






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      lowerCamelCase					(						a_=2 ,						a_=True ,						a_=False	)	->			Union[str, Any]:
							lowerCAmelCase_										=     Accelerator(step_scheduler_with_optimizer=a_ ,						split_batches=a_	)
							lowerCAmelCase_										=     torch.nn.Linear(2 ,						4	)
							lowerCAmelCase_										=     torch.optim.AdamW(model.parameters() ,						lr=1.0	)
							lowerCAmelCase_										=     torch.optim.lr_scheduler.OneCycleLR(a_ ,						max_lr=0.01 ,						steps_per_epoch=2 ,						epochs=1	)
							lowerCAmelCase_						,   lowerCAmelCase_						,   lowerCAmelCase_										=     accelerator.prepare(a_ ,						a_ ,						a_	)

							# 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      lowerCamelCase					(						a_=2 ,						a_=True ,						a_=False	)	->			List[str]:
							lowerCAmelCase_										=     Accelerator(step_scheduler_with_optimizer=a_ ,						split_batches=a_	)
							lowerCAmelCase_										=     torch.nn.Linear(2 ,						4	)
							lowerCAmelCase_										=     torch.optim.AdamW(model.parameters() ,						lr=1.0	)
							lowerCAmelCase_										=     torch.optim.lr_scheduler.LambdaLR(a_ ,						lr_lambda=lambda a_	: 1 - n / 10	)
							lowerCAmelCase_						,   lowerCAmelCase_						,   lowerCAmelCase_										=     accelerator.prepare(a_ ,						a_ ,						a_	)

							# Optimizer has stepped
							lowerCAmelCase_										=     False
							scheduler.step()
							lowerCAmelCase_										=     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
							lowerCAmelCase_										=     True
							scheduler.step()
							if not step_scheduler_with_optimizer:
														lowerCAmelCase_										=     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      lowerCamelCase					(						a_ = 2	)	->			Tuple:
							from transformers import get_linear_schedule_with_warmup

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

														lowerCAmelCase_						,   lowerCAmelCase_						,   lowerCAmelCase_										=     accelerator.prepare(a_ ,						a_ ,						a_	)

														for i in range(10 * num_steps	):
																					with accelerator.accumulate(a_	):
																												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 							a_ (						unittest.TestCase		):


							'''simple docstring'''






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

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

							def      _lowercase       (		self   )					->					str:
														'''simple docstring'''

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

							def      _lowercase       (		self   )					->					Optional[int]:
														'''simple docstring'''

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

							def      _lowercase       (		self   )					->					Union[str, Any]:
														'''simple docstring'''

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

							def      _lowercase       (		self   )					->					str:
														'''simple docstring'''

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

							def      _lowercase       (		self   )					->					Tuple:
														'''simple docstring'''

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

							def      _lowercase       (		self   )					->					Dict:
														'''simple docstring'''

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

							def      _lowercase       (		self   )					->					Tuple:
														'''simple docstring'''

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






							@require_huggingface_suite
							def      _lowercase       (		self   )					->					Tuple:
														'''simple docstring'''

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











import math
def      lowerCamelCase					(						a_	)	->			Dict:
							lowerCAmelCase_										=     0
							if n % 2 == 0:
														count += 1
														while n % 2 == 0:
																					lowerCAmelCase_										=     int(n / 2	)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

							lowerCAmelCase_										=     3

							while i <= int(math.sqrt(a_	)	):
														if n % i == 0:
																					count += 1
																					while n % i == 0:
																												lowerCAmelCase_										=     int(n / i	)
														lowerCAmelCase_										=     i + 2

							# this condition checks the prime
							# number n is greater than 2

							if n > 2:
														count += 1
							return count


if __name__ == "__main__":
		lowerCamelCase_						     =  5_1_2_4_2_1_8_3
		print(f'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
		print(f'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')



