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Pyramid form

We have N stones of various heights laid out in a row. By taking some consecutive section of the stones, we wish to form a pyramid, where the height of the stones start from 1, increase by 1, until it reaches some value x, then decreases by 1 until it reaches 1 again i.e. the stones should be 1, 2, 3, 4…x – 1, x, x – 1, x – 2 … 1. All other stones not part of the pyramid should have a height 0. We cannot move any of the stones from their current position, however, by paying a fee of 1, we can reduce the heights of the stones. We wish to minimize the cost of building a pyramid. Output the minimum cost to build this pyramid. Assume that always a pyramid would be made of the input elements.

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case contains an integer n denoting the size of the array. The last line of input contains n space separated integers forming the array.

Output:
Print the minimum cost to build this pyramid.

Constraints:
1<=T<=10^5
1<=n<=10^5
1<=a[i]<=10^5

Example:
Input:

2
6
1 2 3 4 2 1
3
1 2 1

Output:
4
0

#### ** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Ayush Govil

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Compilation/Execution Result: