




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  lowerCamelCase     (		nn.Module    ):






			'''simple docstring'''





			def __init__(			self      : int							,    lowerCamelCase_      : str							,    lowerCamelCase_      : str=1.0	)    -> int:
								super().__init__()

								__magic_name__				:						Union[str, Any]     				=				cut_size
								__magic_name__				:						Tuple     				=				cut_power


			def 				UpperCAmelCase__							(			self      : Optional[int]							,    lowerCamelCase_      : int							,    lowerCamelCase_      : Optional[Any]	)    -> Optional[int]:
								__magic_name__				,     __magic_name__				:						Any     				=				pixel_values.shape[2:4]
								__magic_name__				:						Dict     				=				min(lowerCamelCase_							,    lowerCamelCase_	)
								__magic_name__				:						List[Any]     				=				min(lowerCamelCase_							,    lowerCamelCase_							,    self.cut_size	)
								__magic_name__				:						Any     				=				[]
								for _ in range(lowerCamelCase_	):
													__magic_name__				:						Dict     				=				int(torch.rand([]	) ** self.cut_power * (max_size - min_size) + min_size	)
													__magic_name__				:						List[str]     				=				torch.randint(0							,    sideX - size + 1							,    ()	)
													__magic_name__				:						Union[str, Any]     				=				torch.randint(0							,    sideY - size + 1							,    ()	)
													__magic_name__				:						Optional[int]     				=				pixel_values[:, :, offsety : offsety + size, offsetx : offsetx + size]
													cutouts.append(F.adaptive_avg_poolad(lowerCamelCase_							,    self.cut_size	)	)
								return torch.cat(lowerCamelCase_	)







def 		lowercase__ (		__A:						Optional[int]				,__A:						Tuple					):





					'''simple docstring'''






					__magic_name__				:						List[Any]     				=				F.normalize(__A				,dim=-1					)
					__magic_name__				:						int     				=				F.normalize(__A				,dim=-1					)
					return (x - y).norm(dim=-1					).div(2					).arcsin().pow(2					).mul(2					)







def 		lowercase__ (		__A:						Union[str, Any]				,__A:						Union[str, Any]					):





					'''simple docstring'''






					for param in model.parameters():
										__magic_name__				:						int     				=				value


class  lowerCamelCase     (		_lowerCamelCase    ):






			'''simple docstring'''





			def __init__(			self      : Any							,    lowerCamelCase_      : AutoencoderKL							,    lowerCamelCase_      : CLIPTextModel							,    lowerCamelCase_      : CLIPModel							,    lowerCamelCase_      : CLIPTokenizer							,    lowerCamelCase_      : UNetaDConditionModel							,    lowerCamelCase_      : Union[PNDMScheduler, LMSDiscreteScheduler, DDIMScheduler, DPMSolverMultistepScheduler]							,    lowerCamelCase_      : CLIPImageProcessor							,    )    -> Any:
								super().__init__()
								self.register_modules(
								    vae=lowerCamelCase_							,    text_encoder=lowerCamelCase_							,    clip_model=lowerCamelCase_							,    tokenizer=lowerCamelCase_							,    unet=lowerCamelCase_							,    scheduler=lowerCamelCase_							,    feature_extractor=lowerCamelCase_							,    )

								__magic_name__				:						Union[str, Any]     				=				transforms.Normalize(mean=feature_extractor.image_mean							,    std=feature_extractor.image_std	)
								__magic_name__				:						Tuple     				=				(
								    feature_extractor.size
								    if isinstance(feature_extractor.size							,    lowerCamelCase_	)
								    else feature_extractor.size['''shortest_edge''']
								)
								__magic_name__				:						Optional[int]     				=				MakeCutouts(self.cut_out_size	)

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

			def 				UpperCAmelCase__							(			self      : int							,    lowerCamelCase_      : Optional[Union[str, int]] = "auto"	)    -> str:
								if slice_size == "auto":
													# half the attention head size is usually a good trade-off between
													# speed and memory
													__magic_name__				:						Union[str, Any]     				=				self.unet.config.attention_head_dim // 2
								self.unet.set_attention_slice(lowerCamelCase_	)

			def 				UpperCAmelCase__							(			self      : List[str]	)    -> int:
								self.enable_attention_slicing(lowerCamelCase_	)

			def 				UpperCAmelCase__							(			self      : int	)    -> Union[str, Any]:
								set_requires_grad(self.vae							,    lowerCamelCase_	)

			def 				UpperCAmelCase__							(			self      : Union[str, Any]	)    -> Optional[int]:
								set_requires_grad(self.vae							,    lowerCamelCase_	)

			def 				UpperCAmelCase__							(			self      : List[str]	)    -> Any:
								set_requires_grad(self.unet							,    lowerCamelCase_	)

			def 				UpperCAmelCase__							(			self      : Union[str, Any]	)    -> Optional[Any]:
								set_requires_grad(self.unet							,    lowerCamelCase_	)

			@torch.enable_grad()
			def 				UpperCAmelCase__							(			self      : str							,    lowerCamelCase_      : int							,    lowerCamelCase_      : int							,    lowerCamelCase_      : List[str]							,    lowerCamelCase_      : Optional[Any]							,    lowerCamelCase_      : Tuple							,    lowerCamelCase_      : int							,    lowerCamelCase_      : Dict							,    lowerCamelCase_      : str							,    lowerCamelCase_      : int=True							,    )    -> Dict:
								__magic_name__				:						Dict     				=				latents.detach().requires_grad_()

								__magic_name__				:						Tuple     				=				self.scheduler.scale_model_input(lowerCamelCase_							,    lowerCamelCase_	)

								# predict the noise residual
								__magic_name__				:						Tuple     				=				self.unet(lowerCamelCase_							,    lowerCamelCase_							,    encoder_hidden_states=lowerCamelCase_	).sample

								if isinstance(self.scheduler							,    (PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)	):
													__magic_name__				:						List[str]     				=				self.scheduler.alphas_cumprod[timestep]
													__magic_name__				:						Optional[int]     				=				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
													__magic_name__				:						Optional[int]     				=				(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

													__magic_name__				:						List[Any]     				=				torch.sqrt(lowerCamelCase_	)
													__magic_name__				:						List[str]     				=				pred_original_sample * (fac) + latents * (1 - fac)
								elif isinstance(self.scheduler							,    lowerCamelCase_	):
													__magic_name__				:						int     				=				self.scheduler.sigmas[index]
													__magic_name__				:						Dict     				=				latents - sigma * noise_pred
								else:
													raise ValueError(F'''scheduler type {type(self.scheduler	)} not supported'''	)

								__magic_name__				:						Optional[Any]     				=				1 / self.vae.config.scaling_factor * sample
								__magic_name__				:						str     				=				self.vae.decode(lowerCamelCase_	).sample
								__magic_name__				:						Optional[int]     				=				(image / 2 + 0.5).clamp(0							,    1	)

								if use_cutouts:
													__magic_name__				:						List[Any]     				=				self.make_cutouts(lowerCamelCase_							,    lowerCamelCase_	)
								else:
													__magic_name__				:						List[str]     				=				transforms.Resize(self.cut_out_size	)(lowerCamelCase_	)
								__magic_name__				:						str     				=				self.normalize(lowerCamelCase_	).to(latents.dtype	)

								__magic_name__				:						Any     				=				self.clip_model.get_image_features(lowerCamelCase_	)
								__magic_name__				:						Any     				=				image_embeddings_clip / image_embeddings_clip.norm(p=2							,    dim=-1							,    keepdim=lowerCamelCase_	)

								if use_cutouts:
													__magic_name__				:						List[str]     				=				spherical_dist_loss(lowerCamelCase_							,    lowerCamelCase_	)
													__magic_name__				:						Optional[int]     				=				dists.view([num_cutouts, sample.shape[0], -1]	)
													__magic_name__				:						Optional[int]     				=				dists.sum(2	).mean(0	).sum() * clip_guidance_scale
								else:
													__magic_name__				:						Optional[int]     				=				spherical_dist_loss(lowerCamelCase_							,    lowerCamelCase_	).mean() * clip_guidance_scale

								__magic_name__				:						str     				=				-torch.autograd.grad(lowerCamelCase_							,    lowerCamelCase_	)[0]

								if isinstance(self.scheduler							,    lowerCamelCase_	):
													__magic_name__				:						Dict     				=				latents.detach() + grads * (sigma**2)
													__magic_name__				:						Any     				=				noise_pred_original
								else:
													__magic_name__				:						Tuple     				=				noise_pred_original - torch.sqrt(lowerCamelCase_	) * grads
								return noise_pred, latents


			@torch.no_grad()
			def __call__(			self      : List[Any]							,    lowerCamelCase_      : Union[str, List[str]]							,    lowerCamelCase_      : Optional[int] = 512							,    lowerCamelCase_      : Optional[int] = 512							,    lowerCamelCase_      : Optional[int] = 50							,    lowerCamelCase_      : Optional[float] = 7.5							,    lowerCamelCase_      : Optional[int] = 1							,    lowerCamelCase_      : float = 0.0							,    lowerCamelCase_      : Optional[float] = 100							,    lowerCamelCase_      : Optional[Union[str, List[str]]] = None							,    lowerCamelCase_      : Optional[int] = 4							,    lowerCamelCase_      : Optional[bool] = True							,    lowerCamelCase_      : Optional[torch.Generator] = None							,    lowerCamelCase_      : Optional[torch.FloatTensor] = None							,    lowerCamelCase_      : Optional[str] = "pil"							,    lowerCamelCase_      : bool = True							,    )    -> int:
								if isinstance(lowerCamelCase_							,    lowerCamelCase_	):
													__magic_name__				:						Optional[Any]     				=				1
								elif isinstance(lowerCamelCase_							,    lowerCamelCase_	):
													__magic_name__				:						int     				=				len(lowerCamelCase_	)
								else:
													raise ValueError(F'''`prompt` has to be of type `str` or `list` but is {type(lowerCamelCase_	)}'''	)

								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
								__magic_name__				:						List[Any]     				=				self.tokenizer(
								    lowerCamelCase_							,    padding='''max_length'''							,    max_length=self.tokenizer.model_max_length							,    truncation=lowerCamelCase_							,    return_tensors='''pt'''							,    )
								__magic_name__				:						List[str]     				=				self.text_encoder(text_input.input_ids.to(self.device	)	)[0]
								# duplicate text embeddings for each generation per prompt
								__magic_name__				:						List[str]     				=				text_embeddings.repeat_interleave(lowerCamelCase_							,    dim=0	)

								if clip_guidance_scale > 0:
													if clip_prompt is not None:
																		__magic_name__				:						Optional[Any]     				=				self.tokenizer(
																		    lowerCamelCase_							,    padding='''max_length'''							,    max_length=self.tokenizer.model_max_length							,    truncation=lowerCamelCase_							,    return_tensors='''pt'''							,    ).input_ids.to(self.device	)
													else:
																		__magic_name__				:						Optional[int]     				=				text_input.input_ids.to(self.device	)
													__magic_name__				:						Tuple     				=				self.clip_model.get_text_features(lowerCamelCase_	)
													__magic_name__				:						List[str]     				=				text_embeddings_clip / text_embeddings_clip.norm(p=2							,    dim=-1							,    keepdim=lowerCamelCase_	)
													# duplicate text embeddings clip for each generation per prompt
													__magic_name__				:						List[str]     				=				text_embeddings_clip.repeat_interleave(lowerCamelCase_							,    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.
								__magic_name__				:						Optional[int]     				=				guidance_scale > 1.0
								# get unconditional embeddings for classifier free guidance
								if do_classifier_free_guidance:
													__magic_name__				:						Optional[Any]     				=				text_input.input_ids.shape[-1]
													__magic_name__				:						List[Any]     				=				self.tokenizer(['''''']							,    padding='''max_length'''							,    max_length=lowerCamelCase_							,    return_tensors='''pt'''	)
													__magic_name__				:						List[Any]     				=				self.text_encoder(uncond_input.input_ids.to(self.device	)	)[0]
													# duplicate unconditional embeddings for each generation per prompt
													__magic_name__				:						Any     				=				uncond_embeddings.repeat_interleave(lowerCamelCase_							,    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
													__magic_name__				:						List[str]     				=				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`.
								__magic_name__				:						List[str]     				=				(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
								__magic_name__				:						List[str]     				=				text_embeddings.dtype
								if latents is None:
													if self.device.type == "mps":
																		# randn does not work reproducibly on mps
																		__magic_name__				:						Dict     				=				torch.randn(lowerCamelCase_							,    generator=lowerCamelCase_							,    device='''cpu'''							,    dtype=lowerCamelCase_	).to(
																		    self.device	)
													else:
																		__magic_name__				:						str     				=				torch.randn(lowerCamelCase_							,    generator=lowerCamelCase_							,    device=self.device							,    dtype=lowerCamelCase_	)
								else:
													if latents.shape != latents_shape:
																		raise ValueError(F'''Unexpected latents shape, got {latents.shape}, expected {latents_shape}'''	)
													__magic_name__				:						int     				=				latents.to(self.device	)

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

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

								# Some schedulers like PNDM have timesteps as arrays
								# It's more optimized to move all timesteps to correct device beforehand
								__magic_name__				:						Optional[Any]     				=				self.scheduler.timesteps.to(self.device	)

								# scale the initial noise by the standard deviation required by the scheduler
								__magic_name__				:						str     				=				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]
								__magic_name__				:						int     				=				'''eta''' in set(inspect.signature(self.scheduler.step	).parameters.keys()	)
								__magic_name__				:						Optional[Any]     				=				{}
								if accepts_eta:
													__magic_name__				:						Any     				=				eta

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

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

													# predict the noise residual
													__magic_name__				:						List[Any]     				=				self.unet(lowerCamelCase_							,    lowerCamelCase_							,    encoder_hidden_states=lowerCamelCase_	).sample

													# perform classifier free guidance
													if do_classifier_free_guidance:
																		__magic_name__				,     __magic_name__				:						int     				=				noise_pred.chunk(2	)
																		__magic_name__				:						str     				=				noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

													# perform clip guidance
													if clip_guidance_scale > 0:
																		__magic_name__				:						List[Any]     				=				(
																		    text_embeddings.chunk(2	)[1] if do_classifier_free_guidance else text_embeddings
																		)
																		__magic_name__				,     __magic_name__				:						str     				=				self.cond_fn(
																		    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    )

													# compute the previous noisy sample x_t -> x_t-1
													__magic_name__				:						str     				=				self.scheduler.step(lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    **lowerCamelCase_	).prev_sample

								# scale and decode the image latents with vae
								__magic_name__				:						Optional[Any]     				=				1 / self.vae.config.scaling_factor * latents
								__magic_name__				:						int     				=				self.vae.decode(lowerCamelCase_	).sample

								__magic_name__				:						Any     				=				(image / 2 + 0.5).clamp(0							,    1	)
								__magic_name__				:						Optional[Any]     				=				image.cpu().permute(0							,    2							,    3							,    1	).numpy()

								if output_type == "pil":
													__magic_name__				:						Optional[int]     				=				self.numpy_to_pil(lowerCamelCase_	)

								if not return_dict:
													return (image, None)

								return StableDiffusionPipelineOutput(images=lowerCamelCase_							,    nsfw_content_detected=lowerCamelCase_	)









def        lowerCamelCase_     (     SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE ):
			'''simple docstring'''
			if n == 0:
						return 1

			elif n % 2 == 1:
						return binary_exponentiation(SCREAMING_SNAKE_CASE       ,						n - 1 ) * a

			else:
						SCREAMING_SNAKE_CASE     =       binary_exponentiation(SCREAMING_SNAKE_CASE       ,						n / 2 )
						return b * b


if __name__ == "__main__":
		try:
				__A    :				Tuple    						=	int(input("""Enter Base : """).strip())
				__A    :				Any    						=	int(input("""Enter Power : """).strip())
		except ValueError:
				print("""Invalid literal for integer""")

		__A    :				Union[str, Any]    						=	binary_exponentiation(BASE, POWER)
		print(f'''{BASE}^({POWER}) : {RESULT}''')






