Maximize

Easy

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Average time to solve is 25m

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Problem statement

You have an integer ‘N’ and an array ‘X’ of ‘N’ integers. You need to maximize the value of the array, which is equal to ⅀ '(X[i] - i)^2' from ‘i’ in the range ‘[0, N-1]’. To do this, you can rearrange the elements of the given array.

Determine the maximum value of the array you can get after rearranging the array ‘X’ elements.

Example:

'N' = 3, ‘X' = [1,2,1] 
If we rearrange our array 'X' to '[2, 1, 1]' .
Then our answer will be (0-2)^2 + (1-1)^2 + (1-2)^2 = 4 + 0 + 1 = 5.
For array ‘[1, 1, 2]’ value will be equal to ‘1 + 0 + 0 = 1’.
For array ‘[1, 2, 1]’ value will be equal to ‘1 + 1 + 1 = 3’.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line contains an integer 'T', which denotes the number of test cases to be run. Then the test cases follow.

The first line of each test case contains an integer 'N’.
The second line contains N integers, denoting the array ‘X’ value.

Output format:

For each test case, return the maximum array value for the given array ‘X’.

Note:

You don’t need to print anything. It has already been taken care of. Just implement the given function.

Constraints :

1 <= T <= 10
1 <= N <= 10^4
1<= X[i] <= 10^5

Time Limit: 1 sec

Sample Input 1 :

Sample Output 1 :

4
2

Explanation Of Sample Input 1 :

For test case 1: 

From this array, we can have 2 arrays i.e. ‘[1,2]’ and ‘[2,1]’
For ‘[1,2]’ the value will be equal to ‘ (1-0)^2 + (2-1)^2’ which is equal to 2.
For ‘[2,1]’ the value will be equal to ‘ (2-0)^2 + (1-1)^2’ which is equal to 4.
Hence answer is ‘4’             

For test case 2:
In this case, there is only one array you can get after rearranging elements of ‘X’.
For array ‘[1,1,1]’ answer will be ‘1+0+1=2’.
Hence the answer is ‘2’.

Sample Input 2:

Sample Output 2:

11
226

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