


def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	str													=   [True] * (num + 1)

				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   2
				while p * p <= num:
								if primes[p]:
												for i in range(p * p    ,    num + 1    ,    __a      ):
																SCREAMING_SNAKE_CASE_   :	Any													=   False
								p += 1

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


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				A        =			int(input('Enter a positive integer: ').strip())
				print(prime_sieve_eratosthenes(user_num))







import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
				import torch_xla.core.xla_model as xm
				import torch_xla.debug.metrics as met


class 							__a							(  __A						):





		'''simple docstring'''



		def __init__(						self ,    *UpperCamelCase__ ,    UpperCamelCase__=None ,    UpperCamelCase__=None ,    **UpperCamelCase__       ):
						super().__init__(*UpperCamelCase__ ,    **UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	Dict													=   eval_examples
						SCREAMING_SNAKE_CASE_   :	int													=   post_process_function


		def   __snake_case			(						self ,    UpperCamelCase__ = None ,    UpperCamelCase__=None ,    UpperCamelCase__ = None ,    UpperCamelCase__ = "eval" ,    **UpperCamelCase__ ,    ):
						SCREAMING_SNAKE_CASE_   :	int													=   gen_kwargs.copy()
						SCREAMING_SNAKE_CASE_   :	Tuple													=   (
						    gen_kwargs['max_length'] if gen_kwargs.get('max_length'       ) is not None else self.args.generation_max_length
						)
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   (
						    gen_kwargs['num_beams'] if gen_kwargs.get('num_beams'       ) is not None else self.args.generation_num_beams
						)
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   gen_kwargs

						SCREAMING_SNAKE_CASE_   :	Tuple													=   self.eval_dataset if eval_dataset is None else eval_dataset
						SCREAMING_SNAKE_CASE_   :	int													=   self.get_eval_dataloader(UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	Any													=   self.eval_examples if eval_examples is None else eval_examples

						# Temporarily disable metric computation, we will do it in the loop here.
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   self.compute_metrics
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   None
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   time.time()
						SCREAMING_SNAKE_CASE_   :	int													=   self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
						try:
										SCREAMING_SNAKE_CASE_   :	List[Any]													=   eval_loop(
										    UpperCamelCase__ ,    description='Evaluation' ,    prediction_loss_only=True if compute_metrics is None else None ,    ignore_keys=UpperCamelCase__ ,    metric_key_prefix=UpperCamelCase__ ,    )
						finally:
										SCREAMING_SNAKE_CASE_   :	Optional[int]													=   compute_metrics
						SCREAMING_SNAKE_CASE_   :	Dict													=   self.args.eval_batch_size * self.args.world_size
						if F'''{metric_key_prefix}_jit_compilation_time''' in output.metrics:
										start_time += output.metrics[F'''{metric_key_prefix}_jit_compilation_time''']
						output.metrics.update(
						    speed_metrics(
						        UpperCamelCase__ ,    UpperCamelCase__ ,    num_samples=output.num_samples ,    num_steps=math.ceil(output.num_samples / total_batch_size       ) ,    )       )

						if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
										# Only the main node write the results by default
										SCREAMING_SNAKE_CASE_   :	List[str]													=   self.post_process_function(UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       )
										SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   self.compute_metrics(UpperCamelCase__       )

										# Prefix all keys with metric_key_prefix + '_'
										for key in list(metrics.keys()       ):
														if not key.startswith(F'''{metric_key_prefix}_'''       ):
																		SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   metrics.pop(UpperCamelCase__       )

										metrics.update(output.metrics       )
						else:
										SCREAMING_SNAKE_CASE_   :	Tuple													=   output.metrics

						if self.args.should_log:
										# Only the main node log the results by default
										self.log(UpperCamelCase__       )

						if self.args.tpu_metrics_debug or self.args.debug:
										# tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
										xm.master_print(met.metrics_report()       )

						SCREAMING_SNAKE_CASE_   :	Dict													=   self.callback_handler.on_evaluate(self.args ,    self.state ,    self.control ,    UpperCamelCase__       )
						return metrics






		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__=None ,    UpperCamelCase__ = "test" ,    **UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   gen_kwargs.copy()

						SCREAMING_SNAKE_CASE_   :	Any													=   self.get_test_dataloader(UpperCamelCase__       )

						# Temporarily disable metric computation, we will do it in the loop here.
						SCREAMING_SNAKE_CASE_   :	Tuple													=   self.compute_metrics
						SCREAMING_SNAKE_CASE_   :	str													=   None
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   time.time()
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
						try:
										SCREAMING_SNAKE_CASE_   :	List[str]													=   eval_loop(
										    UpperCamelCase__ ,    description='Prediction' ,    prediction_loss_only=True if compute_metrics is None else None ,    ignore_keys=UpperCamelCase__ ,    metric_key_prefix=UpperCamelCase__ ,    )
						finally:
										SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   compute_metrics

						SCREAMING_SNAKE_CASE_   :	List[str]													=   self.args.eval_batch_size * self.args.world_size
						if F'''{metric_key_prefix}_jit_compilation_time''' in output.metrics:
										start_time += output.metrics[F'''{metric_key_prefix}_jit_compilation_time''']
						output.metrics.update(
						    speed_metrics(
						        UpperCamelCase__ ,    UpperCamelCase__ ,    num_samples=output.num_samples ,    num_steps=math.ceil(output.num_samples / total_batch_size       ) ,    )       )
						if self.post_process_function is None or self.compute_metrics is None:
										return output

						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   self.post_process_function(UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    'predict'       )
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   self.compute_metrics(UpperCamelCase__       )

						# Prefix all keys with metric_key_prefix + '_'
						for key in list(metrics.keys()       ):
										if not key.startswith(F'''{metric_key_prefix}_'''       ):
														SCREAMING_SNAKE_CASE_   :	Optional[int]													=   metrics.pop(UpperCamelCase__       )
						metrics.update(output.metrics       )
						return PredictionOutput(predictions=predictions.predictions ,    label_ids=predictions.label_ids ,    metrics=UpperCamelCase__       )