A. Pairs
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given $$$n$$$ integers, where $$$n$$$ is an even number. Determine if they can be paired into $$$\frac{n}{2}$$$ pairs such that the sums of the two numbers in each pair are equal for all pairs.

Input

In the first line, there is an integer $$$T$$$, the number of test cases.

For each case, there is a line with an integer $$$n$$$, followed by a line with the $$$n$$$ integers $$$a_1, \ldots, a_n$$$ that need to be paired.

Output

For each case, if the numbers can be paired, write a line with "SI". Otherwise, write a line with "NO".

Scoring

$$$1 \leq T \leq 100$$$

$$$4 \leq n \leq 10^5$$$, $$$n$$$ is an even number, the sum of $$$n$$$ for all cases is less than $$$5 \cdot 10^5$$$

$$$-10^8 \leq a_i \leq 10^8$$$ for $$$1 \leq i \leq n$$$

40 points: $$$n = 6$$$, $$$T \leq 30$$$

50 points: $$$n \leq 1000$$$, the sum of $$$n$$$ for all cases is less than $$$5000$$$

10 points: No additional restrictions

Example
Input
3
4
-2 1 -1 2
6
2 4 0 6 3 5
8
1 1 1 1 1 1 1 1
Output
SI
NO
SI