input: Write a Python function that takes a 2D list `points` and a string `labels`, where `points[i]` represents the coordinates of the i-th point and `labels[i]` indicates the tag of the i-th point. The function should find the maximum number of points that can be contained within a square that has its center at the origin (0, 0), with sides aligned to the coordinate axes, and ensures no two points within this square share the same tag. Points exactly on the boundary of the square are considered inside. 
  
  from typing import List
  
  def max_points_inside_square(points: List[List[int]], labels: str) -> int:
      """
      Returns the maximum number of points that can be inside a valid square as specified.
  
      Args:
      points (List[List[int]]): A 2D list where each element is a list containing the x and y coordinates of a point.
      labels (str): A string where each character represents the tag of the corresponding point in `points`.
  
      Returns:
      int: The maximum number of points contained within a valid square meeting the criteria.
  
      Examples:
      >>> points = [[2,2],[-1,-2],[-4,4],[-3,1],[3,-3]], labels = "abdca"
      2
      >>> points = [[1,1],[-2,-2],[-2,2]], labels = "abb"
      1
      >>> points = [[1,1],[-1,-1],[2,-2]], labels = "ccd"
      0
  
      Constraints:
      1 <= labels.length, points.length <= 10^5
      points[i].length == 2
      -10^9 <= points[i][0], points[i][1] <= 10^9
      labels.length == points.length
      points contains distinct coordinates.
      labels consists only of lowercase English letters.
      """
output: def max_points_inside_square(points: List[List[int]], labels: str) -> int:
      from collections import defaultdict
  
      def is_valid(square_size):
          seen_labels = set()
          for x, y, label in sorted_points:
              if abs(x) <= square_size // 2 and abs(y) <= square_size // 2:
                  if label in seen_labels:
                      return False
                  seen_labels.add(label)
          return True
  
      sorted_points = sorted([(x, y, labels[i]) for i, (x, y) in enumerate(points)], key=lambda p: (abs(p[0]), abs(p[1])))
      
      left, right = 0, 2 * max(max(abs(x), abs(y)) for x, y in points)
      while left < right:
          mid = (left + right) // 2
          if is_valid(mid):
              right = mid
          else:
              left = mid + 1
      return len({label for x, y, label in sorted_points if abs(x) <= left // 2 and abs(y) <= left // 2})