



"""simple docstring"""







from __future__ import annotations

from fractions import Fraction

def 				UpperCamelCase_    (    lowerCAmelCase__      :				int    ,   lowerCAmelCase__      :				int						)						->   bool:

  """simple docstring"""




  return (
      num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
  )

def 				UpperCamelCase_    (    lowerCAmelCase__      :				int						)						->   list[str]:

  """simple docstring"""




  lowerCAmelCase_   :				Dict								= []
  lowerCAmelCase_   :				str								= 11
  lowerCAmelCase_   :				Optional[Any]								= int('1' + '0' * digit_len						)
  for num in range(lowerCAmelCase__    ,   lowerCAmelCase__						):
    while den <= 99:
      if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
        if is_digit_cancelling(lowerCAmelCase__    ,   lowerCAmelCase__						):
          solutions.append(f"{num}/{den}"						)
      den += 1
    num += 1
    lowerCAmelCase_   :				Tuple								= 10
  return solutions

def 				UpperCamelCase_    (    lowerCAmelCase__      :				int = 2						)						->   int:

  """simple docstring"""




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


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










"""simple docstring"""







def 				UpperCamelCase_    (    lowerCAmelCase__      :				int = 100						)						->   int:

  """simple docstring"""




  lowerCAmelCase_   :				Any								= (n * (n + 1) // 2) ** 2
  lowerCAmelCase_   :				Optional[int]								= n * (n + 1) * (2 * n + 1) // 6
  return sum_cubes - sum_squares


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





