

a__												=						[
    (1000, '''M'''),
    (900, '''CM'''),
    (500, '''D'''),
    (400, '''CD'''),
    (100, '''C'''),
    (90, '''XC'''),
    (50, '''L'''),
    (40, '''XL'''),
    (10, '''X'''),
    (9, '''IX'''),
    (5, '''V'''),
    (4, '''IV'''),
    (1, '''I'''),
]



def   __UpperCAmelCase					(      __a :     str      )     ->	int:

					"""simple docstring"""

					_a      :       Optional[int]   =						{'''I''': 1, '''V''': 5, '''X''': 10, '''L''': 50, '''C''': 100, '''D''': 500, '''M''': 1_000}
					_a      :       Union[str, Any]   =						0
					_a      :       List[Any]   =						0
					while place < len(__a      ):
										if (place + 1 < len(__a      )) and (vals[roman[place]] < vals[roman[place + 1]]):
															total += vals[roman[place + 1]] - vals[roman[place]]
															place += 2
										else:
															total += vals[roman[place]]
															place += 1
					return total



def   __UpperCAmelCase					(      __a :     int      )     ->	str:

					"""simple docstring"""

					_a      :       List[str]   =						[]
					for arabic, roman in ROMAN:
										((_a) ,   (_a))      :       Optional[Any]   =						divmod(__a						,__a      )
										result.append(roman * factor      )
										if number == 0:
															break
					return "".join(__a      )


if __name__ == "__main__":
			import doctest

			doctest.testmod()










'''simple docstring'''




def 		__A		(  lowerCamelCase_			,			lowerCamelCase_	):


		"""simple docstring"""



		SCREAMING_SNAKE_CASE :				str		=			1  # To kept the Calculated Value
		# Since C(n, k) = C(n, n-k)
		if k > (n - k):
				SCREAMING_SNAKE_CASE :				Dict		=			n - k
		# Calculate C(n,k)
		for i in range(lowerCamelCase_	):
				result *= n - i
				result //= i + 1
		return result



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



		return catalan_number(lowerCamelCase_	) * factorial(lowerCamelCase_	)


if __name__ == "__main__":
							__UpperCAmelCase            =       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.'''
							)



