B"There is a street with n sights, with sight number i being i miles from the beginning of the street. Sight number i has beauty b_i . You want to start your morning jog l miles and end it r miles from the beginning of the street. By the time you run, you will see sights you run by (including sights at l and r miles from the start). You are interested in the 3 most beautiful sights along your jog, but every mile you run, you get more and more tired. So choose l and r , such that there are at least 3 sights you run by, and the sum of beauties of the 3 most beautiful sights minus the distance in miles you have to run is maximized. More formally, choose l and r , such that b_{i_1} + b_{i_2} + b_{i_3} - (r - l) is maximum possible, where i_1, i_2, i_3 are the indices of the three maximum elements in range [l, r] . The first line contains a single integer t ( 1 <= q t <= q 10^5 ) -- the number of test cases. The first line of each test case contains a single integer n ( 3 <= q n <= q 10^5 ). The second line of each test case contains n integers b_i ( 1 <= q b_i <= q 10^8 ) -- beauties of sights i miles from the beginning of the street. It's guaranteed that the sum of all n does not exceed 10^5 . For each test case output a single integer equal to the maximum value b_{i_1} + b_{i_2} + b_{i_3} - (r - l) for some running range [l, r] . In the first example, we can choose l and r to be 1 and 5 . So we visit all the sights and the three sights with the maximum beauty are the sights with indices 1 , 3 , and 5 with beauties 5 , 4 , and 3 , respectively. So the total value is 5 + 4 + 3 - (5 - 1) = 8 . In the second example, the range [l, r] can be [1, 3] or [2, 4] , the total value is 1 + 1 + 1 - (3 - 1) = 1 . "...