


"""simple docstring"""





from collections import Counter
from functools import total_ordering

from data_structures.heap.heap import Heap

@total_ordering
class  lowercase_  :







      def __init__(      self :							List[str]		,  _lowercase :							str		,  _lowercase :							int    ):
        lowerCAmelCase__    :    List[str]								=					word
        lowerCAmelCase__    :    Dict								=					count







      def __eq__(      self :							Tuple		,  _lowercase :							object    ):
        if not isinstance(_lowercase		,  _lowercase    ):
          return NotImplemented
        return self.count == other.count







      def __lt__(      self :							Dict		,  _lowercase :							object    ):
        if not isinstance(_lowercase		,  _lowercase    ):
          return NotImplemented
        return self.count < other.count





def     lowercase__	(  lowerCamelCase     :  list[str]				,	lowerCamelCase     :  int				)					->     list[str]:
  lowerCAmelCase__    :    Heap[WordCount]								=					Heap()
  lowerCAmelCase__    :    Any								=					Counter(lowerCamelCase				)
  heap.build_max_heap(
      [WordCount(lowerCamelCase				,	lowerCamelCase				) for word, count in count_by_word.items()]				)
  return [heap.extract_max().word for _ in range(min(lowerCamelCase				,	len(lowerCamelCase				)				)				)]


if __name__ == "__main__":
   import doctest

   doctest.testmod()




"""simple docstring"""





from __future__ import annotations

__UpperCAmelCase    				=      [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 :							int		,  _lowercase :							int    ):
        lowerCAmelCase__    :    int								=					-1
        lowerCAmelCase__    :    int								=					-1
        lowerCAmelCase__    :    list[int]								=					[-1] * length
        lowerCAmelCase__    :    Node | None								=					None
        lowerCAmelCase__    :    Node | None								=					None







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





def     lowercase__	(  lowerCamelCase     :  list[int]				)					->     Node | None:
  lowerCAmelCase__    :    Any								=					Node(len(lowerCamelCase				)				)
  lowerCAmelCase__				,		lowerCAmelCase__    :    Any								=					min(lowerCamelCase				), max(lowerCamelCase				)
  # Leaf node case where the node contains only one unique value
  if root.minn == root.maxx:
    return root
  lowerCAmelCase__    :    str								=					(root.minn + root.maxx) // 2

  lowerCAmelCase__    :    list[int]								=					[]
  lowerCAmelCase__    :    list[int]								=					[]

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





def     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     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
  lowerCAmelCase__    :    int								=					(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     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     int:
  if start > end:
    return 0
  lowerCAmelCase__    :    int								=					rank_till_index(lowerCamelCase				,	lowerCamelCase				,	lowerCamelCase				)
  lowerCAmelCase__    :    Optional[Any]								=					rank_till_index(lowerCamelCase				,	lowerCamelCase				,	start - 1				)
  return rank_till_end - rank_before_start





def     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     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]
  lowerCAmelCase__    :    List[str]								=					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     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     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
  lowerCAmelCase__    :    List[str]								=					range_counting(
      node.left				,	(node.map_left[start - 1] if start else 0)				,	node.map_left[end] - 1				,	lowerCamelCase				,	lowerCamelCase				,	)
  lowerCAmelCase__    :    List[str]								=					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()
