Problem title
Difficulty
Avg time to solve

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Moderate
30 mins
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Easy
10 mins
Find the maximum element in the array after update operations.
Moderate
15 mins
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15 mins
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Special Numbers
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All Prime Numbers less than or equal to N
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MaxFreq_Element
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Maximum Sum Path Of A Binary Tree.
Hard
25 mins

# Mining Diamonds

Difficulty: HARD

Problem Statement

#### Vladimir, a dumb miner was assigned the task to mine all diamonds. Since he is dumb he asks for your help to determine the maximum number of coins that he can earn by mining the diamonds in an optimal order.

##### For example:
``````Suppose ‘N’ = 3, and ‘A’ = [7, 1, 8]

The optimal order for mining diamonds will be [2, 1, 3].
State of mine -    [7, 1, 8]    [7, 8]    
Coins earned -    (7*1*8) + (1*7*8) + (1*8*1)  = 56 + 56 + 8 = 120
Hence output will be 120.
``````

#### Input Format:

``````The first line of the input contains a single integer ‘T’ representing the no. of test cases.

The first line of each test case contains a single integer value, ‘N’, denoting the number of diamonds in the mine.

The second line of each test case contains ‘N’ space-separated integers, denoting the size of the diamonds in the mine.
``````

#### Output Format:

``````For each test case, print a single integer value denoting the maximum number of coins that can be earned by mining the diamonds in an optimal order.

Print a separate line for each test case.
``````
##### Note:
``````You are not required to print anything; it has already been taken care of. Just implement the function and return the answer.
``````

#### Constraints:

``````1 ≤ T ≤ 100
1 ≤ N ≤ 100
0 ≤ A[i] ≤ 100
1 ≤ ΣN ≤ 300

Time limit: 1 Sec
``````
##### Sample Input 1 :
``````2
3
7 1 8
2
9 1
``````
##### Sample Output 1 :
``````120
18
``````
##### Explanation For Sample Input 1 :
``````For First Case - Same as explained in above example.

For the second case -

‘N’ = 2, and ‘A’ = [9, 1]

The optimal order for mining diamonds will be [2, 1].
State of mine -    [9, 1]    
Coins earned -    (1*9*1) + (1*9*1) = 9 + 9 = 18
Hence output will be 18..
``````
##### Sample Input 2 :
``````2
5
1 2 3 4 5
4
1 5 2 8
``````
##### Sample Output 2 :
``````110
136
``````   Console