You are given an integer array (a) of length (n). You can perform the following operation: choose a range (l, r) ((1 \le l \le r \le n)) and replace the value of elements (a_l, a_{l+1}, \dots, a_r) with ((l + r)). Your task is to calculate the maximum possible total array sum if you can perform the aforementioned operation at most once. The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The first line of each test case contains a single integer (n) ((1 \le n \le 2 \cdot 10^5)). The second line contains (n) integers (a_1, a_2, \dots, a_n) ((0 \le a_i \le 2n)). Additional constraint on the input: the sum of (n) over all test cases doesn't exceed (2 \cdot 10^5). For each test case, print a single integer — the maximum possible total array sum if you can perform the aforementioned operation at most once. In the first example, you can perform the operation on the subarray (3, 3), resulting in the array (2, 5, 6) and the sum (13). In the second example, you don't need to perform any operation. In the third example, you can perform the operation on the subarray (1, 4), resulting in the array (5, 5, 5, 5) and the sum (20). In the fourth example, you can perform the operation on the subarray (2, 3), resulting in the array (3, 5, 5, 9, 10) and the sum (32).