





"""simple docstring"""


def 							a__			(  _UpperCAmelCase	)    ->  Union[str, Any]:

 '''simple docstring'''






 return n * (2 * n - 1)





def 							a__			(  _UpperCAmelCase	)    ->  int:

 '''simple docstring'''






 snake_case__    							=				(1 + 2_4 * n) ** 0.5
 return ((1 + root) / 6) % 1 == 0





def 							a__			(  _UpperCAmelCase = 1_4_4	)    ->  int:

 '''simple docstring'''






 snake_case__    							=				start
 snake_case__    							=				hexagonal_num(lowercase_	)
 while not is_pentagonal(lowercase_	):
  n += 1
  snake_case__    							=				hexagonal_num(lowercase_	)
 return num


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








"""simple docstring"""


def 							a__			(  _UpperCAmelCase	)    ->  int:

 '''simple docstring'''






 return int(_UpperCAmelCase	) if x - int(_UpperCAmelCase	) <= 0 else int(_UpperCAmelCase	) + 1


if __name__ == "__main__":
   import doctest

   doctest.testmod()

