





def lowerCAmelCase__(__snake_case	,__snake_case							)    ->				Any:







	'''simple docstring'''







	if not root or root not in binary_tree_mirror_dictionary:
		return
	lowerCamelCase__    ,     lowerCamelCase__        =		binary_tree_mirror_dictionary[root][:2]
	lowerCamelCase__        =		[right_child, left_child]
	binary_tree_mirror_dict(_lowerCAmelCase	,_lowerCAmelCase							)
	binary_tree_mirror_dict(_lowerCAmelCase	,_lowerCAmelCase							)





def lowerCAmelCase__(__snake_case	,__snake_case = 1							)    ->				List[Any]:







	'''simple docstring'''







	if not binary_tree:
		raise ValueError('''binary tree cannot be empty'''							)
	if root not in binary_tree:
		lowerCamelCase__        =		F'root {root} is not present in the binary_tree'
		raise ValueError(_lowerCAmelCase							)
	lowerCamelCase__        =		dict(_lowerCAmelCase							)
	binary_tree_mirror_dict(_lowerCAmelCase	,_lowerCAmelCase							)
	return binary_tree_mirror_dictionary


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










from __future__ import annotations

import math
import random





def lowerCAmelCase__(__snake_case	,__snake_case	,__snake_case							)    ->				list[int]:







	'''simple docstring'''







	lowerCamelCase__        =		d * e - 1
	lowerCamelCase__        =		0
	lowerCamelCase__        =		0
	while p == 0:
		lowerCamelCase__        =		random.randint(2	,n - 1							)
		lowerCamelCase__        =		k
		while True:
			if t % 2 == 0:
				lowerCamelCase__        =		t // 2
				lowerCamelCase__        =		(g**t) % n
				lowerCamelCase__        =		math.gcd(x - 1	,__snake_case							)
				if x > 1 and y > 1:
					lowerCamelCase__        =		y
					lowerCamelCase__        =		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()



