





def 	lowerCamelCase_		(							_UpperCamelCase = 1_000					)						->		int:






				"""simple docstring"""


				snake_case_		:       Any           =    -1
				snake_case_		:       Optional[int]           =    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
								snake_case_		:       str           =    (n * n - 2 * a * n) // (2 * n - 2 * a)
								snake_case_		:       Dict           =    n - a - b
								if c * c == (a * a + b * b):
												snake_case_		:       Any           =    a * b * c
												if candidate >= product:
																snake_case_		:       int           =    candidate
				return product


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






"""simple docstring"""






from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
			if not (is_transformers_available() and is_torch_available() and is_transformers_version(""">=""", """4.25.0""")):
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ...utils.dummy_torch_and_transformers_objects import (
			    VersatileDiffusionDualGuidedPipeline,
			    VersatileDiffusionImageVariationPipeline,
			    VersatileDiffusionPipeline,
			    VersatileDiffusionTextToImagePipeline,
			)
else:
			from .modeling_text_unet import UNetFlatConditionModel
			from .pipeline_versatile_diffusion import VersatileDiffusionPipeline
			from .pipeline_versatile_diffusion_dual_guided import VersatileDiffusionDualGuidedPipeline
			from .pipeline_versatile_diffusion_image_variation import VersatileDiffusionImageVariationPipeline
			from .pipeline_versatile_diffusion_text_to_image import VersatileDiffusionTextToImagePipeline