Symmetry

Interview

Time limit1sMemory limit128 MB

Summary

Decide whether the given dots mirror exactly across some vertical line, printing YES or NO for each test case.

Level: Medium5 of 10
Topics: Hash map, Geometry, Sorting
Solved: No attempts yet

Problem

The figure on the left is left-right symmetric: you can fold the sheet of paper along a vertical line (drawn as a dashed line) so that the two halves match exactly. The figure on the right is not left-right symmetric, because no such vertical line exists.

Write a program that decides whether a figure drawn as a set of dots is left-right symmetric. All dots are distinct.

Input

The first line contains the number of test cases $T$ .

Each test case begins with a line containing an integer $N$ ( $1 \le N \le 1000$ ), the number of dots in the figure. Each of the next $N$ lines contains two integers, the $x$ -coordinate and the $y$ -coordinate of a dot. Both coordinates are integers between $-10000$ and $10000$ , inclusive.

Output

For each test case, print a single line: YES if the figure is left-right symmetric, or NO otherwise.

Examples3

Example 1

Input

Expected output

YES
NO
YES

Example 2
Input
```
1
1
0 0
```
Expected output
```
YES
```
Example 3
Input
```
1
2
-3 7
3 7
```
Expected output
```
YES
```