CF1651D Nearest Excluded Points

You are given $ n $ distinct points on a plane. The coordinates of the $ i $ -th point are $ (x_i, y_i) $ . For each point $ i $ , find the nearest (in terms of Manhattan distance) point with integer coordinates that is not among the given $ n $ points. If there are multiple such points — you can choose any of them. The Manhattan distance between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is $ |x_1 - x_2| + |y_1 - y_2| $ .

The first line of the input contains one integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of points in the set. The next $ n $ lines describe points. The $ i $ -th of them contains two integers $ x_i $ and $ y_i $ ( $ 1 \le x_i, y_i \le 2 \cdot 10^5 $ ) — coordinates of the $ i $ -th point. It is guaranteed that all points in the input are distinct.

Print $ n $ lines. In the $ i $ -th line, print the point with integer coordinates that is not among the given $ n $ points and is the nearest (in terms of Manhattan distance) to the $ i $ -th point from the input. Output coordinates should be in range $ [-10^6; 10^6] $ . It can be shown that any optimal answer meets these constraints. If there are several answers, you can print any of them.