CF2092A Kamilka and the Sheep

Kamilka has a flock of $ n $ sheep, the $ i $ -th of which has a beauty level of $ a_i $ . All $ a_i $ are distinct. Morning has come, which means they need to be fed. Kamilka can choose a non-negative integer $ d $ and give each sheep $ d $ bunches of grass. After that, the beauty level of each sheep increases by $ d $ . In the evening, Kamilka must choose exactly two sheep and take them to the mountains. If the beauty levels of these two sheep are $ x $ and $ y $ (after they have been fed), then Kamilka's pleasure from the walk is equal to $ \gcd(x, y) $ , where $ \gcd(x, y) $ denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers $ x $ and $ y $ . The task is to find the maximum possible pleasure that Kamilka can get from the walk.

Each test consists of several test cases. The first line contains one integer $ t $ ( $ 1 \le t \le 500 $ ), the number of test cases. The description of the test cases follows. The first line of each test case contains one integer $ n $ ( $ 2 \leq n \leq 100 $ ), the number of sheep Kamilka has. The second line of each test case contains $ n $ distinct integers $ a_1, a_2, \ldots, a_n \ (1 \le a_i \le 10^9) $ — the beauty levels of the sheep. It is guaranteed that all $ a_i $ are distinct.

For each test case, output a single integer: the maximum possible pleasure that Kamilka can get from the walk.

In the first test case, $ d=1 $ works. In this case, the pleasure is $ \gcd(1+1, \ 1+3)=\gcd(2, \ 4)=2 $ . It can be shown that a greater answer cannot be obtained. In the second test case, let's take $ d=3 $ . In this case, the pleasure is $ \gcd(1+3, \ 5+3)=\gcd(4, \ 8)=4 $ . Thus, for this test case, the answer is $ 4 $ .