PRA4: Shooting Practice // Advanced

Recently Jim decided to improve his pistol shooting skills. Today his coach offered him the following exercise. He placed $n$ cans in a row on a table. Cans are numbered from left to right from $1$ to $n$. Jim has to knock down each can exactly once to finish the exercise. He is allowed to choose the order in which he will knock the cans down.

Jim knows that the durability of the $i^{th}$ can is $a_i$. It means that if Jim has already knocked $x$ cans down and is now about to start shooting the $i^{th}$ one, he will need $a_i \cdot x + 1$ shots to knock it down. You can assume that if Jim starts shooting the $i^{th}$ can, he will be shooting it until he knocks it down.

Your task is to choose such an order of shooting so that the number of shots required to knock each of the $n$ given cans down exactly once is minimum possible.

Input Format

The first line contains the number of test cases, $t$.

For each test case:

The first line contains one integer $n$ ($2 \leq n \leq 1000$) — the number of cans.

The second line of the input contains the sequence $a_1, a_2, ..., a_n$ ($1 \leq a_i \leq 1000$), where $a_i$ is the durability of the $i^{th}$ can.

Sample Input

1
3
20 10 20

Output Format

For each test case, print the minimum number of shots required to knock each of the $n$ given cans down exactly once.

Sample Output

43