


def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  return catalan_number(SCREAMING_SNAKE_CASE_	) * factorial(SCREAMING_SNAKE_CASE_	)


if __name__ == "__main__":
   _snake_case             =     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 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  if divisor % 5 == 0 or divisor % 2 == 0:
    return 0
  lowerCamelCase :					List[Any]    =				1
  lowerCamelCase :					Union[str, Any]    =				1
  while repunit:
    lowerCamelCase :					Union[str, Any]    =				(10 * repunit + 1) % divisor
    repunit_index += 1
  return repunit_index






def 		lowercase_(  SCREAMING_SNAKE_CASE_ = 1000000	):


  '''simple docstring'''

  lowerCamelCase :					List[str]    =				limit - 1
  if divisor % 2 == 0:
    divisor += 1
  while least_divisible_repunit(SCREAMING_SNAKE_CASE_	) <= limit:
    divisor += 2
  return divisor


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



