




"""simple docstring"""





from __future__ import annotations

_lowercase		 =      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]

class  __lowercase    :


				'''simple docstring'''


				def __init__(				self				:       Tuple ,SCREAMING_SNAKE_CASE_				:       int ):
										snake_case__    :   int							     =   -1
										snake_case__    :   int							     =   -1
										snake_case__    :   list[int]							     =   [-1] * length
										snake_case__    :   Node | None							     =   None
										snake_case__    :   Node | None							     =   None





				def __repr__(				self				:       List[Any] ):
										return F'''Node(min_value={self.minn} max_value={self.maxx})'''







def 						lowerCAmelCase							(	lowerCamelCase						):
						'''simple docstring'''


						snake_case__    :   Union[str, Any]							     =   Node(len(lowerCamelCase						)						)
						snake_case__     ,		snake_case__    :   int							     =   min(lowerCamelCase						), max(lowerCamelCase						)
						# Leaf node case where the node contains only one unique value
						if root.minn == root.maxx:
												return root
						snake_case__    :   str							     =   (root.minn + root.maxx) // 2

						snake_case__    :   list[int]							     =   []
						snake_case__    :   list[int]							     =   []

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

def 						lowerCAmelCase							(	lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase						):
						'''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
						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 ,     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 						lowerCAmelCase							(	lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase						):
						'''simple docstring'''


						if start > end:
												return 0
						snake_case__    :   int							     =   rank_till_index(lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase						)
						snake_case__    :   Union[str, Any]							     =   rank_till_index(lowerCamelCase ,     lowerCamelCase ,     start - 1						)
						return rank_till_end - rank_before_start

def 						lowerCAmelCase							(	lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase						):
						'''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]
						snake_case__    :   List[Any]							     =   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 						lowerCAmelCase							(	lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase ,     lowerCamelCase						):
						'''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
						snake_case__    :   Any							     =   range_counting(
						    node.left ,     (node.map_left[start - 1] if start else 0) ,     node.map_left[end] - 1 ,     lowerCamelCase ,     lowerCamelCase ,     )
						snake_case__    :   Tuple							     =   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()








"""simple docstring"""





from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class  __lowercase    :


				'''simple docstring'''


				def __init__(				self				:       List[Any] ,SCREAMING_SNAKE_CASE_				:       Any ):
										snake_case__    :   Any							     =   data
										snake_case__    :   Node | None							     =   None





				def __str__(				self				:       Union[str, Any] ):
										return F'''{self.data}'''







class  __lowercase    :


				'''simple docstring'''


				def __init__(				self				:       Optional[int] ):
										snake_case__    :   Node | None							     =   None
										snake_case__    :   Node | None							     =   None

				def __iter__(				self				:       Optional[int] ):
										snake_case__    :   Optional[int]							     =   self.front
										while node:
																yield node.data
																snake_case__    :   Optional[int]							     =   node.next

				def __len__(				self				:       Any ):
										return len(tuple(iter(self ) ) )

				def __str__(				self				:       Union[str, Any] ):
										return " <- ".join(str(SCREAMING_SNAKE_CASE_ ) for item in self )

				def  _lowerCamelCase   (				self				:       List[str] ):
										return len(self ) == 0

				def  _lowerCamelCase   (				self				:       Optional[int] ,SCREAMING_SNAKE_CASE_				:       Any ):
										snake_case__    :   int							     =   Node(SCREAMING_SNAKE_CASE_ )
										if self.is_empty():
																snake_case__    :   List[Any]							     =   node
										else:
																assert isinstance(self.rear ,SCREAMING_SNAKE_CASE_ )
																snake_case__    :   Union[str, Any]							     =   node
																snake_case__    :   int							     =   node

				def  _lowerCamelCase   (				self				:       int ):
										if self.is_empty():
																raise IndexError('''dequeue from empty queue''' )
										assert isinstance(self.front ,SCREAMING_SNAKE_CASE_ )
										snake_case__    :   List[str]							     =   self.front
										snake_case__    :   str							     =   self.front.next
										if self.front is None:
																snake_case__    :   Optional[Any]							     =   None
										return node.data





				def  _lowerCamelCase   (				self				:       Optional[int] ):
										snake_case__    :   Optional[Any]							     =   None


if __name__ == "__main__":
							from doctest import testmod

							testmod()


