

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    __snake_case	:

  def __init__(       self    ,		_A):
      SCREAMING_SNAKE_CASE_						=    -1
      SCREAMING_SNAKE_CASE_						=    -1
      SCREAMING_SNAKE_CASE_						=    [-1] * length
      SCREAMING_SNAKE_CASE_						=    None
      SCREAMING_SNAKE_CASE_						=    None


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






def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


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

    SCREAMING_SNAKE_CASE_						=    []
    SCREAMING_SNAKE_CASE_						=    []

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


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		Node | None			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		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
    SCREAMING_SNAKE_CASE_						=    (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			, __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			, __snake_case			, index - node.map_left[index]							)


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		Node | None			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		int							):





    """simple docstring"""


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


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		Node | None			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		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]
    SCREAMING_SNAKE_CASE_						=    node.map_left[end] - (
        node.map_left[start - 1] if start else 0
    )
    if num_elements_in_left_tree > index:
        return quantile(
            node.left			, __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        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		Node | None			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		int			, _SCREAMING_SNAKE_CASE       :		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
    SCREAMING_SNAKE_CASE_						=    range_counting(
        node.left			, (node.map_left[start - 1] if start else 0)			, node.map_left[end] - 1			, __snake_case			, __snake_case			, )
    SCREAMING_SNAKE_CASE_						=    range_counting(
        node.right			, start - (node.map_left[start - 1] if start else 0)			, end - node.map_left[end]			, __snake_case			, __snake_case			, )
    return left + right


if __name__ == "__main__":
       import doctest

       doctest.testmod()










"""simple docstring"""



from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

_UpperCamelCase						:    Optional[int]		=						TypeVar('T', bound=bool)

class 			a	(  Generic[T]      ):







    def __init__(     self				,						_lowerCamelCase			):
      lowercase				       =			value
      lowercase				       =			None
      lowercase				       =			None







    @property
    def      UpperCamelCase_ (     self			):
      return self._value







    @staticmethod
    def      UpperCamelCase_ (     _lowerCamelCase				,						_lowerCamelCase			):
      if not roota:
        return roota

      if not roota:
        return roota

      if roota.value > roota.value:
        lowercase       ,	lowercase				       =			roota, roota

      if random.choice([True, False]			):
        lowercase       ,	lowercase				       =			roota.right, roota.left

      lowercase				       =			RandomizedHeapNode.merge(roota.left				,						_lowerCamelCase			)

      return roota


class 			a	(  Generic[T]      ):







    def __init__(     self				,						_lowerCamelCase = ()			):
      lowercase				       =			None

      if data:
        for item in data:
          self.insert(_lowerCamelCase			)







    def      UpperCamelCase_ (     self				,						_lowerCamelCase			):
      lowercase				       =			RandomizedHeapNode.merge(self._root				,						RandomizedHeapNode(_lowerCamelCase			)			)







    def      UpperCamelCase_ (     self			):
      lowercase				       =			self.top()

      if self._root is None:
        return None

      lowercase				       =			RandomizedHeapNode.merge(self._root.left				,						self._root.right			)

      return result







    def      UpperCamelCase_ (     self			):
      if not self._root:
        raise IndexError('Can\'t get top element for the empty heap.'			)
      return self._root.value







    def      UpperCamelCase_ (     self			):
      lowercase				       =			None







    def      UpperCamelCase_ (     self			):
      lowercase				       =			[]
      while self:
        result.append(self.pop()			)

      return result







    def __bool__(     self			):
      return self._root is not None


if __name__ == "__main__":
    import doctest

    doctest.testmod()


