A. Maximise The Score
time limit per test
1 second
memory limit per test
256 megabytes
standard input
standard output

There are $$$2n$$$ positive integers written on a whiteboard. Being bored, you decided to play a one-player game with the numbers on the whiteboard.

You start with a score of $$$0$$$. You will increase your score by performing the following move exactly $$$n$$$ times:

  • Choose two integers $$$x$$$ and $$$y$$$ that are written on the whiteboard.
  • Add $$$\min(x,y)$$$ to your score.
  • Erase $$$x$$$ and $$$y$$$ from the whiteboard.

Note that after performing the move $$$n$$$ times, there will be no more integers written on the whiteboard.

Find the maximum final score you can achieve if you optimally perform the $$$n$$$ moves.


Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 5000$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of integers written on the whiteboard is $$$2n$$$.

The second line of each test case contains $$$2n$$$ integers $$$a_1,a_2,\ldots,a_{2n}$$$ ($$$1 \leq a_i \leq 10^7$$$) — the numbers written on the whiteboard.


For each test case, output the maximum final score that you can achieve.

2 3
1 1 2 1
1 1 1 1 1 1

In the first test case, you can only make one move. You select $$$x=2$$$ and $$$y=3$$$, and your score will be $$$\min(x,y)=2$$$.

In the second test case, the following is a sequence of moves that achieves a final score of $$$2$$$:

  • In the first move, select $$$x=1$$$ and $$$y=1$$$. Then, add $$$\min(x,y)=1$$$ to the score. After erasing $$$x$$$ and $$$y$$$, the integers left on the whiteboard are $$$1$$$ and $$$2$$$.
  • In the second move, select $$$x=1$$$ and $$$y=2$$$. Then, add $$$\min(x,y)=1$$$ to the score. After removing $$$x$$$ and $$$y$$$, no more integers will be left on the whiteboard.
It can be proved that it is not possible to get a score greater than $$$2$$$.

In the third test case, you will perform the move thrice, adding $$$1$$$ to the score each time.