


def      lowerCAmelCase	(						lowerCAmelCase_	,				lowerCAmelCase_	)->	Union[str, Any]:



				if not root or root not in binary_tree_mirror_dictionary:
								return
				lowerCAmelCase_			,					lowerCAmelCase_	: Dict      			=			binary_tree_mirror_dictionary[root][:2]
				lowerCAmelCase_	: Any      			=			[right_child, left_child]
				binary_tree_mirror_dict(lowerCAmelCase_	,				lowerCAmelCase_	)
				binary_tree_mirror_dict(lowerCAmelCase_	,				lowerCAmelCase_	)



def      lowerCAmelCase	(						lowerCAmelCase_	,				lowerCAmelCase_ = 1	)->	int:



				if not binary_tree:
								raise ValueError('''binary tree cannot be empty'''	)
				if root not in binary_tree:
								lowerCAmelCase_	: Union[str, Any]      			=			f"""root {root} is not present in the binary_tree"""
								raise ValueError(lowerCAmelCase_	)
				lowerCAmelCase_	: Optional[int]      			=			dict(lowerCAmelCase_	)
				binary_tree_mirror_dict(lowerCAmelCase_	,				lowerCAmelCase_	)
				return binary_tree_mirror_dictionary


if __name__ == "__main__":
						_UpperCAmelCase     :					Any       ={1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
						print(f"""Binary tree: {binary_tree}""")
						_UpperCAmelCase     :					Any       =binary_tree_mirror(binary_tree, 5)
						print(f"""Binary tree mirror: {binary_tree_mirror_dictionary}""")



from __future__ import annotations



def      lowerCAmelCase	(						lowerCAmelCase_	,				lowerCAmelCase_	,				lowerCAmelCase_	)->	int | float:
				if len(lowerCAmelCase_	) == 0:
								raise ValueError('''find_min() arg is an empty sequence'''	)
				if (
				    left >= len(lowerCAmelCase_	)
				    or left < -len(lowerCAmelCase_	)
				    or right >= len(lowerCAmelCase_	)
				    or right < -len(lowerCAmelCase_	)
				):
								raise IndexError('''list index out of range'''	)
				if left == right:
								return nums[left]
				lowerCAmelCase_	: Any      			=			(left + right) >> 1  # the middle
				lowerCAmelCase_	: Tuple      			=			find_min(lowerCAmelCase_	,				lowerCAmelCase_	,				lowerCAmelCase_	)  # find min in range[left, mid]
				lowerCAmelCase_	: Any      			=			find_min(lowerCAmelCase_	,				mid + 1	,				lowerCAmelCase_	)  # find min in range[mid + 1, right]

				return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)