




from __future__ import annotations

lowerCAmelCase__ :   Optional[Any]						=     [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]




class 	UpperCamelCase__			:

    '''simple docstring'''



    def __init__(					self  ,						UpperCamelCase__  )  ->   int:
           lowerCamelCase     :   List[Any]    				=      -1
           lowerCamelCase     :   int    				=      -1
           lowerCamelCase     :   Union[str, Any]    				=      [-1] * length
           lowerCamelCase     :   Any    				=      None
           lowerCamelCase     :   Union[str, Any]    				=      None







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




def   A   (   _SCREAMING_SNAKE_CASE					)			->				str:
       lowerCamelCase     :   Tuple    				=      Node(len(_SCREAMING_SNAKE_CASE					)					)
       lowerCamelCase				,   lowerCamelCase     :   List[str]    				=      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
       lowerCamelCase     :   Any    				=      (root.minn + root.maxx) // 2

       lowerCamelCase     :   Dict    				=      []
       lowerCamelCase     :   int    				=      []

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

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Tuple:







       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     :   Dict    				=      (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   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Optional[int]:







       if start > end:
              return 0
       lowerCamelCase     :   List[str]    				=      rank_till_index(_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   List[str]    				=      rank_till_index(_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,start - 1					)
       return rank_till_end - rank_before_start

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Optional[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     :   Dict    				=      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   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Optional[Any]:







       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     :   Dict    				=      range_counting(
           node.left				,(node.map_left[start - 1] if start else 0)				,node.map_left[end] - 1				,_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE				,)
       lowerCamelCase     :   List[Any]    				=      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()












from itertools import compress, repeat
from math import ceil, sqrt

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list[int]:

       if num <= 2:
              return []
       if num == 3:
              return [2]

       # Odd sieve for numbers in range [3, num - 1]
       lowerCamelCase     :   str    				=      bytearray(B"\x01"					) * ((num >> 1) - 1)

       for i in range(3				,int(sqrt(_SCREAMING_SNAKE_CASE					)					) + 1				,2					):
              if sieve[(i >> 1) - 1]:
                     lowerCamelCase     :   Tuple    				=      i**2
                     lowerCamelCase     :   str    				=      repeat(
                         0				,ceil((num - i_squared) / (i << 1)					)					)

       return [2] + list(compress(range(3				,_SCREAMING_SNAKE_CASE				,2					)				,_SCREAMING_SNAKE_CASE					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






