

import torch

from accelerate import Accelerator, DistributedType

class    a__  :
			"""simple docstring"""







			def __enter__(      self    )					->  Any:
							'''simple docstring'''






							if self.enabled:
											A__            =     self.model.no_sync()
											self.model_sync_obj.__enter__()

							return self


			def __exit__(      self , lowercase , lowercase , lowercase    )					->  Optional[int]:
							'''simple docstring'''






							if self.enabled:
											# Average all models on exit
											self._sync_and_avg_model_params()
											self.model_sync_obj.__exit__(lowercase , lowercase , lowercase    )


			def __init__(      self , lowercase , lowercase , lowercase , lowercase = True    )					->  Union[str, Any]:
							'''simple docstring'''






							if accelerator.distributed_type not in [
							    DistributedType.NO,
							    DistributedType.MULTI_CPU,
							    DistributedType.MULTI_GPU,
							]:
											raise NotImplementedError("LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)"    )
							A__            =     enabled and accelerator.distributed_type != DistributedType.NO
							A__            =     0
							if self.enabled:
											A__            =     accelerator
											A__            =     model
											A__            =     local_sgd_steps


			def        UpperCamelCase						(      self    )					->  List[str]:
							'''simple docstring'''






							self.num_steps += 1
							if not self.enabled:
											return

							if self.num_steps % self.local_sgd_steps == 0:
											self._sync_and_avg_model_params()


			def        UpperCamelCase						(      self    )					->  List[str]:
							'''simple docstring'''






							self.accelerator.wait_for_everyone()
							with self.accelerator.autocast():
											for param in self.model.parameters():
															A__            =     self.accelerator.reduce(param.data , reduction="mean"    )




import math



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							int )     -> bool:




				'''simple docstring'''





				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5		,    int(math.sqrt(SCREAMING_SNAKE_CASE_ ) + 1 )		,    6 ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							int = 2_0_0_0_0_0_0 )     -> int:




				'''simple docstring'''





				return sum(num for num in range(3		,    SCREAMING_SNAKE_CASE_		,    2 ) if is_prime(SCREAMING_SNAKE_CASE_ ) ) + 2 if n > 2 else 0


if __name__ == "__main__":
	print(f"""{solution() = }""")

