CF1778A Flip Flop Sum

You are given an array of $ n $ integers $ a_1, a_2, \ldots, a_n $ . The integers are either $ 1 $ or $ -1 $ . You have to perform the following operation exactly once on the array $ a $ : - Choose an index $ i $ ( $ 1 \leq i < n $ ) and flip the signs of $ a_i $ and $ a_{i+1} $ . Here, flipping the sign means $ -1 $ will be $ 1 $ and $ 1 $ will be $ -1 $ . What is the maximum possible value of $ a_1 + a_2 + \ldots + a_n $ after applying the above operation?

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 500 $ ). Description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ), the length of the array $ a $ . The next line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ a_i = 1 $ or $ a_i = -1 $ ). The sum of $ n $ over all cases doesn't exceed $ 10^5 $ .

For each test case, print the maximum possible sum of the array $ a $ you can get in a separate line.

In the first case, we can choose index $ 4 $ and flip the signs of $ a_4 $ and $ a_5 $ . After this operation, the sum will be $ -1+1+1+1+1 = 3 $ . We can't make the sum larger than this. In the third case, the only option is to choose the index $ 1 $ .