code: import inspect
  
  from diffusers.utils import is_flax_available
  from diffusers.utils.testing_utils import require_flax
  
  
  if is_flax_available():
  				import jax
  
  
  @require_flax
  class _lowercase					:
  
  
  
  
  
  							"""simple docstring"""
  
  
  
  
  							def     _UpperCAmelCase       (    self  ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														_lowercase				,       _lowercase				=	self.prepare_init_args_and_inputs_for_common()
  
  														_lowercase				=	self.model_class(**UpperCAmelCase  )
  														_lowercase				=	model.init(inputs_dict["""prng_key"""]     ,   inputs_dict["""sample"""]  )
  														jax.lax.stop_gradient(UpperCAmelCase  )
  
  														_lowercase				=	model.apply(UpperCAmelCase     ,   inputs_dict["""sample"""]  )
  
  														if isinstance(UpperCAmelCase     ,   UpperCAmelCase  ):
  																					_lowercase				=	output.sample
  
  														self.assertIsNotNone(UpperCAmelCase  )
  														_lowercase				=	inputs_dict["""sample"""].shape
  														self.assertEqual(output.shape     ,   UpperCAmelCase     ,   """Input and output shapes do not match"""  )
  
  
  
  							def     _UpperCAmelCase       (    self  ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														_lowercase				,       _lowercase				=	self.prepare_init_args_and_inputs_for_common()
  
  														_lowercase				=	16
  														_lowercase				=	(16, 32)
  
  														_lowercase				=	self.model_class(**UpperCAmelCase  )
  														_lowercase				=	model.init(inputs_dict["""prng_key"""]     ,   inputs_dict["""sample"""]  )
  														jax.lax.stop_gradient(UpperCAmelCase  )
  
  														_lowercase				=	model.apply(UpperCAmelCase     ,   inputs_dict["""sample"""]  )
  
  														if isinstance(UpperCAmelCase     ,   UpperCAmelCase  ):
  																					_lowercase				=	output.sample
  
  														self.assertIsNotNone(UpperCAmelCase  )
  														_lowercase				=	inputs_dict["""sample"""].shape
  														self.assertEqual(output.shape     ,   UpperCAmelCase     ,   """Input and output shapes do not match"""  )
  
  
  
  							def     _UpperCAmelCase       (    self  ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														_lowercase				=	"""kwargs""" in inspect.signature(self.model_class.__init__  ).parameters
  														_lowercase				=	len(self.model_class._deprecated_kwargs  ) > 0
  
  														if has_kwarg_in_model_class and not has_deprecated_kwarg:
  																					raise ValueError(
  																					    F'''{self.model_class} has `**kwargs` in its __init__ method but has not defined any deprecated kwargs'''
  																					    """ under the `_deprecated_kwargs` class attribute. Make sure to either remove `**kwargs` if there are"""
  																					    """ no deprecated arguments or add the deprecated argument with `_deprecated_kwargs ="""
  																					    """ [<deprecated_argument>]`"""  )
  
  														if not has_kwarg_in_model_class and has_deprecated_kwarg:
  																					raise ValueError(
  																					    F'''{self.model_class} doesn\'t have `**kwargs` in its __init__ method but has defined deprecated kwargs'''
  																					    """ under the `_deprecated_kwargs` class attribute. Make sure to either add the `**kwargs` argument to"""
  																					    F''' {self.model_class}.__init__ if there are deprecated arguments or remove the deprecated argument'''
  																					    """ from `_deprecated_kwargs = [<deprecated_argument>]`"""  )
  
  
  
style_context: def 					__lowerCAmelCase			(  _A = 998_001					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	0
  							for i in range(999 ,99 ,-1					):  # 3 digit numbers range from 999 down to 100
  														for j in range(999 ,99 ,-1					):
  																					_lowercase				=	str(i * j					)
  																					if product_string == product_string[::-1] and i * j < n:
  																												_lowercase				=	max(_A ,i * j					)
  							return answer
  
  
  if __name__ == "__main__":
  				print(F'''{solution() = }''')
  
  
  