# Minimum Score

Posted: 21 Mar, 2021
Difficulty: Moderate

## PROBLEM STATEMENT

#### Now, you need to find the minimum total triangle score. The total triangle score is the sum of the triangle scores of all the possible triangles.

##### Note:
``````Note that a polygon can be divided into triangles in more than one way. You need to print the minimum sum of triangle values of all the triangles created.
``````
##### Example :
``````Given 'N' = 4, Array = [4, 3, 5, 2], the possible scores for these two triangle score are: (3 * 2 * 5) + (3 * 2 * 4) = 54 and (4 * 2 * 5) + (4 * 3 * 5) = 100.
The minimum of these two triangle scores is 54. So you need to print 54.
``````

##### Input Format:
``````The first line contains an integer ‘T’ which denotes the number of test cases.

The first line of each test case contains a single integer ‘N’, denoting the vertices of the polygon.

The next line contains ‘N’ space-separated integers denoting the value of the vertices of the polygon.
``````
##### Output Format:
``````For each test case, you need to return the minimum triangle score possible from all triangles.

Print the output of each test case in a separate line.
``````
##### Note:
``````You don’t need to print anything; It has already been taken care of. Just implement the given function.
``````
##### Constraints:
``````1 <= T <= 10
3 <=  N  <= 50
1 <= ARR[i] <= 100

Where 'ARR[i]' denotes the Array elements that represent the sides of the polygon.

Time limit: 1 sec
``````