


import inspect
import unittest






class   __lowercase				(  unittest.TestCase  ):





      def        _lowercase				(		self						:					int       )    ->   Tuple:






         """simple docstring"""







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





      def        _lowercase				(		self						:					List[str]       )    ->   List[Any]:






         """simple docstring"""







         import diffusers
         from diffusers.dependency_versions_table import deps

         UpperCAmelCase							=     inspect.getmembers(__lowerCamelCase					,       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":
                     UpperCAmelCase							=     """k-diffusion"""
                  elif backend == "invisible_watermark":
                     UpperCAmelCase							=     """invisible-watermark"""
                  assert backend in deps, F"""{backend} is not in the deps table!"""







from math import sqrt
def   _UpperCamelCase				(						lowerCAmelCase_ = 1_0_0_0_0_0_0   )						->int:
   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   UpperCAmelCase							=     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() = }""")



