
import math







def 							UpperCAmelCase_(  a__					):



    """simple docstring"""



    if not isinstance(__snake_case      ,		__snake_case					):
        SCREAMING_SNAKE_CASE							:							str								=      F"""Input value of [number={number}] must be an integer"""
        raise TypeError(__snake_case					)

    if number < 1:
        SCREAMING_SNAKE_CASE							:							Union[str, Any]								=      F"""Input value of [number={number}] must be > 0"""
        raise ValueError(__snake_case					)
    elif number == 1:
        return 3
    elif number == 2:
        return 5
    else:
        SCREAMING_SNAKE_CASE							:							Tuple								=      int(math.log(number // 3      ,		2					)					) + 2

        SCREAMING_SNAKE_CASE							:							Dict								=      [3, 5]
        SCREAMING_SNAKE_CASE							:							int								=      2
        SCREAMING_SNAKE_CASE							:							Dict								=      3
        for block in range(1      ,		__snake_case					):
            for _ in range(__snake_case					):
                proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]					)
                proth_index += 1
            increment *= 2

    return proth_list[number - 1]


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      for number in range(11):
            a__							:	List[Any]  						=			0
            try:
                  a__							:	Optional[Any]  						=			proth(number)
            except ValueError:
                  print(F"ValueError: there is no {number}th Proth number")
                  continue

            print(F"The {number}th Proth number: {value}")




def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			List[Any]:







 """simple docstring"""


 if b == 0:
  return 1
 if (b % 2) == 0:
  return actual_power(__snake_case     ,						int(b / 2						)						) * actual_power(__snake_case     ,						int(b / 2						)						)
 else:
  return a * actual_power(__snake_case     ,						int(b / 2						)						) * actual_power(__snake_case     ,						int(b / 2						)						)
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			float:







 """simple docstring"""


 if b < 0:
  return 1 / actual_power(__snake_case     ,						__snake_case						)
 return actual_power(__snake_case     ,						__snake_case						)


if __name__ == "__main__":
  print(power(-2, -3))

