def  snake_case  (       snake_case__			:int   ,	snake_case__			:int)						->   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(snake_case__):
              result *= n - i
              result //= i + 1
       return result






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






def  snake_case  (       snake_case__			:int)						->   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  snake_case  (       snake_case__			:int)						->   int:
       return catalan_number(snake_case__) * factorial(snake_case__)


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





def  snake_case  (       snake_case__			:str = "The quick brown fox jumps over the lazy dog"   ,	)						->   bool:
       _A        =  set()

       # Replace all the whitespace in our sentence
       _A        =  input_str.replace(""" """   ,	"""""")
       for alpha in input_str:
              if "a" <= alpha.lower() <= "z":
                     frequency.add(alpha.lower())
       return len(snake_case__) == 26






def  snake_case  (       snake_case__			:str = "The quick brown fox jumps over the lazy dog"   ,	)						->   bool:
       _A        =  [False] * 26
       for char in input_str:
              if char.islower():
                     _A        =  True
              elif char.isupper():
                     _A        =  True
       return all(snake_case__)






def  snake_case  (       snake_case__			:str = "The quick brown fox jumps over the lazy dog"   ,	)						->   bool:
       return len({char for char in input_str.lower() if char.isalpha()}) == 26






def  snake_case  (       )						->   None:
       from timeit import timeit

       _A        =  """from __main__ import is_pangram, is_pangram_faster, is_pangram_fastest"""
       print(timeit("""is_pangram()"""   ,	setup=snake_case__))
       print(timeit("""is_pangram_faster()"""   ,	setup=snake_case__))
       print(timeit("""is_pangram_fastest()"""   ,	setup=snake_case__))
       # 5.348480500048026, 2.6477354579837993, 1.8470395830227062
       # 5.036091582966037, 2.644472333951853,  1.8869528750656173


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    benchmark()




