Problem p03767 - Generation 3

Orig Description

Score : 300 points
Problem StatementThere are 3N participants in AtCoder Group Contest.
The strength of the i-th participant is represented by an integer a_i.
They will form N teams, each consisting of three participants.
No participant may belong to multiple teams.
The strength of a team is defined as the second largest strength among its members.
For example, a team of participants of strength 1, 5, 2 has a strength 2, and a team of three participants of strength 3, 2, 3 has a strength 3.
Find the maximum possible sum of the strengths of N teams.
Constraints
1 ≤ N ≤ 10^5
1 ≤ a_i ≤ 10^{9}
a_i are integers.
InputInput is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
OutputPrint the answer.
Sample Input 12
5 2 8 5 1 5
Sample Output 110
The following is one formation of teams that maximizes the sum of the strengths of teams:
Team 1: consists of the first, fourth and fifth participants.
Team 2: consists of the second, third and sixth participants.
Sample Input 210
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
Sample Output 210000000000
The sum of the strengths can be quite large.

Extracted Specification

An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
A list of 3N integers, where each integer is between 1 and 10^9.

### Example Input:

```
2
5 2 8 5 1 5
```

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

Test Case Generator

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

```python
import random

def tcgen():
    # Generate N
    N = random.randint(1, 10 ** 5)
    
    # Generate 3N integers, each in the range [1, 10^9]
    a = [random.randint(1, 10 ** 9) for _ in range(3 * N)]
    
    return N, a

# Example of using the test case generator
N, a = tcgen()
print(N)
print(" ".join(map(str, a)))
```

### Explanation:

1. **Generating \(N\)**:
   - We generate \(N\) which is an integer in the range \([1, 10^5]\) as per the constraints.

2. **Generating the strengths \(a_i\)**:
   - We generate \(3N\) integers, each in the range \([1, 10^9]\) because there are \(3N\) participants.

3. **Return values**:
   - We return \(N\) and the list of strengths \(a\).

### Example usage:

Running the `tcgen` function will produce random test cases. For instance:
```plaintext
N
a_1 a_2 a_3 ... a_{3N}
```

This generator will help you create a variety of test cases to test the robustness and efficiency of your solution to the problem.

Extract Arguments

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