




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 	__A	(			__lowerCamelCase=2							,    __lowerCamelCase=True							,    __lowerCamelCase=False					)   -> Optional[int]:
	a		       =							Accelerator(step_scheduler_with_optimizer=__lowerCamelCase							,    split_batches=__lowerCamelCase					)
	a		       =							torch.nn.Linear(2							,    4					)
	a		       =							torch.optim.AdamW(model.parameters()							,    lr=1.0					)
	a		       =							torch.optim.lr_scheduler.OneCycleLR(__lowerCamelCase							,    max_lr=0.01							,    steps_per_epoch=2							,    epochs=1					)
	a       ,				a       ,				a		       =							accelerator.prepare(__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)

	# 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 	__A	(			__lowerCamelCase=2							,    __lowerCamelCase=True							,    __lowerCamelCase=False					)   -> int:
	a		       =							Accelerator(step_scheduler_with_optimizer=__lowerCamelCase							,    split_batches=__lowerCamelCase					)
	a		       =							torch.nn.Linear(2							,    4					)
	a		       =							torch.optim.AdamW(model.parameters()							,    lr=1.0					)
	a		       =							torch.optim.lr_scheduler.LambdaLR(__lowerCamelCase							,    lr_lambda=lambda __lowerCamelCase					: 1 - n / 10					)
	a       ,				a       ,				a		       =							accelerator.prepare(__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)

	# Optimizer has stepped
	a		       =							False
	scheduler.step()
	a		       =							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
	a		       =							True
	scheduler.step()
	if not step_scheduler_with_optimizer:
		a		       =							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 	__A	(			__lowerCamelCase = 2					)   -> List[str]:
	from transformers import get_linear_schedule_with_warmup

	a		       =							[1, 2, 4]
	for num_steps in steps:
		a		       =							GradientAccumulationPlugin(num_steps=__lowerCamelCase							,    adjust_scheduler=num_steps > 1					)
		a		       =							Accelerator(gradient_accumulation_plugin=__lowerCamelCase					)
		a		       =							torch.nn.Linear(2							,    4					)
		a		       =							torch.optim.AdamW(model.parameters()							,    lr=10.0					)
		a		       =							get_linear_schedule_with_warmup(optimizer=__lowerCamelCase							,    num_warmup_steps=0							,    num_training_steps=20					)

		a       ,				a       ,				a		       =							accelerator.prepare(__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase					)

		for i in range(10 * num_steps					):
			with accelerator.accumulate(__lowerCamelCase					):
				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 	__lowerCAmelCase			(			unittest.TestCase				):
							def    lowerCamelCase__							(		self		:Union[str, Any]       ):







								'''simple docstring'''







								debug_launcher(partial(__magic_name__	,   num_processes=1       )	,   num_processes=1       )
								debug_launcher(partial(__magic_name__	,   num_processes=1	,   split_batches=__magic_name__       )	,   num_processes=1       )
							def    lowerCamelCase__							(		self		:Optional[Any]       ):







								'''simple docstring'''







								debug_launcher(partial(__magic_name__	,   num_processes=1       )	,   num_processes=1       )
								debug_launcher(partial(__magic_name__	,   num_processes=1	,   split_batches=__magic_name__       )	,   num_processes=1       )
							def    lowerCamelCase__							(		self		:str       ):







								'''simple docstring'''







								debug_launcher(partial(__magic_name__	,   num_processes=1	,   step_scheduler_with_optimizer=__magic_name__       )	,   num_processes=1       )
							def    lowerCamelCase__							(		self		:str       ):







								'''simple docstring'''







								debug_launcher(partial(__magic_name__	,   num_processes=1	,   step_scheduler_with_optimizer=__magic_name__       )	,   num_processes=1       )
							def    lowerCamelCase__							(		self		:Optional[Any]       ):







								'''simple docstring'''







								AcceleratorState._reset_state(__magic_name__       )
								debug_launcher(__magic_name__       )
								debug_launcher(partial(__magic_name__	,   num_processes=1	,   split_batches=__magic_name__       )	,   num_processes=1       )
							def    lowerCamelCase__							(		self		:Optional[int]       ):







								'''simple docstring'''







								AcceleratorState._reset_state(__magic_name__       )
								debug_launcher(__magic_name__       )
								debug_launcher(partial(__magic_name__	,   num_processes=1	,   split_batches=__magic_name__       )	,   num_processes=1       )
							def    lowerCamelCase__							(		self		:Union[str, Any]       ):







								'''simple docstring'''







								AcceleratorState._reset_state(__magic_name__       )
								debug_launcher(partial(__magic_name__	,   step_scheduler_with_optimizer=__magic_name__       )       )
							def    lowerCamelCase__							(		self		:List[str]       ):







								'''simple docstring'''







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





							@require_huggingface_suite
							def    lowerCamelCase__							(		self		:Union[str, Any]       ):







								'''simple docstring'''







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







import math





def 	__A	(			__lowerCamelCase					)   -> bool:

	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 	__A	(			__lowerCamelCase = 6008_5147_5143					)   -> int:

	try:
		a		       =							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."""					)
	a		       =							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					):
				a		       =							n // i
				break
			elif is_prime(__lowerCamelCase					):
				a		       =							i
	return max_number


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

