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, here is the test case generator for the provided problem statement:
```python
import random
def generate_test_case():
# Step 1: Generate a random N within the given constraints
N = random.randint(1, 2000)
# Step 2: Generate the array A of size 3N with values between 1 and N (inclusive)
A = [random.randint(1, N) for _ in range(3 * N)]
return N, A
# Function to print the test case in the required format
def print_test_case(N, A):
print(N)
print(' '.join(map(str, A)))
# Generate and print a test case
N, A = generate_test_case()
print_test_case(N, A)
```
### Explanation:
1. **Step 1:** We start by generating a random integer \( N \) within the range [1, 2000]. This represents the number of different integers that can be on the cards.
2. **Step 2:** We then create a list \( A \) of size \( 3N \) where each element is a random integer between 1 and \( N \). This simulates the cards.
3. **Function `print_test_case`:** This function formats and prints the test case as required by the problem statement.
To generate and print a test case, you can run the code block above. It will output \( N \) followed by the sequence \( A \) in the required format.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
A = list(map(int, fh.readline().strip().split()))
return N, A