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: Wrong Answer)

N=gets.chomp.to_i
array=gets.chomp.split(" ").map(&:to_i)
ret=0
stock={}
stock[array[0]] ||= 0
stock[array[1]] ||= 0
stock[array[0]]+=1
stock[array[1]]+=1
(N-1).times do |n|
    new1 = array[n*3+2]
    new2 = array[n*3+3]
    new3 = array[n*3+4]
    if new1==new2 && new2==new3
        ret+=1
        next
    end
    stock[new1] ||= 0
    stock[new2] ||= 0
    stock[new3] ||= 0
    stock[new1]+=1
    stock[new2]+=1
    stock[new3]+=1
    if new1 != new2 && new1 != new3 && new2 != new3
        if stock[new1] == 3
            stock={}
            stock[new2]=1
            stock[new3]=1
            ret+=1
        elsif stock[new2] == 3
            stock={}
            stock[new1]=1
            stock[new3]=1
            ret+=1
        elsif stock[new3] == 3
            stock={}
            stock[new1]=1
            stock[new2]=1
            ret+=1
        end
    else
        if stock[new1] >= 3
            stock[new1]-=3
            stock.keys.each do |key|
                stock[key] = 1 if stock[key] > 1
            end
            ret+=1
        elsif stock[new2] >= 3
            stock[new2]-=3
            stock.keys.each do |key|
                stock[key] = 1 if stock[key] > 1
            end
            ret+=1
        elsif stock[new3] >= 3
            stock[new3]-=3
            stock.keys.each do |key|
                stock[key] = 1 if stock[key] > 1
            end
            ret+=1
        end
    end
end
if stock[array[3*N-1]] == 2
    ret+=1
end
puts ret