
'''simple docstring'''
import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__=2      ,    SCREAMING_SNAKE_CASE__=True      ,    SCREAMING_SNAKE_CASE__=False       )   ->				Dict:


		'''simple docstring'''


		snake_case   :    Tuple			       =		Accelerator(step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE__      ,    split_batches=SCREAMING_SNAKE_CASE__       )
		snake_case   :    int			       =		torch.nn.Linear(2      ,    4       )
		snake_case   :    Optional[Any]			       =		torch.optim.AdamW(model.parameters()      ,    lr=1.0       )
		snake_case   :    Dict			       =		torch.optim.lr_scheduler.OneCycleLR(SCREAMING_SNAKE_CASE__      ,    max_lr=0.01      ,    steps_per_epoch=2      ,    epochs=1       )
		snake_case       ,snake_case       ,snake_case   :    Dict			       =		accelerator.prepare(SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__       )

		# Optimizer has stepped
		scheduler.step()
		if step_scheduler_with_optimizer or (num_processes == 1):
				assert (
				    scheduler.scheduler.last_epoch == num_processes
				), F'Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})'
		else:
				assert (
				    scheduler.scheduler.last_epoch != num_processes
				), F'Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})'




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__=2      ,    SCREAMING_SNAKE_CASE__=True      ,    SCREAMING_SNAKE_CASE__=False       )   ->				Tuple:


		'''simple docstring'''


		snake_case   :    List[str]			       =		Accelerator(step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE__      ,    split_batches=SCREAMING_SNAKE_CASE__       )
		snake_case   :    List[Any]			       =		torch.nn.Linear(2      ,    4       )
		snake_case   :    Optional[Any]			       =		torch.optim.AdamW(model.parameters()      ,    lr=1.0       )
		snake_case   :    str			       =		torch.optim.lr_scheduler.LambdaLR(SCREAMING_SNAKE_CASE__      ,    lr_lambda=lambda SCREAMING_SNAKE_CASE__       : 1 - n / 10       )
		snake_case       ,snake_case       ,snake_case   :    Optional[int]			       =		accelerator.prepare(SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__       )

		# Optimizer has stepped
		snake_case   :    Optional[Any]			       =		False
		scheduler.step()
		snake_case   :    List[Any]			       =		1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
		assert (
		    scheduler.get_last_lr()[0] == expected_lr
		), F'Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'

		# Optimizer has not stepped
		snake_case   :    Optional[Any]			       =		True
		scheduler.step()
		if not step_scheduler_with_optimizer:
				snake_case   :    Tuple			       =		1 - 2 / 10
		assert (
		    scheduler.get_last_lr()[0] == expected_lr
		), F'Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__ = 2       )   ->				int:


		'''simple docstring'''


		from transformers import get_linear_schedule_with_warmup

		snake_case   :    Optional[Any]			       =		[1, 2, 4]
		for num_steps in steps:
				snake_case   :    Any			       =		GradientAccumulationPlugin(num_steps=SCREAMING_SNAKE_CASE__      ,    adjust_scheduler=num_steps > 1       )
				snake_case   :    int			       =		Accelerator(gradient_accumulation_plugin=SCREAMING_SNAKE_CASE__       )
				snake_case   :    int			       =		torch.nn.Linear(2      ,    4       )
				snake_case   :    List[str]			       =		torch.optim.AdamW(model.parameters()      ,    lr=10.0       )
				snake_case   :    str			       =		get_linear_schedule_with_warmup(optimizer=SCREAMING_SNAKE_CASE__      ,    num_warmup_steps=0      ,    num_training_steps=20       )

				snake_case       ,snake_case       ,snake_case   :    Any			       =		accelerator.prepare(SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__       )

				for i in range(10 * num_steps       ):
						with accelerator.accumulate(SCREAMING_SNAKE_CASE__       ):
								optimizer.step()
								scheduler.step()

						if i == (10 * num_steps - 2):
								assert (
								    scheduler.get_last_lr()[0] != 0
								), F'Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}'
				assert (
				    scheduler.get_last_lr()[0] == 0
				), F'Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}'
				GradientState._reset_state()






@require_cpu
class      snake_case__    (	unittest.TestCase ):







		"""simple docstring"""

		def 	lowerCAmelCase							(	self							:       Tuple	)		->       List[Any]:






				"""simple docstring"""







				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1	)   ,     num_processes=1	)
				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1   ,     split_batches=UpperCamelCase__	)   ,     num_processes=1	)



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






				"""simple docstring"""







				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1	)   ,     num_processes=1	)
				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1   ,     split_batches=UpperCamelCase__	)   ,     num_processes=1	)



		def 	lowerCAmelCase							(	self							:       List[str]	)		->       str:






				"""simple docstring"""







				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1   ,     step_scheduler_with_optimizer=UpperCamelCase__	)   ,     num_processes=1	)



		def 	lowerCAmelCase							(	self							:       Optional[int]	)		->       Any:






				"""simple docstring"""







				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1   ,     step_scheduler_with_optimizer=UpperCamelCase__	)   ,     num_processes=1	)



		def 	lowerCAmelCase							(	self							:       Tuple	)		->       Tuple:






				"""simple docstring"""







				AcceleratorState._reset_state(UpperCamelCase__	)
				debug_launcher(UpperCamelCase__	)
				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1   ,     split_batches=UpperCamelCase__	)   ,     num_processes=1	)



		def 	lowerCAmelCase							(	self							:       Optional[Any]	)		->       Optional[int]:






				"""simple docstring"""







				AcceleratorState._reset_state(UpperCamelCase__	)
				debug_launcher(UpperCamelCase__	)
				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1   ,     split_batches=UpperCamelCase__	)   ,     num_processes=1	)



		def 	lowerCAmelCase							(	self							:       List[Any]	)		->       Dict:






				"""simple docstring"""







				AcceleratorState._reset_state(UpperCamelCase__	)
				debug_launcher(partial(UpperCamelCase__   ,     step_scheduler_with_optimizer=UpperCamelCase__	)	)



		def 	lowerCAmelCase							(	self							:       Tuple	)		->       str:






				"""simple docstring"""







				AcceleratorState._reset_state(UpperCamelCase__	)
				debug_launcher(partial(UpperCamelCase__   ,     step_scheduler_with_optimizer=UpperCamelCase__	)	)



		@require_huggingface_suite
		def 	lowerCAmelCase							(	self							:       str	)		->       Tuple:






				"""simple docstring"""







				AcceleratorState._reset_state(UpperCamelCase__	)
				debug_launcher(partial(UpperCamelCase__   ,     num_processes=1	)	)
				debug_launcher(UpperCamelCase__	)









'''simple docstring'''



import math




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):

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




def       _lowerCAmelCase  ( lowerCamelCase_	:     int = 6_0_0_8_5_1_4_7_5_1_4_3 ):

			try:
						__lowercase   =							int(lowerCamelCase_ )
			except (TypeError, ValueError):
						raise TypeError('''Parameter n must be int or castable to int.''' )
			if n <= 0:
						raise ValueError('''Parameter n must be greater than or equal to one.''' )
			__lowercase   =							0
			if is_prime(lowerCamelCase_ ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase_ ):
						return n
			for i in range(3						,				int(math.sqrt(lowerCamelCase_ ) ) + 1						,				2 ):
						if n % i == 0:
									if is_prime(n // i ):
												__lowercase   =							n // i
												break
									elif is_prime(lowerCamelCase_ ):
												__lowercase   =							i
			return max_number


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





