CF2237A Destroying Towers

Quack the Duck has returned to his homeland and found $ n $ towers standing in a line. The height of the $ i $ -th tower is $ a_i $ . He wants vengeance for the destruction of his ecosystem, and has vowed to wreak as much havoc as possible with his laser gun. Quack will operate on each tower exactly once, in any order he chooses. The operation on tower $ i $ is as follows: - Quack climbs to the top of tower $ i $ and shoots a laser to the right, cutting the first taller tower it hits down to the same height as tower $ i $ .Formally, let $ j $ be the smallest index such that $ j \gt i $ and $ a_j \gt a_i $ , where $ a_i $ and $ a_j $ are the current heights of the towers. If such $ j $ exists, then $ a_j $ is replaced with $ a_i $ . Otherwise, nothing happens. Find the minimum possible final sum of tower heights over all possible orders of operations.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 500 $ ). The description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 1\le n\le 100 $ ) — the number of towers. The following line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1\le a_i\le 1000 $ ) — the heights of the towers.

For each test case, output a single integer — the minimum possible final sum of tower heights over all possible orders of operations.

In the first test case, one optimal order is $ 3,1,2 $ . The heights change as follows: $$$ [1,3,5]\to [1,3,5]\to [1,1,5]\to [1,1,1]. $$$ Thus the final sum is $ 1+1+1=3 $ . In the second test case, no operation can change any tower. For every tower, there is no higher tower to its right. Therefore the final heights remain $ [5,4,3] $ , and the answer is $ 5+4+3=12 $ . In the third test case, one optimal order is $ 4,1,3,2 $ . The heights change as follows: $$$ [3,2,5,1]\to [3,2,5,1]\to [3,2,3,1]\to [3,2,3,1]\to [3,2,2,1]. $$$ Therefore the final sum is $ 3+2+2+1=8 $ .