Count Pairs of Points Within 2 Units on Both Axes

You are given a list of points on a plane with integer coordinates. Two points intersect when their x-coordinates differ by at most 2 and their y-coordinates also differ by at most 2. Return the number of pairs of points that intersect. ### Function Signature ```python def count_intersecting_pairs(points: list[list[int]]) -> int: ``` ### Rules - Each point is given as `[x, y]`. - Points `i` and `j` intersect when `abs(x_i - x_j) <= 2` and `abs(y_i - y_j) <= 2`; both bounds are inclusive. - Count unordered pairs of different indices `i < j`, each pair once. A point is never paired with itself. - Points may repeat: two points at the same coordinates are different points, and they intersect. ### Constraints - `1 <= len(points) <= 10^5` - `-10^9 <= x, y <= 10^9` - the answer can reach `n * (n - 1) / 2`, about `5 * 10^9` when all points coincide, which exceeds `2^31 - 1`; return it as an exact integer ### Examples **Example 1** ```text Input: points = [[0, 0], [2, 2], [3, 0], [5, 5]] Output: 2 ``` `[0, 0]` and `[2, 2]` differ by 2 on both axes, and `[2, 2]` and `[3, 0]` differ by 1 and 2. Every other pair differs by more than 2 on at least one axis. **Example 2** ```text Input: points = [[1, 1], [1, 1], [1, 4]] Output: 1 ``` The two copies of `[1, 1]` intersect; `[1, 4]` is 3 away from both on the y-axis. **Example 3** ```text Input: points = [[0, 0]] Output: 0 ``` A single point forms no pairs.