


"""simple docstring"""




from __future__ import annotations

from collections.abc import Iterator
from typing import Any





class __snake_case		:







   """simple docstring"""




   def __init__(		self							:List[Any]				,  UpperCamelCase__							:Any       ):
          _a          =				data
          _a          =				None




   def __str__(		self							:Any       ):
          return f'{self.data}'






class __snake_case		:







   """simple docstring"""




   def __init__(		self							:Any       ):
          _a          =				None
          _a          =				None




   def __iter__(		self							:List[str]       ):
          _a          =				self.front
          while node:
                 yield node.data
                 _a          =				node.next




   def __len__(		self							:List[str]       ):
          return len(tuple(iter(self       )       )       )




   def __str__(		self							:Union[str, Any]       ):
          return " <- ".join(str(UpperCamelCase__       ) for item in self       )




   def SCREAMING_SNAKE_CASE_      (		self							:Any       ):
          return len(self       ) == 0




   def SCREAMING_SNAKE_CASE_      (		self							:List[str]				,  UpperCamelCase__							:Any       ):
          _a          =				Node(UpperCamelCase__       )
          if self.is_empty():
                 _a          =				_a          =				node
          else:
                 assert isinstance(self.rear				,  UpperCamelCase__       )
                 _a          =				node
                 _a          =				node




   def SCREAMING_SNAKE_CASE_      (		self							:Tuple       ):
          if self.is_empty():
                 raise IndexError("dequeue from empty queue"       )
          assert isinstance(self.front				,  UpperCamelCase__       )
          _a          =				self.front
          _a          =				self.front.next
          if self.front is None:
                 _a          =				None
          return node.data




   def SCREAMING_SNAKE_CASE_      (		self							:int       ):
          _a          =				_a          =				None


if __name__ == "__main__":
   from doctest import testmod

   testmod()




"""simple docstring"""




from __future__ import annotations

__SCREAMING_SNAKE_CASE					=						[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]





class __snake_case		:







   """simple docstring"""




   def __init__(		self							:Optional[Any]				,  UpperCamelCase__							:int       ):
          _a          =				-1
          _a          =				-1
          _a          =				[-1] * length
          _a          =				None
          _a          =				None




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






def 						__a      (  a					):





       """simple docstring"""







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

       _a          =				[]
       _a          =				[]

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



def 						__a      (  a,		a,		a					):





       """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
       _a          =				(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,		a,		node.map_left[index] - 1					)
       else:
              # go to the right subtree and map index to the right subtree
              return rank_till_index(node.right,		a,		index - node.map_left[index]					)



def 						__a      (  a,		a,		a,		a					):





       """simple docstring"""







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



def 						__a      (  a,		a,		a,		a					):





       """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]
       _a          =				node.map_left[end] - (
           node.map_left[start - 1] if start else 0
       )
       if num_elements_in_left_tree > index:
              return quantile(
                  node.left,		a,		(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      (  a,		a,		a,		a,		a					):





       """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
       _a          =				range_counting(
           node.left,		(node.map_left[start - 1] if start else 0),		node.map_left[end] - 1,		a,		a,		)
       _a          =				range_counting(
           node.right,		start - (node.map_left[start - 1] if start else 0),		end - node.map_left[end],		a,		a,		)
       return left + right


if __name__ == "__main__":
   import doctest

   doctest.testmod()
