code: 
  
  
  
  
  
  '''simple docstring'''
  
  from __future__ import annotations
  
  lowercase_       =				[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				,	A )	->     None:
          _SCREAMING_SNAKE_CASE             =    -1
          _SCREAMING_SNAKE_CASE             =    -1
          _SCREAMING_SNAKE_CASE             =    [-1] * length
          _SCREAMING_SNAKE_CASE             =    None
          _SCREAMING_SNAKE_CASE             =    None
  
  
  
  
  
      def __repr__(	self )	->     str:
          return f'Node(min_value={self.minn} max_value={self.maxx})'
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					list[int]					)		->Node | None:
      _SCREAMING_SNAKE_CASE             =    Node(len(__lowerCamelCase					)					)
      _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE             =    min(__lowerCamelCase					), max(__lowerCamelCase					)
      # Leaf node case where the node contains only one unique value
      if root.minn == root.maxx:
          return root
      _SCREAMING_SNAKE_CASE             =    (root.minn + root.maxx) // 2
  
      _SCREAMING_SNAKE_CASE             =    []
      _SCREAMING_SNAKE_CASE             =    []
  
      for index, num in enumerate(__lowerCamelCase					):
          if num <= pivot:
              left_arr.append(__lowerCamelCase					)
          else:
              right_arr.append(__lowerCamelCase					)
          _SCREAMING_SNAKE_CASE             =    len(__lowerCamelCase					)
      _SCREAMING_SNAKE_CASE             =    build_tree(__lowerCamelCase					)
      _SCREAMING_SNAKE_CASE             =    build_tree(__lowerCamelCase					)
      return root
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					Node | None      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int					)		->int:
      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
      _SCREAMING_SNAKE_CASE             =    (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      , __lowerCamelCase      , node.map_left[index] - 1					)
      else:
          # go to the right subtree and map index to the right subtree
          return rank_till_index(node.right      , __lowerCamelCase      , index - node.map_left[index]					)
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					Node | None      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int					)		->int:
      if start > end:
          return 0
      _SCREAMING_SNAKE_CASE             =    rank_till_index(__lowerCamelCase      , __lowerCamelCase      , __lowerCamelCase					)
      _SCREAMING_SNAKE_CASE             =    rank_till_index(__lowerCamelCase      , __lowerCamelCase      , start - 1					)
      return rank_till_end - rank_before_start
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					Node | None      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int					)		->int:
      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]
      _SCREAMING_SNAKE_CASE             =    node.map_left[end] - (
          node.map_left[start - 1] if start else 0
      )
      if num_elements_in_left_tree > index:
          return quantile(
              node.left      , __lowerCamelCase      , (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 lowerCamelCase		(  __lowerCamelCase				:					Node | None      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int					)		->int:
      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
      _SCREAMING_SNAKE_CASE             =    range_counting(
          node.left      , (node.map_left[start - 1] if start else 0)      , node.map_left[end] - 1      , __lowerCamelCase      , __lowerCamelCase      , )
      _SCREAMING_SNAKE_CASE             =    range_counting(
          node.right      , start - (node.map_left[start - 1] if start else 0)      , end - node.map_left[end]      , __lowerCamelCase      , __lowerCamelCase      , )
      return left + right
  
  
  if __name__ == "__main__":
        import doctest
  
        doctest.testmod()
  
  
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  import safs
  
  
  class       a_  (       safs.SaFileSystem ):
  
      '''simple docstring'''
  
  
  
  