




class 	UpperCamelCase__			:

    '''simple docstring'''



    def __init__(					self  )  ->   Tuple:
           lowerCamelCase     :   Dict    				=      [0]
           lowerCamelCase     :   Union[str, Any]    				=      0







    def 					_lowercase  (					self  ,						UpperCamelCase__  )  ->   None:
           lowerCamelCase     :   Tuple    				=      self.__heap[i]
           while i // 2 > 0:
                  if self.__heap[i] > self.__heap[i // 2]:
                         lowerCamelCase     :   int    				=      self.__heap[i // 2]
                         lowerCamelCase     :   Any    				=      temporary
                  i //= 2







    def 					_lowercase  (					self  ,						UpperCamelCase__  )  ->   None:
           self.__heap.append(UpperCamelCase__  )
           self.__size += 1
           self.__swap_up(self.__size  )







    def 					_lowercase  (					self  ,						UpperCamelCase__  )  ->   None:
           while self.__size >= 2 * i:
                  if 2 * i + 1 > self.__size:
                         lowerCamelCase     :   int    				=      2 * i
                  else:
                         if self.__heap[2 * i] > self.__heap[2 * i + 1]:
                                lowerCamelCase     :   List[Any]    				=      2 * i
                         else:
                                lowerCamelCase     :   int    				=      2 * i + 1
                  lowerCamelCase     :   Tuple    				=      self.__heap[i]
                  if self.__heap[i] < self.__heap[bigger_child]:
                         lowerCamelCase     :   str    				=      self.__heap[bigger_child]
                         lowerCamelCase     :   Tuple    				=      temporary
                  lowerCamelCase     :   Optional[Any]    				=      bigger_child







    def 					_lowercase  (					self  )  ->   int:
           lowerCamelCase     :   List[str]    				=      self.__heap[1]
           lowerCamelCase     :   Optional[Any]    				=      self.__heap[self.__size]
           self.__size -= 1
           self.__heap.pop()
           self.__swap_down(1  )
           return max_value







    @property
    def 					_lowercase  (					self  )  ->   Dict:
           return self.__heap[1:]







    def __len__(					self  )  ->   Any:
           return self.__size


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       # create an instance of BinaryHeap
       SCREAMING_SNAKE_CASE__ :   List[str]						=     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

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				list:
       lowerCamelCase     :   int    				=      [None] * (len(_SCREAMING_SNAKE_CASE					) + len(_SCREAMING_SNAKE_CASE					))

       lowerCamelCase     :   Any    				=      0  # pointer to current index for left Half
       lowerCamelCase     :   int    				=      0  # pointer to current index for the right Half
       lowerCamelCase     :   Optional[int]    				=      0  # pointer to current index for the sorted array Half

       while pointera < len(_SCREAMING_SNAKE_CASE					) and pointera < len(_SCREAMING_SNAKE_CASE					):
              if left_half[pointera] < right_half[pointera]:
                     lowerCamelCase     :   Any    				=      left_half[pointera]
                     pointera += 1
                     index += 1
              else:
                     lowerCamelCase     :   Any    				=      right_half[pointera]
                     pointera += 1
                     index += 1
       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   Optional[Any]    				=      left_half[pointera]
              pointera += 1
              index += 1

       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   str    				=      right_half[pointera]
              pointera += 1
              index += 1

       return sorted_array

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list:
       if len(_SCREAMING_SNAKE_CASE					) <= 1:
              return array
       # the actual formula to calculate the middle element = left + (right - left) // 2
       # this avoids integer overflow in case of large N
       lowerCamelCase     :   int    				=      0 + (len(_SCREAMING_SNAKE_CASE					) - 0) // 2

       # Split the array into halves till the array length becomes equal to One
       # merge the arrays of single length returned by mergeSort function and
       # pass them into the merge arrays function which merges the array
       lowerCamelCase     :   Optional[Any]    				=      array[:middle]
       lowerCamelCase     :   Optional[Any]    				=      array[middle:]

       return merge(merge_sort(_SCREAMING_SNAKE_CASE					)				,merge_sort(_SCREAMING_SNAKE_CASE					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






