Orig Description
Problem D: Numbers
Given n, find n consecutive positive integers such that each number has no divisors other than 1 and itself.
Input
The input is given in the following format.
n
The input satisfies the following constraints.
1 ≤ n ≤ 1,500
Output
On the first line, output the smallest of the n selected consecutive positive integers.
From the second to the n+1-th line, output the divisors of each value.
Any value other than 1 or itself can be output as a divisor.
Let x be the value output on the first line and output the divisor of x+i-2 on the i-th line.
The output value must not exceed 5,000 digits.
Sample Input 1
2
Sample Output 1
8
2
3
Sample Input 2
3
Sample Output 2
8
2
3
5
Hint
In Sample Output 2, 8, 9, and 10 are selected as three consecutive integers.
On the second line, 2 is output as the divisor of 8, on the third and fourth lines, 3 and 4 are output as the divisor of 9, and on the fifth line, 5 is output as the divisor of 10.
Extracted Specification
An integer n (1 ≤ n ≤ 1,500), representing some quantity or size.
### Example Input:
```
2
```
### Function Signature:
Write a function f(n) that takes in the input.
```python
def f(n: int):
'''
n: an integer
'''
```
Test Case Generator
Sure! Let's write a test case generator for the given problem statement "Problem D: Numbers". We need to generate random values for \( n \) within the given constraints and then construct the output accordingly.
Here's the code for the test case generator:
```python
import random
def generate_consecutive_numbers(n):
# Starting from a random number that ensures we don't exceed 5000 digits in output
start = random.randint(1, 10**5)
return [start + i for i in range(n)]
def generate_divisors(n):
divisors = []
numbers = generate_consecutive_numbers(n)
for num in numbers:
# Generate a divisor other than 1 and the number itself
if num == 1:
divisors.append(2) # Since 1 only has itself as a divisor, we output 2 instead
else:
divisors.append(random.randint(2, num - 1))
return numbers, divisors
def tcgen():
n = random.randint(1, 1500)
numbers, divisors = generate_divisors(n)
return n, numbers, divisors
def format_output(n, numbers, divisors):
output = [str(numbers[0])]
output.extend(map(str, divisors))
return "\n".join(output)
# Example usage:
n, numbers, divisors = tcgen()
print(n)
print(format_output(n, numbers, divisors))
```
### Explanation:
1. **generate_consecutive_numbers(n)**: Generates `n` consecutive numbers starting from a random integer within a reasonable range.
2. **generate_divisors(n)**: Generates a list of divisors such that each number in the list, except 1, has at least one divisor other than 1 and itself. We handle the special case for 1 by outputting 2 as its divisor.
3. **tcgen()**: Generates a random value for \( n \) within the specified range and then uses the helper functions to generate the numbers and their respective divisors.
4. **format_output(n, numbers, divisors)**: Formats the output in the required way, with the first line being the smallest number in the list, followed by the divisors of each consecutive number.
This should cover the generation of test cases as required by the problem statement.
Extract Arguments
def extract_arguments(fh):
n = int(fh.readline().strip())
return (n,)