Nearest Excluded Points
Description
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.
Input
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.
Output
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.
Samples
6
2 2
1 2
2 1
3 2
2 3
5 5
1 1
1 1
2 0
3 1
2 4
5 4
8
4 4
2 4
2 2
2 3
1 4
4 2
1 3
3 3
4 3
2 5
2 1
2 5
1 5
4 1
1 2
3 2