





import PIL.Image
import PIL.ImageOps
from packaging import version
from PIL import Image


if version.parse(version.parse(PIL.__version__).base_version) >= version.parse("""9.1.0"""):
  _snake_case           =					{
      "linear": PIL.Image.Resampling.BILINEAR,
      "bilinear": PIL.Image.Resampling.BILINEAR,
      "bicubic": PIL.Image.Resampling.BICUBIC,
      "lanczos": PIL.Image.Resampling.LANCZOS,
      "nearest": PIL.Image.Resampling.NEAREST,
  }
else:
  _snake_case           =					{
      "linear": PIL.Image.LINEAR,
      "bilinear": PIL.Image.BILINEAR,
      "bicubic": PIL.Image.BICUBIC,
      "lanczos": PIL.Image.LANCZOS,
      "nearest": PIL.Image.NEAREST,
  }


def _A  (       __magic_name__			):
   lowercase__					  =    (images / 2 + 0.5).clamp(0    ,   1			)
   lowercase__					  =    images.cpu().permute(0    ,   2    ,   3    ,   1			).float().numpy()
   lowercase__					  =    numpy_to_pil(snake_case__			)
   return images







def _A  (       __magic_name__			):


   if images.ndim == 3:
      lowercase__					  =    images[None, ...]
   lowercase__					  =    (images * 255).round().astype("uint8"			)
   if images.shape[-1] == 1:
      # special case for grayscale (single channel) images
      lowercase__					  =    [Image.fromarray(image.squeeze()    ,   mode="L"			) for image in images]
   else:
      lowercase__					  =    [Image.fromarray(snake_case__			) for image in images]

   return pil_images









"""simple docstring"""




def 						A							(  snake_case__		,					snake_case__     ):




			'''simple docstring'''


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

def 						A							(  snake_case__     ):




			'''simple docstring'''


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

def 						A							(  snake_case__     ):




			'''simple docstring'''


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

def 						A							(  snake_case__     ):




			'''simple docstring'''


			return catalan_number(snake_case__     ) * factorial(snake_case__     )


if __name__ == "__main__":
						A_				:      Optional[int]           =			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.'
						)


