12831283 SUSTech Online Judge
Problem 1283 --Cut The Stick Pro [Middle I]

1283: Cut The Stick Pro [Middle I]

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 1030  Solved: 209
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Description

Lanran wants to cut one stick with length L into exactly N sticks with length \(L_i(i=1,2...N)\), so \(L = \sum_{i=1}^{N}{L_i}\). However, the cost to cut one stick into two pieces is the length of the stick, which means cutting a stick with length x will cost x. Now he wants to know the minimal cost if he cuts stick optimally to get N sticks.

Input

The first line will be an integer \(T (1 \leq T \leq 5)\), which is the number of test cases. 

For each test, the first line contains an integer N \((1 \leq N \leq 10^5 )\) — the number of sticks Lanran needs to get. Then the next line contains N  integers, the i-th integer \(L_i (1 \leq p_i \leq 10^5)\) indicates the length of N sticks Lanran wants to get.

Output

For each case print the minimal cost if Lanran cuts stick optimally to get N sticks.

Sample Input

1
4
1 4 2 6

Sample Output

23

HINT

Source

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