

'''simple docstring'''

def 				UpperCamelCase(					UpperCAmelCase_     ):
 return str(UpperCAmelCase_     ) == str(UpperCAmelCase_     )[::-1]




def 				UpperCamelCase(					UpperCAmelCase_     ):
 return int(UpperCAmelCase_     ) + int(str(UpperCAmelCase_     )[::-1]     )




def 				UpperCamelCase(					UpperCAmelCase_ = 1_00_00     ):
 UpperCAmelCase	:     str						 =			[]
 for num in range(1  ,	UpperCAmelCase_     ):
  UpperCAmelCase	:     Optional[int]						 =			0
  UpperCAmelCase	:     Any						 =			num
  while iterations < 50:
   UpperCAmelCase	:     int						 =			sum_reverse(UpperCAmelCase_     )
   iterations += 1
   if is_palindrome(UpperCAmelCase_     ):
    break
  else:
   lychrel_nums.append(UpperCAmelCase_     )
 return len(UpperCAmelCase_     )


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







'''simple docstring'''

import inspect
from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel, VQModel
from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput




class 	A_			(    _snake_case							):






     '''simple docstring'''



     def __init__(		self			:					List[Any]					,      lowercase_			:					VQModel					,      lowercase_			:					UNetaDModel					,      lowercase_			:					DDIMScheduler	)						->     int:
      super().__init__()
      self.register_modules(vqvae=lowercase_					,      unet=lowercase_					,      scheduler=lowercase_	)




     @torch.no_grad()
     def __call__(		self			:					str					,      lowercase_			:					int = 1					,      lowercase_			:					Optional[Union[torch.Generator, List[torch.Generator]]] = None					,      lowercase_			:					float = 0.0					,      lowercase_			:					int = 50					,      lowercase_			:					Optional[str] = "pil"					,      lowercase_			:					bool = True					,      **lowercase_			:					Optional[Any]					,      )						->     Union[Tuple, ImagePipelineOutput]:
      UpperCAmelCase	:     str						 =			randn_tensor(
          (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)					,      generator=lowercase_					,      )
      UpperCAmelCase	:     Any						 =			latents.to(self.device	)

      # scale the initial noise by the standard deviation required by the scheduler
      UpperCAmelCase	:     Optional[Any]						 =			latents * self.scheduler.init_noise_sigma

      self.scheduler.set_timesteps(lowercase_	)

      # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
      UpperCAmelCase	:     Optional[int]						 =			'eta' in set(inspect.signature(self.scheduler.step	).parameters.keys()	)

      UpperCAmelCase	:     Tuple						 =			{}
      if accepts_eta:
       UpperCAmelCase	:     List[str]						 =			eta

      for t in self.progress_bar(self.scheduler.timesteps	):
       UpperCAmelCase	:     Dict						 =			self.scheduler.scale_model_input(lowercase_					,      lowercase_	)
       # predict the noise residual
       UpperCAmelCase	:     Dict						 =			self.unet(lowercase_					,      lowercase_	).sample
       # compute the previous noisy sample x_t -> x_t-1
       UpperCAmelCase	:     Dict						 =			self.scheduler.step(lowercase_					,      lowercase_					,      lowercase_					,      **lowercase_	).prev_sample

      # decode the image latents with the VAE
      UpperCAmelCase	:     Any						 =			self.vqvae.decode(lowercase_	).sample

      UpperCAmelCase	:     Union[str, Any]						 =			(image / 2 + 0.5).clamp(0					,      1	)
      UpperCAmelCase	:     Optional[Any]						 =			image.cpu().permute(0					,      2					,      3					,      1	).numpy()
      if output_type == "pil":
       UpperCAmelCase	:     Tuple						 =			self.numpy_to_pil(lowercase_	)

      if not return_dict:
       return (image,)

      return ImagePipelineOutput(images=lowercase_	)




