


from __future__ import annotations

__UpperCamelCase					:	List[str]          =				[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]





class 			lowerCAmelCase__:






    '''simple docstring'''





    def __init__(						self					: Any							, __snake_case					: int						):





       '''simple docstring'''
       UpperCAmelCase_				:   int							= -1
       UpperCAmelCase_				:   int							= -1
       UpperCAmelCase_				:   list[int]							= [-1] * length
       UpperCAmelCase_				:   Node | None							= None
       UpperCAmelCase_				:   Node | None							= None





    def __repr__(						self					: Optional[Any]						):





       '''simple docstring'''
       return f'''Node(min_value={self.minn} max_value={self.maxx})'''





def   snake_case_    (			__lowercase							):
   UpperCAmelCase_				:   Optional[int]							= Node(len(_lowercase							)							)
   UpperCAmelCase_				:   str							= min(_lowercase							), max(_lowercase							)
   # Leaf node case where the node contains only one unique value
   if root.minn == root.maxx:
      return root
   UpperCAmelCase_				:   Any							= (root.minn + root.maxx) // 2

   UpperCAmelCase_				:   list[int]							= []
   UpperCAmelCase_				:   list[int]							= []

   for index, num in enumerate(_lowercase							):
      if num <= pivot:
         left_arr.append(_lowercase							)
      else:
         right_arr.append(_lowercase							)
      UpperCAmelCase_				:   Dict							= len(_lowercase							)
   UpperCAmelCase_				:   Union[str, Any]							= build_tree(_lowercase							)
   UpperCAmelCase_				:   Dict							= build_tree(_lowercase							)
   return root
def   snake_case_    (			__lowercase      ,							__lowercase      ,							__lowercase							):






   if index < 0 or node is None:
      return 0
   # Leaf node cases
   if node.minn == node.maxx:
      return index + 1 if node.minn == num else 0
   UpperCAmelCase_				:   Tuple							= (node.minn + node.maxx) // 2
   if num <= pivot:
      # go the left subtree and map index to the left subtree
      return rank_till_index(node.left      ,							_lowercase      ,							node.map_left[index] - 1							)
   else:
      # go to the right subtree and map index to the right subtree
      return rank_till_index(node.right      ,							_lowercase      ,							index - node.map_left[index]							)
def   snake_case_    (			__lowercase      ,							__lowercase      ,							__lowercase      ,							__lowercase							):






   if start > end:
      return 0
   UpperCAmelCase_				:   str							= rank_till_index(_lowercase      ,							_lowercase      ,							_lowercase							)
   UpperCAmelCase_				:   Optional[int]							= rank_till_index(_lowercase      ,							_lowercase      ,							start - 1							)
   return rank_till_end - rank_before_start
def   snake_case_    (			__lowercase      ,							__lowercase      ,							__lowercase      ,							__lowercase							):






   if index > (end - start) or start > end or node is None:
      return -1
   # Leaf node case
   if node.minn == node.maxx:
      return node.minn
   # Number of elements in the left subtree in interval [start, end]
   UpperCAmelCase_				:   str							= node.map_left[end] - (
       node.map_left[start - 1] if start else 0
   )
   if num_elements_in_left_tree > index:
      return quantile(
          node.left      ,							_lowercase      ,							(node.map_left[start - 1] if start else 0)      ,							node.map_left[end] - 1      ,							)
   else:
      return quantile(
          node.right      ,							index - num_elements_in_left_tree      ,							start - (node.map_left[start - 1] if start else 0)      ,							end - node.map_left[end]      ,							)
def   snake_case_    (			__lowercase      ,							__lowercase      ,							__lowercase      ,							__lowercase      ,							__lowercase							):






   if (
       start > end
       or node is None
       or start_num > end_num
       or node.minn > end_num
       or node.maxx < start_num
   ):
      return 0
   if start_num <= node.minn and node.maxx <= end_num:
      return end - start + 1
   UpperCAmelCase_				:   Dict							= range_counting(
       node.left      ,							(node.map_left[start - 1] if start else 0)      ,							node.map_left[end] - 1      ,							_lowercase      ,							_lowercase      ,							)
   UpperCAmelCase_				:   Optional[Any]							= range_counting(
       node.right      ,							start - (node.map_left[start - 1] if start else 0)      ,							end - node.map_left[end]      ,							_lowercase      ,							_lowercase      ,							)
   return left + right


if __name__ == "__main__":
       import doctest

       doctest.testmod()



'''simple docstring'''



def       _a      (		_lowercase   :      list    ):





     '''simple docstring'''






     if len(_lowercase    ) <= 1:
          return data
     else:
          return [
              *quick_sort([e for e in data[1:] if e <= data[0]]    ),
              data[0],
              *quick_sort([e for e in data[1:] if e > data[0]]    ),
          ]


if __name__ == "__main__":
      import doctest

      doctest.testmod()