






'''simple docstring'''







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





def 		_UpperCAmelCase   (							__A							:   int      ):
				return binomial_coefficient(2 * node_count						,		__A      ) // (node_count + 1)





def 		_UpperCAmelCase   (							__A							:   int      ):
				if n < 0:
								raise ValueError('''factorial() not defined for negative values'''      )
				a_		:  Dict											=      1
				for i in range(1						,		n + 1      ):
								result *= i
				return result





def 		_UpperCAmelCase   (							__A							:   int      ):
				return catalan_number(__A      ) * factorial(__A      )


if __name__ == "__main__":
		__lowerCAmelCase       		=      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."""
		)












'''simple docstring'''







import sys

__lowerCAmelCase       		=      (
    '73167176531330624919225119674426574742355349194934'
    '96983520312774506326239578318016984801869478851843'
    '85861560789112949495459501737958331952853208805511'
    '12540698747158523863050715693290963295227443043557'
    '66896648950445244523161731856403098711121722383113'
    '62229893423380308135336276614282806444486645238749'
    '30358907296290491560440772390713810515859307960866'
    '70172427121883998797908792274921901699720888093776'
    '65727333001053367881220235421809751254540594752243'
    '52584907711670556013604839586446706324415722155397'
    '53697817977846174064955149290862569321978468622482'
    '83972241375657056057490261407972968652414535100474'
    '82166370484403199890008895243450658541227588666881'
    '16427171479924442928230863465674813919123162824586'
    '17866458359124566529476545682848912883142607690042'
    '24219022671055626321111109370544217506941658960408'
    '07198403850962455444362981230987879927244284909188'
    '84580156166097919133875499200524063689912560717606'
    '05886116467109405077541002256983155200055935729725'
    '71636269561882670428252483600823257530420752963450'
)





def 		_UpperCAmelCase   (							__A							:   str      ):
				a_		:  Tuple											=      1
				for digit in s:
								product *= int(__A      )
				return product





def 		_UpperCAmelCase   (							__A							:   str = N      ):
				a_		:  Dict											=      -sys.maxsize - 1
				a_		:  Optional[int]											=      n[:13]
				a_		:  str											=      13
				while cur_index < len(__A      ) - 13:
								if int(n[cur_index]      ) >= int(substr[0]      ):
												a_		:  Tuple											=      substr[1:] + n[cur_index]
												cur_index += 1
								else:
												a_		:  Dict											=      max(__A						,		str_eval(__A      )      )
												a_		:  List[str]											=      n[cur_index : cur_index + 13]
												cur_index += 13
				return largest_product


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




