


def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		lowercase__	     =						1  # To kept the Calculated Value
		# Since C(n, k) = C(n, n-k)
		if k > (n - k):
				lowercase__	     =						n - k
		# Calculate C(n,k)
		for i in range(__magic_name__	):
				result *= n - i
				result //= i + 1
		return result






def 					UpperCamelCase   (      __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		return binomial_coefficient(2 * node_count       ,       __magic_name__	) // (node_count + 1)






def 					UpperCamelCase   (      __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		if n < 0:
				raise ValueError("""factorial() not defined for negative values"""	)
		lowercase__	     =						1
		for i in range(1       ,       n + 1	):
				result *= i
		return result






def 					UpperCamelCase   (      __magic_name__	:				int	)  ->    int:
		"""simple docstring"""




		return catalan_number(__magic_name__	) * factorial(__magic_name__	)


if __name__ == "__main__":
	A			:						Tuple        =  int(input('Enter the number of nodes: ').strip() or 0)
	if node_count <= 0:
		raise ValueError('We need some nodes to work with.')
	print(
	    F'Given {node_count} nodes, there are {binary_tree_count(node_count)} '
	    F'binary trees and {catalan_number(node_count)} binary search trees.'
	)


'''simple docstring'''


from typing import List, Optional, Tuple, Union

import torch

from ...utils import logging, randn_tensor
from ..pipeline_utils import AudioPipelineOutput, DiffusionPipeline


__lowerCAmelCase						:							List[Any]    							=						logging.get_logger(__name__)  # pylint: disable=invalid-name






class     A ( UpperCAmelCase ):





							def __init__(   self					:				Dict  ,		__a					:				List[Any]  ,		__a					:				Optional[Any]						)				->						Dict:
								super().__init__()
								self.register_modules(unet=__a  ,		scheduler=__a						)






							@torch.no_grad()
							def __call__(   self					:				Tuple  ,		__a					:				int = 1  ,		__a					:				int = 1_0_0  ,		__a					:				Optional[Union[torch.Generator, List[torch.Generator]]] = None  ,		__a					:				Optional[float] = None  ,		__a					:				bool = True  ,		)				->						Union[AudioPipelineOutput, Tuple]:

								if audio_length_in_s is None:
									__UpperCAmelCase      					=      self.unet.config.sample_size / self.unet.config.sample_rate

								__UpperCAmelCase      					=      audio_length_in_s * self.unet.config.sample_rate

								__UpperCAmelCase      					=      2 ** len(self.unet.up_blocks						)
								if sample_size < 3 * down_scale_factor:
									raise ValueError(
									    f"""{audio_length_in_s} is too small. Make sure it's bigger or equal to"""
									    f""" {3 * down_scale_factor / self.unet.config.sample_rate}."""						)

								__UpperCAmelCase      					=      int(__a						)
								if sample_size % down_scale_factor != 0:
									__UpperCAmelCase      					=      (
									    (audio_length_in_s * self.unet.config.sample_rate) // down_scale_factor + 1
									) * down_scale_factor
									logger.info(
									    f"""{audio_length_in_s} is increased to {sample_size / self.unet.config.sample_rate} so that it can be handled"""
									    f""" by the model. It will be cut to {original_sample_size / self.unet.config.sample_rate} after the denoising"""
									    ''' process.'''						)
								__UpperCAmelCase      					=      int(__a						)

								__UpperCAmelCase      					=      next(iter(self.unet.parameters()						)						).dtype
								__UpperCAmelCase      					=      (batch_size, self.unet.config.in_channels, sample_size)
								if isinstance(__a  ,		__a						) and len(__a						) != batch_size:
									raise ValueError(
									    f"""You have passed a list of generators of length {len(__a						)}, but requested an effective batch"""
									    f""" size of {batch_size}. Make sure the batch size matches the length of the generators."""						)

								__UpperCAmelCase      					=      randn_tensor(__a  ,		generator=__a  ,		device=self.device  ,		dtype=__a						)

								# set step values
								self.scheduler.set_timesteps(__a  ,		device=audio.device						)
								__UpperCAmelCase      					=      self.scheduler.timesteps.to(__a						)

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

									# 2. compute previous image: x_t -> t_t-1
									__UpperCAmelCase      					=      self.scheduler.step(__a  ,		__a  ,		__a						).prev_sample

								__UpperCAmelCase      					=      audio.clamp(-1  ,		1						).float().cpu().numpy()

								__UpperCAmelCase      					=      audio[:, :, :original_sample_size]

								if not return_dict:
									return (audio,)

								return AudioPipelineOutput(audios=__a						)
