input: from typing import List
  
  def rectangles_needed_to_cover_points(points: List[List[int]], w: int) -> int:
      """
      Given a list of 2D points, where each point is represented by a pair [x_i, y_i], along with an integer w, your task is to calculate the minimum number of rectangles required to cover all the points.
  
      Each rectangle should have its bottom edge at some point (x1, 0) and its top edge at some point (x2, y2), satisfying x1 <= x2, y2 >= 0, and the condition x2 - x1 <= w must hold for each rectangle.
  
      A point is considered covered by a rectangle if it lies within or on the boundary of that rectangle.
  
      The function should return the minimum number of rectangles needed to ensure that every point is covered by at least one rectangle.
  
      Note: A single point may be covered by multiple rectangles.
  
      Examples:
      >>> points = [[2,1],[1,0],[1,4],[1,8],[3,5],[4,6]], w = 1
      2
      >>> points = [[0,0],[1,1],[2,2],[3,3],[4,4],[5,5],[6,6]], w = 2
      3
      >>> points = [[2,3],[1,2]], w = 0
      2
  
      Constraints:
      1 <= len(points) <= 10^5
      len(points[i]) == 2
      0 <= points[i][0] <= 10^9
      0 <= points[i][1] <= 10^9
      0 <= w <= 10^9
      All points (x_i, y_i) are guaranteed to be unique.
      """
output:     
      points.sort()
  
      rectangles = 0
      i = 0
      while i < len(points):
          rectangles += 1
          limit = points[i][0] + w
          while i < len(points) and points[i][0] <= limit:
              i += 1
              
      return rectangles
  