





'''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       a_  :

    '''simple docstring'''


    def __init__(	self				,	A )	->     None:
        _SCREAMING_SNAKE_CASE             =    -1
        _SCREAMING_SNAKE_CASE             =    -1
        _SCREAMING_SNAKE_CASE             =    [-1] * length
        _SCREAMING_SNAKE_CASE             =    None
        _SCREAMING_SNAKE_CASE             =    None





    def __repr__(	self )	->     str:
        return f'Node(min_value={self.minn} max_value={self.maxx})'





def lowerCamelCase		(  __lowerCamelCase				:					list[int]					)		->Node | None:
    _SCREAMING_SNAKE_CASE             =    Node(len(__lowerCamelCase					)					)
    _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE             =    min(__lowerCamelCase					), max(__lowerCamelCase					)
    # 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(__lowerCamelCase					):
        if num <= pivot:
            left_arr.append(__lowerCamelCase					)
        else:
            right_arr.append(__lowerCamelCase					)
        _SCREAMING_SNAKE_CASE             =    len(__lowerCamelCase					)
    _SCREAMING_SNAKE_CASE             =    build_tree(__lowerCamelCase					)
    _SCREAMING_SNAKE_CASE             =    build_tree(__lowerCamelCase					)
    return root





def lowerCamelCase		(  __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
    _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      , __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				:					Node | None      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int					)		->int:
    if start > end:
        return 0
    _SCREAMING_SNAKE_CASE             =    rank_till_index(__lowerCamelCase      , __lowerCamelCase      , __lowerCamelCase					)
    _SCREAMING_SNAKE_CASE             =    rank_till_index(__lowerCamelCase      , __lowerCamelCase      , start - 1					)
    return rank_till_end - rank_before_start





def lowerCamelCase		(  __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]
    _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      , __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				:					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
    _SCREAMING_SNAKE_CASE             =    range_counting(
        node.left      , (node.map_left[start - 1] if start else 0)      , node.map_left[end] - 1      , __lowerCamelCase      , __lowerCamelCase      , )
    _SCREAMING_SNAKE_CASE             =    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'''

import safs


class       a_  (       safs.SaFileSystem ):

    '''simple docstring'''



