def 						__lowerCamelCase				(UpperCAmelCase__  :				int   ,			UpperCAmelCase__  :				int	):
					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 						__lowerCamelCase				(UpperCAmelCase__  :				int	):
					return binomial_coefficient(2 * node_count   ,			snake_case__	) // (node_count + 1)





def 						__lowerCamelCase				(UpperCAmelCase__  :				int	):






					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 						__lowerCamelCase				(UpperCAmelCase__  :				int	):
					return catalan_number(snake_case__	) * factorial(snake_case__	)


if __name__ == "__main__":
							_lowerCamelCase       : Optional[Any]      					=		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."""
							)












def 	UpperCamelCase	(							snake_case__  : int	):




     '''simple docstring'''






     __snake_case      :List[Any] 							=    0
     while num > 0:
          digit_sum += num % 10
          num //= 10
     return digit_sum






def 	UpperCamelCase	(							snake_case__  : int = 100	):




     '''simple docstring'''






     __snake_case      :Tuple 							=    1
     __snake_case      :Dict 							=    2

     for i in range(2						,max_n + 1	):
          __snake_case      :Optional[int] 							=    pre_numerator
          __snake_case      :List[Any] 							=    2 * i // 3 if i % 3 == 0 else 1
          __snake_case      :Dict 							=    cur_numerator
          __snake_case      :Optional[Any] 							=    e_cont * pre_numerator + temp

     return sum_digits(snake_case__	)


if __name__ == "__main__":
     print(f'''{solution() = }''')


