
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 							lowercase   :



		def __init__(					self							, A_			)    ->   None:
				"""simple docstring"""
				UpperCamelCase            =	-1
				UpperCamelCase            =	-1
				UpperCamelCase            =	[-1] * length
				UpperCamelCase            =	None
				UpperCamelCase            =	None



		def __repr__(					self			)    ->   str:
				"""simple docstring"""
				return F'''Node(min_value={self.minn} max_value={self.maxx})'''






def  A			(   lowercase					)  ->    Node | None:
		'''simple docstring'''

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

		UpperCamelCase            =	[]
		UpperCamelCase            =	[]

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


def  A			(   lowercase       ,			lowercase       ,			lowercase					)  ->    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
		UpperCamelCase            =	(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       ,			lowercase       ,			node.map_left[index] - 1					)
		else:
				# go to the right subtree and map index to the right subtree
				return rank_till_index(node.right       ,			lowercase       ,			index - node.map_left[index]					)


def  A			(   lowercase       ,			lowercase       ,			lowercase       ,			lowercase					)  ->    int:
		'''simple docstring'''

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


def  A			(   lowercase       ,			lowercase       ,			lowercase       ,			lowercase					)  ->    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]
		UpperCamelCase            =	node.map_left[end] - (
		    node.map_left[start - 1] if start else 0
		)
		if num_elements_in_left_tree > index:
				return quantile(
				    node.left       ,			lowercase       ,			(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			(   lowercase       ,			lowercase       ,			lowercase       ,			lowercase       ,			lowercase					)  ->    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
		UpperCamelCase            =	range_counting(
		    node.left       ,			(node.map_left[start - 1] if start else 0)       ,			node.map_left[end] - 1       ,			lowercase       ,			lowercase       ,			)
		UpperCamelCase            =	range_counting(
		    node.right       ,			start - (node.map_left[start - 1] if start else 0)       ,			end - node.map_left[end]       ,			lowercase       ,			lowercase       ,			)
		return left + right


if __name__ == "__main__":
					import doctest

					doctest.testmod()


def  A			(   lowercase					)  ->    int:
		'''simple docstring'''

		return int(lowercase					) if x - int(lowercase					) >= 0 else int(lowercase					) - 1


if __name__ == "__main__":
					import doctest

					doctest.testmod()
