

'''simple docstring'''




from __future__ import annotations

_a				: Dict 							=						[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   , 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       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   list[int]						):
  UpperCAmelCase													=	Node(len(SCREAMING_SNAKE_CASE						)						)
  UpperCAmelCase							,      UpperCAmelCase													=	min(SCREAMING_SNAKE_CASE						), max(SCREAMING_SNAKE_CASE						)
  # 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(SCREAMING_SNAKE_CASE						):
    if num <= pivot:
      left_arr.append(SCREAMING_SNAKE_CASE						)
    else:
      right_arr.append(SCREAMING_SNAKE_CASE						)
    UpperCAmelCase													=	len(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	build_tree(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	build_tree(SCREAMING_SNAKE_CASE						)
  return root


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Node | None       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   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
  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       ,   SCREAMING_SNAKE_CASE       ,   node.map_left[index] - 1						)
  else:
    # go to the right subtree and map index to the right subtree
    return rank_till_index(node.right       ,   SCREAMING_SNAKE_CASE       ,   index - node.map_left[index]						)


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Node | None       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   int						):
  if start > end:
    return 0
  UpperCAmelCase													=	rank_till_index(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	rank_till_index(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   start - 1						)
  return rank_till_end - rank_before_start


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Node | None       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   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]
  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       ,   SCREAMING_SNAKE_CASE       ,   (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__		(						SCREAMING_SNAKE_CASE      :   Node | None       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   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
  UpperCAmelCase													=	range_counting(
      node.left       ,   (node.map_left[start - 1] if start else 0)       ,   node.map_left[end] - 1       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   )
  UpperCAmelCase													=	range_counting(
      node.right       ,   start - (node.map_left[start - 1] if start else 0)       ,   end - node.map_left[end]       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   )
  return left + right


if __name__ == "__main__":
   import doctest

   doctest.testmod()





'''simple docstring'''




from collections import OrderedDict
from dataclasses import fields
from typing import Any, Tuple

import numpy as np

from .import_utils import is_torch_available


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Optional[Any]						):
  if is_torch_available():
    import torch

    if isinstance(SCREAMING_SNAKE_CASE       ,   torch.Tensor						):
      return True

  return isinstance(SCREAMING_SNAKE_CASE       ,   np.ndarray						)



class        lowercase_	(		a ):

  '''simple docstring'''





  def 						snake_case_			(     self     )							->				List[str]:


    """simple docstring"""
    UpperCAmelCase													=	fields(self     )

    # Safety and consistency checks
    if not len(a_     ):
      raise ValueError(F'''{self.__class__.__name__} has no fields.'''     )

    UpperCAmelCase													=	getattr(self   , class_fields[0].name     )
    UpperCAmelCase													=	all(getattr(self   , field.name     ) is None for field in class_fields[1:]     )

    if other_fields_are_none and isinstance(a_   , a_     ):
      for key, value in first_field.items():
        UpperCAmelCase													=	value
    else:
      for field in class_fields:
        UpperCAmelCase													=	getattr(self   , field.name     )
        if v is not None:
          UpperCAmelCase													=	v
  def __delitem__(     self   , *a_   , **a_     )							->				int:


    """simple docstring"""
    raise Exception(F'''You cannot use ``__delitem__`` on a {self.__class__.__name__} instance.'''     )
  def 						snake_case_			(     self   , *a_   , **a_     )							->				Tuple:


    """simple docstring"""
    raise Exception(F'''You cannot use ``setdefault`` on a {self.__class__.__name__} instance.'''     )
  def 						snake_case_			(     self   , *a_   , **a_     )							->				int:


    """simple docstring"""
    raise Exception(F'''You cannot use ``pop`` on a {self.__class__.__name__} instance.'''     )
  def 						snake_case_			(     self   , *a_   , **a_     )							->				Dict:


    """simple docstring"""
    raise Exception(F'''You cannot use ``update`` on a {self.__class__.__name__} instance.'''     )
  def __getitem__(     self   , a_     )							->				Tuple:


    """simple docstring"""
    if isinstance(a_   , a_     ):
      UpperCAmelCase													=	dict(self.items()     )
      return inner_dict[k]
    else:
      return self.to_tuple()[k]
  def __setattr__(     self   , a_   , a_     )							->				Dict:


    """simple docstring"""
    if name in self.keys() and value is not None:
      # Don't call self.__setitem__ to avoid recursion errors
      super().__setitem__(a_   , a_     )
    super().__setattr__(a_   , a_     )
  def __setitem__(     self   , a_   , a_     )							->				str:


    """simple docstring"""
    # Will raise a KeyException if needed
    super().__setitem__(a_   , a_     )
    # Don't call self.__setattr__ to avoid recursion errors
    super().__setattr__(a_   , a_     )





  def 						snake_case_			(     self     )							->				Tuple[Any]:


    """simple docstring"""
    return tuple(self[k] for k in self.keys()     )


