





'''simple docstring'''




from ..utils import DummyObject, requires_backends




class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[int]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[int]      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[str]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Dict      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[Any]      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			str      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[str]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Any      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Union[str, Any]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Dict      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Tuple      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			List[str]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[str]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Dict      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			int      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[Any]      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Any      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			List[str]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Tuple      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)










'''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.'''
							)



