
"""simple docstring"""




import inspect
from typing import List, Optional, Union

import torch
from torch import nn
from torch.nn import functional as F
from torchvision import transforms
from transformers import CLIPImageProcessor, CLIPModel, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    DPMSolverMultistepScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion import StableDiffusionPipelineOutput




class      UpperCamelCase	(       nn.Module      ):

				"""simple docstring"""



				def __init__(				self		,	lowercase__		,	lowercase__=1.0			)    ->    Optional[int]:
									"""simple docstring"""







									super().__init__()

									SCREAMING_SNAKE_CASE				=	cut_size
									SCREAMING_SNAKE_CASE				=	cut_power




				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    int:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE	,    SCREAMING_SNAKE_CASE				=	pixel_values.shape[2:4]
									SCREAMING_SNAKE_CASE				=	min(lowercase__		,	lowercase__			)
									SCREAMING_SNAKE_CASE				=	min(lowercase__		,	lowercase__		,	self.cut_size			)
									SCREAMING_SNAKE_CASE				=	[]
									for _ in range(lowercase__			):
														SCREAMING_SNAKE_CASE				=	int(torch.rand([]			) ** self.cut_power * (max_size - min_size) + min_size			)
														SCREAMING_SNAKE_CASE				=	torch.randint(0		,	sideX - size + 1		,	()			)
														SCREAMING_SNAKE_CASE				=	torch.randint(0		,	sideY - size + 1		,	()			)
														SCREAMING_SNAKE_CASE				=	pixel_values[:, :, offsety : offsety + size, offsetx : offsetx + size]
														cutouts.append(F.adaptive_avg_poolad(lowercase__		,	self.cut_size			)			)
									return torch.cat(lowercase__			)






def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
					SCREAMING_SNAKE_CASE				=	F.normalize(SCREAMING_SNAKE_CASE_,     dim=-1			)
					SCREAMING_SNAKE_CASE				=	F.normalize(SCREAMING_SNAKE_CASE_,     dim=-1			)
					return (x - y).norm(dim=-1			).div(2			).arcsin().pow(2			).mul(2			)

def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
					for param in model.parameters():
										SCREAMING_SNAKE_CASE				=	value




class      UpperCamelCase	(       __magic_name__      ):

				"""simple docstring"""



				def __init__(				self		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	)    ->    Optional[Any]:
									"""simple docstring"""







									super().__init__()
									self.register_modules(
									    vae=lowercase__		,	text_encoder=lowercase__		,	clip_model=lowercase__		,	tokenizer=lowercase__		,	unet=lowercase__		,	scheduler=lowercase__		,	feature_extractor=lowercase__		,	)

									SCREAMING_SNAKE_CASE				=	transforms.Normalize(mean=feature_extractor.image_mean		,	std=feature_extractor.image_std			)
									SCREAMING_SNAKE_CASE				=	(
									    feature_extractor.size
									    if isinstance(feature_extractor.size		,	lowercase__			)
									    else feature_extractor.size['shortest_edge']
									)
									SCREAMING_SNAKE_CASE				=	MakeCutouts(self.cut_out_size			)

									set_requires_grad(self.text_encoder		,	lowercase__			)
									set_requires_grad(self.clip_model		,	lowercase__			)


				def 							A					(				self		,	lowercase__ = "auto"			)    ->    int:
									"""simple docstring"""







									if slice_size == "auto":
														# half the attention head size is usually a good trade-off between
														# speed and memory
														SCREAMING_SNAKE_CASE				=	self.unet.config.attention_head_dim // 2
									self.unet.set_attention_slice(lowercase__			)


				def 							A					(				self			)    ->    Dict:
									"""simple docstring"""







									self.enable_attention_slicing(lowercase__			)


				def 							A					(				self			)    ->    Tuple:
									"""simple docstring"""







									set_requires_grad(self.vae		,	lowercase__			)


				def 							A					(				self			)    ->    Any:
									"""simple docstring"""







									set_requires_grad(self.vae		,	lowercase__			)


				def 							A					(				self			)    ->    Tuple:
									"""simple docstring"""







									set_requires_grad(self.unet		,	lowercase__			)


				def 							A					(				self			)    ->    List[Any]:
									"""simple docstring"""







									set_requires_grad(self.unet		,	lowercase__			)


				@torch.enable_grad()
				def 							A					(				self		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__=True		,	)    ->    Optional[int]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	latents.detach().requires_grad_()

									SCREAMING_SNAKE_CASE				=	self.scheduler.scale_model_input(lowercase__		,	lowercase__			)

									# predict the noise residual
									SCREAMING_SNAKE_CASE				=	self.unet(lowercase__		,	lowercase__		,	encoder_hidden_states=lowercase__			).sample

									if isinstance(self.scheduler		,	(PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)			):
														SCREAMING_SNAKE_CASE				=	self.scheduler.alphas_cumprod[timestep]
														SCREAMING_SNAKE_CASE				=	1 - alpha_prod_t
														# compute predicted original sample from predicted noise also called
														# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
														SCREAMING_SNAKE_CASE				=	(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

														SCREAMING_SNAKE_CASE				=	torch.sqrt(lowercase__			)
														SCREAMING_SNAKE_CASE				=	pred_original_sample * (fac) + latents * (1 - fac)
									elif isinstance(self.scheduler		,	lowercase__			):
														SCREAMING_SNAKE_CASE				=	self.scheduler.sigmas[index]
														SCREAMING_SNAKE_CASE				=	latents - sigma * noise_pred
									else:
														raise ValueError(f'''scheduler type {type(self.scheduler			)} not supported'''			)

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

									if use_cutouts:
														SCREAMING_SNAKE_CASE				=	self.make_cutouts(lowercase__		,	lowercase__			)
									else:
														SCREAMING_SNAKE_CASE				=	transforms.Resize(self.cut_out_size			)(lowercase__			)
									SCREAMING_SNAKE_CASE				=	self.normalize(lowercase__			).to(latents.dtype			)

									SCREAMING_SNAKE_CASE				=	self.clip_model.get_image_features(lowercase__			)
									SCREAMING_SNAKE_CASE				=	image_embeddings_clip / image_embeddings_clip.norm(p=2		,	dim=-1		,	keepdim=lowercase__			)

									if use_cutouts:
														SCREAMING_SNAKE_CASE				=	spherical_dist_loss(lowercase__		,	lowercase__			)
														SCREAMING_SNAKE_CASE				=	dists.view([num_cutouts, sample.shape[0], -1]			)
														SCREAMING_SNAKE_CASE				=	dists.sum(2			).mean(0			).sum() * clip_guidance_scale
									else:
														SCREAMING_SNAKE_CASE				=	spherical_dist_loss(lowercase__		,	lowercase__			).mean() * clip_guidance_scale

									SCREAMING_SNAKE_CASE				=	-torch.autograd.grad(lowercase__		,	lowercase__			)[0]

									if isinstance(self.scheduler		,	lowercase__			):
														SCREAMING_SNAKE_CASE				=	latents.detach() + grads * (sigma**2)
														SCREAMING_SNAKE_CASE				=	noise_pred_original
									else:
														SCREAMING_SNAKE_CASE				=	noise_pred_original - torch.sqrt(lowercase__			) * grads
									return noise_pred, latents




				@torch.no_grad()
				def __call__(				self		,	lowercase__		,	lowercase__ = 512		,	lowercase__ = 512		,	lowercase__ = 50		,	lowercase__ = 7.5		,	lowercase__ = 1		,	lowercase__ = 0.0		,	lowercase__ = 100		,	lowercase__ = None		,	lowercase__ = 4		,	lowercase__ = True		,	lowercase__ = None		,	lowercase__ = None		,	lowercase__ = "pil"		,	lowercase__ = True		,	)    ->    Tuple:
									"""simple docstring"""







									if isinstance(lowercase__		,	lowercase__			):
														SCREAMING_SNAKE_CASE				=	1
									elif isinstance(lowercase__		,	lowercase__			):
														SCREAMING_SNAKE_CASE				=	len(lowercase__			)
									else:
														raise ValueError(f'''`prompt` has to be of type `str` or `list` but is {type(lowercase__			)}'''			)

									if height % 8 != 0 or width % 8 != 0:
														raise ValueError(f'''`height` and `width` have to be divisible by 8 but are {height} and {width}.'''			)

									# get prompt text embeddings
									SCREAMING_SNAKE_CASE				=	self.tokenizer(
									    lowercase__		,	padding='max_length'		,	max_length=self.tokenizer.model_max_length		,	truncation=lowercase__		,	return_tensors='pt'		,	)
									SCREAMING_SNAKE_CASE				=	self.text_encoder(text_input.input_ids.to(self.device			)			)[0]
									# duplicate text embeddings for each generation per prompt
									SCREAMING_SNAKE_CASE				=	text_embeddings.repeat_interleave(lowercase__		,	dim=0			)

									if clip_guidance_scale > 0:
														if clip_prompt is not None:
																			SCREAMING_SNAKE_CASE				=	self.tokenizer(
																			    lowercase__		,	padding='max_length'		,	max_length=self.tokenizer.model_max_length		,	truncation=lowercase__		,	return_tensors='pt'		,	).input_ids.to(self.device			)
														else:
																			SCREAMING_SNAKE_CASE				=	text_input.input_ids.to(self.device			)
														SCREAMING_SNAKE_CASE				=	self.clip_model.get_text_features(lowercase__			)
														SCREAMING_SNAKE_CASE				=	text_embeddings_clip / text_embeddings_clip.norm(p=2		,	dim=-1		,	keepdim=lowercase__			)
														# duplicate text embeddings clip for each generation per prompt
														SCREAMING_SNAKE_CASE				=	text_embeddings_clip.repeat_interleave(lowercase__		,	dim=0			)

									# here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
									# of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
									# corresponds to doing no classifier free guidance.
									SCREAMING_SNAKE_CASE				=	guidance_scale > 1.0
									# get unconditional embeddings for classifier free guidance
									if do_classifier_free_guidance:
														SCREAMING_SNAKE_CASE				=	text_input.input_ids.shape[-1]
														SCREAMING_SNAKE_CASE				=	self.tokenizer(['']		,	padding='max_length'		,	max_length=lowercase__		,	return_tensors='pt'			)
														SCREAMING_SNAKE_CASE				=	self.text_encoder(uncond_input.input_ids.to(self.device			)			)[0]
														# duplicate unconditional embeddings for each generation per prompt
														SCREAMING_SNAKE_CASE				=	uncond_embeddings.repeat_interleave(lowercase__		,	dim=0			)

														# For classifier free guidance, we need to do two forward passes.
														# Here we concatenate the unconditional and text embeddings into a single batch
														# to avoid doing two forward passes
														SCREAMING_SNAKE_CASE				=	torch.cat([uncond_embeddings, text_embeddings]			)

									# get the initial random noise unless the user supplied it

									# Unlike in other pipelines, latents need to be generated in the target device
									# for 1-to-1 results reproducibility with the CompVis implementation.
									# However this currently doesn't work in `mps`.
									SCREAMING_SNAKE_CASE				=	(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
									SCREAMING_SNAKE_CASE				=	text_embeddings.dtype
									if latents is None:
														if self.device.type == "mps":
																			# randn does not work reproducibly on mps
																			SCREAMING_SNAKE_CASE				=	torch.randn(lowercase__		,	generator=lowercase__		,	device='cpu'		,	dtype=lowercase__			).to(
																			    self.device			)
														else:
																			SCREAMING_SNAKE_CASE				=	torch.randn(lowercase__		,	generator=lowercase__		,	device=self.device		,	dtype=lowercase__			)
									else:
														if latents.shape != latents_shape:
																			raise ValueError(f'''Unexpected latents shape, got {latents.shape}, expected {latents_shape}'''			)
														SCREAMING_SNAKE_CASE				=	latents.to(self.device			)

									# set timesteps
									SCREAMING_SNAKE_CASE				=	'offset' in set(inspect.signature(self.scheduler.set_timesteps			).parameters.keys()			)
									SCREAMING_SNAKE_CASE				=	{}
									if accepts_offset:
														SCREAMING_SNAKE_CASE				=	1

									self.scheduler.set_timesteps(lowercase__		,	**lowercase__			)

									# Some schedulers like PNDM have timesteps as arrays
									# It's more optimized to move all timesteps to correct device beforehand
									SCREAMING_SNAKE_CASE				=	self.scheduler.timesteps.to(self.device			)

									# scale the initial noise by the standard deviation required by the scheduler
									SCREAMING_SNAKE_CASE				=	latents * self.scheduler.init_noise_sigma

									# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
									# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
									# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
									# and should be between [0, 1]
									SCREAMING_SNAKE_CASE				=	'eta' in set(inspect.signature(self.scheduler.step			).parameters.keys()			)
									SCREAMING_SNAKE_CASE				=	{}
									if accepts_eta:
														SCREAMING_SNAKE_CASE				=	eta

									# check if the scheduler accepts generator
									SCREAMING_SNAKE_CASE				=	'generator' in set(inspect.signature(self.scheduler.step			).parameters.keys()			)
									if accepts_generator:
														SCREAMING_SNAKE_CASE				=	generator

									for i, t in enumerate(self.progress_bar(lowercase__			)			):
														# expand the latents if we are doing classifier free guidance
														SCREAMING_SNAKE_CASE				=	torch.cat([latents] * 2			) if do_classifier_free_guidance else latents
														SCREAMING_SNAKE_CASE				=	self.scheduler.scale_model_input(lowercase__		,	lowercase__			)

														# predict the noise residual
														SCREAMING_SNAKE_CASE				=	self.unet(lowercase__		,	lowercase__		,	encoder_hidden_states=lowercase__			).sample

														# perform classifier free guidance
														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)

														# perform clip guidance
														if clip_guidance_scale > 0:
																			SCREAMING_SNAKE_CASE				=	(
																			    text_embeddings.chunk(2			)[1] if do_classifier_free_guidance else text_embeddings
																			)
																			SCREAMING_SNAKE_CASE	,    SCREAMING_SNAKE_CASE				=	self.cond_fn(
																			    lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	)

														# compute the previous noisy sample x_t -> x_t-1
														SCREAMING_SNAKE_CASE				=	self.scheduler.step(lowercase__		,	lowercase__		,	lowercase__		,	**lowercase__			).prev_sample

									# scale and decode the image latents with vae
									SCREAMING_SNAKE_CASE				=	1 / self.vae.config.scaling_factor * latents
									SCREAMING_SNAKE_CASE				=	self.vae.decode(lowercase__			).sample

									SCREAMING_SNAKE_CASE				=	(image / 2 + 0.5).clamp(0		,	1			)
									SCREAMING_SNAKE_CASE				=	image.cpu().permute(0		,	2		,	3		,	1			).numpy()

									if output_type == "pil":
														SCREAMING_SNAKE_CASE				=	self.numpy_to_pil(lowercase__			)

									if not return_dict:
														return (image, None)

									return StableDiffusionPipelineOutput(images=lowercase__		,	nsfw_content_detected=lowercase__			)







import math




def        lowerCAmelCase_       (							UpperCamelCase_     )   ->						bool:

       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_ = 600851475143     )   ->						int:

       try:
              UpperCamelCase_      				=     int(UpperCamelCase_     )
       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."     )
       UpperCamelCase_      				=     0
       if is_prime(UpperCamelCase_     ):
              return n
       while n % 2 == 0:
              n //= 2
       if is_prime(UpperCamelCase_     ):
              return n
       for i in range(3    ,						int(math.sqrt(UpperCamelCase_     )     ) + 1    ,						2     ):
              if n % i == 0:
                     if is_prime(n // i     ):
                            UpperCamelCase_      				=     n // i
                            break
                     elif is_prime(UpperCamelCase_     ):
                            UpperCamelCase_      				=     i
       return max_number


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

