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) of integers $$$x$$$ and $$$y$$$.

The task is to find the maximum possible pleasure that Kamilka can get from the walk.

Input

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.

Output

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

Note

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 $$$4$$$.

Kamilka and the Sheep

Examples