WEIGHT - Weighted Sum

You are given N integers, A[1] to A[N]. You have to assign weights to these integers such that their weighted sum is maximized. The weights should satisfy the following conditions :

  1. Each weight should be an positive integer.
  2. W[1] = 1
  3. W[i] should be in the range [2, W[i-1] + 1] for i > 1

Weighted sum is defined as S = A[1] * W[1] + A[2] * W[2] + ... + A[N] * W[N]

Input

There are multiple test cases.
First line contains the number of test cases
Each test case consists of a single line containing N.
This is followed by N lines, each containing A[i]

Output

For each test case, output one line - the maximum weighted sum.

Example

Input:
1
4
1
2
3
-4
Output: 6

Explanation

The weights are 1, 2, 3, 2.

Constraints

N <= 10^6
| A[i] | <= 10^6
Total number of test cases is around 10.


Added by:Kunal Jain
Date:2011-02-07
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:CodeCraft 11

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