




from __future__ import annotations

__lowerCAmelCase		:    Optional[Any]	      =		[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]




class    snake_case__							:
				"""simple docstring"""



				def __init__(				self    :					Optional[Any] ,				__lowerCamelCase    :					int							) ->					None:
							a   =      -1
							a   =      -1
							a   =      [-1] * length
							a   =      None
							a   =      None





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




def       __magic_name__    (			A		: list[int]       ):






			'''simple docstring'''







			a   =      Node(len(A       )       )
			a   ,		a   =      min(A       ), max(A       )
			# Leaf node case where the node contains only one unique value
			if root.minn == root.maxx:
						return root
			a   =      (root.minn + root.maxx) // 2

			a   =      []
			a   =      []

			for index, num in enumerate(A       ):
						if num <= pivot:
									left_arr.append(A       )
						else:
									right_arr.append(A       )
						a   =      len(A       )
			a   =      build_tree(A       )
			a   =      build_tree(A       )
			return root




def       __magic_name__    (			A		: Node | None,  A		: int,  A		: int       ):






			'''simple docstring'''







			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   =      (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       __magic_name__    (			A		: Node | None,  A		: int,  A		: int,  A		: int       ):






			'''simple docstring'''







			if start > end:
						return 0
			a   =      rank_till_index(A,  A,  A       )
			a   =      rank_till_index(A,  A,  start - 1       )
			return rank_till_end - rank_before_start




def       __magic_name__    (			A		: Node | None,  A		: int,  A		: int,  A		: int       ):






			'''simple docstring'''







			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   =      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       __magic_name__    (			A		: Node | None,  A		: int,  A		: int,  A		: int,  A		: int       ):






			'''simple docstring'''







			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   =      range_counting(
			    node.left,  (node.map_left[start - 1] if start else 0),  node.map_left[end] - 1,  A,  A,  )
			a   =      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()












from ..utils import DummyObject, requires_backends




class    snake_case__							(metaclass=_UpperCamelCase       ):
				"""simple docstring"""



				SCREAMING_SNAKE_CASE_	:							List[str]										= ["""torch""", """transformers""", """k_diffusion"""]





				def __init__(				self    :					Optional[int] ,				*__lowerCamelCase    :					Union[str, Any] ,				**__lowerCamelCase    :					List[Any]							) ->					Optional[Any]:
							requires_backends(self ,				["torch", "transformers", "k_diffusion"]							)





				@classmethod
				def 							__UpperCAmelCase							(				cls    :					str ,				*__lowerCamelCase    :					Union[str, Any] ,				**__lowerCamelCase    :					Tuple							) ->					List[Any]:
							requires_backends(cls ,				["torch", "transformers", "k_diffusion"]							)





				@classmethod
				def 							__UpperCAmelCase							(				cls    :					Optional[Any] ,				*__lowerCamelCase    :					List[str] ,				**__lowerCamelCase    :					int							) ->					Dict:
							requires_backends(cls ,				["torch", "transformers", "k_diffusion"]							)






