CF1930A Maximise The Score

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.

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.