




def  snake_case_					(		SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )      ->			Union[str, Any]:
							if not root or root not in binary_tree_mirror_dictionary:
														return
							lowercase__ ,       lowercase__  :	List[Any]        =							binary_tree_mirror_dictionary[root][:2]
							lowercase__  :	Optional[int]        =							[right_child, left_child]
							binary_tree_mirror_dict(SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )
							binary_tree_mirror_dict(SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )
def  snake_case_					(		SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_ = 1    )      ->			dict:
							if not binary_tree:
														raise ValueError("binary tree cannot be empty"    )
							if root not in binary_tree:
														lowercase__  :	Any        =							F"""root {root} is not present in the binary_tree"""
														raise ValueError(SCREAMING_SNAKE_CASE_    )
							lowercase__  :	int        =							dict(SCREAMING_SNAKE_CASE_    )
							binary_tree_mirror_dict(SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )
							return binary_tree_mirror_dictionary


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





from __future__ import annotations

import math
import random
def  snake_case_					(		SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )      ->			list[int]:
							lowercase__  :	List[Any]        =							d * e - 1
							lowercase__  :	Any        =							0
							lowercase__  :	Dict        =							0
							while p == 0:
														lowercase__  :	Dict        =							random.randint(2    ,n - 1    )
														lowercase__  :	int        =							k
														while True:
																					if t % 2 == 0:
																												lowercase__  :	str        =							t // 2
																												lowercase__  :	int        =							(g**t) % n
																												lowercase__  :	List[Any]        =							math.gcd(x - 1    ,SCREAMING_SNAKE_CASE_    )
																												if x > 1 and y > 1:
																																			lowercase__  :	Any        =							y
																																			lowercase__  :	Optional[int]        =							n // y
																																			break  # find the correct factors
																					else:
																												break  # t is not divisible by 2, break and choose another g
							return sorted([p, q]    )


if __name__ == "__main__":
						import doctest

						doctest.testmod()