




"""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      A__   (   nn.Module  ):




	def __init__( self	:						Optional[int]   ,     lowercase	:						Any   ,     lowercase	:						Union[str, Any]=1.0						)       ->			Dict:
						super().__init__()

						__snake_case        =						cut_size
						__snake_case        =						cut_power




	def 				a_		( self	:						Union[str, Any]   ,     lowercase	:						Dict   ,     lowercase	:						Any						)       ->			Union[str, Any]:
						__snake_case   ,   __snake_case        =						pixel_values.shape[2:4]
						__snake_case        =						min(lowercase   ,     lowercase						)
						__snake_case        =						min(lowercase   ,     lowercase   ,     self.cut_size						)
						__snake_case        =						[]
						for _ in range(lowercase						):
											__snake_case        =						int(torch.rand([]						) ** self.cut_power * (max_size - min_size) + min_size						)
											__snake_case        =						torch.randint(0   ,     sideX - size + 1   ,     ()						)
											__snake_case        =						torch.randint(0   ,     sideY - size + 1   ,     ()						)
											__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    snake_case__						(							lowerCAmelCase :		List[Any]					,       lowerCAmelCase :		Dict		):
					__snake_case        =						F.normalize(_UpperCAmelCase					,       dim=-1		)
					__snake_case        =						F.normalize(_UpperCAmelCase					,       dim=-1		)
					return (x - y).norm(dim=-1		).div(2		).arcsin().pow(2		).mul(2		)




def    snake_case__						(							lowerCAmelCase :		Optional[Any]					,       lowerCAmelCase :		Optional[Any]		):
					for param in model.parameters():
										__snake_case        =						value

class      A__   (   lowercase_  ):




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

						__snake_case        =						transforms.Normalize(mean=feature_extractor.image_mean   ,     std=feature_extractor.image_std						)
						__snake_case        =						(
						    feature_extractor.size
						    if isinstance(feature_extractor.size   ,     lowercase						)
						    else feature_extractor.size["""shortest_edge"""]
						)
						__snake_case        =						MakeCutouts(self.cut_out_size						)

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




	def 				a_		( self	:						int   ,     lowercase	:						Optional[Union[str, int]] = "auto"						)       ->			int:






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




	def 				a_		( self	:						Tuple						)       ->			Union[str, Any]:
						self.enable_attention_slicing(lowercase						)




	def 				a_		( self	:						List[str]						)       ->			str:
						set_requires_grad(self.vae   ,     lowercase						)




	def 				a_		( self	:						Optional[int]						)       ->			str:
						set_requires_grad(self.vae   ,     lowercase						)




	def 				a_		( self	:						Optional[int]						)       ->			Optional[int]:
						set_requires_grad(self.unet   ,     lowercase						)




	def 				a_		( self	:						Dict						)       ->			Optional[Any]:
						set_requires_grad(self.unet   ,     lowercase						)




	@torch.enable_grad()
	def 				a_		( self	:						Dict   ,     lowercase	:						Tuple   ,     lowercase	:						str   ,     lowercase	:						Tuple   ,     lowercase	:						str   ,     lowercase	:						Dict   ,     lowercase	:						int   ,     lowercase	:						Union[str, Any]   ,     lowercase	:						Optional[Any]   ,     lowercase	:						Optional[Any]=True   ,     )       ->			int:
						__snake_case        =						latents.detach().requires_grad_()

						__snake_case        =						self.scheduler.scale_model_input(lowercase   ,     lowercase						)

						# predict the noise residual
						__snake_case        =						self.unet(lowercase   ,     lowercase   ,     encoder_hidden_states=lowercase						).sample

						if isinstance(self.scheduler   ,     (PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)						):
											__snake_case        =						self.scheduler.alphas_cumprod[timestep]
											__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
											__snake_case        =						(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

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

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

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

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

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

						__snake_case        =						-torch.autograd.grad(lowercase   ,     lowercase						)[0]

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




	@torch.no_grad()
	def __call__( self	:						str   ,     lowercase	:						Union[str, List[str]]   ,     lowercase	:						Optional[int] = 512   ,     lowercase	:						Optional[int] = 512   ,     lowercase	:						Optional[int] = 50   ,     lowercase	:						Optional[float] = 7.5   ,     lowercase	:						Optional[int] = 1   ,     lowercase	:						float = 0.0   ,     lowercase	:						Optional[float] = 100   ,     lowercase	:						Optional[Union[str, List[str]]] = None   ,     lowercase	:						Optional[int] = 4   ,     lowercase	:						Optional[bool] = True   ,     lowercase	:						Optional[torch.Generator] = None   ,     lowercase	:						Optional[torch.FloatTensor] = None   ,     lowercase	:						Optional[str] = "pil"   ,     lowercase	:						bool = True   ,     )       ->			Optional[Any]:






						if isinstance(lowercase   ,     lowercase						):
											__snake_case        =						1
						elif isinstance(lowercase   ,     lowercase						):
											__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
						__snake_case        =						self.tokenizer(
						    lowercase   ,     padding="""max_length"""   ,     max_length=self.tokenizer.model_max_length   ,     truncation=lowercase   ,     return_tensors="""pt"""   ,     )
						__snake_case        =						self.text_encoder(text_input.input_ids.to(self.device						)						)[0]
						# duplicate text embeddings for each generation per prompt
						__snake_case        =						text_embeddings.repeat_interleave(lowercase   ,     dim=0						)

						if clip_guidance_scale > 0:
											if clip_prompt is not None:
																__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:
																__snake_case        =						text_input.input_ids.to(self.device						)
											__snake_case        =						self.clip_model.get_text_features(lowercase						)
											__snake_case        =						text_embeddings_clip / text_embeddings_clip.norm(p=2   ,     dim=-1   ,     keepdim=lowercase						)
											# duplicate text embeddings clip for each generation per prompt
											__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.
						__snake_case        =						guidance_scale > 1.0
						# get unconditional embeddings for classifier free guidance
						if do_classifier_free_guidance:
											__snake_case        =						text_input.input_ids.shape[-1]
											__snake_case        =						self.tokenizer([""""""]   ,     padding="""max_length"""   ,     max_length=lowercase   ,     return_tensors="""pt"""						)
											__snake_case        =						self.text_encoder(uncond_input.input_ids.to(self.device						)						)[0]
											# duplicate unconditional embeddings for each generation per prompt
											__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
											__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`.
						__snake_case        =						(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
						__snake_case        =						text_embeddings.dtype
						if latents is None:
											if self.device.type == "mps":
																# randn does not work reproducibly on mps
																__snake_case        =						torch.randn(lowercase   ,     generator=lowercase   ,     device="""cpu"""   ,     dtype=lowercase						).to(
																    self.device						)
											else:
																__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}'''						)
											__snake_case        =						latents.to(self.device						)

						# set timesteps
						__snake_case        =						"""offset""" in set(inspect.signature(self.scheduler.set_timesteps						).parameters.keys()						)
						__snake_case        =						{}
						if accepts_offset:
											__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
						__snake_case        =						self.scheduler.timesteps.to(self.device						)

						# scale the initial noise by the standard deviation required by the scheduler
						__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]
						__snake_case        =						"""eta""" in set(inspect.signature(self.scheduler.step						).parameters.keys()						)
						__snake_case        =						{}
						if accepts_eta:
											__snake_case        =						eta

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

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

											# predict the noise residual
											__snake_case        =						self.unet(lowercase   ,     lowercase   ,     encoder_hidden_states=lowercase						).sample

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

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

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

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

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

						if output_type == "pil":
											__snake_case        =						self.numpy_to_pil(lowercase						)

						if not return_dict:
											return (image, None)

						return StableDiffusionPipelineOutput(images=lowercase   ,     nsfw_content_detected=lowercase						)







UpperCAmelCase__  =			10**8





def 				A      (	_UpperCAmelCase							:  int       )							->					bool:







			'''simple docstring'''
			if n % 10 == 0:
						return False
			_UpperCAmelCase									=  str(_UpperCAmelCase       )
			return s == s[::-1]





def 				A      (	)							->					int:







			'''simple docstring'''
			_UpperCAmelCase									=  set()
			_UpperCAmelCase									=  1
			_UpperCAmelCase									=  5
			while sum_squares < LIMIT:
						_UpperCAmelCase									=  first_square + 1
						while sum_squares < LIMIT:
									if is_palindrome(_UpperCAmelCase       ):
												answer.add(_UpperCAmelCase       )
									last_square += 1
									sum_squares += last_square**2
						first_square += 1
						_UpperCAmelCase									=  first_square**2 + (first_square + 1) ** 2

			return sum(_UpperCAmelCase       )


if __name__ == "__main__":
							print(solution())
