

def 					_lowercase     (				a_				:					int = 1_0_0				)				->	int:




					'''simple docstring'''







					__magic_name__							=    (n * (n + 1) // 2) ** 2
					__magic_name__							=    n * (n + 1) * (2 * n + 1) // 6
					return sum_cubes - sum_squares


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







import inspect
import os
import unittest
from dataclasses import dataclass

import torch

from accelerate import Accelerator, DistributedDataParallelKwargs, GradScalerKwargs
from accelerate.state import AcceleratorState
from accelerate.test_utils import execute_subprocess_async, require_cuda, require_multi_gpu
from accelerate.utils import KwargsHandler

@dataclass
class 				__UpperCamelCase				(					SCREAMING_SNAKE_CASE			):
	_lowercase  :   int       				=  0
	_lowercase  :   bool       				=  False
	_lowercase  :   float       				=  3.0




class 				__UpperCamelCase				(					unittest.TestCase			):







	def 	_SCREAMING_SNAKE_CASE							(   self: Tuple      ):

						'''simple docstring'''





						self.assertDictEqual(MockClass().to_kwargs()  , {}      )
						self.assertDictEqual(MockClass(a=2      ).to_kwargs()  , {'a': 2}      )
						self.assertDictEqual(MockClass(a=2  , b=__UpperCamelCase      ).to_kwargs()  , {'a': 2, 'b': True}      )
						self.assertDictEqual(MockClass(a=2  , c=2.25      ).to_kwargs()  , {'a': 2, 'c': 2.25}      )







	@require_cuda
	def 	_SCREAMING_SNAKE_CASE							(   self: Dict      ):

						'''simple docstring'''





						__magic_name__							=    GradScalerKwargs(init_scale=10_24  , growth_factor=2      )
						AcceleratorState._reset_state()
						__magic_name__							=    Accelerator(mixed_precision='fp16'  , kwargs_handlers=[scaler_handler]      )
						print(accelerator.use_fpaa      )
						__magic_name__							=    accelerator.scaler

						# Check the kwargs have been applied
						self.assertEqual(scaler._init_scale  , 1024.0      )
						self.assertEqual(scaler._growth_factor  , 2.0      )

						# Check the other values are at the default
						self.assertEqual(scaler._backoff_factor  , 0.5      )
						self.assertEqual(scaler._growth_interval  , 20_00      )
						self.assertEqual(scaler._enabled  , __UpperCamelCase      )







	@require_multi_gpu
	def 	_SCREAMING_SNAKE_CASE							(   self: Optional[Any]      ):

						'''simple docstring'''





						__magic_name__							=    ['torchrun', F'--nproc_per_node={torch.cuda.device_count()}', inspect.getfile(self.__class__      )]
						execute_subprocess_async(__UpperCamelCase  , env=os.environ.copy()      )


if __name__ == "__main__":
						A__						=							DistributedDataParallelKwargs(bucket_cap_mb=15, find_unused_parameters=True)
						A__						=							Accelerator(kwargs_handlers=[ddp_scaler])
						A__						=							torch.nn.Linear(100, 200)
						A__						=							accelerator.prepare(model)

						# Check the values changed in kwargs
						A__						=							""
						A__						=							model.bucket_bytes_cap // (1024 * 1024)
						if observed_bucket_cap_map != 15:
												error_msg += f"Kwargs badly passed, should have `15` but found {observed_bucket_cap_map}.\n"
						if model.find_unused_parameters is not True:
												error_msg += f"Kwargs badly passed, should have `True` but found {model.find_unused_parameters}.\n"

						# Check the values of the defaults
						if model.dim != 0:
												error_msg += f"Default value not respected, should have `0` but found {model.dim}.\n"
						if model.broadcast_buffers is not True:
												error_msg += f"Default value not respected, should have `True` but found {model.broadcast_buffers}.\n"
						if model.gradient_as_bucket_view is not False:
												error_msg += f"Default value not respected, should have `False` but found {model.gradient_as_bucket_view}.\n"

						# Raise error at the end to make sure we don't stop at the first failure.
						if len(error_msg) > 0:
												raise ValueError(error_msg)




