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 OCaml (4.10.0) (judge verdict: Wrong Answer)

Scanf.scanf "%d" (fun n ->
    let n3 = 3 * n in
    let a = Array.init n3 (fun _ -> Scanf.scanf " %d" (fun a -> a - 1)) in
    let m = 100000 in
    let make_key a b = if a < b then a * m + b else b * m + a in
    let module M = Map.Make (struct type t = int let compare = compare end) in

    let add a b c d e v newmap =
        let key = make_key a b in
        let v = if c = d && d = e then v + 1 else v in
        M.add key (max v (try M.find key newmap with _ -> 0)) newmap
    in

    let rec loop i map =
        if i = n3 - 1 then map else
            let k3 = a.(i) in
            let k4 = a.(i + 1) in
            let k5 = a.(i + 2) in
            let newmap = M.fold (fun key v newmap ->
                let k1 = key / m in
                let k2 = key mod m in
                let newmap = add k1 k2 k3 k4 k5 v newmap in
                let newmap = add k1 k3 k2 k4 k5 v newmap in
                let newmap = add k1 k4 k2 k3 k5 v newmap in
                let newmap = add k1 k5 k2 k3 k4 v newmap in
                let newmap = add k2 k3 k1 k4 k5 v newmap in
                let newmap = add k2 k4 k1 k3 k5 v newmap in
                let newmap = add k2 k5 k1 k3 k4 v newmap in
                let newmap = add k3 k4 k1 k2 k5 v newmap in
                let newmap = add k3 k5 k1 k2 k4 v newmap in
                let newmap = add k4 k5 k1 k2 k5 v newmap in
                newmap
            ) map M.empty in
            loop (i + 3) newmap
    in
    let map = loop 2 (M.singleton (make_key a.(0) a.(1)) 0) in
    M.fold (fun key v acc ->
        let k1 = key / m in
        let k2 = key mod m in
        let v = if k1 = k2 && k2 = a.(n3 - 1) then v + 1 else v in
        max acc v
    ) map 0 |> Printf.printf "%d\n"
)