"""simple docstring"""







def     lowercase__( __SCREAMING_SNAKE_CASE							:  int = 10_00   ):
     lowercase_							,						lowercase_			:       Tuple									=			1, 1
     lowercase_			:       Union[str, Any]									=			[]
     for i in range(1  ,    n + 1   ):
          lowercase_			:       int									=			prev_numerator + 2 * prev_denominator
          lowercase_			:       int									=			prev_numerator + prev_denominator
          if len(str(lowerCAmelCase__   )   ) > len(str(lowerCAmelCase__   )   ):
               result.append(lowerCAmelCase__   )
          lowercase_			:       str									=			numerator
          lowercase_			:       int									=			denominator

     return len(lowerCAmelCase__   )


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


"""simple docstring"""







import numpy as np



def     lowercase__( __SCREAMING_SNAKE_CASE							:  np.array   ):
     return 1 / (1 + np.exp(-vector   ))


if __name__ == "__main__":
       import doctest

       doctest.testmod()

