
Score : 600 points
Problem StatementWe 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
InputInput is given from Standard Input in the following format:
N
A_1 A_2 \cdots A_{3N}
OutputPrint the maximum number of points you can gain.
Sample Input 12
1 2 1 2 2 1
Sample Output 12
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 23
1 1 2 2 3 3 3 2 1
Sample Output 21
Sample Input 33
1 1 2 2 2 3 3 3 1
Sample Output 33
