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 $N$ space-separated 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 $(7, 3, 6, 2)$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'for _ in range(int(input())):\n n = int(input())\n a = list(map(int,input().split()))\n dp = [0]*n\n dp[0] = a[0]\n dp[1] = max(dp[0]+a[1]*2,a[1]*1+a[0]*2)\n for i in range(2,n):\n  dp[i] = max(dp[i-1]+a[i]*(i+1), dp[i-2]+a[i-1]*(i+1)+a[i]*i)\n print(dp[-1])'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13303