input: Write a python function that determines the largest possible area of a square that can fit inside the intersection region of two out of multiple given rectangles, specified by the bottom-left and top-right coordinates respectively.
  
  from typing import List
  
  def max_square_in_intersection(bottomLeft: List[List[int]], topRight: List[List[int]]) -> int:
      """
      You have n rectangles on a 2D plane. Two 0-indexed 2D integer arrays bottomLeft and topRight, each of dimensions n x 2, are given where bottomLeft[i] and topRight[i] denote the bottom-left and top-right corners of the i-th rectangle respectively.
  
      You should identify the largest square area that can be accommodated within the intersection area of any two given rectangles if they overlap. Return the maximum square area achievable, or 0 if no such intersecting regions exist.
  
      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 == bottomLeft.length == topRight.length
      2 <= n <= 10^3
      bottomLeft[i].length == topRight[i].length == 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: def max_square_in_intersection(bottomLeft: List[List[int]], topRight: List[List[int]]) -> int:
      n = len(bottomLeft)
      max_side = 0
  
      for i in range(n):
          for j in range(i + 1, n):
              int_left = max(bottomLeft[i][0], bottomLeft[j][0])
              int_right = min(topRight[i][0], topRight[j][0])
              int_bottom = max(bottomLeft[i][1], bottomLeft[j][1])
              int_top = min(topRight[i][1], topRight[j][1])
  
              if int_left < int_right and int_bottom < int_top:
                  max_side = max(max_side, min(int_right - int_left, int_top - int_bottom))
  
      return max_side * max_side