






__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]












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()




