


from __future__ import annotations

lowerCAmelCase__						=			[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			,						__lowerCamelCase)      ->    Any:
            _A				:	Optional[int]       =			-1
            _A				:	int       =			-1
            _A				:	Optional[Any]       =			[-1] * length
            _A				:	Optional[Any]       =			None
            _A				:	int       =			None


     def __repr__(						self)      ->    List[str]:
            return F"Node(min_value={self.minn} max_value={self.maxx})"





def 							_UpperCAmelCase    (UpperCamelCase__					:  Optional[int]						):
       _A				:	Optional[int]       =			Node(len(UpperCamelCase__						)						)
       _A   ,      _A				:	List[str]       =			min(UpperCamelCase__						), max(UpperCamelCase__						)
       # Leaf node case where the node contains only one unique value
       if root.minn == root.maxx:
              return root
       _A				:	Optional[int]       =			(root.minn + root.maxx) // 2

       _A				:	Tuple       =			[]
       _A				:	int       =			[]

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





def 							_UpperCAmelCase    (UpperCamelCase__					:  Tuple    ,							UpperCamelCase__					:  Union[str, Any]    ,							UpperCamelCase__					:  Dict						):







       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
       _A				:	str       =			(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    ,							UpperCamelCase__    ,							node.map_left[index] - 1						)
       else:
              # go to the right subtree and map index to the right subtree
              return rank_till_index(node.right    ,							UpperCamelCase__    ,							index - node.map_left[index]						)





def 							_UpperCAmelCase    (UpperCamelCase__					:  Any    ,							UpperCamelCase__					:  Optional[Any]    ,							UpperCamelCase__					:  List[str]    ,							UpperCamelCase__					:  Optional[Any]						):







       if start > end:
              return 0
       _A				:	int       =			rank_till_index(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)
       _A				:	str       =			rank_till_index(UpperCamelCase__    ,							UpperCamelCase__    ,							start - 1						)
       return rank_till_end - rank_before_start





def 							_UpperCAmelCase    (UpperCamelCase__					:  Any    ,							UpperCamelCase__					:  List[str]    ,							UpperCamelCase__					:  Optional[int]    ,							UpperCamelCase__					:  List[Any]						):







       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]
       _A				:	Dict       =			node.map_left[end] - (
           node.map_left[start - 1] if start else 0
       )
       if num_elements_in_left_tree > index:
              return quantile(
                  node.left    ,							UpperCamelCase__    ,							(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 							_UpperCAmelCase    (UpperCamelCase__					:  str    ,							UpperCamelCase__					:  Any    ,							UpperCamelCase__					:  int    ,							UpperCamelCase__					:  Any    ,							UpperCamelCase__					:  str						):







       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
       _A				:	Any       =			range_counting(
           node.left    ,							(node.map_left[start - 1] if start else 0)    ,							node.map_left[end] - 1    ,							UpperCamelCase__    ,							UpperCamelCase__    ,							)
       _A				:	List[str]       =			range_counting(
           node.right    ,							start - (node.map_left[start - 1] if start else 0)    ,							end - node.map_left[end]    ,							UpperCamelCase__    ,							UpperCamelCase__    ,							)
       return left + right


if __name__ == "__main__":
    import doctest

    doctest.testmod()




def 							_UpperCAmelCase    (UpperCamelCase__					:  str						):
       _A				:	Tuple       =			str(UpperCamelCase__						).strip()
       if not bin_string:
              raise ValueError("Empty string was passed to the function"						)
       _A				:	Dict       =			bin_string[0] == "-"
       if is_negative:
              _A				:	Any       =			bin_string[1:]
       if not all(char in "01" for char in bin_string						):
              raise ValueError("Non-binary value was passed to the function"						)
       _A				:	Union[str, Any]       =			0
       for char in bin_string:
              _A				:	Union[str, Any]       =			2 * decimal_number + int(UpperCamelCase__						)
       return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
    from doctest import testmod

    testmod()
