
'''simple docstring'''




import math







def 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



    if not isinstance(__lowercase						,							__lowercase		):
        A			:  Union[str, Any]   =		F'Input value of [number={number}] must be an integer'
        raise TypeError(__lowercase		)

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

        A			:  int   =		[3, 5]
        A			:  List[str]   =		2
        A			:  List[Any]   =		3
        for block in range(1						,							__lowercase		):
            for _ in range(__lowercase		):
                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[int]       						=     0
            try:
                  lowercase     :							List[str]       						=     proth(number)
            except ValueError:
                  print(f'''ValueError: there is no {number}th Proth number''')
                  continue

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










'''simple docstring'''







import numpy as np

lowercase      :   str      =       [
    ["""a""", """b""", """c""", """d""", """e"""],
    ["""f""", """g""", """h""", """i""", """k"""],
    ["""l""", """m""", """n""", """o""", """p"""],
    ["""q""", """r""", """s""", """t""", """u"""],
    ["""v""", """w""", """x""", """y""", """z"""],
]







class 					_a :





     '''simple docstring'''



     def __init__(				self							)      ->				None:
          snake_case			:      Dict        =			np.array(__a							)







     def 			snake_case_      (				self							,__a							)      ->				np.ndarray:
          snake_case ,		snake_case			:      Optional[Any]        =			np.where(letter == self.SQUARE							)
          snake_case			:      List[Any]        =			np.concatenate([indexa + 1, indexa + 1]							)
          return indexes







     def 			snake_case_      (				self							,__a							,__a							)      ->				str:
          snake_case			:      List[Any]        =			self.SQUARE[indexa - 1, indexa - 1]
          return letter







     def 			snake_case_      (				self							,__a							)      ->				str:
          snake_case			:      List[Any]        =			message.lower()
          snake_case			:      Dict        =			message.replace(""" """							,""""""							)
          snake_case			:      List[str]        =			message.replace("""j"""							,"""i"""							)

          snake_case			:      Optional[int]        =			np.empty((2, len(__a							))							)
          for letter_index in range(len(__a							)							):
               snake_case			:      Tuple        =			self.letter_to_numbers(message[letter_index]							)

               snake_case			:      Optional[Any]        =			numbers[0]
               snake_case			:      List[str]        =			numbers[1]

          snake_case			:      List[str]        =			first_step.reshape(2 * len(__a							)							)
          snake_case			:      List[Any]        =			""""""
          for numbers_index in range(len(__a							)							):
               snake_case			:      List[str]        =			int(second_step[numbers_index * 2]							)
               snake_case			:      List[Any]        =			int(second_step[(numbers_index * 2) + 1]							)
               snake_case			:      str        =			self.numbers_to_letter(__a							,__a							)
               snake_case			:      Any        =			encoded_message + letter

          return encoded_message







     def 			snake_case_      (				self							,__a							)      ->				str:
          snake_case			:      Any        =			message.lower()
          message.replace(""" """							,""""""							)
          snake_case			:      Dict        =			np.empty(2 * len(__a							)							)
          for letter_index in range(len(__a							)							):
               snake_case			:      str        =			self.letter_to_numbers(message[letter_index]							)
               snake_case			:      Any        =			numbers[0]
               snake_case			:      int        =			numbers[1]

          snake_case			:      List[str]        =			first_step.reshape((2, len(__a							))							)
          snake_case			:      Dict        =			""""""
          for numbers_index in range(len(__a							)							):
               snake_case			:      Optional[Any]        =			int(second_step[0, numbers_index]							)
               snake_case			:      Optional[int]        =			int(second_step[1, numbers_index]							)
               snake_case			:      Tuple        =			self.numbers_to_letter(__a							,__a							)
               snake_case			:      int        =			decoded_message + letter

          return decoded_message



