

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					(			SCREAMING_SNAKE_CASE						:     Optional[Any]=2       ,   SCREAMING_SNAKE_CASE						:     str=True       ,   SCREAMING_SNAKE_CASE						:     Dict=False						)       ->       List[Any]:

 """simple docstring"""






 __lowerCAmelCase:  Any        = Accelerator(step_scheduler_with_optimizer=SCREAMING_SNAKE_CASE       ,   split_batches=SCREAMING_SNAKE_CASE						)
 __lowerCAmelCase:  Union[str, Any]        = torch.nn.Linear(2       ,   4						)
 __lowerCAmelCase:  Tuple        = torch.optim.AdamW(model.parameters()       ,   lr=1.0						)
 __lowerCAmelCase:  Dict        = torch.optim.lr_scheduler.OneCycleLR(SCREAMING_SNAKE_CASE       ,   max_lr=0.0_1       ,   steps_per_epoch=2       ,   epochs=1						)
 __lowerCAmelCase      ,				__lowerCAmelCase      ,				__lowerCAmelCase:  str        = 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 _a					(			SCREAMING_SNAKE_CASE						:     Any=2       ,   SCREAMING_SNAKE_CASE						:     List[str]=True       ,   SCREAMING_SNAKE_CASE						:     int=False						)       ->       int:

 """simple docstring"""






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

 # Optimizer has stepped
 __lowerCAmelCase:  Dict        = False
 scheduler.step()
 __lowerCAmelCase:  Tuple        = 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:  Tuple        = True
 scheduler.step()
 if not step_scheduler_with_optimizer:
  __lowerCAmelCase:  Union[str, Any]        = 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					(			SCREAMING_SNAKE_CASE						:     int = 2						)       ->       Optional[int]:

 """simple docstring"""






 from transformers import get_linear_schedule_with_warmup

 __lowerCAmelCase:  int        = [1, 2, 4]
 for num_steps in steps:
  __lowerCAmelCase:  Optional[int]        = GradientAccumulationPlugin(num_steps=SCREAMING_SNAKE_CASE       ,   adjust_scheduler=num_steps > 1						)
  __lowerCAmelCase:  Union[str, Any]        = Accelerator(gradient_accumulation_plugin=SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  List[str]        = torch.nn.Linear(2       ,   4						)
  __lowerCAmelCase:  Any        = torch.optim.AdamW(model.parameters()       ,   lr=1_0.0						)
  __lowerCAmelCase:  Optional[int]        = get_linear_schedule_with_warmup(optimizer=SCREAMING_SNAKE_CASE       ,   num_warmup_steps=0       ,   num_training_steps=20						)

  __lowerCAmelCase      ,				__lowerCAmelCase      ,				__lowerCAmelCase:  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 				A_					(						unittest.TestCase   ):


     def     UpperCAmelCase    (				self     :						Union[str, Any]   )				->      Optional[Any]:
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1   )     ,    num_processes=1   )
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1     ,    split_batches=UpperCAmelCase   )     ,    num_processes=1   )


     def     UpperCAmelCase    (				self     :						int   )				->      int:
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1   )     ,    num_processes=1   )
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1     ,    split_batches=UpperCAmelCase   )     ,    num_processes=1   )


     def     UpperCAmelCase    (				self     :						List[Any]   )				->      Optional[int]:
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1     ,    step_scheduler_with_optimizer=UpperCAmelCase   )     ,    num_processes=1   )


     def     UpperCAmelCase    (				self     :						Union[str, Any]   )				->      str:
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1     ,    step_scheduler_with_optimizer=UpperCAmelCase   )     ,    num_processes=1   )


     def     UpperCAmelCase    (				self     :						List[str]   )				->      Dict:
      AcceleratorState._reset_state(UpperCAmelCase   )
      debug_launcher(UpperCAmelCase   )
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1     ,    split_batches=UpperCAmelCase   )     ,    num_processes=1   )


     def     UpperCAmelCase    (				self     :						Any   )				->      List[Any]:
      AcceleratorState._reset_state(UpperCAmelCase   )
      debug_launcher(UpperCAmelCase   )
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1     ,    split_batches=UpperCAmelCase   )     ,    num_processes=1   )


     def     UpperCAmelCase    (				self     :						Optional[int]   )				->      Tuple:
      AcceleratorState._reset_state(UpperCAmelCase   )
      debug_launcher(partial(UpperCAmelCase     ,    step_scheduler_with_optimizer=UpperCAmelCase   )   )


     def     UpperCAmelCase    (				self     :						List[str]   )				->      List[str]:
      AcceleratorState._reset_state(UpperCAmelCase   )
      debug_launcher(partial(UpperCAmelCase     ,    step_scheduler_with_optimizer=UpperCAmelCase   )   )


     @require_huggingface_suite
     def     UpperCAmelCase    (				self     :						Optional[Any]   )				->      str:
      AcceleratorState._reset_state(UpperCAmelCase   )
      debug_launcher(partial(UpperCAmelCase     ,    num_processes=1   )   )
      debug_launcher(UpperCAmelCase   )








def _a					(			SCREAMING_SNAKE_CASE						:     int						)       ->       int:

 """simple docstring"""






 return n * (2 * n - 1)







def _a					(			SCREAMING_SNAKE_CASE						:     int						)       ->       bool:

 """simple docstring"""






 __lowerCAmelCase:  List[Any]        = (1 + 24 * n) ** 0.5
 return ((1 + root) / 6) % 1 == 0







def _a					(			SCREAMING_SNAKE_CASE						:     int = 1_44						)       ->       int:

 """simple docstring"""






 __lowerCAmelCase:  Dict        = start
 __lowerCAmelCase:  List[str]        = hexagonal_num(SCREAMING_SNAKE_CASE						)
 while not is_pentagonal(SCREAMING_SNAKE_CASE						):
  n += 1
  __lowerCAmelCase:  Any        = hexagonal_num(SCREAMING_SNAKE_CASE						)
 return num


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





