For two integers (x) and (y) ((x,y\ge 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): Choose a divisor (d) ((d\ge 2)) of (x), then increase (x) by (d). For example, (3) is a generator of (8) since we can perform the following operations: (3 \xrightarrow{d = 3} 6 \xrightarrow{d = 2} 8); (4) is a generator of (10) since we can perform the following operations: (4 \xrightarrow{d = 4} 8 \xrightarrow{d = 2} 10); (5) is not a generator of (6) since we cannot transform (5) into (6) with the operation above. Now, Kevin gives you an array (a) consisting of (n) pairwise distinct integers ((a_i\ge 2)). You have to find an integer (x\ge 2) such that for each (1\le i\le n), (x) is a generator of (a_i), 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\le t\le 10^4)) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer (n) ((1\le n\le 10^5)) — the length of the array (a). The second line contains (n) integers (a_1,a_2,\ldots,a_n) ((2\le a_i\le 4\cdot 10^5)) — 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 (10^5). 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. In the first test case, for (x=2): (2) is a generator of (8), since we can perform the following operations: (2 \xrightarrow{d = 2} 4 \xrightarrow{d = 4} 8); (2) is a generator of (9), sin