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F - Brave CHAIN /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

1 以上 N 以下の整数のうち一つが書かれた 3N 枚のカードが左右一列に並んでいます。 左から i 番目のカードに書かれた整数は A_i です。

• 左から 5 枚のカードを好きな順に並び替える。その後、左から 3 枚のカードを取り除く。このとき、その 3 枚のカードに書かれた整数がすべて等しければ 1 点を得る。

N-1 回の操作の後、残った 3 枚のカードに書かれた整数がすべて等しければ追加で 1 点を得ます。

制約

• 1 \leq N \leq 2000
• 1 \leq A_i \leq N

入力

N
A_1 A_2 \cdots A_{3N}

2
1 2 1 2 2 1

出力例 1

2

カードに書かれた整数は左から順に 1\ 1\ 1 となります。

入力例 2

3
1 1 2 2 3 3 3 2 1

1

入力例 3

3
1 1 2 2 2 3 3 3 1

出力例 3

3

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.

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

1

Sample Input 3

3
1 1 2 2 2 3 3 3 1

3