


'''simple docstring'''






from typing import Optional

import torch
from PIL import Image
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import AutoencoderKL, DDIMScheduler, DiffusionPipeline, UNetaDConditionModel
from diffusers.image_processor import VaeImageProcessor
from diffusers.utils import (
    deprecate,
)






class 					__magic_name__							(		_lowerCAmelCase				):






       def __init__(			self  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case = 0.93  ,							snake_case = True  ,							)						->  int:




          '''simple docstring'''
          _UpperCAmelCase   :   Union[str, Any]							    =mixing_coeff
          _UpperCAmelCase   :   Optional[Any]							    =leapfrog_steps

          super().__init__()
          self.register_modules(
              vae=A__  ,							text_encoder=A__  ,							tokenizer=A__  ,							unet=A__  ,							scheduler=A__  ,							)

          _UpperCAmelCase   :   Optional[Any]							    =2 ** (len(self.vae.config.block_out_channels) - 1)
          _UpperCAmelCase   :   str							    =VaeImageProcessor(vae_scale_factor=self.vae_scale_factor)






       def 			lowerCAmelCase		(			self  ,							snake_case  ,							snake_case = None  ,							snake_case = False)						->  Dict:




          '''simple docstring'''
          _UpperCAmelCase   :   str							    =self.tokenizer(
              A__  ,							padding='max_length'  ,							max_length=self.tokenizer.model_max_length  ,							truncation=A__  ,							return_tensors='pt'  ,							)

          _UpperCAmelCase   :   Dict							    =self.text_encoder(text_inputs.input_ids.to(self.device)).last_hidden_state

          _UpperCAmelCase   :   str							    =prompt_embeds.to(dtype=self.text_encoder.dtype  ,							device=self.device)

          if do_classifier_free_guidance:
             _UpperCAmelCase   :   Tuple							    ='' if negative_prompt is None else negative_prompt

             _UpperCAmelCase   :   Union[str, Any]							    =self.tokenizer(
                 A__  ,							padding='max_length'  ,							max_length=self.tokenizer.model_max_length  ,							truncation=A__  ,							return_tensors='pt'  ,							)

             _UpperCAmelCase   :   Any							    =self.text_encoder(uncond_input.input_ids.to(self.device)).last_hidden_state

             _UpperCAmelCase   :   str							    =torch.cat([negative_prompt_embeds, prompt_embeds])

          return prompt_embeds






       def 			lowerCAmelCase		(			self  ,							snake_case  ,							snake_case)						->  Tuple:




          '''simple docstring'''
          _UpperCAmelCase   :   Dict							    =self.mixing_coeff * x + (1 - self.mixing_coeff) * y
          _UpperCAmelCase   :   Dict							    =self.mixing_coeff * y + (1 - self.mixing_coeff) * x

          return [x, y]






       def 			lowerCAmelCase		(			self  ,							snake_case  ,							snake_case)						->  str:




          '''simple docstring'''
          _UpperCAmelCase   :   str							    =(y - (1 - self.mixing_coeff) * x) / self.mixing_coeff
          _UpperCAmelCase   :   List[str]							    =(x - (1 - self.mixing_coeff) * y) / self.mixing_coeff

          return [x, y]






       def 			lowerCAmelCase		(			self  ,							snake_case)						->  Optional[Any]:




          '''simple docstring'''
          # as self.alphas_cumprod is always in cpu
          _UpperCAmelCase   :   Any							    =int(A__)

          _UpperCAmelCase   :   List[str]							    =self.scheduler.alphas_cumprod[t] if t >= 0 else self.scheduler.final_alpha_cumprod

          return alpha_prod, 1 - alpha_prod






       def 			lowerCAmelCase		(			self  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case  ,							)						->  List[str]:




          '''simple docstring'''
          _UpperCAmelCase   :   Optional[int]							    =timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

          _UpperCAmelCase    ,       _UpperCAmelCase   :   int							    =self._get_alpha_and_beta(A__)
          _UpperCAmelCase    ,       _UpperCAmelCase   :   List[Any]							    =self._get_alpha_and_beta(A__)

          _UpperCAmelCase   :   Tuple							    =(alpha_prod_t_prev / alpha_prod_t) ** 0.5
          _UpperCAmelCase   :   List[Any]							    =-a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5

          _UpperCAmelCase   :   str							    =(base - b_t * model_output) / a_t

          return model_input, next_model_input.to(base.dtype)






       def 			lowerCAmelCase		(			self  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case  ,							)						->  List[str]:




          '''simple docstring'''
          _UpperCAmelCase   :   Optional[Any]							    =timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

          _UpperCAmelCase    ,       _UpperCAmelCase   :   Optional[Any]							    =self._get_alpha_and_beta(A__)
          _UpperCAmelCase    ,       _UpperCAmelCase   :   Tuple							    =self._get_alpha_and_beta(A__)

          _UpperCAmelCase   :   Optional[Any]							    =(alpha_prod_t_prev / alpha_prod_t) ** 0.5
          _UpperCAmelCase   :   List[str]							    =-a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5
          _UpperCAmelCase   :   List[Any]							    =a_t * base + b_t * model_output

          return model_input, next_model_input.to(base.dtype)






       @torch.no_grad()
       def 			lowerCAmelCase		(			self  ,							snake_case)						->  Optional[int]:




          '''simple docstring'''
          _UpperCAmelCase   :   Dict							    =1 / self.vae.config.scaling_factor * latents
          _UpperCAmelCase   :   Optional[Any]							    =self.vae.decode(A__).sample
          _UpperCAmelCase   :   Optional[int]							    =(image / 2 + 0.5).clamp(0  ,							1)
          return image






       @torch.no_grad()
       def 			lowerCAmelCase		(			self  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case = None  ,							)						->  Optional[int]:




          '''simple docstring'''
          _UpperCAmelCase   :   List[Any]							    =guidance_scale > 1.0

          _UpperCAmelCase   :   Optional[Any]							    =image.to(device=self.device  ,							dtype=text_embeds.dtype)
          _UpperCAmelCase   :   List[Any]							    =self.vae.encode(A__).latent_dist.sample(A__)

          _UpperCAmelCase   :   List[str]							    =self.vae.config.scaling_factor * latent

          _UpperCAmelCase   :   str							    =[latent.clone(), latent.clone()]

          for i, t in tqdm(enumerate(A__)  ,							total=len(A__)):
             _UpperCAmelCase   :   Tuple							    =self.noise_mixing_layer(x=coupled_latents[0]  ,							y=coupled_latents[1])

             # j - model_input index, k - base index
             for j in range(2):
                _UpperCAmelCase   :   Union[str, Any]							    =j ^ 1

                if self.leapfrog_steps:
                   if i % 2 == 0:
                      _UpperCAmelCase    ,       _UpperCAmelCase   :   str							    =j, k

                _UpperCAmelCase   :   Any							    =coupled_latents[j]
                _UpperCAmelCase   :   List[Any]							    =coupled_latents[k]

                _UpperCAmelCase   :   Optional[int]							    =torch.cat([model_input] * 2) if do_classifier_free_guidance else model_input

                _UpperCAmelCase   :   Union[str, Any]							    =self.unet(A__  ,							A__  ,							encoder_hidden_states=A__).sample

                if do_classifier_free_guidance:
                   _UpperCAmelCase    ,       _UpperCAmelCase   :   Any							    =noise_pred.chunk(2)
                   _UpperCAmelCase   :   str							    =noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

                _UpperCAmelCase    ,       _UpperCAmelCase   :   Dict							    =self.noise_step(
                    base=A__  ,							model_input=A__  ,							model_output=A__  ,							timestep=A__  ,							)

                _UpperCAmelCase   :   Tuple							    =model_input

          return coupled_latents






       @torch.no_grad()
       def __call__(			self  ,							snake_case  ,							snake_case  ,							snake_case  ,							snake_case = 3.0  ,							snake_case = 5_0  ,							snake_case = 0.8  ,							snake_case = None  ,							snake_case = None  ,							snake_case = "pil"  ,							)						->  List[str]:




          '''simple docstring'''
          _UpperCAmelCase   :   List[str]							    =guidance_scale > 1.0

          _UpperCAmelCase   :   List[Any]							    =self.image_processor.preprocess(A__)

          _UpperCAmelCase   :   int							    =self._encode_prompt(A__  ,							A__  ,							A__)
          _UpperCAmelCase   :   Tuple							    =self._encode_prompt(A__  ,							A__  ,							A__)

          self.scheduler.set_timesteps(A__  ,							self.device)

          _UpperCAmelCase   :   List[Any]							    =num_inference_steps - int(num_inference_steps * strength)
          _UpperCAmelCase   :   str							    =self.scheduler.timesteps[t_limit:]
          _UpperCAmelCase   :   str							    =fwd_timesteps.flip(0)

          _UpperCAmelCase   :   Optional[Any]							    =self.prepare_latents(A__  ,							A__  ,							A__  ,							A__  ,							A__)

          for i, t in tqdm(enumerate(A__)  ,							total=len(A__)):
             # j - model_input index, k - base index
             for k in range(2):
                _UpperCAmelCase   :   Optional[Any]							    =k ^ 1

                if self.leapfrog_steps:
                   if i % 2 == 1:
                      _UpperCAmelCase    ,       _UpperCAmelCase   :   Optional[Any]							    =j, k

                _UpperCAmelCase   :   Dict							    =coupled_latents[j]
                _UpperCAmelCase   :   int							    =coupled_latents[k]

                _UpperCAmelCase   :   int							    =torch.cat([model_input] * 2) if do_classifier_free_guidance else model_input

                _UpperCAmelCase   :   List[Any]							    =self.unet(A__  ,							A__  ,							encoder_hidden_states=A__).sample

                if do_classifier_free_guidance:
                   _UpperCAmelCase    ,       _UpperCAmelCase   :   List[Any]							    =noise_pred.chunk(2)
                   _UpperCAmelCase   :   List[str]							    =noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

                _UpperCAmelCase    ,       _UpperCAmelCase   :   Optional[Any]							    =self.denoise_step(
                    base=A__  ,							model_input=A__  ,							model_output=A__  ,							timestep=A__  ,							)

                _UpperCAmelCase   :   str							    =model_input

             _UpperCAmelCase   :   List[Any]							    =self.denoise_mixing_layer(x=coupled_latents[0]  ,							y=coupled_latents[1])

          # either one is fine
          _UpperCAmelCase   :   Tuple							    =coupled_latents[0]

          if output_type not in ["latent", "pt", "np", "pil"]:
             _UpperCAmelCase   :   Union[str, Any]							    =(
                 f"the output_type {output_type} is outdated. Please make sure to set it to one of these instead: "
                 '`pil`, `np`, `pt`, `latent`'
             )
             deprecate('Unsupported output_type'  ,							'1.0.0'  ,							A__  ,							standard_warn=A__)
             _UpperCAmelCase   :   List[str]							    ='np'

          if output_type == "latent":
             _UpperCAmelCase   :   Dict							    =final_latent
          else:
             _UpperCAmelCase   :   Optional[Any]							    =self.decode_latents(A__)
             _UpperCAmelCase   :   Any							    =self.image_processor.postprocess(A__  ,							output_type=A__)

          return image







def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	int:


      '''simple docstring'''




      return n * (2 * n - 1)

def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	bool:


      '''simple docstring'''




      lowerCamelCase__					     = (1 + 24 * n) ** 0.5
      return ((1 + root) / 6) % 1 == 0

def 	lowerCAmelCase_	(     lowerCamelCase:				int = 1_44  )    ->	int:


      '''simple docstring'''




      lowerCamelCase__					     = start
      lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      while not is_pentagonal(lowerCamelCase  ):
            n += 1
            lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      return num


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