






'''simple docstring'''




def 	__UpperCAmelCase       ( __magic_name__						)->    list[int]:



			"""simple docstring"""



			if num <= 0:
						raise ValueError("Input must be a positive integer"						)

			snake_case_				:					Union[str, Any]   =       [True] * (num + 1)

			snake_case_				:					Any   =       2
			while p * p <= num:
						if primes[p]:
									for i in range(p * p     ,      num + 1     ,      __magic_name__						):
												snake_case_				:					Tuple   =       False
						p += 1

			return [prime for prime in range(2     ,      num + 1						) if primes[prime]]


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		__lowerCamelCase   :					Optional[int]   							=					int(input('''Enter a positive integer: ''').strip())
		print(prime_sieve_eratosthenes(user_num))












'''simple docstring'''




import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu







@require_cpu
class    A_	(unittest.TestCase							):
							"""simple docstring"""




							def 							_A	(		self			:str				)				->  Union[str, Any]:


										'''simple docstring'''




										snake_case_				:					Union[str, Any]   =       torch.nn.Linear(10       ,							10				)
										snake_case_				:					Dict   =       torch.optim.SGD(model.parameters()       ,							0.1				)
										snake_case_				:					Tuple   =       Accelerator()
										snake_case_				:					Optional[Any]   =       accelerator.prepare(lowerCAmelCase__				)
										try:
													pickle.loads(pickle.dumps(lowerCAmelCase__				)				)
										except Exception as e:
													self.fail(F'''Accelerated optimizer pickling failed with {e}'''				)
										AcceleratorState._reset_state()




