Description:
You have an array $$$a$$$ of $$$n$$$ non-negative integers. Let's define $$$f(a, x) = [a_1 \bmod x, a_2 \bmod x, \dots, a_n \bmod x]$$$ for some positive integer $$$x$$$. Find the biggest $$$x$$$, such that $$$f(a, x)$$$ is a palindrome.
Here, $$$a \bmod x$$$ is the remainder of the integer division of $$$a$$$ by $$$x$$$.
An array is a palindrome if it reads the same backward as forward. More formally, an array $$$a$$$ of length $$$n$$$ is a palindrome if for every $$$i$$$ ($$$1 \leq i \leq n$$$) $$$a_i = a_{n - i + 1}$$$.
Input Format:
The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) — the number of test cases.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$).
The second line of each test case contains $$$n$$$ integers $$$a_i$$$ ($$$0 \leq a_i \leq 10^9$$$).
It's guaranteed that the sum of all $$$n$$$ does not exceed $$$10^5$$$.
Output Format:
For each test case output the biggest $$$x$$$, such that $$$f(a, x)$$$ is a palindrome. If $$$x$$$ can be infinitely large, output $$$0$$$ instead.
Note:
In the first example, $$$f(a, x = 1) = [0, 0]$$$ which is a palindrome.
In the second example, $$$f(a, x = 2) = [1, 0, 1, 0, 0, 1, 0, 1]$$$ which is a palindrome.
It can be proven that in the first two examples, no larger $$$x$$$ satisfies the condition.
In the third example, $$$f(a, x) = [0]$$$ for any $$$x$$$, so we can choose it infinitely large, so the answer is $$$0$$$.