

UpperCAmelCase__	:       dict[str, float]			      =      {
    "kilogram": 1,
    "gram": pow(10, 3),
    "milligram": pow(10, 6),
    "metric-ton": pow(10, -3),
    "long-ton": 0.00_09_84_20_73,
    "short-ton": 0.00_11_02_31_22,
    "pound": 2.20_46_24_42_02,
    "stone": 0.15_74_73_17_28,
    "ounce": 35.2_73_99_07_23,
    "carrat": 5_000,
    "atomic-mass-unit": 6.0_22_13_66_52E26,
}

UpperCAmelCase__	:       dict[str, float]			      =      {
    "kilogram": 1,
    "gram": pow(10, -3),
    "milligram": pow(10, -6),
    "metric-ton": pow(10, 3),
    "long-ton": 10_16.0_46_08,
    "short-ton": 9_07.1_84,
    "pound": 0.45_35_92,
    "stone": 6.3_50_29,
    "ounce": 0.0_28_34_95,
    "carrat": 0.00_02,
    "atomic-mass-unit": 1.6_60_54_01_99E-27,
}






def    __lowercase (       _A  ,      _A  ,      _A     )       ->  float:
      if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
            SCREAMING_SNAKE_CASE	: Any					       =				(
                F"Invalid 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
                F"Supported values are: {', '.join(_A     )}"
            )
            raise ValueError(_A     )
      return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]


if __name__ == "__main__":
  import doctest

  doctest.testmod()







from __future__ import annotations

UpperCAmelCase__	:       Optional[int]			      =      [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      :	Optional[Any]			,			UpperCAmelCase__      :	int						)   ->None:
        """simple docstring"""







        SCREAMING_SNAKE_CASE	: int					       =				-1
        SCREAMING_SNAKE_CASE	: int					       =				-1
        SCREAMING_SNAKE_CASE	: list[int]					       =				[-1] * length
        SCREAMING_SNAKE_CASE	: Node | None					       =				None
        SCREAMING_SNAKE_CASE	: Node | None					       =				None




  def __repr__(     self      :	Dict						)   ->str:
        """simple docstring"""







        return f"Node(min_value={self.minn} max_value={self.maxx})"






def    __lowercase (       _A     )       ->  Node | None:
      SCREAMING_SNAKE_CASE	: Tuple					       =				Node(len(_A     )     )
      SCREAMING_SNAKE_CASE       ,		SCREAMING_SNAKE_CASE	: int					       =				min(_A     ), max(_A     )
      # Leaf node case where the node contains only one unique value
      if root.minn == root.maxx:
            return root
      SCREAMING_SNAKE_CASE	: int					       =				(root.minn + root.maxx) // 2

      SCREAMING_SNAKE_CASE	: list[int]					       =				[]
      SCREAMING_SNAKE_CASE	: list[int]					       =				[]

      for index, num in enumerate(_A     ):
            if num <= pivot:
                  left_arr.append(_A     )
            else:
                  right_arr.append(_A     )
            SCREAMING_SNAKE_CASE	: int					       =				len(_A     )
      SCREAMING_SNAKE_CASE	: int					       =				build_tree(_A     )
      SCREAMING_SNAKE_CASE	: Tuple					       =				build_tree(_A     )
      return root






def    __lowercase (       _A  ,      _A  ,      _A     )       ->  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	: List[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  ,      _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  ,      _A  ,      _A  ,      _A     )       ->  int:
      if start > end:
            return 0
      SCREAMING_SNAKE_CASE	: Any					       =				rank_till_index(_A  ,      _A  ,      _A     )
      SCREAMING_SNAKE_CASE	: Optional[int]					       =				rank_till_index(_A  ,      _A  ,      start - 1     )
      return rank_till_end - rank_before_start






def    __lowercase (       _A  ,      _A  ,      _A  ,      _A     )       ->  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	: 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  ,      _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  ,      _A  ,      _A  ,      _A  ,      _A     )       ->  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	: Dict					       =				range_counting(
          node.left  ,      (node.map_left[start - 1] if start else 0)  ,      node.map_left[end] - 1  ,      _A  ,      _A  ,      )
      SCREAMING_SNAKE_CASE	: List[str]					       =				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()




