For two integers x and y (x,y≥2), we will say that x is a generator of y if and only if x can be transformed to y by performing the following operation some number of times (possibly zero):
For example,
Now, Kevin gives you an array a consisting of n pairwise distinct integers (ai≥2).
You have to find an integer x≥2 such that for each 1≤i≤n, x is a generator of ai, or determine that such an integer does not exist.
Each test contains multiple test cases. The first line of the input contains a single integer t (1≤t≤104) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer n (1≤n≤105) — the length of the array a.
The second line contains n integers a1,a2,…,an (2≤ai≤4⋅105) — the elements in the array a. It is guaranteed that the elements are pairwise distinct.
It is guaranteed that the sum of n over all test cases does not exceed 105.
For each test case, output a single integer x — the integer you found. Print −1 if there does not exist a valid x.
If there are multiple answers, you may output any of them.
438 9 1042 3 4 52147 15453 6 8 25 100000
2 -1 7 3
In the first test case, for x=2:
In the second test case, it can be proven that it is impossible to find a common generator of the four integers.
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