





'''simple docstring'''


import copy
from dataclasses import dataclass
from pathlib import Path
from typing import Dict, Optional, Union

@dataclass
class       lowerCAmelCase_						:
 __lowerCamelCase  :							int				     =    None
 __lowerCamelCase  :							Tuple				     =    False
 __lowerCamelCase  :							Optional[int]				     =    False
 __lowerCamelCase  :							Union[str, Any]				     =    False
 __lowerCamelCase  :							Any				     =    None
 __lowerCamelCase  :							List[str]				     =    None
 __lowerCamelCase  :							Optional[Any]				     =    False
 __lowerCamelCase  :							List[Any]				     =    False
 __lowerCamelCase  :							List[str]				     =    False
 __lowerCamelCase  :							Dict				     =    True
 __lowerCamelCase  :							Optional[Any]				     =    None
 __lowerCamelCase  :							Any				     =    1
 __lowerCamelCase  :							Optional[int]				     =    None
 __lowerCamelCase  :							str				     =    False
 __lowerCamelCase  :							List[str]				     =    None
 __lowerCamelCase  :							str				     =    None




 def 							_snake_case      (		self						)			->							int:
     return self.__class__(**{k: copy.deepcopy(lowercase_						) for k, v in self.__dict__.items()}						)



'''simple docstring'''




import math




def 							lowerCamelCase	(      UpperCAmelCase__       :					int )			->      int:

							if not isinstance(UpperCAmelCase__      ,      UpperCAmelCase__ ):
														lowercase_					:			List[Any]										=       F'''Input value of [number={number}] must be an integer'''
														raise TypeError(UpperCAmelCase__ )

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

														lowercase_					:			Any										=       [3, 5]
														lowercase_					:			List[Any]										=       2
														lowercase_					:			Optional[Any]										=       3
														for block in range(1      ,      UpperCAmelCase__ ):
																					for _ in range(UpperCAmelCase__ ):
																												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):
												_lowercase						: Optional[Any]						=						0
												try:
																		_lowercase						: str						=						proth(number)
												except ValueError:
																		print(f"""ValueError: there is no {number}th Proth number""")
																		continue

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





