Problem p02581 - Generation 2

Orig Description

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

Extracted Specification

An integer \(N\) (1 ≤ \(N\) ≤ 2000), representing some quantity or size.
A list of integers \(A\) of size \(3N\), where each integer is between 1 and \(N\).

### Example Input:
```
2
1 2 1 2 2 1
```

### Function Signature:
Write a function `f(N, A)` that takes in the input.
```python
def f(N: int, A: List[int]):
    '''
    N: an integer
    A: a list of integers
    '''
```

Test Case Generator

Sure! Below is a test case generator for the given problem statement.

```python
import random

def tcgen():
    # Generate a random integer N within the constraint 1 ≤ N ≤ 2000
    N = random.randint(1, 2000)
    
    # Generate the list A of size 3N where each element is an integer between 1 and N (inclusive)
    A = [random.randint(1, N) for _ in range(3 * N)]
    
    return N, A

# Example of generating a test case
if __name__ == "__main__":
    N, A = tcgen()
    print(N)
    print(" ".join(map(str, A)))
```

Explanation:
1. **N**: This is a random integer between 1 and 2000 inclusive, representing the number of unique integers that can appear on the cards.
2. **A**: This is a list of integers where each integer is between 1 and N. The length of the list is 3 * N, which satisfies the problem's constraints.

This code will output a random test case adhering to the constraints provided in the problem statement. To use it, you can call the `tcgen` function and it will generate a new test case each time. The output format is designed to match typical competitive programming input formats.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    A = list(map(int, fh.readline().strip().split()))
    return N, A