Maximise The Score
Description
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.
Input
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.
Output
For each test case, output the maximum final score that you can achieve.
3
1
2 3
2
1 1 2 1
3
1 1 1 1 1 1
2
2
3
Note
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.
In the third test case, you will perform the move thrice, adding $1$ to the score each time.