



def 	__a					(   lowerCAmelCase_       : int = 50    )				->			int:






						'''simple docstring'''



						UpperCAmelCase_=       [1] * (length + 1)

						for row_length in range(3      ,length + 1    ):
												for block_length in range(3      ,row_length + 1    ):
																		for block_start in range(row_length - block_length    ):
																								ways_number[row_length] += ways_number[
																								    row_length - block_start - block_length - 1
																								]

																		ways_number[row_length] += 1

						return ways_number[length]


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









from typing import List, Optional, Tuple, Union

import torch

from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






class 		lowercase						(			snake_case__):






	"""simple docstring"""


	def __init__(     self     :						Dict						,  __UpperCAmelCase     :						Tuple						,  __UpperCAmelCase     :						List[Any]					)      ->			List[str]:
							super().__init__()

							# make sure scheduler can always be converted to DDIM
							UpperCAmelCase_=       DDIMScheduler.from_config(scheduler.config					)

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




	@torch.no_grad()
	def __call__(     self     :						Union[str, Any]						,  __UpperCAmelCase     :						int = 1						,  __UpperCAmelCase     :						Optional[Union[torch.Generator, List[torch.Generator]]] = None						,  __UpperCAmelCase     :						float = 0.0						,  __UpperCAmelCase     :						int = 50						,  __UpperCAmelCase     :						Optional[bool] = None						,  __UpperCAmelCase     :						Optional[str] = "pil"						,  __UpperCAmelCase     :						bool = True						,  )      ->			Union[ImagePipelineOutput, Tuple]:

							# Sample gaussian noise to begin loop
							if isinstance(self.unet.config.sample_size						,  __UpperCAmelCase					):
													UpperCAmelCase_=       (
													    batch_size,
													    self.unet.config.in_channels,
													    self.unet.config.sample_size,
													    self.unet.config.sample_size,
													)
							else:
													UpperCAmelCase_=       (batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

							if isinstance(__UpperCAmelCase						,  __UpperCAmelCase					) and len(__UpperCAmelCase					) != batch_size:
													raise ValueError(
													    F"""You have passed a list of generators of length {len(__UpperCAmelCase					)}, but requested an effective batch"""
													    F""" size of {batch_size}. Make sure the batch size matches the length of the generators."""					)

							UpperCAmelCase_=       randn_tensor(__UpperCAmelCase						,  generator=__UpperCAmelCase						,  device=self.device						,  dtype=self.unet.dtype					)

							# set step values
							self.scheduler.set_timesteps(__UpperCAmelCase					)

							for t in self.progress_bar(self.scheduler.timesteps					):
													# 1. predict noise model_output
													UpperCAmelCase_=       self.unet(__UpperCAmelCase						,  __UpperCAmelCase					).sample

													# 2. predict previous mean of image x_t-1 and add variance depending on eta
													# eta corresponds to η in paper and should be between [0, 1]
													# do x_t -> x_t-1
													UpperCAmelCase_=       self.scheduler.step(
													    __UpperCAmelCase						,  __UpperCAmelCase						,  __UpperCAmelCase						,  eta=__UpperCAmelCase						,  use_clipped_model_output=__UpperCAmelCase						,  generator=__UpperCAmelCase					).prev_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,)

							return ImagePipelineOutput(images=__UpperCAmelCase					)




