Yura has (n) homework assignments. For each assignment, its weight (a_i) is known — the number of course points Yura will receive if he completes it. Yura wants to choose a subset of assignments to maximize the total number of points. However, he has one problem: some assignments are too time-consuming. If Yura works on two assignments at positions (i) and (j) ((i \neq j)), there must be enough other assignments between them; otherwise, he will get distracted and fail to complete them. Formally, for any two chosen assignments with indices (i) and (j), the following condition must hold: (|i - j| \gt \max(a_i, a_j)). Find the maximum total weight Yura can obtain by choosing a subset of assignments satisfying this condition. 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 size of the array (a). The second line contains (n) integers (a_1, a_2, \dots, a_n) ((0 \le a_i \le 10^9)) — the elements of the array. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output a single integer — the maximum total weight of the selected assignments. In the first example, it is optimal to choose assignments with indices (1) and (5). In the third example, it is optimal to choose assignments with indices (1) and (6).