



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



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return binomial_coefficient(2 * node_count  ,					SCREAMING_SNAKE_CASE_					) // (node_count + 1)



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



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return catalan_number(SCREAMING_SNAKE_CASE_					) * factorial(SCREAMING_SNAKE_CASE_					)


if __name__ == "__main__":
							lowercase_						=       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 __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			lowercase__   					=			int(SCREAMING_SNAKE_CASE_					)
			if decimal in (0, 1):  # Exit cases for the recursion
						return str(SCREAMING_SNAKE_CASE_					)
			lowercase__					,    lowercase__   					=			divmod(SCREAMING_SNAKE_CASE_  ,					2					)
			return binary_recursive(SCREAMING_SNAKE_CASE_					) + str(SCREAMING_SNAKE_CASE_					)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			lowercase__   					=			str(SCREAMING_SNAKE_CASE_					).strip()
			if not number:
						raise ValueError("No input value was provided"					)
			lowercase__   					=			"-" if number.startswith("-"					) else ""
			lowercase__   					=			number.lstrip("-"					)
			if not number.isnumeric():
						raise ValueError("Input value is not an integer"					)
			return f'''{negative}0b{binary_recursive(int(SCREAMING_SNAKE_CASE_					)					)}'''


if __name__ == "__main__":
							from doctest import testmod

							testmod()




