Dabir, Egor, and Arseniy just got on the train and decided to play a game. Dabir has a backpack with an infinite number of cubes. He built (n) towers from them, where the (i)-th tower has height (h_i) cubes. Egor and Arseniy must choose an integer (x_i) for each tower (i) and increase its height by (x_i) exactly once . For example, if (h) = (1, 3, 2, 2), (x) = (3, 2, 2, 8), then after increasing (h) it will become (4, 5, 4, 10). Their goal is to make the heights of all towers equal. To make the game more interesting, Dabir wants to choose an integer (k) and add a restriction: each (x_i) must satisfy (1 \le x_i \le k). Help him find the smallest (k) for which it is possible to finish the game. The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. Then (t) test cases follow. The first line of each test case contains a single integer (n) ((1 \le n \le 5)). The second line contains (n) integers (h_1, h_2, \dots, h_n) ((1 \le h_i \le 6)). For each test case, output a single integer — the minimum value of (k) such that it is possible to make all towers have equal height.