




import random

def      _SCREAMING_SNAKE_CASE     (				lowercase      :			list      ,				lowercase      :			Tuple	):


      '''simple docstring'''



      lowerCamelCase_							=       [], [], []
      for element in data:
            if element < pivot:
                  less.append(__lowerCamelCase	)
            elif element > pivot:
                  greater.append(__lowerCamelCase	)
            else:
                  equal.append(__lowerCamelCase	)
      return less, equal, greater






def      _SCREAMING_SNAKE_CASE     (				lowercase      :			list      ,				lowercase      :			int	):


      '''simple docstring'''



      if index >= len(__lowerCamelCase	) or index < 0:
            return None

      lowerCamelCase_							=       items[random.randint(0      ,				len(__lowerCamelCase	) - 1	)]
      lowerCamelCase_							=       0
      lowerCamelCase_							=       _partition(__lowerCamelCase      ,				__lowerCamelCase	)
      lowerCamelCase_							=       len(__lowerCamelCase	)
      lowerCamelCase_							=       len(__lowerCamelCase	)

      # index is the pivot
      if m <= index < m + count:
            return pivot
      # must be in smaller
      elif m > index:
            return quick_select(__lowerCamelCase      ,				__lowerCamelCase	)
      # must be in larger
      else:
            return quick_select(__lowerCamelCase      ,				index - (m + count)	)







'''simple docstring'''






from __future__ import annotations

from fractions import Fraction





def lowerCamelCase__     (		__lowerCamelCase			:				int			,       __lowerCamelCase			:				int				):







   '''simple docstring'''




   return (
       num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
   )





def lowerCamelCase__     (		__lowerCamelCase			:				int				):







   '''simple docstring'''




   _UpperCAmelCase  :  Optional[int]				       =[]
   _UpperCAmelCase  :  Union[str, Any]				       =1_1
   _UpperCAmelCase  :  Union[str, Any]				       =int('1' + '0' * digit_len				)
   for num in range(__lowerCamelCase			,       __lowerCamelCase				):
      while den <= 9_9:
         if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
            if is_digit_cancelling(__lowerCamelCase			,       __lowerCamelCase				):
               solutions.append(f"{num}/{den}"				)
         den += 1
      num += 1
      _UpperCAmelCase  :  Optional[int]				       =1_0
   return solutions





def lowerCamelCase__     (		__lowerCamelCase			:				int = 2				):







   '''simple docstring'''




   _UpperCAmelCase  :  Any				       =1.0
   for fraction in fraction_list(__lowerCamelCase				):
      _UpperCAmelCase  :  List[str]				       =Fraction(__lowerCamelCase				)
      result *= frac.denominator / frac.numerator
   return int(__lowerCamelCase				)


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

