input: from typing import List
  from math import inf
  from heapq import nlargest, nsmallest
  
  def minimize_max_distance(points: List[List[int]]) -> int:
      """
      Given a list of integer coordinates representing points on a 2D plane (points[i] = [x_i, y_i]), calculate the minimum possible maximum Manhattan distance between any two points after removing exactly one point.
  
      The Manhattan distance between two points is defined as the sum of the absolute differences of their coordinates.
      Return the minimum value of the maximum distance after removing one point.
  
      Examples:
      >>> points = [[3,10],[5,15],[10,2],[4,4]]
      12
      >>> points = [[1,1],[1,1],[1,1]]
      0
  
      Constraints:
      3 <= points.length <= 10^5
      points[i].length == 2
      1 <= points[i][0], points[i][1] <= 10^8
      """
output:     def manhattan_distance(p1, p2):
          return abs(p1[0] - p2[0]) + abs(p1[1] - p2[1])
  
      def max_distance_without_point(points, idx_to_remove):
          max_dist = 0
          for i in range(len(points)):
              if i == idx_to_remove:
                  continue
              for j in range(i + 1, len(points)):
                  if j == idx_to_remove:
                      continue
                  max_dist = max(max_dist, manhattan_distance(points[i], points[j]))
          return max_dist
  
      min_max_distance = inf
      for i in range(len(points)):
          min_max_distance = min(min_max_distance, max_distance_without_point(points, i))
  
      return min_max_distance