




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

    # 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 					SCREAMING_SNAKE_CASE	(       __UpperCamelCase			:						int=2       ,     __UpperCamelCase			:						Dict=True       ,     __UpperCamelCase			:						Tuple=False      )  ->							str:
    UpperCAmelCase_							 =     Accelerator(step_scheduler_with_optimizer=lowercase_       ,     split_batches=lowercase_      )
    UpperCAmelCase_							 =     torch.nn.Linear(2       ,     4      )
    UpperCAmelCase_							 =     torch.optim.AdamW(model.parameters()       ,     lr=1.0      )
    UpperCAmelCase_							 =     torch.optim.lr_scheduler.LambdaLR(lowercase_       ,     lr_lambda=lambda __UpperCamelCase      : 1 - n / 10      )
    UpperCAmelCase_							 =     accelerator.prepare(lowercase_       ,     lowercase_       ,     lowercase_      )

    # Optimizer has stepped
    UpperCAmelCase_							 =     False
    scheduler.step()
    UpperCAmelCase_							 =     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
    UpperCAmelCase_							 =     True
    scheduler.step()
    if not step_scheduler_with_optimizer:
        UpperCAmelCase_							 =     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 					SCREAMING_SNAKE_CASE	(       __UpperCamelCase			:						int = 2      )  ->							int:
    from transformers import get_linear_schedule_with_warmup

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

        UpperCAmelCase_							 =     accelerator.prepare(lowercase_       ,     lowercase_       ,     lowercase_      )

        for i in range(10 * num_steps      ):
            with accelerator.accumulate(lowercase_      ):
                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   lowerCamelCase_   (	self   :			List[Any]				):
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1				)					,    num_processes=1				)
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1					,    split_batches=_lowerCamelCase				)					,    num_processes=1				)
     def   lowerCamelCase_   (	self   :			List[str]				):
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1				)					,    num_processes=1				)
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1					,    split_batches=_lowerCamelCase				)					,    num_processes=1				)
     def   lowerCamelCase_   (	self   :			Any				):
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1					,    step_scheduler_with_optimizer=_lowerCamelCase				)					,    num_processes=1				)
     def   lowerCamelCase_   (	self   :			Any				):
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1					,    step_scheduler_with_optimizer=_lowerCamelCase				)					,    num_processes=1				)
     def   lowerCamelCase_   (	self   :			List[Any]				):
         AcceleratorState._reset_state(_lowerCamelCase				)
         debug_launcher(_lowerCamelCase				)
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1					,    split_batches=_lowerCamelCase				)					,    num_processes=1				)
     def   lowerCamelCase_   (	self   :			int				):
         AcceleratorState._reset_state(_lowerCamelCase				)
         debug_launcher(_lowerCamelCase				)
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1					,    split_batches=_lowerCamelCase				)					,    num_processes=1				)
     def   lowerCamelCase_   (	self   :			Optional[Any]				):
         AcceleratorState._reset_state(_lowerCamelCase				)
         debug_launcher(partial(_lowerCamelCase					,    step_scheduler_with_optimizer=_lowerCamelCase				)				)
     def   lowerCamelCase_   (	self   :			List[str]				):
         AcceleratorState._reset_state(_lowerCamelCase				)
         debug_launcher(partial(_lowerCamelCase					,    step_scheduler_with_optimizer=_lowerCamelCase				)				)




     @require_huggingface_suite
     def   lowerCamelCase_   (	self   :			List[str]				):
         AcceleratorState._reset_state(_lowerCamelCase				)
         debug_launcher(partial(_lowerCamelCase					,    num_processes=1				)				)
         debug_launcher(_lowerCamelCase				)












"""simple docstring"""





import math




def 		lowerCAmelCase_	(  lowercase_   :							int		):

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




def 		lowerCAmelCase_	(  lowercase_   :							int = 6008_5147_5143		):

 '''simple docstring'''






 try:
  __SCREAMING_SNAKE_CASE :			Any												=       int(lowercase_		)
 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.'''		)
 __SCREAMING_SNAKE_CASE :			List[str]												=       0
 if is_prime(lowercase_		):
  return n
 while n % 2 == 0:
  n //= 2
 if is_prime(lowercase_		):
  return n
 for i in range(3 ,      int(math.sqrt(lowercase_		)		) + 1 ,      2		):
  if n % i == 0:
   if is_prime(n // i		):
    __SCREAMING_SNAKE_CASE :			Optional[int]												=       n // i
    break
   elif is_prime(lowercase_		):
    __SCREAMING_SNAKE_CASE :			Any												=       i
 return max_number


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

