





def _A  (       __magic_name__ = 100_0000			):
   lowercase__					  =    set(range(3    ,   snake_case__    ,   2			)			)
   primes.add(2			)
   for p in range(3    ,   snake_case__    ,   2			):
      if p not in primes:
         continue
      primes.difference_update(set(range(p * p    ,   snake_case__    ,   snake_case__			)			)			)

   lowercase__					  =    [float(snake_case__			) for n in range(limit + 1			)]

   for p in primes:
      for n in range(snake_case__    ,   limit + 1    ,   snake_case__			):
         phi[n] *= 1 - 1 / p

   return int(sum(phi[2:]			)			)


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









"""simple docstring"""




def 						A							(  snake_case__		,					snake_case__     ):




			'''simple docstring'''


			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 						A							(  snake_case__     ):




			'''simple docstring'''


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

def 						A							(  snake_case__     ):




			'''simple docstring'''


			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 						A							(  snake_case__     ):




			'''simple docstring'''


			return catalan_number(snake_case__     ) * factorial(snake_case__     )


if __name__ == "__main__":
						A_				:      Optional[int]           =			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.'
						)


