





from math import factorial




def     A_      (	lowercase_ = 20	)      ->    Union[str, Any]:
       _snake_case   :				List[Any]  					=    2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
       # 2, 3,...
       _snake_case   :				Dict  					=    n // 2

       return int(factorial(__lowercase	) / (factorial(__lowercase	) * factorial(n - k	))	)


if __name__ == "__main__":
   import sys

   if len(sys.argv) == 1:
      print(solution(2_0))
   else:
      try:
         lowerCAmelCase_				= int(sys.argv[1])
         print(solution(n))
      except ValueError:
         print("Invalid entry - please enter a number.")














import numpy as np






def      _snake_case     (__lowercase):
   return 1 / (1 + np.exp(-vector))






def      _snake_case     (__lowercase):
   return vector * sigmoid(__lowercase)


if __name__ == "__main__":
 import doctest

 doctest.testmod()





