'''simple docstring'''




from __future__ import annotations






def __lowerCAmelCase				(							UpperCamelCase__       ,						UpperCamelCase__       ,						UpperCamelCase__       ,						)			->					list[float | int]:
    if not all((nth_term, start_term_a, common_ratio_r)       ):
        return []
    __lowerCamelCase						=						[]
    __lowerCamelCase						=						1
    __lowerCamelCase						=						common_ratio_r
    for _ in range(int(UpperCamelCase__       )       ):
        if not series:
            series.append(UpperCamelCase__       )
        else:
            power += 1
            series.append(float(start_term_a * multiple       )       )
            __lowerCamelCase						=						pow(float(UpperCamelCase__       )       ,						UpperCamelCase__       )
    return series


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  __UpperCAmelCase  							=float(input("Enter the last number (n term) of the Geometric Series"))
  __UpperCAmelCase  							=float(input("Enter the starting term (a) of the Geometric Series"))
  __UpperCAmelCase  							=float(
      input("Enter the common ratio between two terms (r) of the Geometric Series")
  )
  print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
  print(geometric_series(nth_term, start_term_a, common_ratio_r))

'''simple docstring'''




__UpperCAmelCase  							=[chr(i) for i in range(3_2, 1_2_6)]
__UpperCAmelCase  							=list(range(len(alphabets)))
__UpperCAmelCase  							=list(range(len(alphabets)))
__UpperCAmelCase  							=list(range(len(alphabets)))
__UpperCAmelCase  							=list(reversed(range(len(alphabets))))
__UpperCAmelCase  							=[]
__UpperCAmelCase  							=__UpperCAmelCase  							=__UpperCAmelCase  							=0






def __lowerCAmelCase				(							)			->					List[Any]:
    global gear_one_pos
    global gear_two_pos
    global gear_three_pos
    __lowerCamelCase						=						gear_one[0]
    gear_one.append(UpperCamelCase__       )
    del gear_one[0]
    gear_one_pos += 1
    if gear_one_pos % int(len(UpperCamelCase__       )       ) == 0:
        __lowerCamelCase						=						gear_two[0]
        gear_two.append(UpperCamelCase__       )
        del gear_two[0]
        gear_two_pos += 1
        if gear_two_pos % int(len(UpperCamelCase__       )       ) == 0:
            __lowerCamelCase						=						gear_three[0]
            gear_three.append(UpperCamelCase__       )
            del gear_three[0]
            gear_three_pos += 1






def __lowerCAmelCase				(							UpperCamelCase__       )			->					Optional[Any]:
    __lowerCamelCase						=						alphabets.index(UpperCamelCase__       )
    __lowerCamelCase						=						gear_one[target]
    __lowerCamelCase						=						gear_two[target]
    __lowerCamelCase						=						gear_three[target]
    __lowerCamelCase						=						reflector[target]
    __lowerCamelCase						=						gear_three.index(UpperCamelCase__       )
    __lowerCamelCase						=						gear_two.index(UpperCamelCase__       )
    __lowerCamelCase						=						gear_one.index(UpperCamelCase__       )
    code.append(alphabets[target]       )
    rotator()


if __name__ == "__main__":
  __UpperCAmelCase  							=list(input("Type your message:\n"))
  while True:
    try:
      __UpperCAmelCase  							=int(input("Please set token:(must be only digits)\n"))
      break
    except Exception as error:
      print(error)
  for _ in range(token):
    rotator()
  for j in decode:
    engine(j)
  print("\n" + "".join(code))
  print(
      f'\nYour Token is {token} please write it down.\nIf you want to decode '
      "this message again you should input same digits as token!"
  )
