
from __future__ import annotations

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







class     __A:




				def __init__(  self	,  _snake_case       )					->   None:


								'''simple docstring'''




								__a    							=					-1
								__a    							=					-1
								__a    							=					[-1] * length
								__a    							=					None
								__a    							=					None




				def __repr__(  self       )					->   str:


								'''simple docstring'''




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



def 					__lowerCAmelCase    (    a__						) ->						Node | None:
				__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 					__lowerCAmelCase    (    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
				__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 					__lowerCAmelCase    (    a__		,					a__		,					a__		,					a__						) ->						int:
				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 					__lowerCAmelCase    (    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]
				__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 					__lowerCAmelCase    (    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
				__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 itertools import compress, repeat
from math import ceil, sqrt


def 					__lowerCAmelCase    (    a__						) ->						list[int]:

				if num <= 2:
								return []
				if num == 3:
								return [2]

				# Odd sieve for numbers in range [3, num - 1]
				__a    							=					bytearray(B'''\x01'''						) * ((num >> 1) - 1)

				for i in range(3		,					int(sqrt(a__						)						) + 1		,					2						):
								if sieve[(i >> 1) - 1]:
												__a    							=					i**2
												__a    							=					repeat(
												    0		,					ceil((num - i_squared) / (i << 1)						)						)

				return [2] + list(compress(range(3		,					a__		,					2						)		,					a__						)						)


if __name__ == "__main__":
					import doctest

					doctest.testmod()