code: 
  '''simple docstring'''
  
  
  
  
  
  from __future__ import annotations
  def   snake_case_       (							_a     :							list[list[int]] ,					_a     :							int ,					_a     :							int ,					_a     :							int | float			):
        snake_case_       ,	snake_case_						       =							m - 1, 0
        while i >= 0 and j < n:
              if key == mat[i][j]:
                    print(F'''Key {key} found at row- {i + 1} column- {j + 1}'''			)
                    return
              if key < mat[i][j]:
                    i -= 1
              else:
                    j += 1
        print(F'''Key {key} not found'''			)
  def   snake_case_       (							):
        snake_case_						       =							[[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]]
        snake_case_						       =							int(input("Enter the element to be searched:"			)			)
        print(_a			)
        search_in_a_sorted_matrix(_a ,					len(_a			) ,					len(mat[0]			) ,					_a			)
  
  
  if __name__ == "__main__":
       import doctest
  
       doctest.testmod()
       main()
  
  
style_context: 
  '''simple docstring'''
  
  
  
  
  
  from __future__ import annotations
  
  A           =   [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
  
  
  
  class  lowerCAmelCase__   :
  
  
  
    '''simple docstring'''
  
  
  
  
  
  
    def __init__(self  : Optional[int]	, lowerCAmelCase_  : int    )   ->       None:
          snake_case_						       =							-1
          snake_case_						       =							-1
          snake_case_						       =							[-1] * length
          snake_case_						       =							None
          snake_case_						       =							None
  
  
    def __repr__(self  : List[Any]    )   ->       str:
          return f'''Node(min_value={self.minn} max_value={self.maxx})'''
  
  def   snake_case_       (							_a     :							list[int]			):
        snake_case_						       =							Node(len(_a			)			)
        snake_case_       ,	snake_case_						       =							min(_a			), max(_a			)
        # Leaf node case where the node contains only one unique value
        if root.minn == root.maxx:
              return root
        snake_case_						       =							(root.minn + root.maxx) // 2
  
        snake_case_						       =							[]
        snake_case_						       =							[]
  
        for index, num in enumerate(_a			):
              if num <= pivot:
                    left_arr.append(_a			)
              else:
                    right_arr.append(_a			)
              snake_case_						       =							len(_a			)
        snake_case_						       =							build_tree(_a			)
        snake_case_						       =							build_tree(_a			)
        return root
  def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							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
        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 ,					_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   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
        if start > end:
              return 0
        snake_case_						       =							rank_till_index(_a ,					_a ,					_a			)
        snake_case_						       =							rank_till_index(_a ,					_a ,					start - 1			)
        return rank_till_end - rank_before_start
  def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							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]
        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 ,					_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   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int ,					_a     :							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
        snake_case_						       =							range_counting(
            node.left ,					(node.map_left[start - 1] if start else 0) ,					node.map_left[end] - 1 ,					_a ,					_a ,					)
        snake_case_						       =							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()
  
  