"""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      _SCREAMING_SNAKE_CASE							(			UpperCAmelCase				):



   '''simple docstring'''



   def __init__(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = 0.93 ,				_SCREAMING_SNAKE_CASE = True ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					mixing_coeff
      __lowerCamelCase    		=					leapfrog_steps

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

      __lowerCamelCase    		=					2 ** (len(self.vae.config.block_out_channels	) - 1)
      __lowerCamelCase    		=					VaeImageProcessor(vae_scale_factor=self.vae_scale_factor	)







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = False	):


      '''simple docstring'''

      __lowerCamelCase    		=					self.tokenizer(
          a_ ,				padding='max_length' ,				max_length=self.tokenizer.model_max_length ,				truncation=a_ ,				return_tensors='pt' ,				)

      __lowerCamelCase    		=					self.text_encoder(text_inputs.input_ids.to(self.device	)	).last_hidden_state

      __lowerCamelCase    		=					prompt_embeds.to(dtype=self.text_encoder.dtype ,				device=self.device	)

      if do_classifier_free_guidance:
         __lowerCamelCase    		=					'' if negative_prompt is None else negative_prompt

         __lowerCamelCase    		=					self.tokenizer(
             a_ ,				padding='max_length' ,				max_length=self.tokenizer.model_max_length ,				truncation=a_ ,				return_tensors='pt' ,				)

         __lowerCamelCase    		=					self.text_encoder(uncond_input.input_ids.to(self.device	)	).last_hidden_state

         __lowerCamelCase    		=					torch.cat([negative_prompt_embeds, prompt_embeds]	)

      return prompt_embeds







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					self.mixing_coeff * x + (1 - self.mixing_coeff) * y
      __lowerCamelCase    		=					self.mixing_coeff * y + (1 - self.mixing_coeff) * x

      return [x, y]







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					(y - (1 - self.mixing_coeff) * x) / self.mixing_coeff
      __lowerCamelCase    		=					(x - (1 - self.mixing_coeff) * y) / self.mixing_coeff

      return [x, y]







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					int(a_	)

      __lowerCamelCase    		=					self.scheduler.alphas_cumprod[t] if t >= 0 else self.scheduler.final_alpha_cumprod

      return alpha_prod, 1 - alpha_prod







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

      __lowerCamelCase		,__lowerCamelCase    		=					self._get_alpha_and_beta(a_	)
      __lowerCamelCase		,__lowerCamelCase    		=					self._get_alpha_and_beta(a_	)

      __lowerCamelCase    		=					(alpha_prod_t_prev / alpha_prod_t) ** 0.5
      __lowerCamelCase    		=					-a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5

      __lowerCamelCase    		=					(base - b_t * model_output) / a_t

      return model_input, next_model_input.to(base.dtype	)







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

      __lowerCamelCase		,__lowerCamelCase    		=					self._get_alpha_and_beta(a_	)
      __lowerCamelCase		,__lowerCamelCase    		=					self._get_alpha_and_beta(a_	)

      __lowerCamelCase    		=					(alpha_prod_t_prev / alpha_prod_t) ** 0.5
      __lowerCamelCase    		=					-a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5
      __lowerCamelCase    		=					a_t * base + b_t * model_output

      return model_input, next_model_input.to(base.dtype	)







   @torch.no_grad()
   def    _A				(	self ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					1 / self.vae.config.scaling_factor * latents
      __lowerCamelCase    		=					self.vae.decode(a_	).sample
      __lowerCamelCase    		=					(image / 2 + 0.5).clamp(0 ,				1	)
      return image







   @torch.no_grad()
   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = None ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					guidance_scale > 1.0

      __lowerCamelCase    		=					image.to(device=self.device ,				dtype=text_embeds.dtype	)
      __lowerCamelCase    		=					self.vae.encode(a_	).latent_dist.sample(a_	)

      __lowerCamelCase    		=					self.vae.config.scaling_factor * latent

      __lowerCamelCase    		=					[latent.clone(), latent.clone()]

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

         # j - model_input index, k - base index
         for j in range(2	):
            __lowerCamelCase    		=					j ^ 1

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

            __lowerCamelCase    		=					coupled_latents[j]
            __lowerCamelCase    		=					coupled_latents[k]

            __lowerCamelCase    		=					torch.cat([model_input] * 2	) if do_classifier_free_guidance else model_input

            __lowerCamelCase    		=					self.unet(a_ ,				a_ ,				encoder_hidden_states=a_	).sample

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

            __lowerCamelCase		,__lowerCamelCase    		=					self.noise_step(
                base=a_ ,				model_input=a_ ,				model_output=a_ ,				timestep=a_ ,				)

            __lowerCamelCase    		=					model_input

      return coupled_latents







   @torch.no_grad()
   def __call__(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = 3.0 ,				_SCREAMING_SNAKE_CASE = 50 ,				_SCREAMING_SNAKE_CASE = 0.8 ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = "pil" ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					guidance_scale > 1.0

      __lowerCamelCase    		=					self.image_processor.preprocess(a_	)

      __lowerCamelCase    		=					self._encode_prompt(a_ ,				a_ ,				a_	)
      __lowerCamelCase    		=					self._encode_prompt(a_ ,				a_ ,				a_	)

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

      __lowerCamelCase    		=					num_inference_steps - int(num_inference_steps * strength	)
      __lowerCamelCase    		=					self.scheduler.timesteps[t_limit:]
      __lowerCamelCase    		=					fwd_timesteps.flip(0	)

      __lowerCamelCase    		=					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	):
            __lowerCamelCase    		=					k ^ 1

            if self.leapfrog_steps:
               if i % 2 == 1:
                  __lowerCamelCase		,__lowerCamelCase    		=					j, k

            __lowerCamelCase    		=					coupled_latents[j]
            __lowerCamelCase    		=					coupled_latents[k]

            __lowerCamelCase    		=					torch.cat([model_input] * 2	) if do_classifier_free_guidance else model_input

            __lowerCamelCase    		=					self.unet(a_ ,				a_ ,				encoder_hidden_states=a_	).sample

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

            __lowerCamelCase		,__lowerCamelCase    		=					self.denoise_step(
                base=a_ ,				model_input=a_ ,				model_output=a_ ,				timestep=a_ ,				)

            __lowerCamelCase    		=					model_input

         __lowerCamelCase    		=					self.denoise_mixing_layer(x=coupled_latents[0] ,				y=coupled_latents[1]	)

      # either one is fine
      __lowerCamelCase    		=					coupled_latents[0]

      if output_type not in ["latent", "pt", "np", "pil"]:
         __lowerCamelCase    		=					(
             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_	)
         __lowerCamelCase    		=					'np'

      if output_type == "latent":
         __lowerCamelCase    		=					final_latent
      else:
         __lowerCamelCase    		=					self.decode_latents(a_	)
         __lowerCamelCase    		=					self.image_processor.postprocess(a_ ,				output_type=a_	)

      return image











import math
from decimal import Decimal, getcontext

def       A_   (						__a  :					int = 4_000_000		):

				"""simple docstring"""

				try:
								a__					   =		int(__a		)
				except (TypeError, ValueError):
								raise TypeError("""Parameter n must be int or castable to int."""		)
				if n <= 0:
								raise ValueError("""Parameter n must be greater than or equal to one."""		)
				a__					   =		100
				a__					   =		(Decimal(5		) ** Decimal(0.5		) + 1) / Decimal(2		)

				a__					   =		(math.floor(math.log(n * (phi + 2)			,		__a		) - 1		) // 3) * 3 + 2
				a__					   =		Decimal(round(phi ** Decimal(index + 1		)		)		) / (phi + 2)
				a__					   =		num // 2
				return int(__a		)


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

