





"""simple docstring"""





from ....utils import logging


__A											=		logging.get_logger(__name__)






class 					_lowerCAmelCase   (     a       ):
       """simple docstring"""




       def __init__(    self    , __UpperCAmelCase    , __UpperCAmelCase=None    , __UpperCAmelCase=2_0_4_8      ):



         '''simple docstring'''

         lowerCAmelCase__			:List[Any]											=							config.__dict__
         lowerCAmelCase__			:Any											=							modal_hidden_size
         if num_labels:
           lowerCAmelCase__			:Union[str, Any]											=							num_labels







"""simple docstring"""





import math
def  __A   (_SCREAMING_SNAKE_CASE			)					->int:





  """simple docstring"""


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

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

    lowerCAmelCase__			:Optional[Any]											=							[3, 5]
    lowerCAmelCase__			:Optional[Any]											=							2
    lowerCAmelCase__			:List[str]											=							3
    for block in range(1     ,   _SCREAMING_SNAKE_CASE			):
      for _ in range(_SCREAMING_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											=		0
    try:
      __A											=		proth(number)
    except ValueError:
      print(F'''ValueError: there is no {number}th Proth number''')
      continue

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