input: 
  from typing import List
  
  def largest_square_within_intersection(bottomLeft: List[List[int]], topRight: List[List[int]]) -> int:
      """
      You're given n rectangles on a 2D plane, represented by two 0-indexed 2D integer lists, bottomLeft and topRight, each of size n x 2. The i-th rectangle's corners are defined by bottomLeft[i] and topRight[i].
  
      Determine the area of the largest square that can fit inside the overlap of any two rectangles. If there's no overlap, return 0.
  
      Examples:
      >>> bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]
      1
      >>> bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]]
      1
      >>> bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]]
      0
  
      Constraints:
      n == len(bottomLeft) == len(topRight)
      2 <= n <= 1000
      len(bottomLeft[i]) == len(topRight[i]) == 2
      1 <= bottomLeft[i][0], bottomLeft[i][1] <= 10^7
      1 <= topRight[i][0], topRight[i][1] <= 10^7
      bottomLeft[i][0] < topRight[i][0]
      bottomLeft[i][1] < topRight[i][1]
      """
  
output:     max_square_area = 0
  
      for i in range(len(bottomLeft)):
          for j in range(i + 1, len(bottomLeft)):
              # Calculate the overlap area
              overlap_bottom_left_x = max(bottomLeft[i][0], bottomLeft[j][0])
              overlap_bottom_left_y = max(bottomLeft[i][1], bottomLeft[j][1])
              overlap_top_right_x = min(topRight[i][0], topRight[j][0])
              overlap_top_right_y = min(topRight[i][1], topRight[j][1])
              
              # Check if there is an overlap
              if overlap_bottom_left_x < overlap_top_right_x and overlap_bottom_left_y < overlap_top_right_y:
                  # Calculate the dimensions of the overlap rectangle
                  overlap_width = overlap_top_right_x - overlap_bottom_left_x
                  overlap_height = overlap_top_right_y - overlap_bottom_left_y
                  
                  # The side length of the largest square that can fit in this rectangle
                  square_side_length = min(overlap_width, overlap_height)
                  
                  # Calculate the area of this square
                  max_square_area = max(max_square_area, square_side_length ** 2)
      
      return max_square_area