input: from typing import List
  
  def count_valid_pairs(points: List[List[int]]) -> int:
      """
      Given a 2D list of integer coordinates demonstrating points on a 2D plane, where each sublist represents [xi, yi].
  
      Determine how many pairs of points (A, B) exist such that A is positioned on the upper-left side of B, with no other points in the rectangle (or line) they form (including edges).
  
      Return the total count.
  
      Examples:
      >>> points = [[1,1],[2,2],[3,3]]
      0
      >>> points = [[6,2],[4,4],[2,6]]
      2
      >>> points = [[3,1],[1,3],[1,1]]
      2
  
      Constraints:
      2 <= n <= 50
      points[i].length == 2
      0 <= points[i][0], points[i][1] <= 50
      All points[i] are unique.
      """
output:     points.sort()
      total_pairs = 0
  
      for i in range(len(points)):
          for j in range(i + 1, len(points)):
              if points[i][0] < points[j][0] and points[i][1] < points[j][1]:
                  valid = True
                  for k in range(len(points)):
                      if i != k and j != k:
                          if points[i][0] <= points[k][0] <= points[j][0] and points[i][1] <= points[k][1] <= points[j][1]:
                              valid = False
                              break
                  if valid:
                      total_pairs += 1
  
      return total_pairs