
"""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       lowerCAmelCase__				:







     def __init__(							self			:			Optional[int]    ,      _lowerCamelCase			:			str    ,      _lowerCamelCase			:			Optional[Any]    ,      _lowerCamelCase			:			bool = True    ,      _lowerCamelCase			:			bool = False			):
       _snake_case					     =       scheduler
       _snake_case					     =       optimizers if isinstance(_lowerCamelCase    ,      (list, tuple)			) else [optimizers]
       _snake_case					     =       split_batches
       _snake_case					     =       step_with_optimizer
       _snake_case					     =       GradientState()







     def      lowercase	(							self			:			str    ,      *_lowerCamelCase			:			Optional[Any]    ,      **_lowerCamelCase			:			str			):
       if not self.step_with_optimizer:
         # No link between scheduler and optimizer -> just step
         self.scheduler.step(*_lowerCamelCase    ,      **_lowerCamelCase			)
         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(*_lowerCamelCase    ,      **_lowerCamelCase			)
       else:
         # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
         # num_processes steps per training step
         _snake_case					     =       AcceleratorState().num_processes
         for _ in range(_lowerCamelCase			):
           # 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(*_lowerCamelCase    ,      **_lowerCamelCase			)
           else:
             self.scheduler.step(*_lowerCamelCase    ,      **_lowerCamelCase			)







     def      lowercase	(							self			:			List[Any]			):
       return self.scheduler.get_last_lr()







     def      lowercase	(							self			:			Optional[Any]			):
       return self.scheduler.state_dict()







     def      lowercase	(							self			:			str    ,      _lowerCamelCase			:			Optional[Any]			):
       self.scheduler.load_state_dict(_lowerCamelCase			)







     def      lowercase	(							self			:			Tuple			):
       return self.scheduler.get_lr()







     def      lowercase	(							self			:			int    ,      *_lowerCamelCase			:			str    ,      **_lowerCamelCase			:			Dict			):
       return self.scheduler.print_lr(*_lowerCamelCase    ,      **_lowerCamelCase			)





"""simple docstring"""



from math import sqrt
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int = 1_00_00_00		)     ->					int:
  _snake_case					     =       0
  _snake_case					     =       0
  _snake_case					     =       42

  while num_cuboids <= limit:
    max_cuboid_size += 1
    for sum_shortest_sides in range(2 ,					2 * max_cuboid_size + 1		):
      if sqrt(sum_shortest_sides**2 + max_cuboid_size**2		).is_integer():
        num_cuboids += (
            min(__lowerCamelCase ,					sum_shortest_sides // 2		)
            - max(1 ,					sum_shortest_sides - max_cuboid_size		)
            + 1
        )

  return max_cuboid_size


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



