

'''simple docstring'''




# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings('ignore', category=UserWarning, module='torch.optim.lr_scheduler')



class 							lowercase_						:

  '''simple docstring'''





  def __init__(  self ,			a_ ,			a_ ,			a_ = True ,			a_ = False  )				->					Dict:


    """simple docstring"""
    UpperCAmelCase    				=						scheduler
    UpperCAmelCase    				=						optimizers if isinstance(a_ ,			(list, tuple)  ) else [optimizers]
    UpperCAmelCase    				=						split_batches
    UpperCAmelCase    				=						step_with_optimizer
    UpperCAmelCase    				=						GradientState()
  def     snake_case_      (  self ,			*a_ ,			**a_  )				->					str:


    """simple docstring"""
    if not self.step_with_optimizer:
      # No link between scheduler and optimizer -> just step
      self.scheduler.step(*a_ ,			**a_  )
      return

    # Otherwise, first make sure the optimizer was stepped.
    if not self.gradient_state.sync_gradients:
      if self.gradient_state.adjust_scheduler:
        self.scheduler._step_count += 1
      return

    for opt in self.optimizers:
      if opt.step_was_skipped:
        return
    if self.split_batches:
      # Split batches -> the training dataloader batch size is not changed so one step per training step
      self.scheduler.step(*a_ ,			**a_  )
    else:
      # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
      # num_processes steps per training step
      UpperCAmelCase    				=						AcceleratorState().num_processes
      for _ in range(a_  ):
        # Special case when using OneCycle and `drop_last` was not used
        if hasattr(self.scheduler ,			'total_steps'  ):
          if self.scheduler._step_count <= self.scheduler.total_steps:
            self.scheduler.step(*a_ ,			**a_  )
        else:
          self.scheduler.step(*a_ ,			**a_  )
  def     snake_case_      (  self  )				->					int:


    """simple docstring"""
    return self.scheduler.get_last_lr()
  def     snake_case_      (  self  )				->					Union[str, Any]:


    """simple docstring"""
    return self.scheduler.state_dict()
  def     snake_case_      (  self ,			a_  )				->					Dict:


    """simple docstring"""
    self.scheduler.load_state_dict(a_  )
  def     snake_case_      (  self  )				->					Any:


    """simple docstring"""
    return self.scheduler.get_lr()





  def     snake_case_      (  self ,			*a_ ,			**a_  )				->					Union[str, Any]:


    """simple docstring"""
    return self.scheduler.print_lr(*a_ ,			**a_  )





'''simple docstring'''




def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : int = 1000    ):
  UpperCAmelCase    				=						-1
  UpperCAmelCase    				=						0
  for a in range(1							, n // 3    ):
    # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
    UpperCAmelCase    				=						(n * n - 2 * a * n) // (2 * n - 2 * a)
    UpperCAmelCase    				=						n - a - b
    if c * c == (a * a + b * b):
      UpperCAmelCase    				=						a * b * c
      if candidate >= product:
        UpperCAmelCase    				=						candidate
  return product


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


