
'''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()



'''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()

