Given an array, the task is to complete the function which finds the maximum sum subarray, where you may remove atmost one element to get the maximum sum.

Examples:

Input : A[] = {1, 2, 3, -4, 5}
Output : 11
Explanation : We can get maximum sum subarray by
removing -4.
Input : A[] = [-2, -3, 4, -1, -2, 1, 5, -3]
Output : 9
Explanation : We can get maximum sum subarray by
removing -2 as, [4, -1, 1, 5] summing 9, which is
the maximum achievable sum.

**Input:**

The first line of input contains an integer T denoting the number of test cases. The description of T test cases follows. The first line of each test case contains a single integer N denoting the size of array. The second line contains N space-separated integers A1, A2, ..., AN denoting the elements of the array.

**Output:**

For each test case in a new line output will be the maximum sum subarray.

**Constraints:**

1<=T<=100

1<=N<=100

-1000<=A[]<=1000

**Example(To be used only for expected output):**

Input:

2

5

1 2 3 -4 5

8

-2 -3 4 -1 -2 1 5 -3

**Output:**

11

9

**Note:**The **Input/Ouput** format and **Example** given are used for system's internal purpose, and should be used by a user for **Expected Output** only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.

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