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   lowercase			(   a   ):




							def __init__(  self      :    List[Any]		,							_UpperCamelCase      :    AutoencoderKL		,							_UpperCamelCase      :    CLIPTextModel		,							_UpperCamelCase      :    CLIPTokenizer		,							_UpperCamelCase      :    UNetaDConditionModel		,							_UpperCamelCase      :    DDIMScheduler		,							_UpperCamelCase      :    float = 0.9_3		,							_UpperCamelCase      :    bool = True		,							)    -> Any:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				mixing_coeff
												SCREAMING_SNAKE_CASE				=				leapfrog_steps

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

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




							def 		__snake_case(  self      :    Union[str, Any]		,							_UpperCamelCase      :    str		,							_UpperCamelCase      :    Optional[str] = None		,							_UpperCamelCase      :    bool = False					)    -> Optional[int]:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				self.tokenizer(
												    _UpperCamelCase		,							padding="max_length"		,							max_length=self.tokenizer.model_max_length		,							truncation=_UpperCamelCase		,							return_tensors="pt"		,							)

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

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

												if do_classifier_free_guidance:
																	SCREAMING_SNAKE_CASE				=				"" if negative_prompt is None else negative_prompt

																	SCREAMING_SNAKE_CASE				=				self.tokenizer(
																	    _UpperCamelCase		,							padding="max_length"		,							max_length=self.tokenizer.model_max_length		,							truncation=_UpperCamelCase		,							return_tensors="pt"		,							)

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

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

												return prompt_embeds




							def 		__snake_case(  self      :    int		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor					)    -> str:



												'''simple docstring'''

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

												return [x, y]




							def 		__snake_case(  self      :    Optional[Any]		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor					)    -> Tuple:



												'''simple docstring'''

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

												return [x, y]




							def 		__snake_case(  self      :    List[Any]		,							_UpperCamelCase      :    torch.Tensor					)    -> List[str]:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				int(_UpperCamelCase					)

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

												return alpha_prod, 1 - alpha_prod




							def 		__snake_case(  self      :    Tuple		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							)    -> List[Any]:



												'''simple docstring'''

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

												SCREAMING_SNAKE_CASE	,      SCREAMING_SNAKE_CASE				=				self._get_alpha_and_beta(_UpperCamelCase					)
												SCREAMING_SNAKE_CASE	,      SCREAMING_SNAKE_CASE				=				self._get_alpha_and_beta(_UpperCamelCase					)

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

												SCREAMING_SNAKE_CASE				=				(base - b_t * model_output) / a_t

												return model_input, next_model_input.to(base.dtype					)




							def 		__snake_case(  self      :    Union[str, Any]		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							)    -> Union[str, Any]:



												'''simple docstring'''

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

												SCREAMING_SNAKE_CASE	,      SCREAMING_SNAKE_CASE				=				self._get_alpha_and_beta(_UpperCamelCase					)
												SCREAMING_SNAKE_CASE	,      SCREAMING_SNAKE_CASE				=				self._get_alpha_and_beta(_UpperCamelCase					)

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

												return model_input, next_model_input.to(base.dtype					)




							@torch.no_grad()
							def 		__snake_case(  self      :    Optional[Any]		,							_UpperCamelCase      :    torch.Tensor					)    -> Tuple:



												'''simple docstring'''

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




							@torch.no_grad()
							def 		__snake_case(  self      :    Any		,							_UpperCamelCase      :    Image.Image		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    torch.Tensor		,							_UpperCamelCase      :    float		,							_UpperCamelCase      :    Optional[torch.Generator] = None		,							)    -> Optional[int]:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				guidance_scale > 1.0

												SCREAMING_SNAKE_CASE				=				image.to(device=self.device		,							dtype=text_embeds.dtype					)
												SCREAMING_SNAKE_CASE				=				self.vae.encode(_UpperCamelCase					).latent_dist.sample(_UpperCamelCase					)

												SCREAMING_SNAKE_CASE				=				self.vae.config.scaling_factor * latent

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

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

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

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

																						SCREAMING_SNAKE_CASE				=				coupled_latents[j]
																						SCREAMING_SNAKE_CASE				=				coupled_latents[k]

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

																						SCREAMING_SNAKE_CASE				=				self.unet(_UpperCamelCase		,							_UpperCamelCase		,							encoder_hidden_states=_UpperCamelCase					).sample

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

																						SCREAMING_SNAKE_CASE	,      SCREAMING_SNAKE_CASE				=				self.noise_step(
																						    base=_UpperCamelCase		,							model_input=_UpperCamelCase		,							model_output=_UpperCamelCase		,							timestep=_UpperCamelCase		,							)

																						SCREAMING_SNAKE_CASE				=				model_input

												return coupled_latents





							@torch.no_grad()
							def __call__(  self      :    Tuple		,							_UpperCamelCase      :    str		,							_UpperCamelCase      :    str		,							_UpperCamelCase      :    Image.Image		,							_UpperCamelCase      :    float = 3.0		,							_UpperCamelCase      :    int = 50		,							_UpperCamelCase      :    float = 0.8		,							_UpperCamelCase      :    Optional[str] = None		,							_UpperCamelCase      :    Optional[torch.Generator] = None		,							_UpperCamelCase      :    Optional[str] = "pil"		,							)    -> List[Any]:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE				=				guidance_scale > 1.0

												SCREAMING_SNAKE_CASE				=				self.image_processor.preprocess(_UpperCamelCase					)

												SCREAMING_SNAKE_CASE				=				self._encode_prompt(_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase					)
												SCREAMING_SNAKE_CASE				=				self._encode_prompt(_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase					)

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

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

												SCREAMING_SNAKE_CASE				=				self.prepare_latents(_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase		,							_UpperCamelCase					)

												for i, t in tqdm(enumerate(_UpperCamelCase					)		,							total=len(_UpperCamelCase					)					):
																	# j - model_input index, k - base index
																	for k in range(2					):
																						SCREAMING_SNAKE_CASE				=				k ^ 1

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

																						SCREAMING_SNAKE_CASE				=				coupled_latents[j]
																						SCREAMING_SNAKE_CASE				=				coupled_latents[k]

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

																						SCREAMING_SNAKE_CASE				=				self.unet(_UpperCamelCase		,							_UpperCamelCase		,							encoder_hidden_states=_UpperCamelCase					).sample

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

																						SCREAMING_SNAKE_CASE	,      SCREAMING_SNAKE_CASE				=				self.denoise_step(
																						    base=_UpperCamelCase		,							model_input=_UpperCamelCase		,							model_output=_UpperCamelCase		,							timestep=_UpperCamelCase		,							)

																						SCREAMING_SNAKE_CASE				=				model_input

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

												# either one is fine
												SCREAMING_SNAKE_CASE				=				coupled_latents[0]

												if output_type not in ["latent", "pt", "np", "pil"]:
																	SCREAMING_SNAKE_CASE				=				(
																	    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"		,							_UpperCamelCase		,							standard_warn=_UpperCamelCase					)
																	SCREAMING_SNAKE_CASE				=				"np"

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

												return image





import math





def 		__lowerCamelCase							(UpperCAmelCase__   :							int     ):

					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5					,       int(math.sqrt(UpperCAmelCase__     ) + 1     )					,       6     ):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True





def 		__lowerCamelCase							(UpperCAmelCase__   :							int = 2_0_0_0_0_0_0     ):
					return sum(num for num in range(3					,       UpperCAmelCase__					,       2     ) if is_prime(UpperCAmelCase__     )     ) + 2 if n > 2 else 0


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




