G. Illuminating Lights
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are given the positions of a collection of lights in the plane. At time $$$0$$$ they are all simultaneously activated, and at time $$$T$$$ each light illuminates an axis-aligned square of side length $$$2T$$$ centered on itself. You must decide whether there is a time $$$T \gt 0$$$ when the illuminated area is a rectangle.
Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 2 \cdot 10^5$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1\leq n\leq 2\cdot10^5$$$) — the number of lights.

Each of the next $$$n$$$ lines of each test case contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^9\leq x_i,\,y_i\leq 10^9$$$) — the coordinates of the $$$i$$$-th light. The positions of the lights are guaranteed to be distinct.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print YES if the illuminated area is at some point a rectangle, and NO otherwise.

You can output YES and NO in any case (for example, yES, yes, and Yes will be accepted).

Example
Input
4
4
0 0
0 1
1 0
1 1
4
2 2
0 5
5 0
3 3
3
6 1
6 2
6 3
2
-1000 -1000
1000 1000
Output
YES
NO
YES
NO
Note

In the second test case, which is shown in the statement, it can be shown that regardless of how much time passes, the illuminated area will never be a rectangle.