

# 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      lowerCamelCase_      :




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




	def        lowerCAmelCase_       (     self						:     Dict					,      *__A						:     int					,      **__A						:     List[Any]							):
		if not self.step_with_optimizer:
			# No link between scheduler and optimizer -> just step
			self.scheduler.step(*__A					,      **__A							)
			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(*__A					,      **__A							)
		else:
			# Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
			# num_processes steps per training step
			__A :			str		    =			AcceleratorState().num_processes
			for _ in range(__A							):
				# 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(*__A					,      **__A							)
				else:
					self.scheduler.step(*__A					,      **__A							)




	def        lowerCAmelCase_       (     self						:     Any							):
		return self.scheduler.get_last_lr()




	def        lowerCAmelCase_       (     self						:     Optional[Any]							):
		return self.scheduler.state_dict()




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     int							):
		self.scheduler.load_state_dict(__A							)




	def        lowerCAmelCase_       (     self						:     Optional[int]							):
		return self.scheduler.get_lr()




	def        lowerCAmelCase_       (     self						:     List[Any]					,      *__A						:     Optional[Any]					,      **__A						:     List[str]							):
		return self.scheduler.print_lr(*__A					,      **__A							)








from math import sqrt





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''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(sqrt(UpperCamelCase__ ) + 1 )  ,				6 ):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True





def    __lowerCamelCase      (					UpperCamelCase__ = 10001 ):







							'''simple docstring'''






							snake_case_     							=       0
							snake_case_     							=       1
							while count != nth and number < 3:
														number += 1
														if is_prime(UpperCamelCase__ ):
																					count += 1
							while count != nth:
														number += 2
														if is_prime(UpperCamelCase__ ):
																					count += 1
							return number


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




