



"""simple docstring"""


def  _lowerCAmelCase      (   lowercase_		,	lowercase_						):
						UpperCAmelCase             = 1  # To kept the Calculated Value
						# Since C(n, k) = C(n, n-k)
						if k > (n - k):
												UpperCAmelCase             = n - k
						# Calculate C(n,k)
						for i in range(lowercase_						):
												result *= n - i
												result //= i + 1
						return result

def  _lowerCAmelCase      (   lowercase_						):
						return binomial_coefficient(2 * node_count		,	lowercase_						) // (node_count + 1)

def  _lowerCAmelCase      (   lowercase_						):
						if n < 0:
												raise ValueError('factorial() not defined for negative values'						)
						UpperCAmelCase             = 1
						for i in range(1		,	n + 1						):
												result *= i
						return result

def  _lowerCAmelCase      (   lowercase_						):
						return catalan_number(lowercase_						) * factorial(lowercase_						)


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.'''
				)









'''simple docstring'''
def 					a__       (					lowerCAmelCase__						)    ->	int:
    UpperCAmelCase__			:		Tuple													=				0
    while num > 0:
        digit_sum += num % 10
        num //= 10
    return digit_sum





def 					a__       (					lowerCAmelCase__ = 1_00						)    ->	int:
    UpperCAmelCase__			:		Dict													=				1
    UpperCAmelCase__			:		str													=				2

    for i in range(2  ,					max_n + 1						):
        UpperCAmelCase__			:		Tuple													=				pre_numerator
        UpperCAmelCase__			:		Tuple													=				2 * i // 3 if i % 3 == 0 else 1
        UpperCAmelCase__			:		str													=				cur_numerator
        UpperCAmelCase__			:		List[str]													=				e_cont * pre_numerator + temp

    return sum_digits(lowerCAmelCase__						)


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