = 0
  dp2[x][y] = 0
end
base = 0
q = []

(1 ... N).each do |i|
  a,b,c = S[3 * i - 1, 3].sort
  if a == c
    base += 1
    next
  elsif a == b
    (1 .. N).each do |x|
      next if dp2[x][a] < 0 && dp2[a][x] < 0
      if x < a
        q << [x, c, dp2[x][a] + 1]
      elsif x < c
        q << [x, c, dp2[a][x] + 1]
      else
        q << [c, x, dp2[a][x] + 1]
      end
    end
    if dp2[c][c] >= 0
      q << [a, a, dp2[c][c] + 1]
    end
  elsif b == c
    (1 .. N).each do |x|
      next if dp2[x][c] < 0 && dp2[c][x] < 0
      if x < a
        q << [x, a, dp2[x][c] + 1]
      elsif x < c
        q << [a, x, dp2[x][c] + 1]
      else
        q << [a, x, dp2[c][x] + 1]
      end
    end
    if dp2[a][a] >= 0
      q << [c, c, dp2[a][a] + 1]
    end
  else
    q << [a, b, dp2[c][c] + 1]
    q << [a, c, dp2[b][b] + 1]
    q << [b, c, dp2[a][a] + 1]
  end
  
  q << [a, b, dp1[0]]
  q << [a, c, dp1[0]]
  q << [b, c, dp1[0]]

  (1 .. N).each do |x|
    next if dp1[x] < 0
    [a,b,c].each do |y|
      if x < y
        q << [x, y, dp1[x]]
      else
        q << [y, x, dp1[x]]
      end
    end
  end
  
  until q.empty?
    a,b,v = q.shift
    if dp2[a][b] < v
      dp2[a][b] = v
      dp1[0] = v if dp1[0] < v
      dp1[a] = v if dp1[a] < v
      dp1[b] = v if dp1[b] < v
    end
  end
end
puts base + [dp1[0], dp2[S[-1]][S[-1]] + 1].max