




'''simple docstring'''




from __future__ import annotations




def 						snake_case__    ( lowerCamelCase__				:   list[int]			,		lowerCamelCase__				:   int			)   ->   list[int]:
					A_ :     dict[int, int] =							{}
					for index, val in enumerate(lowerCamelCase__			):
										A_ :     str =							target - val
										if compl in chk_map:
															return [chk_map[compl], index]
										A_ :     Any =							index
					return []


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(F'{two_sum([2, 7, 11, 15], 9) = }')









'''simple docstring'''




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     UpperCamelCase_     :







						"""simple docstring"""


						def __init__(     self      :       Dict							, _lowerCamelCase      :       int    ):





											"""simple docstring"""







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







						def __repr__(     self      :       List[str]    ):





											"""simple docstring"""







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






def 						snake_case__    ( lowerCamelCase__				:   list[int]			)   ->   Node | None:
					A_ :     Optional[Any] =							Node(len(lowerCamelCase__			)			)
					A_ ,A_ :     str =							min(lowerCamelCase__			), max(lowerCamelCase__			)
					# 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_ :     list[int] =							[]
					A_ :     list[int] =							[]

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




def 						snake_case__    ( 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
					A_ :     List[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 						snake_case__    ( lowerCamelCase__				:   Node | None			,		lowerCamelCase__				:   int			,		lowerCamelCase__				:   int			,		lowerCamelCase__				:   int			)   ->   int:
					if start > end:
										return 0
					A_ :     Union[str, Any] =							rank_till_index(lowerCamelCase__			,		lowerCamelCase__			,		lowerCamelCase__			)
					A_ :     Union[str, Any] =							rank_till_index(lowerCamelCase__			,		lowerCamelCase__			,		start - 1			)
					return rank_till_end - rank_before_start




def 						snake_case__    ( 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]
					A_ :     List[str] =							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 						snake_case__    ( 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
					A_ :     int =							range_counting(
					    node.left			,		(node.map_left[start - 1] if start else 0)			,		node.map_left[end] - 1			,		lowerCamelCase__			,		lowerCamelCase__			,		)
					A_ :     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()



