Flipping Coins Problem

Gary has N coins placed in a straight line. Some coins have their head side up, and others have the tail side up.

Convention:

1 denotes the HEAD side is up. 
0 denotes the TAIL side is up. 

Gary wants to achieve the maximum number of head-side up coins. He is allowed to perform at most one flip (possibly zero) in which he can flip the coins of a continuous segment (a continuous subarray).

Example:

In the given array (0-based indexing), { 1, 0, 0, 1, 0, 0, 1 }, the maximum number of head-side up coins can be achieved by flipping the coins in the range 1 to 5. The array will then become { 1, 1, 1, 0, 1, 1, 1 }.

Task:

Return the maximum number of heads side up Gary can obtain.

Input:

The first line contains an integer 'T' which denotes the number of test cases.
 For each test case:
 - The first line contains an integer 'N' denoting the number of coins.
 - The second line contains 'N' space-separated integers (0 or 1) representing the orientation of the coins.

Output:

For each test case, print the maximum number of head-side up coins obtainable in a single line.
 Output for each test case is printed on a separate line.

Constraints:

• 1 <= T <= 10
• 1 <= N <= 10^5
• 0 <= arr[i] <= 1