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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分