A14908. 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.