

def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_		):
							A      :					List[Any]      		=					1  # To kept the Calculated Value
							# Since C(n, k) = C(n, n-k)
							if k > (n - k):
														A      :					Any      		=					n - k
							# Calculate C(n,k)
							for i in range(lowercase_		):
														result *= n - i
														result //= i + 1
							return result






def        snake_case__		(    lowerCamelCase_		):
							return binomial_coefficient(2 * node_count     ,				lowercase_		) // (node_count + 1)






def        snake_case__		(    lowerCamelCase_		):
							if n < 0:
														raise ValueError('''factorial() not defined for negative values'''		)
							A      :					Optional[int]      		=					1
							for i in range(1     ,				n + 1		):
														result *= i
							return result






def        snake_case__		(    lowerCamelCase_		):
							return catalan_number(lowercase_		) * factorial(lowercase_		)


if __name__ == "__main__":
		lowercase			:				Dict   =     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."
		)













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							(   lowerCamelCase__	):




      """simple docstring"""







      def __init__(		self   ,				a__   ,				a__   ,				a__):



             """simple docstring"""





             super().__init__()
             self.register_modules(vqvae=a__   ,				unet=a__   ,				scheduler=a__)



      @torch.no_grad()
      def __call__(		self   ,				a__ = 1   ,				a__ = None   ,				a__ = 0.0   ,				a__ = 50   ,				a__ = "pil"   ,				a__ = True   ,				**a__   ,				):



             """simple docstring"""





             _lowerCamelCase				:  Tuple						=		randn_tensor(
                 (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)   ,				generator=a__   ,				)
             _lowerCamelCase				:  Optional[int]						=		latents.to(self.device)

             # scale the initial noise by the standard deviation required by the scheduler
             _lowerCamelCase				:  Tuple						=		latents * self.scheduler.init_noise_sigma

             self.scheduler.set_timesteps(a__)

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

             _lowerCamelCase				:  Union[str, Any]						=		{}
             if accepts_eta:
                    _lowerCamelCase				:  List[Any]						=		eta

             for t in self.progress_bar(self.scheduler.timesteps):
                    _lowerCamelCase				:  List[Any]						=		self.scheduler.scale_model_input(a__   ,				a__)
                    # predict the noise residual
                    _lowerCamelCase				:  Optional[int]						=		self.unet(a__   ,				a__).sample
                    # compute the previous noisy sample x_t -> x_t-1
                    _lowerCamelCase				:  List[str]						=		self.scheduler.step(a__   ,				a__   ,				a__   ,				**a__).prev_sample

             # decode the image latents with the VAE
             _lowerCamelCase				:  Optional[int]						=		self.vqvae.decode(a__).sample

             _lowerCamelCase				:  Dict						=		(image / 2 + 0.5).clamp(0   ,				1)
             _lowerCamelCase				:  List[str]						=		image.cpu().permute(0   ,				2   ,				3   ,				1).numpy()
             if output_type == "pil":
                    _lowerCamelCase				:  List[Any]						=		self.numpy_to_pil(a__)

             if not return_dict:
                    return (image,)

             return ImagePipelineOutput(images=a__)

