Paint the Array

题意翻译

$T$ 组数据。 对于每组数据，给定一个长度为 $n$ 的序列。 问是否存在一个数 $d$ ，将所有能被 $d$ 整除的数标记为红色，所有不能被 $d$ 整除的数标记为蓝色，使得序列中没有相邻的元素具有相同的颜色。 若存在，则输出任意一个满足条件的 $d$ ；若不存在，则输出 $0$ 。

题目描述

You are given an array $ a $ consisting of $ n $ positive integers. You have to choose a positive integer $ d $ and paint all elements into two colors. All elements which are divisible by $ d $ will be painted red, and all other elements will be painted blue. The coloring is called beautiful if there are no pairs of adjacent elements with the same color in the array. Your task is to find any value of $ d $ which yields a beautiful coloring, or report that it is impossible.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of testcases. The first line of each testcase contains one integer $ n $ ( $ 2 \le n \le 100 $ ) — the number of elements of the array. The second line of each testcase contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^{18} $ ).

输出格式

For each testcase print a single integer. If there is no such value of $ d $ that yields a beautiful coloring, print $ 0 $ . Otherwise, print any suitable value of $ d $ ( $ 1 \le d \le 10^{18} $ ).

输入输出样例

输入样例 #1

5
5
1 2 3 4 5
3
10 5 15
3
100 10 200
10
9 8 2 6 6 2 8 6 5 4
2
1 3

输出样例 #1

2
0
100
0
3