def      _a					(   lowercase__	:      int  ,	lowercase__	:      int			):







     '''simple docstring'''


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







def      _a					(   lowercase__	:      int			):







     '''simple docstring'''


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







def      _a					(   lowercase__	:      int			):







     '''simple docstring'''


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







def      _a					(   lowercase__	:      int			):







     '''simple docstring'''


     return catalan_number(SCREAMING_SNAKE_CASE_			) * factorial(SCREAMING_SNAKE_CASE_			)


if __name__ == "__main__":
      SCREAMING_SNAKE_CASE__		:       Union[str, 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__  (     SCREAMING_SNAKE_CASE_	:	int = 2_00_00_00       )  ->     int:
						_lowercase					       =					[0 for i in range(n + 1       )]
						_lowercase					       =					1
						_lowercase					       =					1

						for i in range(2		,   int(n**0.5       ) + 1       ):
												if primality_list[i] == 0:
																		for j in range(i * i		,   n + 1		,   SCREAMING_SNAKE_CASE_       ):
																								_lowercase					       =					1
						_lowercase					       =					0
						for i in range(SCREAMING_SNAKE_CASE_       ):
												if primality_list[i] == 0:
																		sum_of_primes += i
						return sum_of_primes


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