Problem p03197 - Generation 2

Orig Description

Score : 500 points
Problem StatementThere is an apple tree that bears apples of N colors. The N colors of these apples are numbered 1 to N, and there are a_i apples of Color i.
You and Lunlun the dachshund alternately perform the following operation (starting from you):
Choose one or more apples from the tree and eat them. Here, the apples chosen at the same time must all have different colors.
The one who eats the last apple from the tree will be declared winner. If both you and Lunlun play optimally, which will win?
Constraints
1 \leq N \leq 10^5
1 \leq a_i \leq 10^9
All values in input are integers.
InputInput is given from Standard Input in the following format:
N
a_1
a_2
:
a_N
OutputIf you will win, print first; if Lunlun will win, print second.
Sample Input 12
1
2
Sample Output 1first
Let Color 1 be red, and Color 2 be blue. In this case, the tree bears one red apple and two blue apples.
You should eat the red apple in your first turn. Lunlun is then forced to eat one of the blue apples, and you can win by eating the other in your next turn.
Note that you are also allowed to eat two apples in your first turn, one red and one blue (not a winning move, though).
Sample Input 23
100000
30000
20000
Sample Output 2second

Extracted Specification

An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
A list of integers A of size N, where each integer is between 1 and 1e9.

### Example Input:

```
2
1
2
```

### 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! Let's create a test case generator for the given problem statement. The generator will create random valid inputs based on the given constraints.

Here's the generator:

```python
import random

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

# Example usage:
if __name__ == "__main__":
    N, A = tcgen()
    print(N)
    for a in A:
        print(a)
```

### Explanation:
1. **N**: It generates a random integer between 1 and \(10^5\) (inclusive). This represents the number of different colors of apples.
2. **A**: It generates a list of \(N\) integers, each between 1 and \(10^9\) (inclusive). Each integer \(A[i]\) represents the number of apples of color \(i+1\).

When you run the `tcgen()` function, it will print \(N\) and the list of integers \(A\) representing the number of apples of each color.

### Example Output:
Here’s an example of what the output might look like:
```
5
345
678
12345
67890
234567
```

This output means there are 5 different colors of apples, and the counts of apples for each color are 345, 678, 12345, 67890, and 234567, respectively.

You can use this generator to create various test cases for the problem, ensuring that the solution can handle a wide range of inputs.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    A = [int(fh.readline().strip()) for _ in range(N)]
    return N, A