


from __future__ import annotations

_snake_case				=			[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       :			Tuple							,     _a       :			Union[str, Any]					)     ->      List[str]:
      UpperCAmelCase    :					int			=      -1
      UpperCAmelCase    :					int			=      -1
      UpperCAmelCase    :					list[int]			=      [-1] * length
      UpperCAmelCase    :					Node | None			=      None
      UpperCAmelCase    :					Node | None			=      None

 def __repr__(      self       :			str					)     ->      Union[str, Any]:
      return f'Node(min_value={self.minn} max_value={self.maxx})'







def 	A (		A__			):
     UpperCAmelCase    :					List[str]			=      Node(len(lowerCamelCase_			)			)
     UpperCAmelCase    :					Any			=      min(lowerCamelCase_			), max(lowerCamelCase_			)
     # Leaf node case where the node contains only one unique value
     if root.minn == root.maxx:
          return root
     UpperCAmelCase    :					str			=      (root.minn + root.maxx) // 2

     UpperCAmelCase    :					list[int]			=      []
     UpperCAmelCase    :					list[int]			=      []

     for index, num in enumerate(lowerCamelCase_			):
          if num <= pivot:
               left_arr.append(lowerCamelCase_			)
          else:
               right_arr.append(lowerCamelCase_			)
          UpperCAmelCase    :					Tuple			=      len(lowerCamelCase_			)
     UpperCAmelCase    :					Optional[Any]			=      build_tree(lowerCamelCase_			)
     UpperCAmelCase    :					Optional[Any]			=      build_tree(lowerCamelCase_			)
     return root







def 	A (		A__		,		A__		,		A__			):





     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    :					Any			=      (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 	A (		A__		,		A__		,		A__		,		A__			):





     if start > end:
          return 0
     UpperCAmelCase    :					int			=      rank_till_index(lowerCamelCase_		,		lowerCamelCase_		,		lowerCamelCase_			)
     UpperCAmelCase    :					List[Any]			=      rank_till_index(lowerCamelCase_		,		lowerCamelCase_		,		start - 1			)
     return rank_till_end - rank_before_start







def 	A (		A__		,		A__		,		A__		,		A__			):





     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    :					Tuple			=      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 	A (		A__		,		A__		,		A__		,		A__		,		A__			):





     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    :					Any			=      range_counting(
         node.left		,		(node.map_left[start - 1] if start else 0)		,		node.map_left[end] - 1		,		lowerCamelCase_		,		lowerCamelCase_		,		)
     UpperCAmelCase    :					List[str]			=      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()




'''simple docstring'''


def    _lowerCamelCase       ( lowerCamelCase_   :				list  ):



     """simple docstring"""





     UpperCAmelCase_				:  Optional[int]  = len(lowerCamelCase_  )

     # Set the gap value to be decreased by a factor of 1.3
     # after each iteration
     UpperCAmelCase_				:  Optional[Any]  = 1.3

     # Continue sorting until the gap is 1
     while gap > 1:
          # Decrease the gap value
          UpperCAmelCase_				:  Optional[Any]  = int(gap / shrink  )

          # Sort the elements using insertion sort
          for i in range(lowerCamelCase_      ,	len(lowerCamelCase_  )  ):
               UpperCAmelCase_				:  Optional[int]  = collection[i]
               UpperCAmelCase_				:  Tuple  = i
               while j >= gap and collection[j - gap] > temp:
                    UpperCAmelCase_				:  Tuple  = collection[j - gap]
                    j -= gap
               UpperCAmelCase_				:  Optional[int]  = temp

     return collection


if __name__ == "__main__":
 import doctest

 doctest.testmod()






