
'''simple docstring'''





def   A			(							A_				:       int							):
						return n * (2 * n - 1)

def   A			(							A_				:       int							):
						snake_case							:  Optional[Any]			=     (1 + 24 * n) ** 0.5
						return ((1 + root) / 6) % 1 == 0

def   A			(							A_				:       int = 144							):
						snake_case							:  Any			=     start
						snake_case							:  Any			=     hexagonal_num(A_							)
						while not is_pentagonal(A_							):
												n += 1
												snake_case							:  Optional[Any]			=     hexagonal_num(A_							)
						return num


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



'''simple docstring'''





from ..utils import DummyObject, requires_backends

class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[int],     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					int,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					int,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					int,     *SCREAMING_SNAKE_CASE_						:					Tuple,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					Tuple,     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[int],     *SCREAMING_SNAKE_CASE_						:					Any,     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					int,     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					Tuple,     **SCREAMING_SNAKE_CASE_						:					Any   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					int,     **SCREAMING_SNAKE_CASE_						:					Union[str, Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					int,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					int,     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					Tuple,     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[int],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					Union[str, Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					Optional[Any],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					Tuple,     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[int],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					Any   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					Optional[Any],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					Union[str, Any],     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					Union[str, Any],     **SCREAMING_SNAKE_CASE_						:					Union[str, Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					Union[str, Any],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[int],     *SCREAMING_SNAKE_CASE_						:					int,     **SCREAMING_SNAKE_CASE_						:					Any   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[str],     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					Any   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[int],     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					int   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					Any,     **SCREAMING_SNAKE_CASE_						:					Any   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					List[str],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					Any,     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					Tuple,     **SCREAMING_SNAKE_CASE_						:					Optional[int]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					Union[str, Any],     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					List[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					Any   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					int,     *SCREAMING_SNAKE_CASE_						:					Any,     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					Dict,     **SCREAMING_SNAKE_CASE_						:					Optional[int]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Dict,     *SCREAMING_SNAKE_CASE_						:					Union[str, Any],     **SCREAMING_SNAKE_CASE_						:					Tuple   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Tuple,     *SCREAMING_SNAKE_CASE_						:					Optional[Any],     **SCREAMING_SNAKE_CASE_						:					Dict   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Union[str, Any],     *SCREAMING_SNAKE_CASE_						:					List[Any],     **SCREAMING_SNAKE_CASE_						:					str   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					str,     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					List[Any],     *SCREAMING_SNAKE_CASE_						:					str,     **SCREAMING_SNAKE_CASE_						:					Optional[Any]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Optional[Any],     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					Optional[int]   ):
										requires_backends(self,     ['''vision''']   )




class     a (					metaclass=__magic_name__     ):
				_snake_case		     =			['''vision''']




				def __init__(				self						:					Any,     *SCREAMING_SNAKE_CASE_						:					Optional[int],     **SCREAMING_SNAKE_CASE_						:					List[str]   ):
										requires_backends(self,     ['''vision''']   )

