



import inspect
import unittest

class        UpperCAmelCase_  (       unittest.TestCase	):

						'''simple docstring'''




						def 	_A     (   self		):







													'''simple docstring'''

													try:
																				import diffusers  # noqa: F401
													except ImportError:
																				assert False






						def 	_A     (   self		):







													'''simple docstring'''

													import diffusers
													from diffusers.dependency_versions_table import deps

													__SCREAMING_SNAKE_CASE									= inspect.getmembers(_A				,							inspect.isclass		)

													for cls_name, cls_module in all_classes:
																				if "dummy_" in cls_module.__module__:
																											for backend in cls_module._backends:
																																		if backend == "k_diffusion":
																																									__SCREAMING_SNAKE_CASE									= 'k-diffusion'
																																		elif backend == "invisible_watermark":
																																									__SCREAMING_SNAKE_CASE									= 'invisible-watermark'
																																		assert backend in deps, f"""{backend} is not in the deps table!"""











def      __lowercase       (			a__ = 10_00       )    ->			int:
							__SCREAMING_SNAKE_CASE									= -1
							__SCREAMING_SNAKE_CASE									= 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
														__SCREAMING_SNAKE_CASE									= (n * n - 2 * a * n) // (2 * n - 2 * a)
														__SCREAMING_SNAKE_CASE									= n - a - b
														if c * c == (a * a + b * b):
																					__SCREAMING_SNAKE_CASE									= a * b * c
																					if candidate >= product:
																												__SCREAMING_SNAKE_CASE									= candidate
							return product


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






