






def   lowercase__   (  __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[Any]   =		[True for i in range(n + 1						)]
					UpperCAmelCase_					:   Union[str, Any]   =		[i - 1 for i in range(n + 1						)]
					UpperCAmelCase_					:   List[str]   =		[]
					for i in range(2  , n + 1						):
										if is_prime[i]:
															primes.append(__snake_case						)
										for j in range(0  , len(__snake_case						)						):
															if i * primes[j] >= n:
																				break
															UpperCAmelCase_					:   Any   =		False

															if i % primes[j] == 0:
																				UpperCAmelCase_					:   Dict   =		totients[i] * primes[j]
																				break

															UpperCAmelCase_					:   int   =		totients[i] * (primes[j] - 1)

					return totients


if __name__ == "__main__":
		import doctest

		doctest.testmod()














from __future__ import annotations



class 						lowerCamelCase   :







		'''simple docstring'''



		def __init__(							self       ,	_UpperCamelCase = 0     )			->							None:
							UpperCAmelCase_					:   int   =		value
							UpperCAmelCase_					:   Node | None   =		None
							UpperCAmelCase_					:   Node | None   =		None





def   lowercase__   (  __snake_case					:							Node | None  , __snake_case					:							Node | None						):


					'''simple docstring'''


					if treea is None:
										return treea
					if treea is None:
										return treea

					UpperCAmelCase_					:   List[Any]   =		treea.value + treea.value
					UpperCAmelCase_					:   Dict   =		merge_two_binary_trees(treea.left  , treea.left						)
					UpperCAmelCase_					:   str   =		merge_two_binary_trees(treea.right  , treea.right						)
					return treea




def   lowercase__   (  __snake_case					:							Node | None						):


					'''simple docstring'''


					if root:
										print(root.value						)
										print_preorder(root.left						)
										print_preorder(root.right						)


if __name__ == "__main__":
		__UpperCAmelCase										=		Node(1)
		__UpperCAmelCase										=		Node(2)
		__UpperCAmelCase										=		Node(3)
		__UpperCAmelCase										=		Node(4)

		__UpperCAmelCase										=		Node(2)
		__UpperCAmelCase										=		Node(4)
		__UpperCAmelCase										=		Node(6)
		__UpperCAmelCase										=		Node(9)
		__UpperCAmelCase										=		Node(5)

		print('Tree1 is: ')
		print_preorder(treea)
		print('Tree2 is: ')
		print_preorder(treea)
		__UpperCAmelCase										=		merge_two_binary_trees(treea, treea)
		print('Merged Tree is: ')
		print_preorder(merged_tree)






