






import numpy as np
import torch
from imwatermark import WatermarkEncoder


# Copied from https://github.com/Stability-AI/generative-models/blob/613af104c6b85184091d42d374fef420eddb356d/scripts/demo/streamlit_helpers.py#L66
__UpperCamelCase   :   List[str]      =    0B10_11_00_11_11_10_11_00_10_01_00_00_01_11_10_11_10_11_00_01_10_01_11_10
# bin(x)[2:] gives bits of x as str, use int to convert them to 0/1
__UpperCamelCase   :   List[Any]      =    [int(bit) for bit in bin(WATERMARK_MESSAGE)[2:]]


class 							__UpperCamelCase     :







	def __init__(	self   :				int      )		->			List[Any]:
		"""simple docstring"""







		__lowercase   							=	WATERMARK_BITS
		__lowercase   							=	WatermarkEncoder()

		self.encoder.set_watermark("""bits"""							,					self.watermark      )







	def 			_a (	self   :				List[Any]							,					_lowerCAmelCase   :				torch.FloatTensor      )		->			Union[str, Any]:
		"""simple docstring"""







		if images.shape[-1] < 256:
			return images

		__lowercase   							=	(255 * (images / 2 + 0.5)).cpu().permute(0							,					2							,					3							,					1      ).float().numpy()

		__lowercase   							=	[self.encoder.encode(_lowerCAmelCase							,					"""dwtDct"""      ) for image in images]

		__lowercase   							=	torch.from_numpy(np.array(_lowerCAmelCase      )      ).permute(0							,					3							,					1							,					2      )

		__lowercase   							=	torch.clamp(2 * (images / 255 - 0.5)							,					min=-1.0							,					max=1.0      )
		return images








'''simple docstring'''




def 		__A		(  lowerCamelCase_			,			lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



		return catalan_number(lowerCamelCase_	) * factorial(lowerCamelCase_	)


if __name__ == "__main__":
							__UpperCAmelCase            =       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.'''
							)



