Swapping

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### Read problem statements in [Hindi](http://www.codechef.com/download/translated/LTIME74/hindi/SFRV.pdf), [Bengali](http://www.codechef.com/download/translated/LTIME74/bengali/SFRV.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/LTIME74/mandarin/SFRV.pdf), [Russian](http://www.codechef.com/download/translated/LTIME74/russian/SFRV.pdf), and [Vietnamese](http://www.codechef.com/download/translated/LTIME74/vietnamese/SFRV.pdf) as well. You are given a sequence $A_1, A_2, \ldots, A_N$. You may perform the following operation an arbitrary number of times (including zero): choose two adjacent elements of this sequence, i.e. $A_i$, $A_{i+1}$ for some valid $i$, and swap them. However, for each valid $i$, it is not allowed to choose $A_i$ (the element with the index $i$, regardless of its value at any point in time) more than once in total during this process. Find the maximum of the sum $S = \sum_{i=1}^N A_i \cdot i$. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains a single integer $N$.  The second line contains $N$ spaceseparated integers $A_1, A_2, \ldots, A_N$. ### Output For each test case, print a single line containing one integer ― the maximum possible value of $S$. ### Constraints  $1 \le T \le 1,000$  $1 \le N \le 10^5$  $1 \le A_i \le 10^9$ for each valid $i$  the sum of $N$ over all test cases does not exceed $10^6$ ### Subtasks **Subtask #1 (50 points):**  $N \le 20$  the sum of $N$ over all test cases does not exceed $200$ **Subtask #2 (50 points):** original constraints ### Example Input ``` 2 4 2 1 4 3 4 7 6 3 2 ``` ### Example Output ``` 30 39 ``` ### Explanation **Example case 1:** Swap the first and second element of the initial sequence. Then, swap the third and fourth element of the resulting sequence. The final sequence $A$ is $(1, 2, 3, 4)$. **Example case 2:** Swap the second and third element to make the sequence $(7, 3, 6, 2)$.Author:  kingofnumbers 
Editorial  https://discuss.codechef.com/problems/SFRV 
Tags  dynamicprogramming, easy, kingofnumbers, ltime74 
Date Added:  26072019 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, SQL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS 
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