CF2124B Minimise Sum

This problem differs from problem G. In this problem, you must output the minimum sum of prefix minimums after at most one operation. You are given an array $ a $ of length $ n $ , with elements satisfying $ \boldsymbol{0 \le a_i \le n} $ . You can perform the following operation at most once: - Choose two indices $ i $ and $ j $ such that $ i < j $ . Set $ a_i := a_i + a_j $ . Then, set $ a_j = 0 $ . Output the minimum possible value of $ \min(a_1) + \min(a_1,a_2) + \ldots + \min(a_1, a_2, \ldots, a_n) $ that you can get.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 2 \leq n \leq 2\cdot 10^5 $ ) — the length of $ a $ . The following line contains $ n $ space-separated integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le n $ ) — denoting the array $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, output an integer on a new line, the minimum possible value of $ \min(a_1) + \min(a_1,a_2) + \ldots + \min(a_1, a_2, \ldots, a_n) $ .

In the second test case, it is optimal to perform the operation with $ i=2 $ and $ j=3 $ . In the third test case, it is optimal to not perform any operations. The answer is $ 3 $ .