code: 
  
  
  """simple docstring"""
  
  
  
  
  def 						__a      (  a,		a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         _a          =				1.0
         for i in range(1,		r + 1					):
                ret *= (n + 1 - i) / i
         return round(a					)
  
  
  
  def 						__a      (  a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         return choose(8 + n,		a					) + choose(9 + n,		a					) - 1_0
  
  
  
  def 						__a      (  a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         return sum(non_bouncy_exact(a					) for i in range(1,		n + 1					)					)
  
  
  
  def 						__a      (  a = 1_0_0					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         return non_bouncy_upto(a					)
  
  
  if __name__ == "__main__":
     print(f'{solution() = }')
  
style_context: 
  
  
  """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()
  