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 \(100000\)