




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

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase)      ->					int:
     return binomial_coefficient(2 * node_count		, __UpperCamelCase) // (node_count + 1)

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase)      ->					int:
     if n < 0:
          raise ValueError("factorial() not defined for negative values")
     a     =				1
     for i in range(1		, n + 1):
          result *= i
     return result

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase)      ->					int:
     return catalan_number(__UpperCamelCase) * factorial(__UpperCamelCase)


if __name__ == "__main__":
   lowercase__				:      Optional[int]	   = 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.'
   )







import math
import sys

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase)      ->					int:
     if number != int(__UpperCamelCase):
          raise ValueError("the value of input must be a natural number")
     if number < 0:
          raise ValueError("the value of input must not be a negative number")
     if number == 0:
          return 1
     a     =				[-1] * (number + 1)
     a     =				0
     for i in range(1		, number + 1):
          a     =				sys.maxsize
          a     =				int(math.sqrt(__UpperCamelCase))
          for j in range(1		, root + 1):
               a     =				1 + answers[i - (j**2)]
               a     =				min(__UpperCamelCase		, __UpperCamelCase)
          a     =				answer
     return answers[number]


if __name__ == "__main__":
   import doctest

   doctest.testmod()

