Detect Squares Python Solution with Tests

lcpy gen -n 2013   # by problem number
lcpy gen -s detect_squares   # by problem name

Input
["DetectSquares", "add", "add", "add", "count", "count", "add", "count"]
[[], [[3, 10]], [[11, 2]], [[3, 2]], [[11, 10]], [[14, 8]], [[11, 2]], [[11, 10]]]
Output
[null, null, null, null, 1, 0, null, 2]

Explanation
DetectSquares detectSquares = new DetectSquares();
detectSquares.add([3, 10]);
detectSquares.add([11, 2]);
detectSquares.add([3, 2]);
detectSquares.count([11, 10]); // return 1.
detectSquares.count([14, 8]);  // return 0.
detectSquares.add([11, 2]);    // Adding duplicate points is allowed.
detectSquares.count([11, 10]); // return 2.

from collections import Counter


class DetectSquares:
    # Time: O(1) per add
    # Space: O(n) for unique points
    def __init__(self) -> None:
        self.point_counts: Counter[tuple[int, int]] = Counter()

    # Time: O(1)
    # Space: O(1)
    def add(self, point: list[int]) -> None:
        self.point_counts[(point[0], point[1])] += 1

    # Time: O(n) - n unique points
    # Space: O(1)
    def count(self, point: list[int]) -> int:
        qx, qy = point
        total = 0

        for (px, py), count in self.point_counts.items():
            # Look for points on the diagonal: equal nonzero distance on both axes.
            if abs(px - qx) != abs(py - qy) or px == qx:
                continue
            total += count * self.point_counts[(px, qy)] * self.point_counts[(qx, py)]

        return total