D. Nearest Excluded Points
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$|x_1 - x_2| + |y_1 - y_2|$$$.

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.

Examples
Input
6
2 2
1 2
2 1
3 2
2 3
5 5
Output
1 1
1 1
2 0
3 1
2 4
5 4
Input
8
4 4
2 4
2 2
2 3
1 4
4 2
1 3
3 3
Output
4 3
2 5
2 1
2 5
1 5
4 1
1 2
3 2