

"""simple docstring"""




def       lowercase__						(       snake_case_   :int    ):
	__UpperCAmelCase      		= (1 + 24 * n) ** 0.5
	return ((1 + root) / 6) % 1 == 0





def       lowercase__						(       snake_case_   :int = 5_000    ):
	__UpperCAmelCase      		= [(i * (3 * i - 1)) // 2 for i in range(1			,		snake_case_    )]
	for i, pentagonal_i in enumerate(snake_case_    ):
		for j in range(snake_case_			,		len(snake_case_    )    ):
			__UpperCAmelCase      		= pentagonal_nums[j]
			__UpperCAmelCase      		= pentagonal_i + pentagonal_j
			__UpperCAmelCase      		= pentagonal_j - pentagonal_i
			if is_pentagonal(snake_case_    ) and is_pentagonal(snake_case_    ):
				return b

	return -1


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







# 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 							__SCREAMING_SNAKE_CASE       :






							def __init__(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase = True	,			__lowerCAmelCase = False	):
														UpperCamelCase__					  =      scheduler
														UpperCamelCase__					  =      optimizers if isinstance(__lowerCAmelCase	,			(list, tuple)	) else [optimizers]
														UpperCamelCase__					  =      split_batches
														UpperCamelCase__					  =      step_with_optimizer
														UpperCamelCase__					  =      GradientState()






							def 					_lowerCamelCase		(    self	,			*__lowerCAmelCase	,			**__lowerCAmelCase	):
														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
																					UpperCamelCase__					  =      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 					_lowerCamelCase		(    self	):
														return self.scheduler.get_last_lr()






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.state_dict()






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	):
														self.scheduler.load_state_dict(__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.get_lr()







							def 					_lowerCamelCase		(    self	,			*__lowerCAmelCase	,			**__lowerCAmelCase	):
														return self.scheduler.print_lr(*__lowerCAmelCase	,			**__lowerCAmelCase	)




