

'''simple docstring'''
import numpy as np







def 					_A		(	snake_case     )			->	np.array:
   return (2 / (1 + np.exp(-2 * vector     ))) - 1


if __name__ == "__main__":
    import doctest

    doctest.testmod()







"""simple docstring"""






from __future__ import annotations

from fractions import Fraction



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  bool:
   return (
       num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
   )



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  list[str]:
   lowercase__:   str					=      []
   lowercase__:   str					=      1_1
   lowercase__:   str					=      int('''1''' + '''0''' * digit_len )
   for num in range(__UpperCAmelCase       ,    __UpperCAmelCase ):
      while den <= 9_9:
         if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
            if is_digit_cancelling(__UpperCAmelCase       ,    __UpperCAmelCase ):
               solutions.append(F"""{num}/{den}""" )
         den += 1
      num += 1
      lowercase__:   Dict					=      1_0
   return solutions



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase = 2 )  ->  int:
   lowercase__:   List[str]					=      1.0
   for fraction in fraction_list(__UpperCAmelCase ):
      lowercase__:   List[str]					=      Fraction(__UpperCAmelCase )
      result *= frac.denominator / frac.numerator
   return int(__UpperCAmelCase )


if __name__ == "__main__":
       print(solution())
