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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import Control.Monad
import Data.List
import Data.Maybe
import Data.Ord
import qualified Data.ByteString.Char8 as BS

solveSub as
    | a == b && b ==c = as'
    | otherwise = sort as
    where
        as' = sortBy (comparing (\a -> (- (abs a)))) as
        a = as'!!0
        b = as'!!1
        c = as'!!2

solve [] = 0
solve an
    | a == b && b == c = 1 + solve (drop 3 an')
    | otherwise = solve (drop 3 an)
        where
            an' = if length an >= 5 then (solveSub $ take 5 an) ++ (drop 5 an) else solveSub an
            a = an'!!0
            b = an'!!1
            c = an'!!2
main = do
    n <- readLn :: IO Int
    an <- map read . words <$> getLine :: IO [Int]
    print $ (solveSub $ take 5 an) ++ (drop 5 an)
    print $ solve an