
"""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 __lowerCAmelCase						( nn.Module     ):





     def __init__(      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase=1.0 ):

      '''simple docstring'''




      super().__init__()

      __UpperCamelCase							    =			cut_size
      __UpperCamelCase							    =			cut_power







     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase ):

      '''simple docstring'''




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






def 				A		(							snake_case :Any							,   snake_case :List[Any]						) ->      Tuple:
 __UpperCamelCase							    =			F.normalize(snake_case							,   dim=-1						)
 __UpperCamelCase							    =			F.normalize(snake_case							,   dim=-1						)
 return (x - y).norm(dim=-1						).div(2						).arcsin().pow(2						).mul(2						)






def 				A		(							snake_case :Any							,   snake_case :Union[str, Any]						) ->      Tuple:
 for param in model.parameters():
  __UpperCamelCase							    =			value





class __lowerCAmelCase						( __SCREAMING_SNAKE_CASE     ):





     def __init__(      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	):

      '''simple docstring'''




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

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

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





     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase = "auto" ):

      '''simple docstring'''




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





     def 		UpperCAmelCase   (      self ):

      '''simple docstring'''




      self.enable_attention_slicing(__UpperCAmelCase )





     def 		UpperCAmelCase   (      self ):

      '''simple docstring'''




      set_requires_grad(self.vae      ,	__UpperCAmelCase )





     def 		UpperCAmelCase   (      self ):

      '''simple docstring'''




      set_requires_grad(self.vae      ,	__UpperCAmelCase )





     def 		UpperCAmelCase   (      self ):

      '''simple docstring'''




      set_requires_grad(self.unet      ,	__UpperCAmelCase )





     def 		UpperCAmelCase   (      self ):

      '''simple docstring'''




      set_requires_grad(self.unet      ,	__UpperCAmelCase )





     @torch.enable_grad()
     def 		UpperCAmelCase   (      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase      ,	__UpperCAmelCase=True      ,	):

      '''simple docstring'''




      __UpperCamelCase							    =			latents.detach().requires_grad_()

      __UpperCamelCase							    =			self.scheduler.scale_model_input(__UpperCAmelCase      ,	__UpperCAmelCase )

      # predict the noise residual
      __UpperCamelCase							    =			self.unet(__UpperCAmelCase      ,	__UpperCAmelCase      ,	encoder_hidden_states=__UpperCAmelCase ).sample

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

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

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

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

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

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

      __UpperCamelCase							    =			-torch.autograd.grad(__UpperCAmelCase      ,	__UpperCAmelCase )[0]

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







     @torch.no_grad()
     def __call__(      self      ,	__UpperCAmelCase      ,	__UpperCAmelCase = 512      ,	__UpperCAmelCase = 512      ,	__UpperCAmelCase = 50      ,	__UpperCAmelCase = 7.5      ,	__UpperCAmelCase = 1      ,	__UpperCAmelCase = 0.0      ,	__UpperCAmelCase = 100      ,	__UpperCAmelCase = None      ,	__UpperCAmelCase = 4      ,	__UpperCAmelCase = True      ,	__UpperCAmelCase = None      ,	__UpperCAmelCase = None      ,	__UpperCAmelCase = "pil"      ,	__UpperCAmelCase = True      ,	):

      '''simple docstring'''




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

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

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

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

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

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

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

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

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

       # predict the noise residual
       __UpperCamelCase							    =			self.unet(__UpperCAmelCase      ,	__UpperCAmelCase      ,	encoder_hidden_states=__UpperCAmelCase ).sample

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

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

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

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

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

      if output_type == "pil":
       __UpperCamelCase							    =			self.numpy_to_pil(__UpperCAmelCase )

      if not return_dict:
       return (image, None)

      return StableDiffusionPipelineOutput(images=__UpperCAmelCase      ,	nsfw_content_detected=__UpperCAmelCase )





"""simple docstring"""

UpperCamelCase      :							int          =					1_0**8






def 				A		(							snake_case :int						) ->      bool:
 if n % 1_0 == 0:
  return False
 __UpperCamelCase							    =			str(snake_case						)
 return s == s[::-1]






def 				A		(							) ->      int:
 __UpperCamelCase							    =			set()
 __UpperCamelCase							    =			1
 __UpperCamelCase							    =			5
 while sum_squares < LIMIT:
  __UpperCamelCase							    =			first_square + 1
  while sum_squares < LIMIT:
   if is_palindrome(snake_case						):
    answer.add(snake_case						)
   last_square += 1
   sum_squares += last_square**2
  first_square += 1
  __UpperCamelCase							    =			first_square**2 + (first_square + 1) ** 2

 return sum(snake_case						)


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



