Nearest Excluded Points

Description:

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.

Sample Input:

6
2 2
1 2
2 1
3 2
2 3
5 5

Sample Output:

1 1
1 1
2 0
3 1
2 4
5 4

Sample Input:

8
4 4
2 4
2 2
2 3
1 4
4 2
1 3
3 3

Sample Output:

4 3
2 5
2 1
2 5
1 5
4 1
1 2
3 2