B. Lunatic Never Contenttime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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}.InputThe 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.OutputFor each test case output the biggest x, such that f(a, x) is a palindrome. If x can be infinitely large, output 0 instead.ExampleInput
421 283 0 1 2 0 3 2 1103100 1 1000000000Output
1
2
0
999999900
NoteIn 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.
421 283 0 1 2 0 3 2 1103100 1 1000000000
1 2 0 999999900 
['math', 'number theory', '*1100']