code: 
  
  
  
  
  
  
  __A  							=  [0.485, 0.456, 0.406]
  __A  							=  [0.229, 0.224, 0.225]
  __A  							=  [0.5, 0.5, 0.5]
  __A  							=  [0.5, 0.5, 0.5]
  __A  							=  [0.4814_5466, 0.457_8275, 0.4082_1073]
  __A  							=  [0.2686_2954, 0.2613_0258, 0.2757_7711]
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  __A  							=  [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
  
  
  
  class 							_A :
      """simple docstring"""
  
      def __init__(							self			:    List[str]   ,    __SCREAMING_SNAKE_CASE			:    int			)			->       None:
             __UpperCAmelCase    							=-1
             __UpperCAmelCase    							=-1
             __UpperCAmelCase    							=[-1] * length
             __UpperCAmelCase    							=None
             __UpperCAmelCase    							=None
  
  
  
      def __repr__(							self			:    Optional[int]			)			->       str:
             return f'''Node(min_value={self.minn} max_value={self.maxx})'''
  
  
  
  
  
  
  
  def 			lowercase__  (				A_:	list[int]		)  ->							Node | None:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         __UpperCAmelCase    							=Node(len(A_		)		)
         __UpperCAmelCase							,   __UpperCAmelCase    							=min(A_		), max(A_		)
         # Leaf node case where the node contains only one unique value
         if root.minn == root.maxx:
                return root
         __UpperCAmelCase    							=(root.minn + root.maxx) // 2
  
         __UpperCAmelCase    							=[]
         __UpperCAmelCase    							=[]
  
         for index, num in enumerate(A_		):
                if num <= pivot:
                       left_arr.append(A_		)
                else:
                       right_arr.append(A_		)
                __UpperCAmelCase    							=len(A_		)
         __UpperCAmelCase    							=build_tree(A_		)
         __UpperCAmelCase    							=build_tree(A_		)
         return root
  
  
  
  
  
  
  
  def 			lowercase__  (				A_:	Node | None     ,			A_:	int     ,			A_:	int		)  ->							int:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         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    							=(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     ,			A_     ,			node.map_left[index] - 1		)
         else:
                # go to the right subtree and map index to the right subtree
                return rank_till_index(node.right     ,			A_     ,			index - node.map_left[index]		)
  
  
  
  
  
  
  
  def 			lowercase__  (				A_:	Node | None     ,			A_:	int     ,			A_:	int     ,			A_:	int		)  ->							int:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         if start > end:
                return 0
         __UpperCAmelCase    							=rank_till_index(A_     ,			A_     ,			A_		)
         __UpperCAmelCase    							=rank_till_index(A_     ,			A_     ,			start - 1		)
         return rank_till_end - rank_before_start
  
  
  
  
  
  
  
  def 			lowercase__  (				A_:	Node | None     ,			A_:	int     ,			A_:	int     ,			A_:	int		)  ->							int:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         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    							=node.map_left[end] - (
             node.map_left[start - 1] if start else 0
         )
         if num_elements_in_left_tree > index:
                return quantile(
                    node.left     ,			A_     ,			(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 			lowercase__  (				A_:	Node | None     ,			A_:	int     ,			A_:	int     ,			A_:	int     ,			A_:	int		)  ->							int:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         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    							=range_counting(
             node.left     ,			(node.map_left[start - 1] if start else 0)     ,			node.map_left[end] - 1     ,			A_     ,			A_     ,			)
         __UpperCAmelCase    							=range_counting(
             node.right     ,			start - (node.map_left[start - 1] if start else 0)     ,			end - node.map_left[end]     ,			A_     ,			A_     ,			)
         return left + right
  
  
  if __name__ == "__main__":
     import doctest
  
     doctest.testmod()
  
  
  
  
  