




"""simple docstring"""







from math import factorial




class       lowerCAmelCase__       :


				"""simple docstring"""





				def __init__(     self					:	Any    ,   lowercase__					:	Dict    ,   lowercase__					:	List[Any]						):
						__lowercase				:		Optional[int]												=				real
						if isinstance(lowercase__    ,   lowercase__						):
								__lowercase				:		Optional[Any]												=				[1] * rank
						else:
								__lowercase				:		Optional[int]												=				rank



				def __repr__(     self					:	Optional[Any]						):
						return (
						    f'{self.real}+'
						    f'{"+".join(str(lowercase__						)+"E"+str(n+1						)for n,dual in enumerate(self.duals						)						)}'
						)



				def       snake_case    (     self					:	Tuple						):
						__lowercase				:		Dict												=				self.duals.copy()
						while cur[-1] == 0:
								cur.pop(-1						)
						return Dual(self.real    ,   lowercase__						)



				def __add__(     self					:	List[Any]    ,   lowercase__					:	str						):
						if not isinstance(lowercase__    ,   lowercase__						):
								return Dual(self.real + other    ,   self.duals						)
						__lowercase				:		Tuple												=				self.duals.copy()
						__lowercase				:		int												=				other.duals.copy()
						if len(lowercase__						) > len(lowercase__						):
								o_dual.extend([1] * (len(lowercase__						) - len(lowercase__						))						)
						elif len(lowercase__						) < len(lowercase__						):
								s_dual.extend([1] * (len(lowercase__						) - len(lowercase__						))						)
						__lowercase				:		Union[str, Any]												=				[]
						for i in range(len(lowercase__						)						):
								new_duals.append(s_dual[i] + o_dual[i]						)
						return Dual(self.real + other.real    ,   lowercase__						)

				__UpperCAmelCase :     Dict       =      __add__



				def __sub__(     self					:	List[Any]    ,   lowercase__					:	int						):
						return self + other * -1



				def __mul__(     self					:	Optional[Any]    ,   lowercase__					:	Optional[int]						):
						if not isinstance(lowercase__    ,   lowercase__						):
								__lowercase				:		Any												=				[]
								for i in self.duals:
										new_duals.append(i * other						)
								return Dual(self.real * other    ,   lowercase__						)
						__lowercase				:		Optional[int]												=				[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    ,   lowercase__						)

				__UpperCAmelCase :     Union[str, Any]       =      __mul__



				def __truediv__(     self					:	List[str]    ,   lowercase__					:	List[Any]						):
						if not isinstance(lowercase__    ,   lowercase__						):
								__lowercase				:		Dict												=				[]
								for i in self.duals:
										new_duals.append(i / other						)
								return Dual(self.real / other    ,   lowercase__						)
						raise ValueError



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



				def __pow__(     self					:	str    ,   lowercase__					:	Optional[int]						):
						if n < 0 or isinstance(lowercase__    ,   lowercase__						):
								raise ValueError("power must be a positive integer"						)
						if n == 0:
								return 1
						if n == 1:
								return self
						__lowercase				:		Any												=				self
						for _ in range(n - 1						):
								x *= self
						return x





def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase				)			->str:






		"""simple docstring"""


		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"				)
		__lowercase				:		int												=				Dual(_lowerCamelCase,  1				)
		__lowercase				:		Optional[int]												=				func(_lowerCamelCase				)
		if order == 0:
				return result.real
		return result.duals[order - 1] * factorial(_lowerCamelCase				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						def 						snake_case__       (					_lowerCamelCase				)			->List[Any]:






								"""simple docstring"""


								return y**2 * y**4





						print(differentiate(f, 9, 2))






"""simple docstring"""







class       lowerCAmelCase__       :


				"""simple docstring"""





				def __init__(     self					:	int    ,   lowercase__					:	List[Any]						):
						__lowercase				:		Tuple												=				val
						__lowercase				:		Optional[Any]												=				None
						__lowercase				:		Tuple												=				None



				def       snake_case    (     self					:	Optional[Any]    ,   lowercase__					:	List[str]						):
						if self.val:
								if val < self.val:
										if self.left is None:
												__lowercase				:		Tuple												=				Node(lowercase__						)
										else:
												self.left.insert(lowercase__						)
								elif val > self.val:
										if self.right is None:
												__lowercase				:		Any												=				Node(lowercase__						)
										else:
												self.right.insert(lowercase__						)
						else:
								__lowercase				:		Optional[Any]												=				val





def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->Any:






		"""simple docstring"""


		if root:
				inorder(root.left,  _lowerCamelCase				)
				res.append(root.val				)
				inorder(root.right,  _lowerCamelCase				)

def 						snake_case__       (					_lowerCamelCase				)			->Optional[Any]:






		"""simple docstring"""


		if len(_lowerCamelCase				) == 0:
				return arr
		__lowercase				:		int												=				Node(arr[0]				)
		for i in range(1,  len(_lowerCamelCase				)				):
				root.insert(arr[i]				)
		# Traverse BST in order.
		__lowercase				:		Tuple												=				[]
		inorder(_lowerCamelCase,  _lowerCamelCase				)
		return res


if __name__ == "__main__":
						print(tree_sort([1_0, 1, 3, 2, 9, 1_4, 1_3]))
