
import itertools




def 						A_			(				snake_case				: int = 1000000			)   ->     int:



						'''simple docstring'''

						__UpperCamelCase  	=      [1]

						for i in itertools.count(len(snake_case			)			):
												__UpperCamelCase  	=      0
												for j in itertools.count(1			):
																		__UpperCamelCase  	=      -1 if j % 2 == 0 else +1
																		__UpperCamelCase  	=      (j * j * 3 - j) // 2
																		if index > i:
																								break
																		item += partitions[i - index] * sign
																		item %= number
																		index += j
																		if index > i:
																								break
																		item += partitions[i - index] * sign
																		item %= number

												if item == 0:
																		return i
												partitions.append(snake_case			)

						return 0


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				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''']   )

