


# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings('''ignore''', category=UserWarning, module='''torch.optim.lr_scheduler''')





class  _a							:




	def __init__( self						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		Optional[int]		, _SCREAMING_SNAKE_CASE						:		bool = True		, _SCREAMING_SNAKE_CASE						:		bool = False		)->	str:
			lowerCAmelCase__       :      Dict   					= scheduler
			lowerCAmelCase__       :      int   					= optimizers if isinstance(_SCREAMING_SNAKE_CASE		, (list, tuple)		) else [optimizers]
			lowerCAmelCase__       :      List[str]   					= split_batches
			lowerCAmelCase__       :      Dict   					= step_with_optimizer
			lowerCAmelCase__       :      List[str]   					= GradientState()




	def 							UpperCAmelCase__( self						:		int		, *_SCREAMING_SNAKE_CASE						:		Optional[int]		, **_SCREAMING_SNAKE_CASE						:		List[Any]		)->	Optional[int]:
			if not self.step_with_optimizer:
					# No link between scheduler and optimizer -> just step
					self.scheduler.step(*_SCREAMING_SNAKE_CASE		, **_SCREAMING_SNAKE_CASE		)
					return

			# Otherwise, first make sure the optimizer was stepped.
			if not self.gradient_state.sync_gradients:
					if self.gradient_state.adjust_scheduler:
							self.scheduler._step_count += 1
					return

			for opt in self.optimizers:
					if opt.step_was_skipped:
							return
			if self.split_batches:
					# Split batches -> the training dataloader batch size is not changed so one step per training step
					self.scheduler.step(*_SCREAMING_SNAKE_CASE		, **_SCREAMING_SNAKE_CASE		)
			else:
					# Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
					# num_processes steps per training step
					lowerCAmelCase__       :      Dict   					= AcceleratorState().num_processes
					for _ in range(_SCREAMING_SNAKE_CASE		):
							# Special case when using OneCycle and `drop_last` was not used
							if hasattr(self.scheduler		, '''total_steps'''		):
									if self.scheduler._step_count <= self.scheduler.total_steps:
											self.scheduler.step(*_SCREAMING_SNAKE_CASE		, **_SCREAMING_SNAKE_CASE		)
							else:
									self.scheduler.step(*_SCREAMING_SNAKE_CASE		, **_SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		List[str]		)->	str:
			return self.scheduler.get_last_lr()




	def 							UpperCAmelCase__( self						:		Optional[int]		)->	int:
			return self.scheduler.state_dict()




	def 							UpperCAmelCase__( self						:		Tuple		, _SCREAMING_SNAKE_CASE						:		str		)->	int:
			self.scheduler.load_state_dict(_SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		Optional[Any]		)->	int:
			return self.scheduler.get_lr()




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, *_SCREAMING_SNAKE_CASE						:		int		, **_SCREAMING_SNAKE_CASE						:		Tuple		)->	Union[str, Any]:
			return self.scheduler.print_lr(*_SCREAMING_SNAKE_CASE		, **_SCREAMING_SNAKE_CASE		)








from math import isqrt






def 					lowerCamelCase_   (	_a	):




		"""simple docstring"""






		lowerCAmelCase__       :      Dict   					= [True] * max_number
		for i in range(2     ,       isqrt(max_number - 1	) + 1	):
				if is_prime[i]:
						for j in range(i**2     ,       _a     ,       _a	):
								lowerCAmelCase__       :      int   					= False

		return [i for i in range(2     ,       _a	) if is_prime[i]]






def 					lowerCamelCase_   (	_a = 10**8	):




		"""simple docstring"""






		lowerCAmelCase__       :      Any   					= calculate_prime_numbers(max_number // 2	)

		lowerCAmelCase__       :      Tuple   					= 0
		lowerCAmelCase__       :      List[Any]   					= 0
		lowerCAmelCase__       :      Optional[int]   					= len(_a	) - 1
		while left <= right:
				while prime_numbers[left] * prime_numbers[right] >= max_number:
						right -= 1
				semiprimes_count += right - left + 1
				left += 1

		return semiprimes_count


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




