Solve the programming task below in a Python markdown code block.
Monica decides that she would like to get to know the neighbours in the apartment better. She makes a batch of wonderful chocolates and hangs them on the door in a basket hoping that her neighbors will take some and they can meet. The neighbours (including Joey) eventually go crazy over the candy and demand more. Eventually, she keeps a bowl full of chocolates at the door for the last time.

There are N neighbours. The i^{th} neigbhour has initial energy equal to A_{i}. There is one bowl filled with chocolates. The neighbours are made to stand in a row and the bowl is passed around by obeying the following rules:

Any person can hold the bowl initially. 
If the person holding the bowl has positive energy, he/she passes the bowl to the person on the immediate right of him/her. The rightmost person in the row passes the bowl to the leftmost person in the row. 
The act of passing the bowl takes 1 second. 
If the person holding the bowl has non-positive energy, he/she drops the bowl.  
After each pass, the energy of the person reduces by 1. 

Among all possible ways in which the N neighbours start the game, find the maximum time until the bowl is dropped.

------ Input Format ------ 

- First line will contain T, number of testcases. Then the testcases follow.
- First line of each testcase contains one integer N.
- Second line of each testcase contains of N integers, denoting the elements of array A.

------ Output Format ------ 

For each testcase, output in a single line the maximum time until the bowl is dropped.

------ Constraints ------ 

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$0 ≤ A[i] ≤ 10^{6}$
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$

----- Sample Input 1 ------ 
3
3
2 1 1
3
0 5 0
4
3 0 2 1

----- Sample Output 1 ------ 
4
1
3

----- explanation 1 ------ 
Test case 1: One of the optimal orders in which all the neighbours can stand in the row is:   
$1$ $\rightarrow$ $2$ $\rightarrow$ $3$ $\rightarrow$ $1$. The bowl is initially with person $1$. 
- Person $1$, in one second, passes the bowl to person $2$ and his/her own energy becomes $1$. 
- Person $2$, in one second, passes the bowl to person $3$ and his/her own energy becomes $0$.
- Person $3$, in one second, passes the bowl to person $1$ and his/her own energy becomes $0$.
- Person $1$, in one second, passes the bowl to person $2$ and his/her own energy becomes $0$.
- Person $2$ has $0$ energy, so he/she drops the bowl. 
Thus, the bowl is dropped after $4$ seconds.

Test case 2: One of the optimal orders in which all the neighbours can stand in the row is:   
$2$ $\rightarrow$ $1$ $\rightarrow$ $3$ $\rightarrow$ $2$. The bowl is initially with person $2$. Thus, it would travel as $2$ $\rightarrow$ $1$. The bowl can not be passed further due to $0$ energy of person $1$.