Belt Packing with 2D Item Sizes (Distance Threshold Triplet)

Problem: 2D Triplet Packing (Distance Threshold) Items arrive online. Each item is a 2D point p = [x, y]. A triplet p1, p2, p3 is packable if the maximum pairwise Euclidean distance among them is < threshold. Implement Packer2D(threshold) with method add(p): Insert point p. If any valid triplet exists after insertion, return one such triplet and remove it from the system. Otherwise return empty. Constraints: up to 1e5 insertions; coordinates up to 1e9. Note: This is a reconstructed version based on the interview write-up; the exact condition may differ. Example Input threshold=3, points: (0,0),(1,1),(2,0) Output one valid triplet