Given an array you have to find the max sum of i*A[i] where i is the index of the array obtained by rotating the element of the array one by one . Your task is to complete the function **max_sum** which takes one argument which is the array A [ ] and returns an integer value denoting the required max sum .

**Input:**

The first line of input is the number of test cases T . Then T test cases follow . The first line of each test case is an integer N denoting the size of the array . Then in the next line are N space separated values of the array A [ ] .

**Output:**

For each test case output will be the required max sum.

**Constraints:**

1<=T<=100

1<=N<=10^{5}

1<=A[]<1000

**Example:**

**Input**

1

4

8 3 1 2

**Output**

29

**Explanation**

Above the configuration possible by rotating elements are

3 1 2 8 here sum is 3*0+1*1+2*2+8*3 = 29

1 2 8 3 here sum is 1*0+2*1+8*2+3*3 = 27

2 8 3 1 here sum is 2*0+8*1+3*2+1*3 = 17

8 3 1 2 here sum is 8*0+3*1+1*2+2*3 = 11

Here the max sum is 29

**Note:**The **Input/Ouput** format and **Example** given are used for system's internal purpose, and should be used by a user for **Expected Output** only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.

Author: Shubham Joshi 1

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