'''simple docstring'''




__SCREAMING_SNAKE_CASE       :     Dict     =  8.3_1_4_4_6_2  # Unit - J mol-1 K-1

def 	UpperCamelCase_							(					_UpperCAmelCase  :      float			,	_UpperCAmelCase  :      float			,	_UpperCAmelCase  :      float    )    ->    float:


       """simple docstring"""







       if moles < 0 or kelvin < 0 or volume < 0:
              raise ValueError("Invalid inputs. Enter positive value."    )
       return moles * kelvin * UNIVERSAL_GAS_CONSTANT / volume

def 	UpperCamelCase_							(					_UpperCAmelCase  :      float			,	_UpperCAmelCase  :      float			,	_UpperCAmelCase  :      float    )    ->    float:


       """simple docstring"""







       if moles < 0 or kelvin < 0 or pressure < 0:
              raise ValueError("Invalid inputs. Enter positive value."    )
       return moles * kelvin * UNIVERSAL_GAS_CONSTANT / pressure


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

  testmod()


'''simple docstring'''




def 	UpperCamelCase_							(					_UpperCAmelCase  :      int			,	_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







       return catalan_number(_UpperCAmelCase    ) * factorial(_UpperCAmelCase    )


if __name__ == "__main__":
  __SCREAMING_SNAKE_CASE       :     Dict     =  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.'
  )

