




from math import factorial

class 		__lowerCAmelCase	:
							def __init__(						self						:Any		,      __magic_name__						:int		,      __magic_name__						:List[str]				):







								'''simple docstring'''







								a										=							real
								if isinstance(__magic_name__		,      __magic_name__				):
									a										=							[1] * rank
								else:
									a										=							rank
							def __repr__(						self						:Optional[Any]				):







								'''simple docstring'''







								return (
								    F'{self.real}+'
								    F'{"+".join(str(__magic_name__				)+"E"+str(n+1				)for n,dual in enumerate(self.duals				)				)}'
								)
							def       lowerCamelCase__							(						self						:Dict				):







								'''simple docstring'''







								a										=							self.duals.copy()
								while cur[-1] == 0:
									cur.pop(-1				)
								return Dual(self.real		,      __magic_name__				)
							def __add__(						self						:Optional[int]		,      __magic_name__						:List[Any]				):







								'''simple docstring'''







								if not isinstance(__magic_name__		,      __magic_name__				):
									return Dual(self.real + other		,      self.duals				)
								a										=							self.duals.copy()
								a										=							other.duals.copy()
								if len(__magic_name__				) > len(__magic_name__				):
									o_dual.extend([1] * (len(__magic_name__				) - len(__magic_name__				))				)
								elif len(__magic_name__				) < len(__magic_name__				):
									s_dual.extend([1] * (len(__magic_name__				) - len(__magic_name__				))				)
								a										=							[]
								for i in range(len(__magic_name__				)				):
									new_duals.append(s_dual[i] + o_dual[i]				)
								return Dual(self.real + other.real		,      __magic_name__				)

							UpperCamelCase__					     =  __add__
							def __sub__(						self						:Dict		,      __magic_name__						:Tuple				):







								'''simple docstring'''







								return self + other * -1
							def __mul__(						self						:Union[str, Any]		,      __magic_name__						:Tuple				):







								'''simple docstring'''







								if not isinstance(__magic_name__		,      __magic_name__				):
									a										=							[]
									for i in self.duals:
										new_duals.append(i * other				)
									return Dual(self.real * other		,      __magic_name__				)
								a										=							[0] * (len(self.duals				) + len(other.duals				) + 1)
								for i, item in enumerate(self.duals				):
									for j, jtem in enumerate(other.duals				):
										new_duals[i + j + 1] += item * jtem
								for k in range(len(self.duals				)				):
									new_duals[k] += self.duals[k] * other.real
								for index in range(len(other.duals				)				):
									new_duals[index] += other.duals[index] * self.real
								return Dual(self.real * other.real		,      __magic_name__				)

							UpperCamelCase__					     =  __mul__
							def __truediv__(						self						:Optional[Any]		,      __magic_name__						:Any				):







								'''simple docstring'''







								if not isinstance(__magic_name__		,      __magic_name__				):
									a										=							[]
									for i in self.duals:
										new_duals.append(i / other				)
									return Dual(self.real / other		,      __magic_name__				)
								raise ValueError
							def __floordiv__(						self						:Dict		,      __magic_name__						:Any				):







								'''simple docstring'''







								if not isinstance(__magic_name__		,      __magic_name__				):
									a										=							[]
									for i in self.duals:
										new_duals.append(i // other				)
									return Dual(self.real // other		,      __magic_name__				)
								raise ValueError





							def __pow__(						self						:Optional[int]		,      __magic_name__						:Dict				):







								'''simple docstring'''







								if n < 0 or isinstance(__magic_name__		,      __magic_name__				):
									raise ValueError("""power must be a positive integer"""				)
								if n == 0:
									return 1
								if n == 1:
									return self
								a										=							self
								for _ in range(n - 1				):
									x *= self
								return x







def 		__A		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase    )      ->       int:
	if not callable(__lowerCamelCase    ):
		raise ValueError("""differentiate() requires a function as input for func"""    )
	if not isinstance(__lowerCamelCase							,			(float, int)    ):
		raise ValueError("""differentiate() requires a float as input for position"""    )
	if not isinstance(__lowerCamelCase							,			__lowerCamelCase    ):
		raise ValueError("""differentiate() requires an int as input for order"""    )
	a										=							Dual(__lowerCamelCase							,			1    )
	a										=							func(__lowerCamelCase    )
	if order == 0:
		return result.real
	return result.duals[order - 1] * factorial(__lowerCamelCase    )


if __name__ == "__main__":
		import doctest

		doctest.testmod()





		def 		__A		(	__lowerCamelCase    )      ->       Union[str, Any]:
			return y**2 * y**4



		print(differentiate(f, 9, 2))







def 		__A		(	__lowerCamelCase    )      ->       int:
	a										=							hex_num.strip()
	if not hex_num:
		raise ValueError("""No value was passed to the function"""    )

	a										=							hex_num[0] == """-"""
	if is_negative:
		a										=							hex_num[1:]

	try:
		a										=							int(__lowerCamelCase							,			16    )
	except ValueError:
		raise ValueError("""Invalid value was passed to the function"""    )

	a										=							""""""
	while int_num > 0:
		a										=							str(int_num % 2    ) + bin_str
		int_num >>= 1

	return int(("""-""" + bin_str) if is_negative else bin_str    )


if __name__ == "__main__":
		import doctest

		doctest.testmod()

