
class  _lowerCamelCase			:

     def __init__(  self    ):
            __snake_case						       =   [0]
            __snake_case						       =   0

     def 						__lowerCamelCase				(  self							,       SCREAMING_SNAKE_CASE_    ):
            __snake_case						       =   self.__heap[i]
            while i // 2 > 0:
                   if self.__heap[i] > self.__heap[i // 2]:
                          __snake_case						       =   self.__heap[i // 2]
                          __snake_case						       =   temporary
                   i //= 2

     def 						__lowerCamelCase				(  self							,       SCREAMING_SNAKE_CASE_    ):
            self.__heap.append(SCREAMING_SNAKE_CASE_    )
            self.__size += 1
            self.__swap_up(self.__size    )

     def 						__lowerCamelCase				(  self							,       SCREAMING_SNAKE_CASE_    ):
            while self.__size >= 2 * i:
                   if 2 * i + 1 > self.__size:
                          __snake_case						       =   2 * i
                   else:
                          if self.__heap[2 * i] > self.__heap[2 * i + 1]:
                                 __snake_case						       =   2 * i
                          else:
                                 __snake_case						       =   2 * i + 1
                   __snake_case						       =   self.__heap[i]
                   if self.__heap[i] < self.__heap[bigger_child]:
                          __snake_case						       =   self.__heap[bigger_child]
                          __snake_case						       =   temporary
                   __snake_case						       =   bigger_child

     def 						__lowerCamelCase				(  self    ):
            __snake_case						       =   self.__heap[1]
            __snake_case						       =   self.__heap[self.__size]
            self.__size -= 1
            self.__heap.pop()
            self.__swap_down(1    )
            return max_value

     @property
     def 						__lowerCamelCase				(  self    ):
            return self.__heap[1:]

     def __len__(  self    ):
            return self.__size


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 # create an instance of BinaryHeap
 lowerCamelCase_				:							Union[str, Any]       =    BinaryHeap()
 binary_heap.insert(6)
 binary_heap.insert(10)
 binary_heap.insert(15)
 binary_heap.insert(12)
 # pop root(max-values because it is max heap)
 print(binary_heap.pop())  # 15
 print(binary_heap.pop())  # 12
 # get the list and size after operations
 print(binary_heap.get_list)
 print(len(binary_heap))


from __future__ import annotations







class  _lowerCamelCase			:

     def __init__(  self							,       SCREAMING_SNAKE_CASE_ = 0    ):
            __snake_case						       =   value
            __snake_case						       =   None
            __snake_case						       =   None





def        __lowercase(							__snake_case				:		Node | None    ,__snake_case				:		Node | None					)       ->   Node | None:
       if treea is None:
              return treea
       if treea is None:
              return treea

       __snake_case						       =   treea.value + treea.value
       __snake_case						       =   merge_two_binary_trees(treea.left    ,treea.left					)
       __snake_case						       =   merge_two_binary_trees(treea.right    ,treea.right					)
       return treea
def        __lowercase(							__snake_case				:		Node | None					)       ->   None:
       if root:
              print(root.value					)
              print_preorder(root.left					)
              print_preorder(root.right					)


if __name__ == "__main__":
 lowerCamelCase_				:							int       =    Node(1)
 lowerCamelCase_				:							Tuple       =    Node(2)
 lowerCamelCase_				:							Tuple       =    Node(3)
 lowerCamelCase_				:							int       =    Node(4)

 lowerCamelCase_				:							Tuple       =    Node(2)
 lowerCamelCase_				:							List[Any]       =    Node(4)
 lowerCamelCase_				:							List[Any]       =    Node(6)
 lowerCamelCase_				:							Optional[Any]       =    Node(9)
 lowerCamelCase_				:							List[str]       =    Node(5)

 print("Tree1 is: ")
 print_preorder(treea)
 print("Tree2 is: ")
 print_preorder(treea)
 lowerCamelCase_				:							int       =    merge_two_binary_trees(treea, treea)
 print("Merged Tree is: ")
 print_preorder(merged_tree)
