





def 	__UpperCamelCase (	lowercase__		:				int						)		->					Dict:
    '''simple docstring'''





    return n * (2 * n - 1)
def 	__UpperCamelCase (	lowercase__		:				int						)		->					int:
    '''simple docstring'''





    lowerCAmelCase_    :		List[str] 						=      (1 + 24 * n) ** 0.5
    return ((1 + root) / 6) % 1 == 0
def 	__UpperCamelCase (	lowercase__		:				int = 144						)		->					str:
    '''simple docstring'''





    lowerCAmelCase_    :		Union[str, Any] 						=      start
    lowerCAmelCase_    :		Union[str, Any] 						=      hexagonal_num(lowercase__						)
    while not is_pentagonal(lowercase__						):
        n += 1
        lowerCAmelCase_    :		List[Any] 						=      hexagonal_num(lowercase__						)
    return num


if __name__ == "__main__":
  print(f"""{solution()} = """)






'''simple docstring'''







import math






def       lowerCAmelCase__       (				lowerCamelCase     :			int   ):
       _A     :	int      =					math.log(2  ,10   ) * number
       _A     :	List[Any]      =					round((log_number - int(lowerCamelCase   ))  ,15   )

       return difference






def       lowerCAmelCase__       (				lowerCamelCase     :			int = 678910   ):
       _A     :	List[str]      =					90
       _A     :	List[Any]      =					0

       _A     :	List[str]      =					math.log(1.23  ,10   )
       _A     :	Any      =					math.log(1.24  ,10   )
       _A     :	Union[str, Any]      =					0

       while position < number:
              _A     :	Dict      =					log_difference(lowerCamelCase   )

              if difference >= upper_limit:
                     power_iterator += 93

              elif difference < lower_limit:
                     power_iterator += 196

              else:
                     _A     :	str      =					power_iterator
                     power_iterator += 196
                     position += 1

       return previous_power


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   print(f"""{solution() = }""")






