





from typing import Union

import torch
from PIL import Image
from torchvision import transforms as tfms
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)







class 						_lowerCAmelCase(						_a):

  """simple docstring"""







  def __init__( self  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    )-> Optional[int]:
     super().__init__()

     self.register_modules(vae=UpperCAmelCase  ,    text_encoder=UpperCAmelCase  ,    tokenizer=UpperCAmelCase  ,    unet=UpperCAmelCase  ,    scheduler=UpperCAmelCase     )

  def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> int:
     with torch.no_grad():
        __A				 =       self.vae.encode(tfms.ToTensor()(UpperCAmelCase     ).unsqueeze(0     ).to(self.device     ) * 2 - 1     )
        __A				 =       0.18215 * latent.latent_dist.sample()
     return latent

  def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> List[str]:
     __A				 =       (1 / 0.18215) * latent
     with torch.no_grad():
        __A				 =       self.vae.decode(UpperCAmelCase     ).sample
     __A				 =       (img / 2 + 0.5).clamp(0  ,    1     )
     __A				 =       img.detach().cpu().permute(0  ,    2  ,    3  ,    1     ).numpy()
     __A				 =       (img * 2_55).round().astype('''uint8'''     )
     return Image.fromarray(img[0]     )

  def 		SCREAMING_SNAKE_CASE__	( self  ,    UpperCAmelCase     )-> Union[str, Any]:
     __A				 =       self.tokenizer(
         UpperCAmelCase  ,    padding='''max_length'''  ,    max_length=self.tokenizer.model_max_length  ,    truncation=UpperCAmelCase  ,    return_tensors='''pt'''  ,    )

     __A				 =       self.text_encoder(text_input.input_ids.to(self.device     )     )[0]

     __A				 =       self.tokenizer(
         ''''''  ,    padding='''max_length'''  ,    max_length=self.tokenizer.model_max_length  ,    truncation=UpperCAmelCase  ,    return_tensors='''pt'''  ,    )

     __A				 =       self.text_encoder(uncond_input.input_ids.to(self.device     )     )[0]

     return torch.cat([uncond_embedding, text_embedding]     )





  def __call__( self  ,    UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase = 0.3  ,    UpperCAmelCase = 0.6  ,    UpperCAmelCase = 0.5  ,    UpperCAmelCase = 42  ,    UpperCAmelCase = 50  ,    UpperCAmelCase = 7.5  ,    )-> Image.Image:
     __A				 =       steps - int(kmin * steps     )
     __A				 =       steps - int(kmax * steps     )

     __A				 =       self.prep_text(UpperCAmelCase     )

     self.scheduler.set_timesteps(UpperCAmelCase     )

     __A ,						__A				 =       img.size
     __A				 =       self.encode(UpperCAmelCase     )

     torch.manual_seed(UpperCAmelCase     )
     __A				 =       torch.randn(
         (1, self.unet.config.in_channels, height // 8, width // 8)  ,    ).to(self.device     )

     __A				 =       self.scheduler.add_noise(
         UpperCAmelCase  ,    UpperCAmelCase  ,    timesteps=self.scheduler.timesteps[tmax]  ,    )

     __A				 =       torch.cat([latents] * 2     )

     __A				 =       self.scheduler.scale_model_input(UpperCAmelCase  ,    self.scheduler.timesteps[tmax]     )

     with torch.no_grad():
        __A				 =       self.unet(
            UpperCAmelCase  ,    self.scheduler.timesteps[tmax]  ,    encoder_hidden_states=UpperCAmelCase  ,    ).sample

     __A ,						__A				 =       pred.chunk(2     )
     __A				 =       pred_uncond + guidance_scale * (pred_text - pred_uncond)

     __A				 =       self.scheduler.step(UpperCAmelCase  ,    self.scheduler.timesteps[tmax]  ,    UpperCAmelCase     ).prev_sample

     for i, t in enumerate(tqdm(self.scheduler.timesteps     )     ):
        if i > tmax:
           if i < tmin:  # layout generation phase
              __A				 =       self.scheduler.add_noise(
                  UpperCAmelCase  ,    UpperCAmelCase  ,    timesteps=UpperCAmelCase  ,    )

              __A				 =       (mix_factor * latents) + (
                  1 - mix_factor
              ) * orig_latents  # interpolating between layout noise and conditionally generated noise to preserve layout sematics
              __A				 =       torch.cat([input] * 2     )

           else:  # content generation phase
              __A				 =       torch.cat([latents] * 2     )

           __A				 =       self.scheduler.scale_model_input(UpperCAmelCase  ,    UpperCAmelCase     )

           with torch.no_grad():
              __A				 =       self.unet(
                  UpperCAmelCase  ,    UpperCAmelCase  ,    encoder_hidden_states=UpperCAmelCase  ,    ).sample

           __A ,						__A				 =       pred.chunk(2     )
           __A				 =       pred_uncond + guidance_scale * (pred_text - pred_uncond)

           __A				 =       self.scheduler.step(UpperCAmelCase  ,    UpperCAmelCase  ,    UpperCAmelCase     ).prev_sample

     return self.decode(UpperCAmelCase     )








def 				__UpperCamelCase  (		snake_case = 1_0_0     )  ->						int:


   '''simple docstring'''







   __A				 =       [[0 for _ in range(snake_case     )] for _ in range(m + 1     )]
   for i in range(m + 1     ):
      __A				 =       1

   for n in range(m + 1     ):
      for k in range(1    ,	snake_case     ):
         memo[n][k] += memo[n][k - 1]
         if n > k:
            memo[n][k] += memo[n - k - 1][k]

   return memo[m][m - 1] - 1


if __name__ == "__main__":
    print(solution(int(input("""Enter a number: """).strip())))

