





def        __SCREAMING_SNAKE_CASE	(				__lowercase:		Optional[int] = 1_00):



  '''simple docstring'''






  __lowerCAmelCase								=					[[0 for _ in range(__snake_case)] for _ in range(m + 1)]
  for i in range(m + 1):
    __lowerCAmelCase								=					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())))




from typing import List, Optional, Tuple, Union

import torch

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







class  lowerCamelCase__  (			lowerCAmelCase):
     SCREAMING_SNAKE_CASE__      =     42
     SCREAMING_SNAKE_CASE__      =     42





     def __init__(self						,	UpperCAmelCase						,	UpperCAmelCase			)	->  Tuple:
      super().__init__()

      _lowercase				 =PNDMScheduler.from_config(scheduler.config			)

      self.register_modules(unet=UpperCAmelCase						,	scheduler=UpperCAmelCase			)





     @torch.no_grad()
     def __call__(self						,	UpperCAmelCase = 1						,	UpperCAmelCase = 5_0						,	UpperCAmelCase = None						,	UpperCAmelCase = "pil"						,	UpperCAmelCase = True						,	**UpperCAmelCase						,	)	->  Union[ImagePipelineOutput, Tuple]:
      _lowercase				 =randn_tensor(
          (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)						,	generator=UpperCAmelCase						,	device=self.device						,	)

      self.scheduler.set_timesteps(UpperCAmelCase			)
      for t in self.progress_bar(self.scheduler.timesteps			):
       _lowercase				 =self.unet(UpperCAmelCase						,	UpperCAmelCase			).sample

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

      _lowercase				 =(image / 2 + 0.5).clamp(0						,	1			)
      _lowercase				 =image.cpu().permute(0						,	2						,	3						,	1			).numpy()
      if output_type == "pil":
       _lowercase				 =self.numpy_to_pil(UpperCAmelCase			)

      if not return_dict:
       return (image,)

      return ImagePipelineOutput(images=UpperCAmelCase			)

