



'''simple docstring'''



def 							__UpperCAmelCase				(				UpperCamelCase__				:Any   ,				UpperCamelCase__				:Optional[int]			)		->						Tuple:
				if len(str(UpperCamelCase__			)			) == 1 or len(str(UpperCamelCase__			)			) == 1:
								return a * b

				snake_case__      :   List[str]      =    max(len(str(UpperCamelCase__			)			)   ,				len(str(UpperCamelCase__			)			)			)
				snake_case__      :   Union[str, Any]      =    ma // 2

				snake_case__  ,      snake_case__      :   Any      =    divmod(UpperCamelCase__   ,				10**ma			)
				snake_case__  ,      snake_case__      :   int      =    divmod(UpperCamelCase__   ,				10**ma			)

				snake_case__      :   Tuple      =    karatsuba(UpperCamelCase__   ,				UpperCamelCase__			)
				snake_case__      :   Any      =    karatsuba((aa + aa)   ,				(ba + ba)			)
				snake_case__      :   Union[str, Any]      =    karatsuba(UpperCamelCase__   ,				UpperCamelCase__			)

				return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)


def 							__UpperCAmelCase				(				)		->						int:
				print(karatsuba(1_5463   ,				2_3489			)			)


if __name__ == "__main__":
				main()









from collections.abc import Callable

__magic_name__       =     Callable[[float], float]  # type alias for a real -> real function





def 		__snake_case						(    _UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			):
					"""simple docstring"""






					lowercase						   =       float(_UpperCAmelCase				)
					while True:
										try:
															lowercase						   =       prev_guess - function(_UpperCAmelCase				) / derivative(_UpperCAmelCase				)
										except ZeroDivisionError:
															raise ZeroDivisionError('Could not find root'				) from None
										if abs(prev_guess - next_guess				) < 10**-5:
															return next_guess
										lowercase						   =       next_guess





def 		__snake_case						(    _UpperCAmelCase				):
					"""simple docstring"""






					return (x**3) - (2 * x) - 5





def 		__snake_case						(    _UpperCAmelCase				):
					"""simple docstring"""






					return 3 * (x**2) - 2


if __name__ == "__main__":
		print(newton(f, fa, 3))






