Find the Number of Ways to Place People II

The title alone is not enough to safely name one algorithm. Ask whether people are points on a grid, whether a valid placement means an axis-aligned rectangle, a visibility pair, or a nonattacking arrangement, and whether coordinates are unique. For rectangle-like counting, sort or group points by one coordinate and count compatible pairs on the other; for visibility problems, a sweep may maintain the nearest blocking point or a Fenwick tree over compressed coordinates. State the invariant before implementation, such as the data structure containing exactly points processed with smaller x. Explicitly ask whether answer counts can exceed 32-bit range and whether a modulus is required. Test one point, collinear points, duplicate x or y values, and input order unrelated to geometric order. Complexity depends on the clarified task: sorting-based grouping is often O(n log n) time and O(n) space, while naive pair checking is O(n squared). Do not fabricate a specific LeetCode formulation from this partial report.