You are a car seller. You have $N$ cars and the profit for each of the cars is given by an array $P$. The profit of cars are $P_1,\ P_2,\ P_3,\ ...,\ P_N$. Since you got a huge profit in the last month so you decide to get $(N-1)$ more sets of such cars. You already have one car. Now, you have $N^2$ cars. Basically, there are $N$ number of cars of each profit such as $N$ cars for profit $P_1$, $N$ cars of profit $P_2$, and so on up to $N$ cars of profit $P_N$.

You can perform the following operations any number of times:

• If the last car is sold for profit $P$, then you can sell a car for profit $P_c >P$ .

Note: You can select a car of any profit in the first operation as there are no cars that are sold earlier.

Find out the maximum profit that you can make.

For example, $N=4$ and prices are $P_1,\ P_2,\ P_3,\ P_4$. Since $N$ is 4, therefore you can have four sets of cars and the prices are $P_1,\ P_2,\ P_3,\ P_4,\ P_1,\ P_2,\ P_3,\ P_4 ,\ P_1,\ P_2,\ P_3,\ P_4 ,\ P_1,\ P_2,\ P_3,\ P_4$ .

See the sample explanation for more details. 

Input format

• The first line contains a single integer $T$ denoting the number of test cases.
• The first line of each test case consists of an integer $N$.
• The second line consists of $N$ space-separated integers $P_1,\ P_2,\ P_3,\ ...,\ P_N$

Output format

For each test case, print a single integer denoting the maximum amount of profit that you can make.

Constraints

$1 \leq T \leq 100$

$1\leq N\leq 100000$

$1\leq P_i<=1e9 \forall i \in [1,N]$

Sum of $N$ over all test cases does not exceed $100000$