code: from typing import Union
  
  import torch
  from PIL import Image
  from torchvision import transforms as tfms
  from tqdm.auto import tqdm
  from transformers import CLIPTextModel, CLIPTokenizer
  
  from diffusers import (
      AutoencoderKL,
      DDIMScheduler,
      DiffusionPipeline,
      LMSDiscreteScheduler,
      PNDMScheduler,
      UNetaDConditionModel,
  )
  
  class 				_lowercase						(    UpperCAmelCase__ ):
  
  
  
  
  
  
      '''simple docstring'''
  
  
  
  
      def __init__(						self					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__					,	):
         super().__init__()
  
         self.register_modules(vae=lowerCamelCase__					,	text_encoder=lowerCamelCase__					,	tokenizer=lowerCamelCase__					,	unet=lowerCamelCase__					,	scheduler=lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__   ):
         with torch.no_grad():
            lowerCAmelCase_:       Union[str, Any]         =  self.vae.encode(tfms.ToTensor()(lowerCamelCase__   ).unsqueeze(0   ).to(self.device   ) * 2 - 1   )
            lowerCAmelCase_:       Union[str, Any]         =  0.1_8_2_1_5 * latent.latent_dist.sample()
         return latent
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__   ):
         lowerCAmelCase_:       Tuple         =  (1 / 0.1_8_2_1_5) * latent
         with torch.no_grad():
            lowerCAmelCase_:       int         =  self.vae.decode(lowerCamelCase__   ).sample
         lowerCAmelCase_:       List[str]         =  (img / 2 + 0.5).clamp(0					,	1   )
         lowerCAmelCase_:       Optional[Any]         =  img.detach().cpu().permute(0					,	2					,	3					,	1   ).numpy()
         lowerCAmelCase_:       List[Any]         =  (img * 255).round().astype("uint8"   )
         return Image.fromarray(img[0]   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__   ):
         lowerCAmelCase_:       List[str]         =  self.tokenizer(
             lowerCamelCase__					,	padding="max_length"					,	max_length=self.tokenizer.model_max_length					,	truncation=lowerCamelCase__					,	return_tensors="pt"					,	)
  
         lowerCAmelCase_:       int         =  self.text_encoder(text_input.input_ids.to(self.device   )   )[0]
  
         lowerCAmelCase_:       Any         =  self.tokenizer(
             ""					,	padding="max_length"					,	max_length=self.tokenizer.model_max_length					,	truncation=lowerCamelCase__					,	return_tensors="pt"					,	)
  
         lowerCAmelCase_:       Dict         =  self.text_encoder(uncond_input.input_ids.to(self.device   )   )[0]
  
         return torch.cat([uncond_embedding, text_embedding]   )
  
  
  
  
      def __call__(						self					,	lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__ = 0.3					,	lowerCamelCase__ = 0.6					,	lowerCamelCase__ = 0.5					,	lowerCamelCase__ = 42					,	lowerCamelCase__ = 50					,	lowerCamelCase__ = 7.5					,	):
         lowerCAmelCase_:       Dict         =  steps - int(kmin * steps   )
         lowerCAmelCase_:       Optional[int]         =  steps - int(kmax * steps   )
  
         lowerCAmelCase_:       List[Any]         =  self.prep_text(lowerCamelCase__   )
  
         self.scheduler.set_timesteps(lowerCamelCase__   )
  
         lowerCAmelCase_:       Union[str, Any]         =  img.size
         lowerCAmelCase_:       str         =  self.encode(lowerCamelCase__   )
  
         torch.manual_seed(lowerCamelCase__   )
         lowerCAmelCase_:       Any         =  torch.randn(
             (1, self.unet.config.in_channels, height // 8, width // 8)					,	).to(self.device   )
  
         lowerCAmelCase_:       Optional[Any]         =  self.scheduler.add_noise(
             lowerCamelCase__					,	lowerCamelCase__					,	timesteps=self.scheduler.timesteps[tmax]					,	)
  
         lowerCAmelCase_:       Dict         =  torch.cat([latents] * 2   )
  
         lowerCAmelCase_:       Any         =  self.scheduler.scale_model_input(lowerCamelCase__					,	self.scheduler.timesteps[tmax]   )
  
         with torch.no_grad():
            lowerCAmelCase_:       Tuple         =  self.unet(
                lowerCamelCase__					,	self.scheduler.timesteps[tmax]					,	encoder_hidden_states=lowerCamelCase__					,	).sample
  
         lowerCAmelCase_:       Optional[int]         =  pred.chunk(2   )
         lowerCAmelCase_:       str         =  pred_uncond + guidance_scale * (pred_text - pred_uncond)
  
         lowerCAmelCase_:       Any         =  self.scheduler.step(lowerCamelCase__					,	self.scheduler.timesteps[tmax]					,	lowerCamelCase__   ).prev_sample
  
         for i, t in enumerate(tqdm(self.scheduler.timesteps   )   ):
            if i > tmax:
               if i < tmin:  # layout generation phase
                  lowerCAmelCase_:       Tuple         =  self.scheduler.add_noise(
                      lowerCamelCase__					,	lowerCamelCase__					,	timesteps=lowerCamelCase__					,	)
  
                  lowerCAmelCase_:       Any         =  (mix_factor * latents) + (
                      1 - mix_factor
                  ) * orig_latents  # interpolating between layout noise and conditionally generated noise to preserve layout sematics
                  lowerCAmelCase_:       Dict         =  torch.cat([input] * 2   )
  
               else:  # content generation phase
                  lowerCAmelCase_:       Union[str, Any]         =  torch.cat([latents] * 2   )
  
               lowerCAmelCase_:       Any         =  self.scheduler.scale_model_input(lowerCamelCase__					,	lowerCamelCase__   )
  
               with torch.no_grad():
                  lowerCAmelCase_:       int         =  self.unet(
                      lowerCamelCase__					,	lowerCamelCase__					,	encoder_hidden_states=lowerCamelCase__					,	).sample
  
               lowerCAmelCase_:       Tuple         =  pred.chunk(2   )
               lowerCAmelCase_:       Dict         =  pred_uncond + guidance_scale * (pred_text - pred_uncond)
  
               lowerCAmelCase_:       Optional[Any]         =  self.scheduler.step(lowerCamelCase__					,	lowerCamelCase__					,	lowerCamelCase__   ).prev_sample
  
         return self.decode(lowerCamelCase__   )
  
  
  
  
style_context: import itertools
  def 		snake_case__  (		lowercase				):
     return (
         int("".join(combination[0:2]				)				) * int("".join(combination[2:5]				)				)
         == int("".join(combination[5:9]				)				)
     ) or (
         int("".join(combination[0]				)				) * int("".join(combination[1:5]				)				)
         == int("".join(combination[5:9]				)				)
     )
  def 		snake_case__  (		):
     return sum(
         {
             int("".join(pandigital[5:9]				)				)
             for pandigital in itertools.permutations("123456789"				)
             if is_combination_valid(lowercase				)
         }				)
  
  
  if __name__ == "__main__":
   print(solution())