code: 
  
  from typing import Any, Callable, Dict, List, Optional, Union
  
  import PIL.Image
  import torch
  from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer
  
  from diffusers import (
      AutoencoderKL,
      DDIMScheduler,
      DiffusionPipeline,
      LMSDiscreteScheduler,
      PNDMScheduler,
      StableDiffusionImgaImgPipeline,
      StableDiffusionInpaintPipelineLegacy,
      StableDiffusionPipeline,
      UNetaDConditionModel,
  )
  from diffusers.configuration_utils import FrozenDict
  from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
  from diffusers.utils import deprecate, logging
  
  
  A_:      List[Any]        =			logging.get_logger(__name__)  # pylint: disable=invalid-name
  
  
  class _lowercase					(       _UpperCAmelCase						):
  
  
  
  
  
  							"""simple docstring"""
  
  
  
  
  							lowerCAmelCase__       =					['safety_checker', 'feature_extractor']
  
  
  
  							def __init__(    self     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase = True     ,   ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														super().__init__()
  														if hasattr(scheduler.config     ,   """steps_offset"""  ) and scheduler.config.steps_offset != 1:
  																					_lowercase				=	(
  																					    F'''The configuration file of this scheduler: {scheduler} is outdated. `steps_offset`'''
  																					    F''' should be set to 1 instead of {scheduler.config.steps_offset}. Please make sure '''
  																					    """to update the config accordingly as leaving `steps_offset` might led to incorrect results"""
  																					    """ in future versions. If you have downloaded this checkpoint from the Hugging Face Hub,"""
  																					    """ it would be very nice if you could open a Pull request for the `scheduler/scheduler_config.json`"""
  																					    """ file"""
  																					)
  																					deprecate("""steps_offset!=1"""     ,   """1.0.0"""     ,   UpperCAmelCase     ,   standard_warn=UpperCAmelCase  )
  																					_lowercase				=	dict(scheduler.config  )
  																					_lowercase				=	1
  																					_lowercase				=	FrozenDict(UpperCAmelCase  )
  
  														self.register_modules(
  														    vae=UpperCAmelCase     ,   text_encoder=UpperCAmelCase     ,   tokenizer=UpperCAmelCase     ,   unet=UpperCAmelCase     ,   scheduler=UpperCAmelCase     ,   safety_checker=UpperCAmelCase     ,   feature_extractor=UpperCAmelCase     ,   )
  														self.register_to_config(requires_safety_checker=UpperCAmelCase  )
  
  
  
  							@property
  							def     _UpperCAmelCase       (    self  ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														return {k: getattr(self     ,   UpperCAmelCase  ) for k in self.config.keys() if not k.startswith("""_"""  )}
  
  
  
  							def     _UpperCAmelCase       (    self     ,   UpperCAmelCase = "auto"  ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														if slice_size == "auto":
  																					# half the attention head size is usually a good trade-off between
  																					# speed and memory
  																					_lowercase				=	self.unet.config.attention_head_dim // 2
  														self.unet.set_attention_slice(UpperCAmelCase  )
  
  
  
  							def     _UpperCAmelCase       (    self  ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														self.enable_attention_slicing(UpperCAmelCase  )
  
  
  
  							@torch.no_grad()
  							def     _UpperCAmelCase       (    self     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase = 0.8     ,   UpperCAmelCase = 50     ,   UpperCAmelCase = 7.5     ,   UpperCAmelCase = None     ,   UpperCAmelCase = 1     ,   UpperCAmelCase = 0.0     ,   UpperCAmelCase = None     ,   UpperCAmelCase = "pil"     ,   UpperCAmelCase = True     ,   UpperCAmelCase = None     ,   UpperCAmelCase = 1     ,   ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														return StableDiffusionInpaintPipelineLegacy(**self.components  )(
  														    prompt=UpperCAmelCase     ,   image=UpperCAmelCase     ,   mask_image=UpperCAmelCase     ,   strength=UpperCAmelCase     ,   num_inference_steps=UpperCAmelCase     ,   guidance_scale=UpperCAmelCase     ,   negative_prompt=UpperCAmelCase     ,   num_images_per_prompt=UpperCAmelCase     ,   eta=UpperCAmelCase     ,   generator=UpperCAmelCase     ,   output_type=UpperCAmelCase     ,   return_dict=UpperCAmelCase     ,   callback=UpperCAmelCase     ,   )
  
  
  
  							@torch.no_grad()
  							def     _UpperCAmelCase       (    self     ,   UpperCAmelCase     ,   UpperCAmelCase     ,   UpperCAmelCase = 0.8     ,   UpperCAmelCase = 50     ,   UpperCAmelCase = 7.5     ,   UpperCAmelCase = None     ,   UpperCAmelCase = 1     ,   UpperCAmelCase = 0.0     ,   UpperCAmelCase = None     ,   UpperCAmelCase = "pil"     ,   UpperCAmelCase = True     ,   UpperCAmelCase = None     ,   UpperCAmelCase = 1     ,   **UpperCAmelCase     ,   ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														return StableDiffusionImgaImgPipeline(**self.components  )(
  														    prompt=UpperCAmelCase     ,   image=UpperCAmelCase     ,   strength=UpperCAmelCase     ,   num_inference_steps=UpperCAmelCase     ,   guidance_scale=UpperCAmelCase     ,   negative_prompt=UpperCAmelCase     ,   num_images_per_prompt=UpperCAmelCase     ,   eta=UpperCAmelCase     ,   generator=UpperCAmelCase     ,   output_type=UpperCAmelCase     ,   return_dict=UpperCAmelCase     ,   callback=UpperCAmelCase     ,   callback_steps=UpperCAmelCase     ,   )
  
  
  
  							@torch.no_grad()
  							def     _UpperCAmelCase       (    self     ,   UpperCAmelCase     ,   UpperCAmelCase = 512     ,   UpperCAmelCase = 512     ,   UpperCAmelCase = 50     ,   UpperCAmelCase = 7.5     ,   UpperCAmelCase = None     ,   UpperCAmelCase = 1     ,   UpperCAmelCase = 0.0     ,   UpperCAmelCase = None     ,   UpperCAmelCase = None     ,   UpperCAmelCase = "pil"     ,   UpperCAmelCase = True     ,   UpperCAmelCase = None     ,   UpperCAmelCase = 1     ,   ):
  
  
  
  
  
  
  
  														'''simple docstring'''
  
  
  
  
  
  
  														return StableDiffusionPipeline(**self.components  )(
  														    prompt=UpperCAmelCase     ,   height=UpperCAmelCase     ,   width=UpperCAmelCase     ,   num_inference_steps=UpperCAmelCase     ,   guidance_scale=UpperCAmelCase     ,   negative_prompt=UpperCAmelCase     ,   num_images_per_prompt=UpperCAmelCase     ,   eta=UpperCAmelCase     ,   generator=UpperCAmelCase     ,   latents=UpperCAmelCase     ,   output_type=UpperCAmelCase     ,   return_dict=UpperCAmelCase     ,   callback=UpperCAmelCase     ,   callback_steps=UpperCAmelCase     ,   )
  
  
  
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() = }''')
  
  
  