




from __future__ import annotations

__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   :
 def __init__(  self		,   snake_case__						)	->							None:
       '''simple docstring'''





       UpperCAmelCase    : str      =-1
       UpperCAmelCase    : int      =-1
       UpperCAmelCase    : Optional[int]      =[-1] * length
       UpperCAmelCase    : str      =None
       UpperCAmelCase    : Union[str, Any]      =None






 def __repr__(  self						)	->							str:
       '''simple docstring'''





       return f'''Node(min_value={self.minn} max_value={self.maxx})'''





def   lowerCAmelCase_ (				__lowerCAmelCase						)->  List[Any]:






      '''simple docstring'''





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

      UpperCAmelCase    : List[str]      =[]
      UpperCAmelCase    : List[str]      =[]

      for index, num in enumerate(lowercase__						):
            if num <= pivot:
                  left_arr.append(lowercase__						)
            else:
                  right_arr.append(lowercase__						)
            UpperCAmelCase    : Dict      =len(lowercase__						)
      UpperCAmelCase    : Tuple      =build_tree(lowercase__						)
      UpperCAmelCase    : int      =build_tree(lowercase__						)
      return root





def   lowerCAmelCase_ (				__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase						)->  Any:






      '''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
      UpperCAmelCase    : 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		,					lowercase__		,					node.map_left[index] - 1						)
      else:
            # go to the right subtree and map index to the right subtree
            return rank_till_index(node.right		,					lowercase__		,					index - node.map_left[index]						)





def   lowerCAmelCase_ (				__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase						)->  List[Any]:






      '''simple docstring'''





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





def   lowerCAmelCase_ (				__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase						)->  Optional[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]
      UpperCAmelCase    : Optional[int]      =node.map_left[end] - (
          node.map_left[start - 1] if start else 0
      )
      if num_elements_in_left_tree > index:
            return quantile(
                node.left		,					lowercase__		,					(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		,					__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase		,					__lowerCAmelCase						)->  Dict:






      '''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
      UpperCAmelCase    : List[str]      =range_counting(
          node.left		,					(node.map_left[start - 1] if start else 0)		,					node.map_left[end] - 1		,					lowercase__		,					lowercase__		,					)
      UpperCAmelCase    : List[Any]      =range_counting(
          node.right		,					start - (node.map_left[start - 1] if start else 0)		,					end - node.map_left[end]		,					lowercase__		,					lowercase__		,					)
      return left + right


if __name__ == "__main__":
     import doctest

     doctest.testmod()

from collections import defaultdict





def   lowerCAmelCase_ (				__lowerCAmelCase = 5						)->  int:






      '''simple docstring'''





      UpperCAmelCase    : List[str]      =defaultdict(__lowerCAmelCase						)
      UpperCAmelCase    : Tuple      =0

      while True:
            UpperCAmelCase    : Any      =get_digits(__lowerCAmelCase						)
            freqs[digits].append(__lowerCAmelCase						)

            if len(freqs[digits]						) == max_base:
                  UpperCAmelCase    : Optional[int]      =freqs[digits][0] ** 3
                  return base

            num += 1





def   lowerCAmelCase_ (				__lowerCAmelCase						)->  str:






      '''simple docstring'''





      return "".join(sorted(str(num**3						)						)						)


if __name__ == "__main__":
     print(f'{solution() = }')
